ProtoSociology Vol 12 After the Received View: Developments in the Theory of Science (Contents &...

ProtoSociologyAn International Journal of Interdisciplinary Research

Vol. 12 -1998

After the Received View - Developments in theTheory of Science

P Editor: Gerhard Preyer

P Editorial Staff: Georg Peter, Alexander Ulfig

P Editorial of the Vol. 12 1998: Georg Peter, Alexander Ulfig

P Layout and Technical Conception: Georg Peter

P Editorial Office: ProtoSociology, Stephan-Heise-Str. 56, 60488Frankfurt am Main, RFA, Phone: 069-769461, E-Mail:[email protected]

PROTOSOCIOLOGYAn International Journal of Interdisciplinary Research

VOL. 12, 1998 – Special Edition

AFTER THE RECEIVED VIEW – Developments in the Theory of Science

Gerhard Preyer, Georg Peter, Alexander Ulfig (Eds.)

in memoriamWolfgang Stegmüller

Content

Introduction: Developments in the Theory of Science 4Gerhard Preyer, Georg Peter, Alexander Ulfig

LOGICAL OPERATIONALISM – SIGNIFICANCE AND MEANING

Wilhelm K. Essler 12Truth and Knowledge. Some Considerations concerning the Task of Philosophy of Science

Gerhard Preyer 40The Received View, Incommensurability and Comparison of Theories – Beliefs as the Basis of Theorizing

Robert Schwartz 59Reflections on Projection

Jeffrey E. Foss 66The Logical and Sociological Structure of Science

STRUCTURALISM – MEANINGFUL MEASUREMENT – THE CONCEPTION OF

PHYSICAL LAW

C. Ulises Moulines 78Structuralism vs. Operationalism

Nicholas Rescher 92Meaningless Numbers

R. I. G. Hughes 113Laws of Nature, Laws of Physics, and the Representational Account of Theories

James R. Brown 144Einstein’s Principle Theory

INDUCTIVE INFERENCES – INTERPRETATION OF PROBABILITY – GAME

THEORY

Kevin T. Kelly, Cory Juhl 158Transcendental Deductions and Universal Architectures for InductiveInferences

Howard H. Harriott 177R.A. Fisher and the Interpretation of Probability

Brian Skyrms 194Evolution of an Anomaly

PROPERTIES – UNDERDETERMINATION – SCIENTIFIC REALISM

George N. Schlesinger 212Degrees of Characterizations

Carl A. Matheson 225Observational Adequacy as distinct from the Truth about Observables

Thomas R. Grimes 238Scientific Realism and the Problem of Underdetermination

Paul C. L. Tang 249On Paul Churchland’s Treatment of the Argument from Introspection and Scientific Realism

RATIONALITY – METAPHORS – VALUES IN SCIENCE

David Resnik 258Scientific Rationality and Epistemic Goals

Aldo Montesano 290Rationality in Economics: A General Framework

Joseph Agassi 297Science Real and Ideal: Popper and the Dogmatic Scientist

Michael Bradie 305Models and Metaphors in Science

David Gruender 319Values and the Philosophy of Science Authors 333

Impressum 334

On ProtoSociology 335 Forthcoming and published Volumes 336

Publications within the Project ProtoSociology 339

Subscription 355

Electronic Publications – Special Offer! 356

4 G. Preyer, G. Peter, A. Ulfig

Introduction: Developments in the Theory of Science

In the twentieth century the syntactic model in the theory and philosophy ofscience, the so called Received View – R. Carnap, C. G. Hempel, H. Reichen-bach, E. Nagel –, is paradigmatic for answering questions on meaning,significance and validation of theoretical statements and of our scientificknowledge. Since the 1960’s the Received View is challenged by the naturalis-tic (realistic), the sociological, the structuralistic and the constructive empiri-cist (representational) accounts of the “correct view” on our scientificknowledge. We take the Received View to frame the recent developments asan initial systematization. Today, there is a shift to a semantic account andthe main interest is in transparadigmatic orientation. This is reflected by theontologies of theory-languages, the theory of meaningful measurement andby analyzing the structure of experience, especially. It is there, we have toask how ontology and empirical knowledge (beliefs) are interconnected withthe issues of underdetermination. The description and systematization oftheory change are the major topics here. Theory change is not just a problemof a dyachronous perspective but of our theorizing on the dynamics of beliefs– of our theory of decision and rationality. A lot of former scientific con-cepts, e.g. of Newton, Einstein, Duhem, Fisher are to be revisited then.

By shifting from object-level of empirical science to the meta-level ofphilosophy of science, we mention the means the scientist uses. But pickingout the logico-linguistic distinction of ‘use’ and ‘mention’ as a central themehas to be supplemented and precisely defined by the instruments of classicallogic. Wilhelm K. Essler – in the context of his suppositionalism andconditionalism – conceives of his logical operationalism as cognitive seman-tics. Following Tarski, he analyzes parts of the philosophy of science in termsof a level-ordered language. These levels are of different power in generatingempirical knowledge. Essler gives an elementary exposition of the languageof classification and comparison. This exposition conceptually clarifies ourelementary perception and observation as well as parts of comparative expe-rimental measurement. Application in detail is referred to epistemology.Leveling languages shows a way from the philosophy of science to “somemetaphysics of experience” for physics as well as it shows for our empiricalknowledge in general to be part of philosophy of science. Logicaloperationalism – different from a more or less “radical” structuralism in thisrespect – takes into account the metalogical research on antinomies. Conse-

Introduction: Developments in the Theory of Science 5

quentially, in systemizing empirical laws and their background assumptionsOckham’s razor is applied. Choosing a theory-language and its ontology iseconomy-minded.

It is common to contemporary extensionalist approaches towards phi-losophy of mind, cognitive science and artificial intelligence to assume thereis a distinction between pure syntax and semantic interpretation. The originof the syntactic account and of the term ‘pure syntax’ is traced back toCarnap’s distinction between pure and applied syntax and semantics, and toformalist analysis of mathematical systems as uninterpreted token manipula-ting games. Yet, sciences aim at developing empirically adequate theoriesresting on both the analysis of the semantical structure of scientific knowled-ge (theories/language) as well as the analysis of the concept of ob-servable/empirical objects. Gerhard Preyer discusses the semantics of thesyntactic account, i. e. the junctim of significance (confirmation) and mea-ning. References are made to the method of reduction – as of Carnap, C.I.Lewis, A. Pap – and to the structuralism of W. Stegmüller and J. D. Sneed. Itis the sociological and historical account of scientific discovery going back –more or less – to Kuhn and the controversy on incommensurability undcomparison of theories that dominates this discussion of the logico-semanti-cal structure of scientific knowledge. Yet, it is to name in this context alsoN.R. Hanson, M. Fleck and M. Polany. In particular Fleck has firstly develo-ped an account like Kuhn in his The Structure of Scientific Revolution. Preyerargues Popper can be defended against the critique of P. Kuhn, P. Feyer-abend, I. Lakatos, H. Putnam. Hence, the Popper-Kuhn-controversy shouldbe done with D. Davidson’s critique of Kuhn’s incommensurability-thesiswhich is directed against this third dogma of empiricism and its conceptualrelativism rooted in a fundamental distinction of conceptual scheme (predic-tion, organizing, facing, or fitting) from neutral content (nature, reality,sensory promptings). Following Davidson here there is no way back to thedungeon of paradigms and the Kuhnian misconception of scientific activityand endeavor. Contrary to Kuhn: comparing theories is possible, even ifthere is a shift of meaning and reference. All validating scientific knowledgeis taking place towards a background of beliefs which themselves can not bequestioned all the time. These background-beliefs guarantee for any singlebelief’s being true. An interpreter’s actually translating beliefs embedded in(utterance-, sentence-) meanings proves the dichotomy of scheme and con-tent implausible.

In the tradition of the syntactic account there is a special problem calledthe “Goodman-Paradox” and “Goodman’s theory of projectibility” of hypo-theses – for Goodman entrenchment of predicates is only one feature of


projectibility. Schwarz explores three issues concerning Goodman’s so called“new riddle of induction”. They are first: considerations of extensionality,second: limitations of the present theory of projection, and third: entrench-ment and appeals to innate quality space. Schwarz argues the solution to the“new riddle” depends on psychological notions rather than syntactic orformal semantic properties.

The sociological and the historical account of scientific knowledge do notask for trans-paradigmatically validating and justifying scientific knowledge.Answering this question on the other hand is “one” task in the theory andphilosophy of science, i.e. science aims at supplying us with theories whichare empirically adequate – through the change of scientific knowledge, aswell. Jeffrey E. Foss shows in detail the error of both views the syntactic andsociological account, and – to take their place – he offers a new account, theinformation-economic account, which reveals the structure of science both ata time and through time. This regards the description and systematization oftheory change by the syntactic account, i. e. thesis that new theories reduceolder theories and the incommensurability thesis as part of the sociologicalaccount of theorizing. Foss constructs a five-fold unity of science for theubiquitous exchange of information between the various scientific discipli-nes: 1. sociological, 2. logical, 3. ontological, 4. epistemological, and5. temporal. Following this account, science grew both by elimination andaccumulation.

Structuralism (W. Stegmüller, J. D. Sneed) carries on to the question,which language is used and to the consequential problem of immunizingtheories against “recalcitrant experiences”. The example here may be the ruleof auto-determination, i. e. a theory defining the scope of its applications byitself. Therefore, at first, it is necessary to explicate what natural or physicallaw means and how these laws relate to scientific knowledge. C. UlisesMoulines, successor of W. Stegmüller at Munich University, takes (naive) set-theory not to be characteristic for the non-statement-view. He takes it just tobe technically useful and the background-theory of structuralism to be amoderate (conceptual) holism. For Moulines the major difference betweenstructuralism and different versions of operationalism – P.M. Bridgman,Carnap’s method of reduction sentences in the 1930’s et al. – consists in thesemantic structure of scientific knowledge. The major question is: What isfixing the meaning of quantitative functions, e.g. of mass, distance? – orrespectively: How is the extension of functions fixed in general? Moulinesdisputes the semantic analyses of quantitative functions that in the end comeup with: the operation is the meaning. He votes for a moderate holisticpicture of semantic concepts of scientific theories. This is contrary to P.


Duhm and W. Quine. Moulines takes clusters of concepts to be characteristicfor scientific theories. Hence, identity of a theory does not consist in a singlebut in a specific group of concepts and its correlation. Systematic connectionof concepts usually is called a law of a given theory, e.g. Newton’s me-chanics as a cluster of concepts of particle, time, distance, mass and force.

The building of empirically adequate theories is primarily concerned withtheoretically and semantically analyzing quantitative concepts. It is common-ly supposed that each and every observationally based quantifications repre-sents a measurement. But this is erroneous. Many perfectly good quantitiesdo not measure anything e.g. the number of 3’s in the distance in kilometersbetween two cities. Nicholas Rescher clarifies what it is that makes a quantitya meaningful measurement. It is easy to list necessary conditions here e.g.effective determinability, reproducibility, robustness, validity, nomic involve-ment, predictive utility, and descriptive dimensionality. But unfortunatelythe issue of sufficiency is less easily handled and in fact has not really beenresolved to date. Among the quantities whose claims to measuring somethingare distinctly questionable are quality of life and human intelligence (IQ).Rescher intends to conceptualize meaningful measurement by surveying socalled fallacies of quantifications, e.g. what one can not quantify is notimportant, everything can be quantified, quantification and measurement areone of the same.

The problematic aspects of the concept of a physical law are well known.R.I.G. Hughes examines three of them in his contribution: the problem ofmodal force, the problem of accidental generalizations, and the problem ofceteris paribus clauses. It is argued that these problems are inescapable iflaws are seen as a privileged class of empirical generalizations, but disappearif we consider laws as they appear in theories – provided that we view theo-ries in the way that the representational account of theories suggests. Thisaccount is a version of the semantic view of theories proposed by van Fraa-sen and R. Giere. Hughes fixes the place of theoretical laws on the represen-tational account, i. e. all theoretical laws are true in a model a theory de-fines. A model is a theoretical structure intended to represent parts of theworld – in contrast to structuralism. Newton’s law of motion provides a casestudy; and the representational account sheds light on the way they aredeployed in Newton’s “Principia”, and so defuses the criticisms of Newton’sprocedure made by Poincaré. In this context, Einstein’s approach of theori-zing is informative. James R. Brown examines Einstein’s distinction betweenconstructive and principle theories and discusses several of the properties ofprinciple theories in relation to visualization, thought experiments, and thequestion: Did Einstein change his mind and move of from a youthful positi-


vism to a mature realism? Brown argues that understanding principle theo-ries sheds much light on these matters. He interprets principle theories bylinking them to what are called “phenomena”.

Rather than summarizing or explaining historical scientific practice orattempting to justify individual beliefs, learning theory is concerned with theexistence of inductive methods converging on the truth of increasing empiri-cal data. Kevin T. Kelly and Cory Juhl illustrate the learning-theoretic ap-proach in their paper by establishing necessary and sufficient conditions for“almost stable” identifications. Which requires that the method be guaran-teed to stabilize the state producing only correct hypotheses drawn form afinite set. Kelly and Juhl show that the proof of the theorem involves theconstruction of a universal architecture for almost stable identification. Thiselaboration amounts to theorizing on the change (dynamics) of beliefs fromold to new. R.A. Fisher is rightly credited with developing many statisticalmethods, yet paradoxically while statistical inference requires the use ofprobability, few appreciate the distinctness of Fisher’s account of probabilityand its intuitive relationship to his statistical philosophy. Harriott recallsFishers merits for introducing the discipline of statistics. He presents asympathetic reading of Fisher’s account of probability, his style, his accountof statistical inference, and his interpreting on probability. And it is shownhow this dovetails with his underlying philosophy of statistical inference.

Laboratory experiments have shown behavior in the ultimatum gamewhich commentators have found anomalous from the point of view of ra-tional choice paradigm (decision/game theory), e.g. economic theory (R.Thaler). So, we are confronted with the problem: “How could such behaviorhave evolved?” Brian Skyrms investigates the evolutionary dynamic of a sym-metrized ultimatum game. There is one population and members of thatpopulation sometimes assume the role of ultimatum givers and sometimesthe role of ultimatum receivers. Skyrms’ study supplements the investigationof the ultimatum game between two populations by J. Gale, K. Binmore andL. Samuelson. In both cases there are (somewhat different) conditions underwhich the “anomalous” behavior can evolve. In the case investigated in hisstudy, even when the anomalous behavior does not evolve, other weaklydominated strategies typically survive in a population polymorphism. Resultscall into question the descriptive adequacy of sequential rationality andsubgame perfect equilibrium.

Quine’s scientific realism means, we are ontologically committed to whata theory says there is. He formalizes ontic decisions of modern science andour scientific knowledge, i. e. the (modern) ontological commitments, suchthat properties (universals), concepts or forms are removed from the scope of


science. George N. Schlesinger focuses on properties basing on “degrees ofcharacterizations”. A full-fledged predicate ‘J’ which applies to anindividual i has complete power of characterization through its capacity toset i apart from every other particular that lacks ‘J’. On the other end ofthe spectrum there are predicates with zero power of setting i apart fromanything. In between, there are predicates with varying degrees of differen-tiating capacities. Special references are made to M. Black’s critique of theprinciple of the identity of indiscernible and D. Amstrong’s insistence that“being identical with ...” is a pseudo-property. Following illustrative ex-amples, it is shown that his inquiry, which may have seemed to belongexclusively to the abstract study of ontological commitments has severaldown-to-earth implications. The issue shows that ontology and the scientificknowledge are to be seen interconnected.

B. van Fraasen disputes Quine’s scientific realism and various issues inunderdetermination of theories. In effect, van Fraasen’s constructive empiri-cism rejects the syntactic account of theories and also in part, thestructuralist account. The interconnection between ontology and scientificknowledge is the theme of Carl A. Matheson’s critique of van Fraassen’sconstructive empiricism. His account is based on a selective scepticismconcerning our knowledge of unobservable, which in turn is motivated bythe underdetermination of theory by observation. He argues that the ob-servable components of our theory are equally prone to underdeterminationarguments; theories can be observationally adequate without making trueclaims about observables. Thomas R. Grimes completes Matheson’s issue. Hedevelops a new solution to the problem of underdetermination as it appliesto the account of scientific realism and argues that the solution is an im-provement over other proposals that have been offered for overcoming thisproblem. Tang scrutinizes scientific realism as eminent in Paul and PatriciaChurchland’s eliminative materialism, i. e. their version of identity-theory.They attempt to refute the argument from introspection – as used by thedualist to support his non-materialist position. They present several parallelarguments to show that the dualist’s arguments are invalid. Tang examinesall these arguments and argues that the Churchland’s beg the question of theidentity of mental states with brain states as much as the dualist begs thequestion of the non-identity of these states. This result is due to theunderdetermination of the two positions. He then goes on to analyze whythe Churchland’s claim the identity of these two states and argues that theydo so by blurring the “is of predication” with the “is of identity”; by confu-sing contingent identity with necessary identity; and by conflating two sensesof scientific realism, which Paul C.L. Tang calls the “immanent sense” and


the “metaphysical sense”. Normally, we hold scientific knowledge to be intrinsically rational and

science traditionally is taken to be a model of rationality. But there aredifferent interpretations of scientific rationality and conduct. David Resnikexplores the limitations of the instrumentalist model of scientific rationalityand discuss alternative models: the dynamic accounts “conventionalism”,“reflective equilibrium” and “naturalism”. He does not suggest that weabandon the instrumentalist model, since it still has many useful applica-tions. However, we need to recognize its limitations and be open to alternati-ve approaches to scientific rationality that can successfully account for thephenomena that this traditional view cannot accommodate. The instrumenta-list model most clearly applies to local decisions relating to specific epistemicgoals and methods, but another model should be invoked in order to under-stand global decisions concerning general epistemic goals and methods. Heargues that an dynamic and naturalistic model of scientific rationality provi-des us with the most promising approach to understanding global decisionsin science. Aldo Montesano examines the different meanings of the termrationality in economics and proposes a framework where they can be pla-ced. He introduces a distinction among the rationality of theory, i. e. econo-mic theory is deductive, the rationality of action, i.e. agents actions areintentional, and the rationality of agents’ preferences on actions, whichimplies three different sub-rationalities: the rationality of preferences onconsequences, the rationality of expectations and the rationality of thefunction which determines agents’ preferences on actions. Further on, heintroduces a formal representation of these rationalities and their role ineconomics commented upon.

For Popper scientific practice is intrinsically rational. His view of scienceas a social phenomenon and of scientific theories as refutable renders sciencemuch less ideal than the traditional account of it as proof. Joseph Agassiargues nevertheless, pluralism requires further relaxation of Popper’s ac-count. Viewing science as the result of our filtering from the world what wevalue, renders it much less ideal, since what we value may and usually doescome in a mixed bag. Agassi shows that Popper’s view of normal science asdangerous, then, is an exaggeration, since it is a social phenomenon; we mayjudge its output post hoc and decide what part of it we value.

Although metaphors are not well esteemed as part of scientific language,we realize they can not be secluded. So, they seem to be functional. MichaelBradie demonstrates that the heuristic dimension of metaphors in scienceinvolves the use of metaphors in the construction and development of newtheories or new formulations of the old based upon perceived or created


analogies or similarities extrapolated from prior theories or from analogiesor similarities extrapolated from experiential realm – i. e. not from anyformal theory. The cognitive or epistemic dimension of the role of meta-phors in science involves the application of theories to reality. Bradie arguesthat the cognitive or epistemic role of metaphors in science is more signifi-cant than is often realized. When theories are applied to the world, theapplication of the theory results in a metaphorical redescription of the phe-nomena to be understood. In normal science, the range of application oftheory is extended via exemplars – worked out examples which, when suc-cessful, are shown to fit the data. Bradie presents some illustrations fromvarious disciplines and concludes with a brief consideration of some objec-tions and some remarks on the implications of his analysis for some centralepistemological and metaphysical issues of our scientific knowledge.

As others have remarked, discussion of the values relevant to work is rarein the science literature, in spite of the great and growing importance of suchissues e.g. Putnam. David Gruender briefly explores possible reasons for this,and revisits the fact-value-distinction. Above all he examines major ethicaltheories for their possible bearing on value issues in the sciences. Referencesare made to the semantics von value-statements of logical empiricism, theemotivists (A. J. Ayer, C.L. Stevenson), the naturalistic fallacy (G.E. Moore),to R. M. Hare’s approach and J. Dewey’s application of value theory to thesciences. A version of the theory identifying values as existing or as potentialfacts important to human beings is sketched showing its application toindividuals and social groups. Some consequent global implications aresketched, as well. Anyway, we should remember: Wertfreiheit remains anunquestionable constraint on object-theories of scientific conduct.Wertfreiheit guarantees for objectivity, rationality and acceptance of ourscientific knowledge. That does not exclude scientists from being committedmeta-theoretically to a demanding ethics they use during their commonscientific affairs. But they do not have to.

The collection was planned by the project Protosociology (http://www.rz.uni-frankfurt.de/protosociology). It is owed to many people. We want to thankthem for their contributions. Above all our senior, W.K. Essler gave strongsupport in developing the project but also M. Roth cooperated in outliningthe content of the project. We dedicate this volume to Wolfgang Stegmüller,the most influential of the first-generation philosophers of science in post-war Germany.

Gerhard Preyer, Georg Peter, Alexander UlfigFrankfurt am Main, Germany

12 Wilhelm K. Essler

LOGICAL OPERATIONALISM – SIGNIFICANCE AND MEANING

Wilhelm K. Essler

Truth and Knowledge: Some Considerations concerning the Task of Philosophy of Science

1. Preliminary Remarks on Philosophy of Science

Investigating empirical science consists in investigating what exactly scien-tists doing by practic empirical science.

Investigating empirical science itself may be performed according to rulesof empirical science leading mainly to psychological, sociological, politicaland historical statements on actions and assertions of scientists, being thensome science of science; or it may be done according to rules of a prioriscience in using solely methods of deduction and definition, the resultingstatements belonging then to some philosophy of science.1

Thus it is very easy to draw a clear distinction between these twometadisciplines via nominal definition. However, it is not very easy, whenworking within the framework of one of these two disciplines, to alwaysclearly keep this distinction in mind. Moreover, it is not always useful not tooverstep this dividing line: Because a philosopher of science, while workingon his idealizing rational reconstructions, will not lose his footing if he keepstrack of the work – successful, for the most part – done in the sciences; anda scientist of science, while investigating the object empirical science – towhich he himself belongs, as seen from the outside – , will surely profit if heincorporates the results of philosophy of science.

Philosophy of science – and this is what this paper is about – is thus a me-tadiscipline; for its object of research consists in the activities of the empiri-cal scientists. These activities, however, are quite varied: they consist partlyin formulating measuring results, statistical treatments of those results, lawsand theories, partly in justifying or rejecting theories by means of experiencesas well as justifying or rejecting experiences by means of theories, and partlyin applying measuring theories in order to obtain empirical data. In phi-

Truth and Knowledge: The Task of Philosophy of Science 13

losophy of science the activities of an empirical scientist will therefore beitems of reflection; or, in other words: whatever means the empirical scien-tist uses to obtain and to formulate the results of his domain of research willnow be mentioned as a new domain of research where analyses being carriedout in such a way that the means of the a priori analyzing are used, i. e. themethods of deducing and defining. The transition from using to mentioningin using tools of the reflection level marks the transition from an empiricalscientist’s level of working to the meta-level of working of a philosopher ofscience as an a priori scientist.

This is a preliminary and very rough determination of the distinct realmsof investigation by leveling language. If there were no more precise andsubtle determination one could, of course, be content with it. But there existintellectual instruments to determine the levels of this reflection processmore subtle. And it is the logic which empirical scientists are using in theirendeavor for the purpose of systematizing their results, which will show ushow to determine these levels.

Until now they always used without exception some classical logic takenas basis for the mathematics they are applying. The justification of such asystem of logical arguments entails either the immediate reference to thedefinition of the classical two-valued concept of truth or the mediatelyestablishing of some system of axioms in order to produce classical deduc-tions as well as the evidence of its correctness by an argumentative referenceto this particular concept of truth.

Since the respective investigations of Tarski we know that this concept ofcomplete interpretation, with which the concept of complete truth is to bedefined, determines the stages of semantic reflecting in an unsurpassedsubtlety as follows. If a certain language is taken and afterwards its variety ofexpressions gets enlarged, then two different results may happen: (a) Withinthe language newly developed in this way the concept of complete inter-pretation and with it the complete two-valued concept of truth for the previ-ous old language are not expressible; then the new language belongs to thesame semantical level of reflection as the old one. (b) Within this newlanguage such complete semantic concepts for that old language are ex-pressible; then the new language belongs to a higher semantic level of reflec-tion. And a minimal such enlargement of the old language will then laydown the subsequent semantic level of reflection, thus being the standardlanguage of that level.2

Each new semantical level will then presuppose a more extensive ontolo-gy than the previous one; in doing so, the size of these ontologies can bemeasured by some ordinal number. The more extensive the ontology is the


more means of arithmetics can be expressed in it, and therefore the moreand the more fine-meshed conceptual nets for finding the truth, for determi-ning truths, for gaining knowledge the semantics will contain; or, in short:some ontology enlarged in this way will contain more and also strongerintensions which are instruments for extensionally determining the domainof the interpretation of the old language as well as the extensions of thecognitive concepts of that language, and as a consequence the truth values ofthe sentences of that language and therefore finally the extension of theconcept of truth.

It is the aim of this paper to give indications of how such a concept ofworking within the field of theory of science can be started as a programme.Because as far as I can see this approach has until now not yet been taken upby anyone and being dealt with as a program of research: Mathematiciansand logicians like Frege, Hilbert, Gödel and Tarski obviously were not inte-rested in questions of this kind. And among the philosophers, on the otherhand, only a few like Reichenbach, Carnap and Hempel carried out investi-gations in order to exactly describe the logical structure of these intensions.Of course they did this by skillfully using the instruments of modern logic,but without incorporating the metalogical results obtained by Gödel, Tarskiand others. And after they got stuck in questions of details they raised thewhite flag instead of procuring stronger and sharper weapons.

I now burn this white flag. Because their way of philosophy of science,being a logical operationalism, opens up unexpected insights for those whotake it while including the metalogical results in a deliberate and skillful way.It will open up insights into what is the contribution of the human mind -represented by communication systems of languages of different degrees ofexpressibility arranged in the form of levels – during the process of obtainingempirical knowledge. It consequently enables a philosopher of science whomaintains some position of relativism rather than of absolutism, to determine– while adopting some basic thoughts of Kant – what in empirical sciencesand especially in physics may be regarded as perceptions or measuring result,as observations or confirmed measuring results, as experiences or generalizedconfirmed measuring results, how the additional empirical knowledge is tobe classified according to usefully applied categories of epistemology, andwhat philosophical insights may be gained in analysing those categories; inshort: it enables to develop some relativistic métaphysics3 of experience.

2. The language of classifying and comparing

Scientific working starts with investigating attributes of things of a universewhich one is interested in as can easily be observed in looking at science both


from a historical and a systematical point of view. In Aristotle’s philosophyof science the unary concepts are those concepts of experience which he re-garded exclusively. But even in present-day empirical science where peopleare working experimentally the empirical base consists of unary concepts.These concepts may be given as it is with a normal-sighted human’s percepti-on e.g. of color, or may be artificially created, as it is with the intervals ofmeasuring units. And no matter how reliable or unreliable this measuringdevice may be, if it gets used on an object of the universe one receives aresult which, in view of the factor to be determined, is to be found withinone of those intervals.To determine philosophically this situation of classifying and comparing it isrecommended – in accordance with William of Ockham’s principle “Entianon sint multiplicanda praeter necessitate” – to choose a language includingthe ontology required for its use, which contains all the measuring conceptsof some science as well as the respective comparative concepts, but notconceptual tools which are not required here. For this purpose the entirelanguage of first order quantificational logic is unsuited; for it containsexpressions for all n-ary relations where n is some positive natural number,while in situations of classifying and comparing only 1-ary and 2-ary con-cepts are needed among the undefined concepts. Therefore such a first orderlanguage does not yield any additional profit, but enormously complicatesthe drawing-up of a semantics for this language on a meta-level.

The language used here, i.e. M0L, contains a term “U”, designating someuniverse of discourse and being defined in this simple language of a finitetype theory as:

Df1 “U = λx: x=x”

Now, normally measurements are not performed on all objects of the uni-verse, be it, since there is no point in it for some elements, or be it, since themeasuring instruments are not suited for them; then the field of investiga-tions is limited to a subclass F f U in short: to the field F. If, for example,objects of the physical universe are investigated and classified upon theircolours, then F is the visual part of this U.

The measuring intervals on a measuring device – and even the human eyecan serve as one, for instance when colours have to be determined – may beregarded here as classes which are excluding each other in pairs. On thislevel of the analysis of empirical knowledge the measuring instruments arenot yet anything to worry about; on the contrary, the attention gets ex-clusively directed at the objects of field F. In comparing the elements of Fwith regard to colors the respective classes must contain standard objectsrepresenting these classes, e.g. small color plates representing the standard


colors during the perception of colors; and therefore these classes cannot beempty.4 And in their entirety they have to exhaust the field F which repre-sents the area of investigation. This establishes the following three axioms ofclassification:

Cl1 “vGH ε M:G … H 6G 1 H=i” Cl2 “vG ε M: G…i”Cl3 “ = F”MU

When the entirety M is finite and, in addition to that, contains a knownamount of classes, then these axioms can be rendered in a well-known wayin first order quantificational logic: the universal quantifications of Cl1 andCl2 will be rendered in conjunctions; and the existantial quantifications ofCl3 will be rendered in an adjunction.

In each actual measuring situation M is finite; and in addition, that finitenumber is known to the scientist. If that number is very large, he sometimeswill identify it with !0, regarding this as an idealization. It is then to bedetermined empirically which and how many elements of F are elements ofthe sets of M which are e.g. colors or measuring intervals. The axioms {Cl1,Cl2, Cl3}, on the contrary, are describing how to classify the elements of F;therefore, in M0L they constitute the structure of experience and are thus apriori for the still to be obtained experiences.

While Frege took the view that the intensions of the basic expressions ofsome axiomatic system determine the truth values of the axioms, Hilbert, onthe contrary, asserted that precisely these sentences determine the intensionsof those concepts in determinating the class of their models. I take Hilbert’sview; – in analysing the differentiation using-mentioning more exactly, thebackground of what is happening here will become more clear.

Concernig Hilbert’s misleading mode of expressing, that an axiom systemwould define its basic concepts, Frege rightly pointed out that herewith notthese concepts, but some concept of second level related to them gets defined,in taking the concepts of the axioms system as bare variables and the con-junction of the axioms as definiens of the definiendum.5

“Partition” – in short: “Ptt” – is here the higher level concept with respectto {Cl1, Cl2, Cl3}, expressing that M is a partition of F using as definiens thestructure of those axioms:

Df2 “v MF: <M, F > ε Ptt : vGH ε M [G … H 6 G 1 H =i] v vG ε M [G …i ]v = F”MU

In order to determine what class of some fixed M – where M may be colors,lengths, weights, positions, etc. – contains some given object of F, this object


has to be compared with the respective standard objects. They are comparedby using some equivalence relation of colors, or of lengths, etc.; and themeasuring instrument some biological or mechanical object regarded as agood realization of the following axioms {Eq1, Eq2, Eq3} of comparingobjects according to equality – perceives whether or not both objects areequivalent in the given respect. This instrument need not be in F and noteven in U.

The three following axioms describe the characteristic attributes of anequivalence relation Q over F as a transitive and symmetrical relation whereevery element of F is some member of Q:

Eq1 “< Q,F > ε Trs”Eq2 “< Q,F > ε Sym”Eq3 “F = mem(Q)”

The concept “member of Q” is hereby defined as usual:

Df3 “vQ: mem(Q) =λx wy: < x,y > ε Q c Q-1”

By using these characteristic attributes of equality with regard to the respecti-ve contents of color, length, etc., we obtain knowledge on which objects areequal and which are unequal in that respect. In this way we consequentlydetermine – step by step, and in fact at each step partially only – the exten-sions of the elements of M, like the extensions of the colors as color classes.

The structure or logical form of this abstract form of equality is again tobe introduced as a higher-rank concept, “equivalence relation”, as follows:

Df4 “vQF: < Q,F > ε Equ : < Q,F > ε Trs vv < Q, F > ε Sym vv F = mem(Q)”

In order to see how such an equivalence relation Q generates a partition Mof the field F, we first introduce the function concept “ƒ„”, spoken: “relatof”:

Df5 “vQFx: ƒx„Q,F =λy ε F: < x,y >ε Q”

For some equivalence relation Q the relat of an object is the equivalence classcontaining this object and being thus represented by it.

Such an equivalence relation Q divides F up completely into non-emptyand disjunct subclasses. For that reason the concept “quotient set” can bedefined by the function symbol “/” – read: “divided by” – as follows:

Df6 “vQF: F/Q =λG wx ε F:ƒx„Q,F = G”

Then it can be proved that each equivalence relation generates a partition:6

Th1 “vQF: < Q,F > ε Equ 6 < F/Q,F > ε Ptt”

Reversely, each partition uniquely determines the respective equivalencerelation:


Th2 “vMF: < M, F > ε Ptt 6 wQ: < Q, F > ε Equ v F/Q = M

The extension of this equivalence relation – being a class of ordered pairs –is thus uniquely determined by the given partition; beyond that, with theconceptual means available at this level, there are no different intensionsleading to the same extension. For the axioms {Eq1, Eq2, Eq3} are the onlyrules given a priori. In that situation of perceiving and measuring all othersentences accepted as knowledge are accepted later on as a result of applyingthese rules to the elements of F, and are therefore regarded as empiricalassertions in that.

A partition and therewith an equivalence relation constitutes a nominalscale; here the sequence of the equivalence classes generated in such a way isstill completely at random. With an ordinal scale or a comparative order,however, these classes are arranged in a series. Hence such a comparativeorder is obtained by adding a series R to an equivalence relation Q; such aseries R is transitive, excludes Q and is connex outside of Q:

Sr1 “< R, F > ε Trs”Sr2 “< Q,R,F > ε Excl”Sr3 “< Q,R,F > ε ExtCon”

The concepts of exclusion and of the external connexity are thereby definedas:

Df7 “vQRF: < Q,R,F > ε Excl : vxy ε F: < x,y > ε Q 6 < x,y > R”/ε

Df8 “vQRF: <Q,R,F > ε ExtCon : vxy ε F: < x,y > Q 6 < x,y > ε R c R-1”/εThe concept of a comparative order is then, by using the structure of theaxioms {Eqi,..., Sr3} as definiens, to be determined as a higher-rank conceptrespective explicit concept as follows:

Df9 “vQRF: < Q,R,F > ε CpOrd : < Q,F > ε Equ v < R,F >ε Trs v < Q,R,F > ε Excl v < Q,R,F >

ε ExtCon”

With this set of conceptual instruments a philosophy of science can not onlyconceptually record and reconstructingly show the usual perceiving andobserving, but also those parts of measuring which get done in a comparativeway and without underlying metrics. In sciences, a large amount of ob-servations are gained in this way and are then compared with proposed laws.

It is the task of the epistemiology to describe in detail how to work withthese concepts, how they get used for thereby obtaining singular knowledgefirst, and with this then general knowledge. In this branch of philosophy of


science it has to be shown in detail which conditions have to be realized sothat one can accept a particular judgement as knowledge.

It is, however, the task of the métaphysics as a further part of philosophyof science to present those conditions – within the frame of the given possibi-lities – systematically and in a complete or at least completed way.7 In thecase at issue the métaphysical fundamentals of experience consist of thenamed systems of axioms, that is to say of {Cl1, Cl2, Cl3}, {Eq1, Eq2, Eq3}and {Eq1, ..., Sr

3}, and this applies respectively to each quantity that comes

into question. No further foundation is possible at this stage of the conceptu-al analysis of working in empirical sciences.

3. Defining “Truth” and Finding Truth

Those three systems of sentences {Cl1, Cl2, Cl3}, {Eq1, Eq2, Eq3} and {Eq1,..., Sr3} have to be regarded, indeed, as three families of systems of axioms.Therefore, for example M1 may be the entirety of the basic colors red, yel-low, and blue, M2 the entirety of the spectral colors, M3 the entirety –understood to be a discret union – of spectral colours plus the border colorsblack and white, and M4 the entirety – understood to be a continuous union– of all colors producible from them by a continuous transition. By analogyMi' may be entireties of classes of height with a different degree of fineness inthe determination of heights, and Mi" may be entireties of classes of weightwith tolerance widths which are different in each case.

These entireties are brought about by the equivalence relations Qi, Qi' andQi". No series are assigned to the different relations of color equality; theindividual relations of height and weight equality, on the other hand, arenow aligned topologically by such relations Ri' and Ri".

The language without additional means of expressiveness, being in thesense of William of Ockham’s razor the smallest language which containsthose axioms and the resulting theorems, is thus a second-order languageM0L of the following kind: on rank 0 it only contains terms for individualsand for ordered pairs of individuals, on rank 1 only expressions for 1-ary and2-ary relations, and on rank 2 only expressions for classes of classes.8

The language used until that point is now mentioned; this is indicatedhere by replacing the numeral “0” on the top in front of the previously usedcognitive expressions of M0L. The previously used expressions “a”, “U”,“R”,... are thus now written like “0a”, “0U”, “0R”,. . . ; to simplify matters,however, this index is omitted in connection with the logical symbols.9

The expressions of M0L are elements of the universe U; this class U, too,is determined on this level of reflection as the class of objects being identicalwith themselves. Elements of this U, however, are also those statements


which were, are or will be produced when M0L is used, and moreover: whichare candidates for such usage, even if they are never used. The expression asa type is then the equivalence class of the expressions equivalent to a stan-dard expression as tokens.10 A suitable equivalence relation which partlyshows consideration for the external shapes of these objects and partly forthe functional correlations thus lays down the types of expressions for therespective given tokens. The syntactical rules of M0L concerning the voca-bulary consists of the descriptions of the general characteristic attributes ofthese expressions.11 In addition to this, the syntax of M0L’s grammar con-tains an operation or function { which combines two such elements X andY to a new element Z: {(X,Y) = X{Y = Z.

In order to trace what was done before on this level of reflecting, asemantics must now be developed – also according to Ockham’s razor – forM0L which will thus get syntactically determined. For that purpose first ofall Tarski’s method of homogenizing types12 or some related method has tobe applied to the various types of designata. Then an interpretation J is to beintroduced as a function, mapping the domain of J, i.e. those elements of Uwhich consist of cognitive expressions of M0L, into that homogenized classof entities, thus being the range of J. The concept of truth13 is then definedby referring to those interpretations on the basis of non-empty14 universes;and the concepts of deduction are introduced in the usual way by using thisconcept of truth.

The axiom systems of M0L can easily be proved to be consistent; for thereexist models in arithmetics which satisfy them simultaneously.15 But we arenot interested in some model of those axioms but in that interpretation onthat universe of discourse we were speaking about when using the sentencesof M0L. As long as we were using M0L the cognitive expressions of M0L wereregarded as rigidly connected with their designata. In reflecting M0L wecatch the syntax and, in doing so, lose this connection J on some domain; wetherefore have to use methods of semantics and of epistemology to get themback step by step.

On this semantical level M1L the ontology which is presupposed in usingM1L is richer than that of M0L. Of course, it need not be that epistemologyis referring to these additional means; thus it does not use them. This hap-pens e.g. when in M1L the expressions “Q” and “R” are related, via J, tosome relations / and ¤, without specifying them in epistemological respectsaccording to that additional ontology which is some more subtle net forclassifying objects. In this case, metaphysics is definitively completed for us:the axioms of M0L then constitute our system of conditions of physicalexperience. This is the métaphysics we get, when on the level M1L we re-


member only the results of epistemological work used in semantics, but notthe way of gaining those results.

But perhaps we remember, in using M1L, what we did before in episte-mological respects which lead to assertions of M0L, e.g. when we had toassert that x is equal to y with regard to color, or that x is smaller than ywith regard to length, or that x is larger than y with regard to weight. Thenwe perceive how we perceived: we identified the objects of the field ofinvestigation, and then we investigated them according to specific methods.

In the case of color perception we identified the objects of field F accor-ding to the pars pro toto principle with their surface; and then we broughtthem sufficiently close together and examined their color relation by ap-plying some suitable test-result method. In case of determining length weidentify the objects of the field with certain distances leading from twocorner points through these bodies; and then we examined their lengthrelations. And in the case of weight determination we identified them withtheir centers of gravity; and after that we examined them in a suitable way.

The test conditions as well as the test results contain substantially moreconceptual possibilities than were available in M0L. This can be seen veryclearly in the following case of length comparison, which will be described ina short and simple way – although through the shortness which is called forhere far too simplified: “A” be the test condition, “B” the result of thelength-equality test, and “C” the result of the shorter-relation test. They shallbe determined by suitable definitions according to the following indications:

“A(x,y,z,w)” for “The objects x and y, understood to be distances, aremoved in such a way that afterwards, at the time z, they are parallel in allthree dimensions of physical space, and that there exists a perpendicularw – for instance, by means of parallel light, or an appropriate shifting ofa physical right angle – such that one edge point of each x and y sharesome ray of w and two inner points of x and y share some other ray ofw”,“B(x,y,z,w)” for “At z, the other edge points of x and y share some ray ofas well as“C(x,y,z,w)” for “At z, the other edge point of x and some inner point ofy share some other ray of w”.

Thus reference to geometrical attributes of these objects is made, to theirmovement in space, to points of time or sufficiently short intervals of time astemporal cross-sections of the space-time-continuum, and to many otherattributes, which in the shortness called for here must be passed over.

Analogous to that the respective test and reaction conditions have to beformulated for orderings weight and color comparisons. In all these cases it


then turns out that for finding the interpretation of M0L and thus for findingthe truth values of all the statements16 of M0L there is more to presupposethan is available in M0L.

It is the task of the respective science – or rather: the foundational rese-arch of this science, its métaphysics – to determine how these conditions areto be formulated. It is, however, the genuine task of the philosopher ofscience to determine the precise logical formulation of this test-result relati-on, and with it the presuppositions which have to be given for an applicationof such an operational determination of relations / and ¤. The auxiliaryconcept ‘total uniformity of A with respect to B” – in short: “TU(A,B)” –may be defined as follows:17

Df'1 “vxy ε F: < x,y > ε TU(A,B) : [wzw [A(x,y,z,w) v B(x,y,z,w)] 6 vzw [A(x,y,z,w) 6 B(x,y,z,w)]”

The comparative relations / and ¤ cannot be determined operationally bytotal definitions. For it has to be presupposed that the test gets performedonce – in the past, present or future –, and that total uniformity is given withregard to that test-result relation, the latter to be understood as an idealizati-on.18 Should, on the other hand, the objects x and y be identical, then / is tobe equated with identity and ¤ with diversity:

Df'2 (a) “vxy ε F: x = y 6 [x /y : x=x]” (b) “vxy ε F: [x … y v< x,y >ε TU(A,B) vwzw:A(x,y,z,w)] 6 [x / y : vzw:A(x,y,z,w) 6 B(x,y,z,w)]”

Df'3 (a) “vxy ε F: x=y 6 [x ¤ y : x … x]” (b) “vxy ε F: [x …y v < x,y > ε TU(A,C) v

wzw: A(x,y,z,w)]6 [x ¤ y : vzw: A(x,y,z,w)6 C(x,y,z,w)]”

Applications of such partial definitions therefore require auxiliary objects w1,

w2, ..., which are the realizations of those partial definitions as the analytic

parts of the a priori background; these objects of U need not be elements ofJ(“0F”) and not even of J(“0U”).

The realm of such a realization w is the set of objects of U so that theresults of the operation satisfy the axioms {Eq1, ..., Sr3}. According to meta-empirical results the class of those auxiliary objects may be divided accordingto equal strength or to equality of realm; then reformulations of “B” and “C”refer to such an equivalence class of realizations.

Let w be some realization, being an element of some class H of realiza-tions equal to w. Then, on account of applying w, it may happen that certain


observations are gained and, based on them, further certain general condi-tional equivalences of the form of Df'2 (b) and Df'3 (b) with a differentcondition “A'” and different results “B'” and “C'”. Suppose that the field F'of that candidate of operationalizing / and ¤ largely overlaps both F andand U \ F. Then, in this later situation of scientific research, scientists willaccept this generalization on F 1 F' as empirical truth; and, being confidentof it, they will therefore use it outside, i.e. on (U \ F) 1 F', as an additionalinstrument to get new empirical truth not receivable up to now, thus cons-tituting experience. In this simple case, such a priori accepted sentences areused as analytic truths, since they are logically equivalent to new partialdefinitions, to be added to Df'2 and Df'3:

19

Df'2 (c) “vxy ε F'* \ F*: ...”Df'3 (c) “vxy ε F'* \ F*: ...”

In epistemology of M1L for M0L, we have to determine the minimal set ofpresuppositions which are required in every stage of operationalization. Inmétaphysics of M1L for M0L we have to systematize these intensions whichare the instruments for finding out the extensions of the cognitive conceptsof M0L; here we have to establish a simple and homogeneous systematizationof that set of presuppositions for each epistemological stage. If, for the sakeof economy, it then turns out that the operationalizations of kind (c) aremore fundamental than those of kind (b), then scientists will rearrange thesequence of operationalizations according to that métaphysics. In our fast-living times shiftings of the corpus of empirical and a priori truths arecarried out from time to time, according to the progress of empiricalknowledge.

So, in developing experimental methods, physicists got the result that1.650.763,73 wavelengths of red light of the 86Kr in the vacuum are roughlyof an equal length to the standard meter in Paris. In rearranging the méta-physics of physics later on, this empirical knowledge was shifted to oneaccepted as a priori in 1960, when it was declared to be the new definition ofstandard measuring unit of length; the previously a priori knowledge becamethen an empirical one. In 1983 the Conférence Général des Poids et Mesurestook the former empirical laws that 1 meter is equal to the length of lightrays in vacuum during 299792458-1 seconds as the new definition of “me-ter”, so that the former definitions were shifted to the empirical laws; there-fore it now be measured that the length of the standard meter is changing tosome degree.

To justify such rearrangements empirical laws containing metric conceptsare needed; for – to formulate a metaempirical hypothesis – without suchconceptual instruments the subtle interconnections and differences between


the old method and the new one cannot be pointed out to the requiredextent.

Metric concepts designate functions from F or from conservative extensi-ons of F into the class ú of real numbers. Such sets of numbers can bedetermined in M1L by referring to some categorical description of theirattributes.20 The operation of combining elements of F is then, by suchmetric functions, mapped to adding numbers. The attributes of the combi-ning of elements of F can be formulated in M1L according to Hölder asfollows:21

Hd1 “< / ¤ F > ε CpOrd”Hd2 “vx ε F wy ε F: y ¤ x”Hd3 “o: F × F 6 F”Hd4 “vxy ε F: x ¤ x o y v y ¤ x o y”Hd5 “vxy ε F: x ¤ y 6 wz ε F [x o z /y ] v wu ε F [u o x /y]”Hd6 “vGH: < {G,H},F > ε Ptt v vx ε G vy ε H [x ¤ y ] 6

wz ε F vx ε F: (x ¤ z v x ε G) w (z ¤ x v x ε H)”

Taking the operation o as the combining of objects of F as to their length,then Hd2 and Hd3 say that there is neither a smallest nor a largest length,while Hd4 excludes elements of length 0. Hd5 guarantees the existence ofdifferences of lengths; and Hd6 postulates the existence of Dedekindian cutsso that F is a complete set with regard to the combining operation. Taking oas the combining of objects of F as to their weights, these axioms are to beread analogously.

The logical form or structure of these operations is expressed by the ex-plicit concept “Hölder system”, in short: “Hld”; again, we take the axioms{Hd1, ..., Hd6} as definiens, regarding their cognitive concepts now as varia-bles:

Df'4 “vF o / ¤: < /,¤,o,F > ε Hld : ...”

For some purposes of application it may be suitable to weaken Hd6, e.g. tothe Archimedian axiom Hd7 saying that for each two elements x and y of Fwhere x ¤ y there is some finite number of x’s – to be more exactly: ofcopies of x, of elements of F being equivalent to x – so that the result ofcombining them is not smaller than y. The respective explicit concept“Hld*” is then to be defined according to {Hd1, ..., Hd5, Hd7}.

In M1L, metric concepts in the sense of basic measurement are introdu-ced by mapping some Hölder system into some set of numbers:22

Et1 “< /, ¤, o, F > ε Hld”Et2 “g: F 6ú+”Et3 “vxy ε F: x / y 6 g(x) = g(y)”


Et4 “vxy ε F: g(x o y) = g(x) + g(y)”Et5 “u ε F v g(u) = 1”

In the sense of Hilbert, these axioms implicitely define the concept “ex-tensive additive magnitude”, in short: “Eta”:

Df'5 “vF guo/¤: < /, ¤, o, g, u, F >ε Eta : ...”

In the case of length measurement the elements of the then observed field Fare objects of a physical space which has the attributes described by somegeometry; and in the case of time measurement the elements of F are pointsin physical time which has the attributes of some chronometry.

Additivity need not be a component of metric concepts. Of course, veloci-ty in classical mechanics is additive: for if we combine two objects a1 and a2

according to velocity v, we have: v(a1 o a2) = v(a1)+ v(a2). But in the case ofthe special theory of relativity this equation is regarded as some limit valueof: v(a1 o a2) = (v(a1)+ v(a2)) /(1+ v(a1) @ v(a2) @ c-2), where c is the velocityof light in vacuum. Thus, the intensions of concept at least partially dependon implications of the theory to which they belong.

Thus M1L contains the total concept of truth for statements of M0L, sothat the concept of logical consequence, as the central method for scientistsas well as for philosophers of science, is definable in M1L for M0L in theusual way; and additionally M1L contains conceptual instruments, whoserealizations by physical instruments allow scientists to decide whether or notsentences of M0L are true, i.e. to find truths.

The means available in M1L to find truths also contain certain two-valued functions, which are defined on pairs of statements of M0L and havevalues in [0; 1] f ú; these methods of epistemology are then regarded asepistemological probabilities. Another method of M1L consists of a two-valued function from pairs of sets of objects into [0; 1] f ú understood tobe the objective probability and identified in final cases with relative frequen-cy. Epistemological probabilities can effectively be applied when they arerelated to objective probability.

4. The End of Métaphysics

Furthermore, respective métaphysics of a given physical theory contains thatbackground knowledge which is necessary to read mathematical equations asphysical laws. For instance, Galileo’s law “s = ½ @ b @ t2” is related to timeand space as well as to some field of physical bodies identified with theirpoint of gravity: and it presupposes conditions of application like frictionles-ness, nearness to the earth’s surface etc. as far as M1L contains vocabulary to


formulate them. A complete reformulation of that law in M1L will then be ofthe form:

“vx ε F: ...s(x) ... t(x)... b... 6 s(x) = (b/2) @ t(x)2”

Thus, pure métaphysics for that physical theory formulated in M1L containsall the background knowledge presupposed in that theory like geometry,chronometry, theory of bodies, and theory of measurement. And appliedmétaphysics tries to establish the respective conditions of the laws of thattheory.

But in speaking like that, M1L is no longer used but mentioned. For Istarted here to reflect about M1L, even if this is done in very rough and indis-tinct remarks. The – still to be produced – task of the syntactic, semantic andpragmatic aspects of such a reflecting process thus consist in:

The syntax of the language used before has to be developed in harmonywith Ockham’s razor. To develop a rational reconstruction of the theoriesand laws used before to determine the intensions of the concepts of thetheories of M0L, the syntactical forms of that concepts of M1L as n-aryconcepts for different natural numbers n has to be established, as well as itslowest syntactical rank with respect to theory of types: as long as such ex-plications do not produce other results, we locate the concepts of eachtheory at rank 0. Then the laws and theories containing those concepts are tobe reformulated so that proof of consistency can be carried out.

The semantics of this language M1L then has to be established by determi-ning the class of possible interpretations, thereby using some more powerfulontology; referring to that class the concept of truth for statements of M1Lis then to be defined, being the basis for introduce the concept of logicalconsequence.

The pragmatics of M1L establishes instruments for establishing the intend-ed interpretation. In M1L, for example, the term “1o” was used according to{Hd1 , .. .,Hd6}. However, the attributes expressed in this set of rules are notthe only ones. On the contrary, this set only determines the logical form orstructure of what was intended with “1o” while using M1L; and this structureis, of course, common to all such combining operations, independent of itsspecific kind like combining objects according to length or according toweight.

Perhaps additional partial definitions are formulated in M1L, defining“1o” in other concepts and finally in other basic concepts of theories in M1L;then, seen from M2L, these theories also only determine the structure of theirintended interpretation, but not the specific interpretation itself. Thesetheories and definitions can be reformulated in M2L without change; it stillremains to be clarified whether M2L contains the same background knowled-


ge as the one which was used before in M1L, or whether the pragmatics inM2L for M1L entails additional conceptual as well as epistemological meansso that the basic concepts of the theories of M1L can now be referred to morespecific and differentiated attributes which refer not only to the logical formof their intensions, but to these intensions itself.

Ultimately, these defined concepts refer to concepts of geometry andchronometry,23 then understood to have a physical content; and this contentbecomes manifest in situations when experiments are performed to determi-ne values of physical magnitudes. But these performances are – formulatingagain some metaempirical hypothesis – always human actions related to andin agreement with physical theories being known either consciously or assome semi-conscious background knowledge: be it the craftman’s knowled-ge, or be it the utilization of our present-day scientific knowledge.24 Atearlier stages of this succession of empirical knowledge geometrical andchronomical theories will be enriched by referring their concepts opera-tionally to empirical knowledge which is now used a priori to get empiricalresults. But this need not always be so.

With regard to the métaphysics used in M2L for determining the inten-sions of the terms of M1L, two cases are to be considered: (a) It may turn outthat this métaphysics used now is not richer than the one which was usedbefore in M1L and which is under investigation now, so that both are in factlogically equivalent. (b) It may turn out that also at this stage of using M2Lits pragmatics is richer than the one of M1L, for which we now try to de-termine the intensions used before. Which particular case is given heredepends on the amount of métaphysics of the users of M2L; and the answermay be therefore different for different persons or even for one person atdifferent times.

In the case (a), métaphysics came to a standstill at least at this point; forthe additional instruments of syntax and semantics, which are used in M2L toreflect scientific operations at level M1L, are not used in pragmatics of M2L.At this point, epistemology as well as métaphysics do not take advantage ofthis more powerful ontology which is available here, or which will be availa-ble in future when going on to still higher language levels: The backgroundknow-ledge used now is already present in the investigated métaphysics.Therefore any epistemological reduction of the basic terms of this métaphy-sics can be carried out only in the vocabulary of that same metaphysics anddoes not lead out of it; no other background knowledge containing moredifferentiating concepts is available, even though the ontology to which M2Lrefers contains additional possibilities for classification. In cases where a setof users of M1L is unable to make any distinction within the intensions of


their vocabulary, this pragmatic stage of métaphysics may be suitable, atleast in their current situation. Of course, this situation of commonly usedmétaphysics may change in future, without the user having any idea nowhow to then enrich their conceptual network.

In the case (b), in reflecting M1L, the pragmatic situation on the levelM2L is similar to the situation of using M1L to reflect M0L. The used ontolo-gy contains even stronger means to classify and to differentiate these classifi-cations and differentiations, and so on, up to the level of the interpretationfunction for M1L; and the pragmatics contains intellectual instruments togenerate such classifications and differentiations, which are interneted alongthe ontological ranks, and which are therefore not expressible in M1L.

In M1L, as an example, natural numbers may be placed at rank 0 of typetheory, but also at rank 2, according to Peano’s axioms. At rank 0 they areisolated, but not at rank 2. For M1L contains means to define the basicconcepts of this axiom system in the vocabulary of logic; and because of suchdefinitions four of the axioms become theorems of logic.25 These naturalnumbers of ontological rank 2 can then be used in M1L in a natural way tocount sets, and therefore to establish relative frequencies.

Real numbers, on the contrary, can be placed only at ontological rank 0in stating Tarski’s axioms; for the ontology presupposed in using M1L is notrich enough to constitute these real number at some higher rank along theline of how rational numbers in idealized measuring situations are used, i.e.in associating them with the limits of an infinite sequence of refinements ofthe measuring intervals. However, at rank 0 they are objects isolated fromother objects, including those which are regarded as natural numbers; and inlooking at M1L therefore – and using M2L – we see that the respective theo-ries are isolated in M1L, too.

Of course, in using M1L we declared some suitable function g mapping Finto or onto the set of real numbers to represent measurement; and for thosepurposes where M1L is a suitable instrument to deal with this way of procee-ding is surely sufficient.

But in finding out and establishing in M2L the intended intensions ofTarski’s axioms, according to the specific attributes of real numbers – likethere are used in measuring situations –, some ontology has to be used whichis rich enough for that purpose; and this ontology is available in M2L, sincetotal interpretation functions for M1L can be constituted in it.

Thus, we refer the basic concepts of the axiom systems of M1L to thoseknots in the network of intensions in M2L, which constitute exactly thatstructure which is expressed by the respective axiom systems taking thenetwork as means to establish the truth for the a priori accepted axioms of


M1L; in doing so, among the possible interpretations of M1L we determinethe a priori structure of the intended one, and therefore the frame of theworld we were speaking on about M1L.

As an additional example, in using M1L space points were regarded aselemeuts of rank 0, according to the attributes expressed by the axioms ofgeometry. Now, in using M2L they are constituted in accordance with ideali-zations of measurements as limits of certain sequences of physical bodies onthe line of the established real numbers. Of course, de facto each such succes-sion of more and more refined measuring intervals will break off at somestage; taking this as a metaempirical fact, it is a future task to investigate theexact philosophical meaning of idealizations of that kind.

I doubt wether M2L is rich enough to present métaphysics – being one ofthe preconditions for a completed physics – so completely in the sense ofphilosophical foundational research that according to Tarski the terms ofthis complete theory are derivable from the terms of its underlying physicalgeometry and chronometry26, and a general and uniform field theory canthus be obtained. Yet this goal is achievable in principle by using the ontolo-gical instruments of one of the languages M3L, M4L and M5L; i.e. from anontological point of view the instruments for mastering the respective pro-blems of theoretical physics are available. Such a combined general theory ofphysical space and time will presumably be categorically in some strict orweakened sense of the word, then its models have to be isomorphic, whichmeans that two users of this theory’s vocabulary are unable to discoverdifferences of their models and may therefore conclude that they are equal.27

At this end of the line of development of physics theoretical researchingwill then come to a closing of métaphysics; and then any further physicalactivities will only consist in filling any remaining gaps in this picture ofreality, then already outlined in its main features: Only a fundamentally newapproach and therefore the opening of a new line of the basics in the form ofsteps, and the theoretical presentation of experiments could then set anotherphysics in motion, and, accompanying it, another métaphysics.28

As long as no new combined system of physics and métaphysics is devel-oped, the pragmatic stage will then be as follows: No means are available tolead métaphysics to a further foundation in some semantically and pragma-tically enriched higher-level language; for at this stage only the structures ofthe basic concepts of the axiom systems are available, being in the sense ofHilbert and Frege second-order concepts. But means have to be available toconstitute those entities which were used at lower stages of epistemologicalreflecting as starting points on the way to that métaphysics which is devel-oped now as some systematization of completely exhausted and explicated


background knowledge of physics; thereto belong especially the criteriawhen and according to which theory a mass point is handled as a physicalbody being a thing expanded in space and spatially connected in all of itsparts, opposing penetrations of other bodies of a similar kind with a certaincharacteristic resistance.29 While using this métaphysics we thus have todetermine factors which mark the kind of resistance as well as the degree ofresistance in each case.

It belongs to the tasks of métaphysics to determine the factors being usedin physical laws by developing the intensions of the concepts involved; andmoreover, this also has to be done according to those factors or physicalfoundations which are mentioned explicitly or tacitly in the conditions ofthose laws, as factors which have to be excluded in shielding the applicationsof laws from them or in neutralizing their effects by employing contraryfactors.

Magnitudes or factors as functions of that kind were not used in M0L, butfrom M1L onwards. In reflecting M1L on the level M2L, we only foundfunction concepts which we then had to interpret in semantical as well aspragmatical respects. The factors of M1L, and therefore of the worlds beingcompatible with the métaphysics of M1L, are those which are expressible interms of that métaphysics. Then, of course, it may happen that the usedlanguage M2L contains disruptive factors which are not expressible in M1L;in these cases, on the level M2L, the conditions of these laws are to be supp-lemented respectively.

And looking at M2L from M3L we may, in a related way, still receive newfactors which will help us to continue to complete the conditions of theempirical laws and to sharpen their applications.30

In this sense each language level together with its métaphysics constitutethe frame of the possible worlds; in these worlds exactly those entities exist,which are determined by its métaphysics.

When, at some language level, métaphysics will come to an end, then epi-stemological work is not yet terminated. Among the tasks of epistemologywhich are still open is then the question of how and to what extent, theobjects which are constituted in that métaphysics may differ in the differentcases of realizations of experimental instructions, with regard to these in-structions, i.e. to constitute unsharpness intervals which depend on thedemands of the situations where those instructions are applied. In fact, whatwe get and what we need here is not a sharply defined interval of unsharp-ness, but a phased-out distribution of this unsharpness of those coarse ma-crophysical objects. Thus the work of epistemology will not end as long asexperimental work is done. Such unavoidable unsharpnesses in experimental


situations, however, allow in principle to pursue ways which lead to anotherdetermination of those concepts to which the mathematical equations of thephysical laws are related. With a new reflection about what is done in theexperiments and how these actions have to be formulated, an alternative ex-perience may be obtained, which – according to the unsharpness mentionedbefore – may be worked into another background to be established accor-ding to this new reflection, that is to say, the way to another métaphysicsmay be taken. As a philosopher one must not speculate about whether or notthings like that will happen in the future and into which direction this willdevelop, but rather wait for the onset of such a turning point and then analy-ze it with the means of logic.

In proceeding from M1L to M2L and from M2L to M3L, the means ofdeductive logic increase, and with it the means of defining, and especially thecases of definability of concepts in theories. The questions, too, how criteriaof simplicity have to be applied to theories, require – along with an increa-sing formation of theories in ever more expressive languages – increasinglydifferentiated solutions. Methodological problems of that kind belong toepistemology which is a parts of pragmatics; after all, even some de factoending of métaphysics of physics does not cause a philosopher of science tobecome unemployed.

5. Concluding Remarks

A lot of most important questions whose analysis is seen as a priority taskin logical operationalism have not even been mentioned yet in this paper.They include those forms of recourse in measurement which – at first sight– must appear to be circular.31 For example, the fundamental introduction ofthe metric concept of temperature presupposes the metric concept of length.However, in order to determine length independently of fixed values of tem-perature, just that metric concept of temperature is required so it can be usedas a correcting factor. If we bring to mind the historical development of bothconcepts then we will see clearer that we are not moving here in some vici-ous circle, but in a kind of empirical recursion along the lines of the histori-cal levels of more and more refined determinations of the two mutuallyrelated concepts and therefore to more and more refined measuring procedu-res. And in disentangling this circularity, following the principle of economy,we then have to make sure that on each step of that recursion we use theinvolved empirical laws restricted to that field of application which is requi-red here to determine measuring concepts for the purpose of using them asa priori rules to receive new a posteriori results; using these laws unrestrictedor at least not carefully restricted may indeed lead to vicious circles.


Investigations of logical operationalism are primarily concerned withanalysing the conditions of empirical laws, where these laws are regarded asbeing of the form

“vx ε F: ... h(x)... 6 h(x) = r*”

where “h” designats a – normally compounded – physical magnitude andwhere “r*” is some specific numerical constant; therefore “... h(x)...” and“x ε F” are taken as objects of explication, thereby using the means of logic.Secondarily, however, within these conditions very often equations of thekind “g(x) = r'” have to be used; therefore this main part of the law, too,must be kept in mind.

Empirical laws of that kind may later on turn out to be false. But inrestricting the field F of applications to some suitable domain, e.g. to someclass of measuring instruments, it may happen that the mistake being madein applying them may be taken as neglectable with regard to the given inter-val of unsharpness. In testing such a law for objects of such a restricteddomain, this law is then taken as unrejected and therefore as a posterioritrue. In using it as member of a more differentiated intension of some measu-ring concept this part of the law is then taken as one which constitutesexperiences and therefore as a priori true. And in reformulating the back-ground knowledge it may happen that the resulting métaphysics may gra-dually change the intensions of the involved concepts, thereby indicatingwhy it is appropriate to use this restricted law in such measuring situations.

All in all, logical operationalism is a non-holistic procedure of philosophi-cally analysing procedures of empirical science. Hereby scientific theoriesare taken as sets of sentences; these are bases for determining their structu-res. Methods of science are regarded as instructions or rules and therefore asstatements of some higher language level. Then a non-holistic point of viewwhich is concerned with sentences as well as with their structures, as wasdone by Carnap, will lead to important philosophical insights in addition tothose where the statement aspect of scientific theories and methods is neg-lected or where the non-holistic categories “a priori – a posteriori” as well asthe shifting of sentences – according to these categories – is ignored.

Many important results were obtained by the school of structuralism32,established by Stegmüller, especially in reconstructing the main parts of em-pirical laws, namely statements of the kind “h(x) = r*” or to be more ex-actly: in proceeding from these statements to their logical forms, in Car-nap’s words: to the explicit concepts of those statements; these explicitconcepts or structures are this philosophical school’s domain of investigati-on.


While logical operationalism – being non-holistic not only with regard tothe pragmatic state of scientific sentences formulated within some language,but also with regard to the language themselves – is reconstructing empiricaltheories in languages suited for them and is similarly reconstructing scientificmethods for sciences in suitable languages, structuralism or non-statementview of scientific theories takes a universal language as its base for its recon-structing of all empirical theories. In keeping in mind of the results of foun-dational research in logic and mathematics, the methodological aim oflogical operationalism is to presuppose – in the sense of Ockham’s razor –only as much ontology as is required for the purpose in question; languagesin which empirical theory is to be reconstructed and which, when being used,presuppose some amount of ontology, are therefore constructed according toeconomical aspects. Structuralism, however, does not involve these aspectsof metalogic, but chooses a universal language for its purposes, which cannotbe enlarged any more ontologically. Now there exists only one kind of lan-guages which, according to the metalogical results obtained in this century,cannot be enlarged any more as far as ontology and expressibility are con-cerned, namely those which contain antinomies. Therefore, for its analyses,a language of naive set theory is chosen in structuralism, and the problem ofantinomies is avoided by not paying attention to them.

Now if some problem is not paid attention to or even gets tabooed, itthen does not stop to exist. Of course, this philosophical attitude is harmlessif it is regarded as a first step towards explication or rational reconstruction,where further steps are to follow; for then this language is ultimate not used.But suppose that a structuralist asserts that this first step is already the lastone.33 Taking this metaphilosophical assertions seriously and coolly, thenthe situation for listeners or readers may shortly be described as follows: Allthe assertions of structuralists are statements of an antinomic language; init, because of the ex falsum quod libet principle, every statement is bothprovable und refutable. Therefore, proofs given for theorems of this languageare worthless unless they are reformulated in some consistent language.

Therefore, one should interpret this attitude of structuralism with awarmhearted mind; this is done by reformulating it in some language of thesimple type theory which is rich enough for the respective purpose butcontains no superfluous ingredients. It seems to me that, when such a refor-mulation takes place, all non-antinomically used sentences of structuralismmust then, along the lines of language leveling, be placed in the languageM1L; for all mathematical and physical entities are presented there at rank 0,and especially the mathematical entities will not get constituted as logicalentities of higher rank.


This leads to the assertion that the following metaempirical statement isnot a thesis, but rather a working hypothesis: Every sound result obtained inthe language frame of structuralism can be reformulated in the language frameof logical operationalism, but not vice versa. The latter is obvious; because ifwe discuss for example how to introduce dispositional concepts or even mainconcepts like “force” via partial definitions, how to determine the conceptsof interpretation, of truth and of logical truth, how to apply measuringinstructions to coarse-grained objects as well as the results of such investiga-tions, we need statements as objects of philosophical analysis.

Some other minor differences will remain. While in logical operationa-lism the word “theory” is used in its traditional way, for instance applied to{Hd1, ..., Hd6}, and expressions “explicit concepts” or “logical form” or“structure” are applied to “Hld” or – which works out to the same – to theclass of interpretations of {Hd1, ..., Hd6}, structuralists renamed “theory” to“model” or “application”, and “explicit concept” to “theory”. As long aspeople are aware of this translation key, there is nothing wrong in changingterminology; for statements of structuralism can then easily be reconstructedinto sentences of logical operationalism salva veritate.

Also at this super-meta-level, concepts – being expressions used accordingto some set of rules – are always concepts of some conceptual frame. There-fore super-meta-level statements like “Theories are not sets of statements butstructures of such sets” and “Theories are sets of statements whose structureis defined by some explicit concept” are both analytically true in their ownrespective frame, and contradictory in the other.

There is some other seeming difference between structuralism and logicaloperationalism, which has no logical basis. For structuralism created somesort of school identity card for its members: The explicit concept is notdefined like it was done in the sections before, but in the following kind:

“vX: X ε NN :wY0 Y1 ... Yn: X=< Y0,Y1, ..., Yn > v ...”

Concerning the example of the Hölder system the explicit concept then readshere:

“vX: X ε Hld : wF o / ¤: X = < F, o, / ¤ > v ...”

If we want to include this form of presenting the explicit concept – which isneither a simple nor an elegant form, but a recognizably complicated one forlogical argumentations – in such a language of simple type theory, then wehave to add to that language variables for ordered n-tuples; this is the easiestthing to do. In doing so, the two following equivalences are logically true:

“< Y0,Y1. . . ,Yn >ε NN :wX: X = < Y0,Y1..., Yn >v X ε NN”

“< Y0,Y1.. . ,Yn > ε NN :vX: X= < Y0,Y1... ,Yn > 6 X ε NN”


The first of these two laws of logic justifies the presentation of the explicitconcept when an existential quantifier gets used in definiens; but the secondone shoes more directly and clearly the intended universality of the structure.Nevertheless structuralists always use the right part of the first equivalenceand never the right part of the second one. I can see no logical reason fordoing this; therefore, in order to determine the reason for this choice ofstructuralism, being some philosophy of science, one has to apply historical,psychological and sociological methods, i.e. the means of a science of phi-losophy of science.

In those areas of the philosophy of science in which one can profitablywork with explicit concepts extracted from sentence systems, structuralismhas achieved an impressive amount of important results; no other directionor even school of philosophy of science can show a similar amount ofaccomplished philosophical work. This is at least partially due to the factthat structuralists are exclusively related to each other in their own works,following the latent dogma “A current philosophy of science can only be theone of the non-statement view”. For this credo leads the adepts of this schoolto work commonly and exclusively on a narrowed-down sector of philoso-phy of science.

In logical operationalism there is no place for such a tendency towardsabsolutism and dogmatism; in fact, this philosophical position is not a schoolat all. The field of investigation is neither limited to some non-statementview nor to some solely-statement view; but the results of higher and non-elementary logic as well as of metalogic are not out of sight. Reconstructingempirical theories as well as their structures within some formal language asthe final steps of explication is aimed at applying the results of metalogic inorder to receive philosophical insights to the preconditions of truth and offinding truth; but the starting point of explication are, according to Carnapand others, those informal languages which are used by working scientists.

Informal languages as well as formal ones both have advantages and pro-duce benefit, if applied carefully, sensitively and with sure instinct. For theyare intellectual tools and therefore, like manual instruments, fruitful in somecases of application and less fruitful in other cases of working with language.In the process of explication or rational reconstruction, coarse-grained toolsare useful in the beginning; but later we require precision instruments. Thisholds for languages as well as for means of philosophical analysis.

But also this principle of philosophical analysis is regarded as a workingbasis and not as a dogma to generate some school. In this sense logicaloperationalism regards philosophical methods as tools of the mind whichmust not tie up the mind.


Of course, I do not expect that during my lifetime it will become necessa-ry for me to use other kinds of languages of thinking and other philosophicalmeans than those which I have referred to above; however, there are nological reasons which are superior to all kinds of languages used and whichexclude the possibility of other means of constituting reality and of findingtruth which gets done by fruitfully applying the language-formed instrumentsof the human mind as they are operationalized in human speaking andwriting. Notes1 This distinction between science of science and philosophy of science is due to Carnap who usedthe terms “Wissenschaftslehre” and “Wissenschaftslogik”; cf. Carnap (1934), 205. Using theseterms, Carnap tried to determine the distinction between Neurath’s way and his own way ofinvestigating empirical science.2 Cf. Tarski (1935a). At the present state of metalogical research it cannot be said yet whether there exists only someminimal enlargement and therefore some subsequent level of reflection, or in addition to that thesmallest enlargement and thus the subsequent level of reflection. It is conceivable that there existsmore than one possibility to determine an initial link of this succession of language levels, as wellas that there are more and different possibilities of enlarging a given language in this sense.In the following chapters I will proceed as follows: Some object language is determined by reducingthe variety of defined expressions of the respective language level according to its given definitions;afterwards the concept of interpretation is developed, and it is pointed out where more ontologicalmeans are called for than the investigated language level can offer.My interest in the following investigation will, however, not be focused on such metalogicalrefinements, but on those semantic levels relevant for the theory of science; and for that I mightaccept that the leveling turns out a bit more rough than this is indicated by the metalogics. I will doso if in that way the gradual development of the métaphysics experience can be traced better.In a loose analogy with multiplying and raising to a higher power, for instance in the expression fora function “xny”, I will use the notation “MnL” for finite language levels and by that I have thefollowing abbreviations for the first three cases: “M0L” for “L”, “M1L” for “ML”, and “M2L” for“MML”.3 The putting of the accent marks one of the two modes of use of this word with Kant. In com-pliance with this metaphysics are those philosophical disciplines offering proofs for statements onGod, the World, and the I.4 Of course, it may happen that F does not contain representatives for some color classes of U, e.g.if F is chosen as some set of balls in an urn where each ball is either red or green. In that world ofF these two colors are the only existing ones, while the world of U will then contain additionalcolors.5 Cf. Frege (1967), 395-422, and Carnap (1929) using there the concept “Explizitbegriff” insteadof “Begriff zweiter Stufe”. Cf. also Essler (1970).If this transition is to be presented more precisely, one should formulate the axioms by cognitiveconstants – e.g. “M*” and “F*” instead of the variables “M” and “F”; and in taking the conjunctionof these axioms as definiens for the higher-rank concept, those constants then have to be sub-stituted by those variables. But since multiplying terminology sometimes causes confusion, I decidedto use some lack of subtle exactness here, while hoping that the well-informed reader will not beconfuses by this.6 For details see e.g.: Essler-Brendel (1993), ch. IV.


7 In the interesting cases no completeness can be reached, not because of the profound incom-pleteness which was made evident for the first time by Gödel, but because the investigations in anarea of research normally are never brought to a closure.The concept of completion of a system of axioms does not yet have such a general and precisedefinition. In this sense categorical systems are completed, and so are such systems of sentences,which are categoric in power or which, in another weakened sense, have a model set with certainisomorphical characteristic attributes.8 Since it contains no expressions for 2-ary relations on rank 2, no concept of interpretation for agenuine part language is representable in it; and since it contains no expressions for 3-ary relations– and therefore no 2-ary functions – on rank 1, it does not contain any means to formulate somesyntax of a language.9 One could also choose the following way of symbolization for the logical symbols: According tothe implication one uses “->” in M0L, “=>” in M1L, “/>” in M2L, etc; and the other logicalsymbols get used similarly.Since logical symbols are never used without cognitive symbols here, one can always unmistakablysee from the context to which language level they belong in each case.The respective used language is written without such additional numerals here; in that the naivityof using may be expressed. In reflecting this using such an index as a symbol of this expression’slevel of reflexion is then as signed to it.10 The more tokens are included in such a type, the more linguistic potential can then be realizedlinguistically. In an idealizing way it is assumed that each type contains an unlimited and non-ending entirety of tokens, that is to say: countably infinitely many.11 This equivalence relation will then be operationalized on the next level of reflexion M 2L; thecognitive concepts of M1L are first formalized and then supplied with contents by means of suchoperationalizations. This takes place in the same way as when M0L is developed in using M1L,where in order to do so the observational concepts of M0L are first formalized and then opera-tionalized, involving the perceiver.12 Cf. Tarski (1935a).13 Cf. Tarski (1935a), Scholz-Hasenjaeger (1961), Hermes (1963), and Essler-Martínez (1991).14 In using M0L we produced physical objects used according to syntactical categories; in reflectingM0L, these objects and their categories are those entities which we can register easily. But, inaddition to this, we used M0L to refer to something; and this something can not so easily beperceived as the syntax of M0L.15 General methods of proving satisfiability are normally more sophisticated; cf. Skolem (1923),as well as Gödel (1930).In fact, I discovered the creativity of Carnap’s bilateral reduction sentences by transferring Suppes’arguments on non-creativity regarding total definitions to the case of partial definitions. Cf. Suppes(1957), ch. §8.16 In constituting the set of possible worlds of M0L as the class of interpretations satisfying theaxioms of M0L, finding the truth values of all the statements is nothing but finding the reality ofM0L. Cf. Essler (1972), ch. III and IV.17 In “TU(A,B)”, in order to simplify matters, just “A” and “B” gets written instead of “λxyzwA(x,y,z,w)” and “λxyzw B(x,y,z,w)”.18 Cf. Carnap (T&M); cL also Essler (1975) and (1985).By the way: Whether the operational instruction it is formulated as definiens in Df'2 and Df'3 is tobe seen (a) as a call for individual or general actions, therefore being an order, or (b) as a des-cription of singular actions or of the general connection between those actions, or (c) as a des-cription of the individual or general results of such actions, is in my view a matter of aspects underwhich operations are performed. With regard to the aspect of reflecting the cognitive content ofoperationally determined intensions of concepts the syntactical forms used above are sufficient.19 In fact, the methodological situation will be usually more complex. For this method of con-servatively extending the original field F of application already starts at the stage of Df'2 (b) andDf'3 (b) by using different standard objects w1, w2, ... of different equivalence classes H1, H2, ...


which are either more rough or more subtle realizations of the method of operationalization; theconservative extensions of F in the case (b) are then:(U \ F)1 F1, (U \ F \ F1)1 F2, ... In each factual situation of scientific process this sequence is finite.Similarly in the case (c) there usually exist – or will be obtained – more and more non-equivalentrealizations w’1, w’2 ... of respective equivalence classes H’1, H’2 ..., leading to extensions

(U\F\ {Fi}) 1 F'1, (U\F\ {Fi} \F'1) 1 F'2, ..., and so on also for cases (d), (e), ... of newin=1U i

n=1U

ways of operationalizations of the given relations.Furthermore, these interlocked sequences of conservative extensions are not permanently fixed, butmay be exchanged in future like, in fact, they were exchanged in the past.20 On this score cf. Peano (1895) as well as Tarski (1937), ch. X. Concerning the importance ofcategoricity, cf. Carnap - Bachmann (1936) and Hermes (1963), ch. IV §4.1.21 Cf. Hölder (1901). It is one of Suppes’ merits to have discovered this early and importantcontribution of Hblder; cf. Suppes (1957), §8.22 With regard to the operational aspects of that mapping cf. e.g. Carnap (1926), Hempel (1952)and Carnap (1966). Concerning the structural aspects of it cf. Suppes – Zinnes (1963) and Krantzetc. (1971).23 Cf. Carnap (1925).24 It may be that this scientific knowledge will in some millennia be regarded, too, as pre-scientifictheories.25 Reduction of the concepts of some theory to those of an other theory does not entail reductionof the axioms of the first theory to those of the second one!26 According to Tarski (1935b), the concepts of a complete physical theory must be definable interms of some physical geometry combined with some physical chronometry which has to beadded.27 In fact, they believe that these models are identical; for according to their métaphysical situationthere exist no means to establish differences. Cf. Essler (1993).28 On the one hand, from a logical point of view, further refinement of métaphysics cannot eventhen be excluded when it appears to be impossible according to the physical theories prevailing atthe moment. On the other hand the assumption that there would, after all, be something like a limitof the physical theories, including their respective métaphysics, is pure metaphysics in the othersense of the word: No current progress or standstill in the development of these disciplinesdiscloses the way of further development or guarantees the standstill, and no total system, even ifit appears plausible, will be able to prevent physicists in future centuries from seeing the hithertoexisting way as a dead end, and therefore they will choose totally different lines of métaphysicallyinterpreting the physical results.But in any case, such a thesis which seems to deal with all systems and therefore with all languagesis no statement of a language for which a concept of interpretation and, building up on this, aconcept of truth can be introduced; therefore it is, contrary to its appearance – which is given to itby the languages of every-day life – only a sentence-like sequence of words without any real contentand without any truth value; i.e. it is an activity of métaphysics.NB: Such a different and possibly future line of developing métaphysical systems will assign diffe-rent intensions to the basic concepts of the former experimental instructions and therefore inparticular to those of the operational definitions, even if the old word still remains. The currentline of developing more and more refined systems of métaphysics does not show how to enrich thelanguage so that future systems of métaphysics within such enriched languages are predictable.29 Among these bodies which are constituted according to this métaphysics are also those whichwere used earlier in lower-level languages, like measuring instruments and even linguistic signs.Among those physicists who were not only interested in philosophy, but who also possessed theability of the philosophical analysis, Mach was clearly the first and until now the only one torecognize the extent of philosophical preconditions in an atom theory, and who, because of theshortcommings of these preconditions, preferred a theory of continuum; Cf. Mach (1912), ch.IV/4.


Sommerfeld’s rejection of these thougths of Mach, which simply consists in labeling these viewswith the expression “positivistic”, is representative of how much physicists métaphysically cling tobasic métaphysical preconditions like, for instance, the precondition of the atom theory as a theoryof a theory-independent existence of indivisible, three-dimensionally expanded things. Cf. Sommer-feld (1964), 3.NB: If certain forms of the current elementary part theory ascribe a point-shaped existence to thequarks, then this is still an atom theory, because – if a sufficiently small proximity is given – thesequarks will, in a reciprocal way, oppose a further approximation with sufficiently large resistance.Because along Kant’s lines, a body does not get represented by its point of mass, but instead of thatby precisely that virtual room around the point of mass, into which other bodies of this kind cannotenter under non-extreme conditions.30 Factors are always factors constituted on some métaphysics at some language level, like all kindsof entities we are dealing with.31 Cf. Carnap (1926) and (1966), §7 and 9.32 Cf. the list of papers and monographs of structuralism in: “Erkenntnis” 30 (1989), 41(1994).33 Cf. Stegmüller (1979), p. 4f.“It is now more than twenty years since Suppes advanced the claim that philosophers of scienceshould use set-theoretical instead of metamathematical methods ...By statement view1 (st.v.1) I refer only to the Carnap or formal language approach and by non-st.v.1. I refer to the structuralist approach. I now formulate a main thesis:Thesis 1: To carry out the program suggested by statement view1 is not humanly possible. Thusst.v.1 is not a realistic alternative to the structuralist view. Whoever compares the advantages anddisadvantages of non-st.v.1 and st.v.1 weighs something that does exist against something that doesnot, and will not, for a long time to come, exist at all.”

I am indebted to Wolfgang Wilhelmy and Joachim Labude for their helpful comments on earlierversions of this paper.

92 Nicholas Rescher

Nicholas Rescher

Meaningless Numbers

“Deus fecit omnia in pondere, in numero, etmensura.”

– Old Testament

“The business of pinning numbers on things– which is what we mean by measurement –has become a pandemic activity in modemscience and human affairs.”

– S.S. Stevens, “Measurement, Psychophysics, and Utility”

1. The Problem

Notwithstanding an extensive literature on the subject, the existing state ofthe art is such that our understanding of exactly what measurement is allabout still leaves much to be desired.1 The present discussion will focus onthe problem of distinguishing genuine measurements/quantity – specifica-tions that are informatively significant and meaningful – from those quantifi-cations that lack this sort of substance. Ist problem domain is that of thequestion: What vantures in quantification are not just feckless number-juggling but actually in measure something?

Many treatises on the subject routinely assume that each and every ob-servationally based quantification represents a measurement.2 But this isnonsense. Quantification as such does not automatically constitute measure-ment. To see this, consider some examples of effectively meaningless quanti-ties

* the number of 3’s in the distance (in kilometers) between two cities.

* the number of times (on average) that the sentences of a given En-glish text end with a proper name.

It is very doubtful that such numbers do any measuring. For surely not everyquantity represents a measurement. “How many of those girls remind you ofyour mother?” you ask me. “Two,” I respond. A lovely quantity, that! Butwhat in heaven’s name am I in measuring? It is thus all too clear that wemust reject the claim of S.S. Stevens that measurement [is] the assignment ofnumerals to objects or events according to a rule-any rule.”3

Philosophers of science all too often sidestep the problem. They incline toease their task by simply supposing that the problem of distinguishing bet-

Meaningless Numbers 93

ween meaningless quantities and actual measurements will go away if wesimply ignore it. But this tactic, however convenient, is very questionable. Ameasurement, after all, has to be a quantitative characterization of somemeaningfully descriptive facet of reality, as opposed to one that is arbitraryand uninformative.

But exactly what is at issue here? A well-known pair of philosophicalauthors has told us that measurement consists in “indicating the quantitativerelations between [intensive] qualities.”4 But this idea that quantitative mea-surements must represent actually qualitative features of things is deeplyproblematic. Presumably the rate of exchange between dollars and yenconstitutes some sort of measurement. But it is far from clear that the quali-ties or attributes of anything are at issue. Again, birth rates or inflation ratesdo not discernibly reflect qualities of anything-unless we blatantly ~ so-mething (a social or economic or political system) for them to be qualitiesof.5 We can measure the annual snowfall of a place, but it is far from evidentthat one of ist qualities is at stake.

Perhaps, then, one should abandon any reference to qualities in thiscontext. Perhaps getting numbers is all that counts for measurement. Follo-wing in the footsteps of the operationalist school of P.W. Bridgman, theBritish philosopher of science Herbert Dingle has insisted that “instead ofsupposing a pre-existing ‘property’ which our operation measures, we shouldbegin with our operation and ist result, and then if we wish to speak of aproperty (which I do not think that we should do) define it in terms ofthat.”6 But here we are caught in a dilemma. If we tie measurement to speci-fically physical processes of quantity determination-linking it to apparatusmanipulation and instrument pointer readings as with the measurement oflength or mass-then we proceed in so restrictive a way that we have difficul-ties accommodating the sorts of quantities at issue with social affairs. Interestrates or the velocity of money circulation are some examples. In macroeco-nomics, after all, we get our quantities-not by reading off the position of apointer from a scale, but by copying suitably related numbers from pieces ofpaper. And yet the claims of these quantities to count as measurements seemsto be conceded on all sides. It is thus very problematic to insist that measure-ments have to result from a physical measuring process of some sort. If, onthe other hand, if we loosen up the linkage of measuring to measurement toomuch, we lose our cognitive hold on what measurement is. In particular, ifwe reject the distinction between genuine measurements and merely meaning-less quantities altogether – if the phenomenology we take into view is that ofindiscriminate number-assignments –then there at once ceases to be any real

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reason why anyone should be interested in the topic of measurement at thisabsurdly general and undiscriminating level.

But how are we to understand this difference between real measurementsand meaningless quantities? It would be all very well to say “I know a mea-surement when I see one,” but this convenient approach facilitates under-standing no more in the present context than in any other. In the absence ofa sensible answer to the question of what it is to measure, there is clearly alarge hole in our understanding of the scientific enterprise.

2. Quantification vs. measurement: What makes a number meaningful?

One sensible idea, it would seem, is that the only sort of quantity specificati-on that deserves the name of measurement is that which plays an ampliativerole in enabling us to extend our information regarding the items whosequantitative aspects are at issue. Thus contrast the preceding examples ofproblematic number allocation with such items as:

* inches of rainfall per annum (at a particular place) * the number of inhabitants (of a particular town)

The situation here is very different. The salient difference seems to be one ofcognitive utility. Information of this sort is genuinely informative. Given ourknowledge of how things work in the world, we can draw various informati-ve conclusions from it –regarding agricultural potential in the case of rainfall(say), and requirements for food and water in the case of population.

On this basis, the meaningfulness of quantities is clearly a reflection ofthe extent to which they are bearers of information. And it is evident thatdifferent albeit interrelated considerations are at work in making a numbermeaningful in this regard. An adequate inventory is hound to include thefollowing:

1. Effective Determinability

An actual measurement has to be the result of a practicable and imple-mentable process. And this is simply lacking in various cases. Consider, forexample:

* the number of Latin words whose meaning a person once knew buthas forgotten. Or again, for living individuals contrast years frombirth with years to death-that is, with

* a person’s remaining lifespan.

The problem with such quantities is that they are effectively impossible todetermine. We can make sense of the relative frequency with which a certainword is used by the writers of a certain language or the number of times their


written discussions refer to a certain person, but there is little if anything wecan do with

* the percentage of persons to whom a certain idea has occurred. Wecannot plausibly construe such problem quantities as meaningfulmeasurements.

Clearly, measurement has to be an operationally implementable procedure ofsome sort.

2. Reproducibility

An actual measurement has to be well defined-the stable result of a re-producible process and procedure. Real measurements must yield essentiallythe same result on different occasions when carried out by the same opera-tor, and must also yield essentially same results when carried out concurrent-ly by different operators. This requirement is illustrated by contrasting thenumber of “wrongdoers” with “the number of people found guilty of specificoffenses (from some specified list).” or again, contrast the number of unhap-py people in a community with the number of suicides or the extent of istpurchase of headache remedies.

3. Context Invariance/Robustness

A genuine measurement should reflect a substantially context-invariantquantity. Since talent and skill for taste-performance is generally comparativeand context variable, industrial statistics regarding “skilled” vs. “unskilled”workers are automatically suspect-particularly because the same product canbe made from the same materials by processes and methods requiring verydifferent sorts of talents.

In particular a genuine measurement must not be sensitive to factorswhich – as best we can tell – are not causally linked to the sort of thing atissue. For example, it just does not – and should not – matter whether wemeasure the amount of rainfall at a certain place on an odd or an even-numbered day, a workday or a holiday. In quantifying highly context-depen-dent relational and interactional aspects of things – say hair vibration asopposed to pulse rate – we are not in general carrying out actual measure-ments. (Hair vibration will vary with wind exposure, body movements,headscratching, etc.)

4. Validity/Coherence

With genuine measurements, there must be good reason to think that theresult of the measurement is the true value of the quantity at issue. And this

96 Nicholas Rescher

is only possible where measurements cohere. Wherever there are differentmeasuring processes and procedures- different ways of measuring what issupposed to be the same item-they must agree. Thus whenever the operatorsand their mode of operation themselves enter into the measurement processin a result-influencing way (as some physicists claim for the “measurements”of quantum phenomena, but as certainly holds for various sociologicalquantifications), the claims of the resulting numbers to represent measure-ments are ipso facto compromised.

5. Predictive Utility

It is clear that the usefulness of a number in predictive contexts is apivotal feature of ist meaningfulness. If we know a town’s population we canuse this datum to say something about this locality’s consumption of wateror ist need for housing, while the age of ist mayor or the average velocity ofist winds from the east are, by comparison at least, meaningless quantitiesbecause few if any other quantities relevant to the constitution of towns canbe predicted on the basis of these data.

This factor of the predictive serviceability of measurement is closelylinked to yet another crucial aspect of measurement, namely:

6. Nomic Involvement

Measurements should result in quantities that function informatively inthe context of general laws or law-like statistical relationships.7 This means,in particular, that, while any mathematical compounding of quantities will ofcourse yield yet another quantity, there is no cogent reason for thinking thatthis is so with measurements. Even when the input quantities actually measu-re something, the functionally combined output quantities need not do so aswell, owing to an absence of informative interrelationships. We would thusbe highly disinclined to see

as measuring some aspect of a person’s makeup. Given this quantity, there iseffectively nothing else of any interest with which it stands in lawful interre-lationships.

It is tempting to distinguish between “fundamental” measurements whichwe carry out “directly” by some suitably contrived process of physical mani-pulation with material objects and “derived” measurements which we effectby calculations with numbers resulting from prior measurements.8 But – asthe previous examples show – even we put perfectly good measurements to


work, it is clear that their arbitrary arithmetical compounding does notautomatically measure anything. And this circumstance blocks the prospectof any recursive approach to the specification of legitimate measurements. Inthis light, it is the laws of nature that ultimately determine the meaningful-ness of complex quantities. Consider the gas law to the effect that (at leastapproximately) the product of pressure and volume divided by temperatureis constant:

Given this law, the product P × V . T represents a perfectly meaningfulquantity that provides us with a means of measuring temperature. But thequantity

fails to measure anything because it lacks any plausible physical meaningowing to ist failure to operate as a significant whole in the context of service-able laws. As this example shows, when we combine perfectly meaningfuland measurable quantities by throwing them together arbitrarily via rules ofcalculation, the upshot may well be something altogether nonsensical. Theresult of a real measurement has to be something that functions as a mea-ningful unit in the context of laws.

Genuine measurements accordingly have to be theory-laden: when wecannot embed quantities in a theoretical context of some sort and fit theirresults into our theories, then these number specifications are clearly unableto qualify as authentic measurements.9 And if the theories into which they fitare patently invalid, absurd, or crazy, then the quantities at issue cannotqualify as genuine measurements. The range of evil-eye potency or theintensity of a person’s “spiritual aura” are putative measures that vanish intonothingness with the disappearance of the theories on which they are predi-cated.

On the other hand, the mere fact that quantities do indeed behave inlawful coordination is of itself not enough to mean that they represent mea-ningful measurements.

98 Nicholas Rescher

Thus consider once again the gas law:

P × V . TAnd let

P* = P × Mand

T* = T × Mwhere M represents some otherwise irrelevant feature of the system at issue– ist aggregate mass – or, if you prefer, the time of sunrise in ist location.Then those star-quantities are clearly rubbish. Yet nevertheless, they stand insplendid lawful coordination via the gas law. As this example indicates, thelaw-connectedness of determinable quantities does not suffice to establishthem as meaningful measurements.

We arrive at the recognition that each of the six measurement-characteri-zing factors considered individually – determinability, reproducibility, ro-bustness, nomicity, and the rest – has ist problems. More ominously yet, itemerges that, even in combination, they do not suffice to assure meaningful-ness. They are all necessary for genuine measurement, but even jointly theyare still not sufficient. Consider, for example, the following person-des-criptive parameter:

* the sum of a person’s age in years plus their systolic blood pressure.

Not only is this well-defined, determinable, and contextually stable, but italso has nomic involvement and predictive value in relation to such issues asgeneral health and life expectancy. All the same, it is not something we couldregard as a meaningful measurement because of the rather eccentric way inwhich it mixes apples and oranges. As such considerations indicate, some-thing more is needed – over and above all of the preceding factors – toestablish the claims of a quality to representing a meaningful measurement.A clearly appropriate further step moves in the direction of:

7. Dimensionality

Actually to measure something is to affix a numerical yardstick to somequantitative parameter that has ist operative foothold in the world’s schemeof things – length, temperature, mass, electric charge, money-circulation orthe like. Measurement must present an objective and well-defined quantitati-ve aspect of the qualitative make-up of things in the real world. A measure-ment, after all, is a number assignment made under a particular descriptionsuch as:

* is x inches long* measures x units on the Richter scale


* rates x units of acquisitiveness on the Spencer phrenology scale.

And when numerical assignments fall to capture such lawfully descriptivefeatures of things, then they just do not measure anything.

With a genuine measurement two questions arise:

(1) What is it that one is measuring? (The object question.)(2) How is it that one is measuring what is at issue? (The processquestion.)

And, moreover, the issues involved in (1) and (2) must be separable anddistinct-that is, one must in principle be able to provide an answer to thewhat question independently of one’s answer to the how question. Thus aperson’s weight or age represent cogent measurements, but not:

* age in years divided by waistline in inches* height in feet plus years resided at present address

It is clear in this context that a wide roadway leading from meaningful tomeaningless numbers is provided by mathematical compounding. This isindicated by such examples as:

* the product of the longest and shortest side of a polygon* weight of a person in kg minus months resided at present address* volume of an object (in cc3) divided by ist age (in years)

Such amalgamations are problematic precisely because there is no noncircu-lar reply to the question: Just what is it that is being purportedly measured inthis way? That is, we have no workable way of distinguishing the what of theputative measurement from ist how.

The issue of dimensionality is clearly serviceable in providing a cogentfactor disqualifies such Rube Goldberg quantities from counting as genuinemeasurements. Regrettably, however, it is not easy to say just what is at issuehere (which may explain why recent treatments of measurement in generalsimply bypass this issue of descriptive dimensionality). Philosophers ofscience have in recent years deliberated a good deal about what is or is not anatural kind when it comes to classification, but they have largely ignored theclosely parallel and inherently no less important issue of what constitutes anatural dimension in point of mensuration.10 Yet however difficult this issuemay be to resolve, it is clear that such descriptive dimensionality – or so-mething very like it – must be added to our list of requisites.

Our deliberations have indicated that the following features all representnecessary conditions for meaningful measurements:

* effective determinability* reproducibility* context stability/robustness

100 Nicholas Rescher

* coherence/validity* nomic involvement* predictive utility* descriptive dimensionality

The yet (unresolved) problem we face is whether now at last these severalnecessary conditions for genuine measurement are jointly sufficient. Onemay be tempted to surmise that this is indeed the case. But there is goodreason to think that it is not. For one thing even perfectly meaningful quanti-ties can be contextually problematic. It makes sense to ask for the marketprice of gold or of lead specifically but not of metal in general. We can makegood sense of the idea of the average birth-weight of a human female inspecific, but can make little of the color of the average death-weight of a fishin general. But an even graver difficulty lurks around the corner. Consider,for the sake of an example, the person-correlative quantity:

This clearly quantifies an aspect of a person’s individual makeup in a waythat (I) has a meaningful dimension (viz. chronological age, seeing that thefractional multiplier is dimensionless), and (2) behaves lawfully since fromthe vast majority of humans fage = age and a person’s age factors lawfully inmany contexts and as biological development and life expectancy. Despite allthis, however, the Rube Goldberg nature of the conception would leave onedisinclined to consider “fage”-determination as a meaningful measurementprocess. What we want and need is a more cogent and discriminating ac-count. But it is one thing to ask for such an account and another to knowwhere it can be found.

And so, in the end, it appears that we are confronted with a distinctlydiscomfiting situation. It is clear that we need a cogent way of distinguishingbetween meaningless quantities and genuine measurements. But it is far fromclear how we are to draw this distinction.

In the philosophy of science, there are a number of structurally analogousproblems of distinction and demarcation-between natural kinds and hapha-zard collections, between genuine laws and accidental generalizations, bet-ween ad hoc explanations and genuine ones, and even between real scienceand pseudo-science. The problem of distinguishing between mere quantifica-tion and real measurement is of this same general sort. But unlike the rest, itis a problem that has received precious little attention in the literature of the


field. In this case even more than with others we have to do with an in-strumentality of communication about science that is clearly useful, butwhich, nevertheless, we are simply unable to render clear and precise inanything like a satisfactory way. On all indications, the distinction betweenactual measurements and meaningless qualities remains enigmatic.

Some numbers can be acknowledged as measurements because, likeweight and distance, they are paradigmatic of the very concept. Others areclearly not measurements because they violate one or another of the necessa-ry conditions of the conception. But there is a considerable grey area wherewe do not see the way clear, and where we have good reason for caution andunease. And nowhere does this lack of a clear-cut way of drawing the linemanifest itself more painfully manifest than in the social sciences. Let usexplore some of the ramifications of this situation.

3. Problematic measurements

The need for maintaining the distinction between measurement and merequantification along the lines of the preceding deliberations, raises somedisturbing questions regarding the status of various putative “measurements”that people nowadays conjure with in the social sciences-particularly in areasthat have implications for and applications to matters of practical policy. Ineconomics, for example, we deal with quantities-such as interest rates-thatare neither determined by actually measuring anything, nor yet by calculati-on from such quantities, but which emerge from calculations with numbersthat crop u~mysteriously or otherwise-as writing on bits of paper. The ideaof a meaningfully descriptive dimensionality in this domain is particularlyproblematic with respect to many of the quantities used in social analysesand social studies, where people throw numbers together in ways that oughtto raise one’s theoretician’s hackles. A good illustration of such a problemnumber is provided by the IQ tester’s idea of a pervasive “intelligence.” Howcognitively competent people are is clearly of interest to us in many contexts.For, all too evidently, people have very different levels of ability-be it bodilyor mental. But there is no good reason to expect that someone’s physical orintellectual dexterity or versatility can be represented by a single number.And the fact that it would be convenient if this was so from the angle of ourprograms of educational planning and management just does not make ittrue. Intelligence quotients throw together ability to decode language withanalogy spotting and competence at calculation. Those tests explore verydifferent sorts of abilities, and there is no reason to think that these cansimply be aggregated by weighted addition to yield a meaningful compositeresult. Even a student’s performance on one of those objective tests, on


which we Americans place so much weight in college admissions processing,and in scholarship awards, actually indicates little about ability for intellectu-ally demanding work-or for doing anything substantially different fromtaking objective tests.

And of course calculating with such quantities poses further problems. Asour preceding deliberations have shown all too clearly, when one combinesdifferent quantitative factors by mathematical compounding one will ge-nerally get not a measurement but a mess. And while this mess may possiblybehave lawfully in some respects, nevertheless from the angle of understan-ding – of facilitating a conceptualized grasp of things – it remains a messunless and until it comes to play a substantial role in a systematic law-frame-work of theoretical systematization.

4. Quality of life as an example

For another example of problematic qualification in the social domain,consider the nowadays fashionable quality of life measures for differenttowns, areas, or countries. Here income data, housing costs, crime statistics,cultural facilities are somehow quantified and then thrown together in somesort of aggregation. But there is clearly no good reason to think that a mea-ningful result emerges. Conceivably such QOL figures could be used topredict migration patterns, although this has apparently never been attemp-ted. (“Other things equal, people abandon low QOL areas for high (QOLones” is hard to test and unlikely to survive testing in unqualified generality.)But clearly some embedding in a structure of lawful order is needed, and hasnever been supplied. And there is an even more fundamental problem here.

In general, things have many different value-aspects and we have noworkable single-valued “function of combination” enabling us to extract asingle, all-embracing measure of overall value from them. We have to dealwith a plurality of distinct considerations that are not easily weighed offagainst one another. Even if we assume (perhaps rashly) that measurability ispossible within each of these parametric dimensions, there is generally noway of making quantitative exchanges across different value parameters byway of weighing them off against each other in a common scale. The ele-ments of a good journey are clearly not commensurable: adding more specta-cular scenery cannot make up for bad food, even as adding more salt, nomatter how much, will not compensate for a cake’s lack of sugar. We canreadily quantify various features of urban life-crime rates, housing costs,park acreage per capita, and so on. But does that mean we can combine suchnumbers into one single meaningful index of quality-of-life? Surely ourprospects in this direction are no better than those of the 19th-century


French physicians who thought that “health” was a property of the humanbody and attempted to provide a measure of a patient’s “health” or “cons-titution” by means of a single number concocted out of a witches’ brew ofdiverse factors.11 With quality of life, or health or other such factors, thevarious evaluative aspects of the good are not interchangeable. In general,when we have to appraise a profile or complex of desiderata, preferabilitybecomes a matter of a contextually determined stucturaI harmonizationrather than of mensurational maximization.12

The idea of “The social value of a life” affords yet another example of adeeply problematic quantity. We shall deal with it in detail in the nextchapter.

5. Fallacies of quanticipation

So far we have been concerned to argue that it is wrong to maintain that:whenever one can quantify one will obtain cognitively meaningful measure-ments. The other side of the coin also deserves examination. Is it correct toargue: whenever one cannot quantify one cannot accomplish cognitivelysignificant work? Out deliberations about this issue will consider four widelycurrent “Fallacies of Quantification” and their implications.

The first of these fallacies is that of the thesis:

What one cannot quantify is not important.

The modem mania for numbers is notorious (especially in the U.S.A.!).Statistics have become a latter-day Baconian “idol of the tribe.” We love torate and the rank- everything from the world’s best tennis player (eventhough performance varies substantially with playing surface) to the world’sfavorite soft drink or airline company. We worship at the altar of statistics:the thirst for measurements and quantities is a salient characteristic or ourculture. Living in a society and in an era that is bedazzled by quantification,we have become Homo numerans, quantifying man. The splendid successesof natural science have enticed even the least numerate of us to the temptingidea that measurement and quantification afford the only true pathway andgenuine understanding. Modem bureaucracy’s commerce in paperwork andreports is just one more illustration of a dedication to statistic-not necessarilywith a view to any pressing particular need, but nowadays often seeminglyfor their own sake.

It is this idolatry of numbers that underlies the great characteristic delusi-on of the times represented by the aforementioned fallacy. A laudable impe-tus to quantify the things that are important tempts us into the folly ofdeeming the things we cannot quantify to be negligible.


Testifying before the Presidential Inquiry Commission on the explosion ofthe shuttle Challenger, the representative of Morton Thiokol, the contractorthat produced the booster rockets, explained their frustrations in persuadingtheir NASA counterparts that it was unsafe to launch in the low temperatureconditions of the morning of January 26, 1986. Thiokol’s representative feltthat “we had to prove to them (NASA) that we weren’t ready to fly”. Andthis was difficult to do because, when it came to the effect of cold on theseals that were at the heart of the problem, “I recognized that it’s very diffi-cult to quite quantify at which temperature these seals may be acceptable andat which they aren’t acceptable. Now based on that data-some of it certainlywas inconclusive-there was no doubt in my mind. And that’s a difficult thingto quantify “13 Given this circumstance, NASA refused to be convinced.There was little doubt in the mind of this witness that some shortcomings ofquantifiability led to the discounting of his data.

This approach is, quite clearly, the height of folly. “What you can’tquantify doesn’t matter” is about as silly a thesis as “What you don’t seecan’t hurt you.” This “Quantification Fallacy” is just that-a fallacy. Thatnight’s debate in Florida between Thiokol and NASA puts before us a vividand terrible illustration of the Quantification Fallacy at work.

The converse of the present fallacy, the idea that whatever can be quanti-fied is also has ist problems, It too is clearly a fallacy, given the wide scopethere is for quantitative trivia. But it is easy to fool ourselves into thinkingthat the things we can readily measure are the ones that count.

Numbers do not always tell the story. The wise strategist realizes thatGod is not always on the side of the big battalions. “How many divisions hasthe Pope?” Stalin asked. It is not a question that bemused General Jaruzelskyin Poland. By all quantitative yardsticks the U.S. was ahead throughout theViet Nam conflict and duly won the battles- but lost the war. The numbersjust do not always reflect conveniently the impact things will eventually exertupon the world’s course. In complex situations, the quantitative factors maybe the easiest to get hold of, but they are not necessarily the most pivotal.Certainties are more easily measured than uncertainties, simplicities thancomplexities. But they are not necessarily the determining factors.

Our sense of legitimacy no longer relies on perceived quality or reputati-on, but demands validation through numerical rating-indices. We demandquantitative performance ratings for our products, livability ratings for ourcities, and quality indices for our schools. We rank colleges not on the com-petence of their graduates but in terms of “quality point averages” and theirscores on “objective” examinations. With tennis players performance on thecourts is not an end in itself but a mere means to good computer rankings.


Time and again we need to be reminded of the importance of a concern forthe things we cannot quantify-or cannot yet quantify in the existing state ofinformation Public opinion polls or the statistical content analysis of newspa-per articles in the local press may have provided “hard data”, but certainlywere of little help to someone trying to judge how well entrenched or vulne-rable the position of the Shah was in Iran. To judge by the coverage of socialissues in the media, thoughtful policy debate is impossible without a relianceon statistics. Common sense and historical analogy count for little. And yetnumbers too can speak with a forked tongue. (Extrapolation is a dangeroussport; be it with hemlines or employment statistics, a one percent shift thisyear seldom presages a ten percent shift a decade further on.)

We forget all too easily that there are “lies, damned lies, and statistics”,as Benjamin Disraeli put it. The numbers are not a substitute four soundjudgment. On the contrary, it is generally only on the basis of sound judge-ment that they themselves are useful. Admittedly, the sensible appraisal ofsituations is often encouraged and facilitated by numerical data. But statisticsonly carry a meaningful message to the prepared mind.

There is no need to deny that plain fact that quantitative informati-on is often illuminating and useful. The point, rather, is that there is noearthly reason to think some sort of correlation exists between the ease andaccuracy of the quantifiability of some consideration and the significance ofist rile in the matters to which it relates. The remedy of the fallacy at issuelies in the recognizing that: the things vou cannot quantify in the context f aninquiry may well turn out to be the most important. As long as we persist inadhering to the Quantification Fallacy by thinking that what one cannotqualify just is not important and can safely be ignored, we shall also persistin trying to send aloft rockets, economic policies, and social programs thatjust will not fly.

Let us now turn to our second fallacy, which is clearly related to thepreceding one:

Everything (at any rate everything that is even remotely interesting)can be quantified.

Fallacy No. 1 maintained that whatever is important can be quantified; thepresent fallacy says that whatever is really interesting can be.

A good illustration of this fallacy is provided by the IQ tester’s idea of apervasive “intelligence.” How intellectually able people are is generally ofgreat interest to us. Clearly, people have very different levels of ability-be itbodily or mental. But there is no good reason to expect that someone’sphysical or intellectual dexterity or versatility can be represented by a singlenumber. And the fact that it would be convenient if this was so from the


angle of our educational or managerial programs just does not make it true.Even a student’s performance on one of those objective tests on which weAmericans place so much weight in college admissions processing, or Na-tional Merit Scholarship awards, indicates little about real ability for acade-mic work or for doing anything substantially different from taking objectivetests.

Rational choice among alternatives is undoubtedly a matter of selecting“the best option.” But since this preferability cannot in general be quantifiedin most real-world situations, its comparative determination is a matter ofqualitative judgment rather that quantitative measurement.

The appraisal at issue is generally not a matter of quantitative evaluationbut of comparison and contrast with other cases-of analogy and assimilation.The experienced judge often evaluates but seldom calculates.

In many of our deliberations we do well to adopt this judicial model ofdecision-making rather than that of quantitative comparison – not a modelof calculating but of appraising by “weighing arguments”. And the idea of“strength of evidence” is an example of a situation in which quantitativeresources leave us in the lurch. The crux is not a matter of scientific compu-tation but of informal estimation – of making: “judgment calls” on the basisof seasoned experience that may not have a quantitative foundation. Wegenerally cannot assess the bearing of evidence in quantitative terms.

The crucial lesson is that even where quantification is impracticable – oreven though in principle feasible where numerical data are lacking – it isperfectly appropriate to place reliance on informed and tested judgment.There are situations in ordinary life, in engineering, and even in science,where we would do well to put our trust not in such shaky numbers as canbe had, but in the informed estimates of experienced and knowledgeableminds. In the cognitive and practical affairs of man there are all sorts ofissues where quantification is infeasible and we must proceed by qualitativejudgement based on assimilation and analogy.

To avert the fallacy at issue we must accordingly recognize that, despitewhat people may think to the contrary, some highly significant and interestingmatters simply cannot be quantified.

This brings us to yet another of our quantificational fallacies:

Quantification and measurement are one and the same.

This thesis is also emphatically incorrect. The fact is that quantities may notbe descriptively meaningful at all. Numbers need not measure anything; noteverything quantitative is a measure. “How many of those girls remind youof your mother?” you ask me. “Two”, I respond. A lovely quantity, that! But


what in heaven’s name am I measuring? Quantification is not necessarilymeasurement

Science has succeeded in mathematicizing the realm of our knowledge tosuch an extent that we tend to lose sight of the fact that the realm of ourexperience is not always all that congenial to measurement. It is full of co-lors, odors, and tastes, of likes and dislikes, apprehensions and expectations,loves and hates that allow precious little room for measurement We readilyforget how very special a situation measurability is – even in contexts ofseeming precision.

To measure (in any appropriate sense of the term) is to affix a numericalyardstick to some quantitative parameter that has ist own foothold in theworld’s scheme of thing – length, temperature, money-circulation or the like,an objective and well – defined aspect of the make-up of things in “the realworld”. Measurement reflect those particular descriptive features of thingsthat can be reflected in quantitative terms. And when quantities fail to captu-re such descriptive features, they just do not measure anything.

An important conclusion emerges. Quantities may not measure any thingat all. It is by not means the case that every quantity we can specify is ameasure of some well-defined and pre-existing parameter in the natural orsocial realm.

Consideration of the preceding fallacy leads naturally towards the reco-gnition of yet another:

The quantities that measure various distinct factors can always becombined in a meaningful aggregate. They can ultimately be seen asexchangeable parts of a composite whole.

This idea that different sorts of quantities can be lumped together as con-vertible constituents of one single composite –that they can be seen as ex-changeable parts of an aggregate whole – runs deep in modern thought. Allthe same, it is highly unrealistic. Consider, for example, some of the pointsof merit that relate to the effectiveness of a car:

* maximum speed;* starting reliability;* operating reliability (freedom from breakage);* passenger safety;* economy of operation.

If the top speed of a car is 5 m.p.h., no augmentation is passenger safety oroperating reliability can make up for the shortcoming. Again, if the car iseminently unsafe, an increase in ist other virtues cannot offset this. Wherethe various merits of a car are concerned, there simply is no free exchange


among the relevant value-parameters, but only complicated (non-linear)trade-offs over a limited range. And this illustrated a general situation.

In general, things have many different value-aspects and we have noworkable single-valued “function of combination” enabling us to extract asingly, all-embracing measure of overall value from them. We have to dealwith a plurality of distinct “parameters of value”. Even if we assume (per-haps rashly) that measurability is possible w~ each of these parametricdimensions, there is generally no way of making quantitative exchangesacross different value parameter by way of weighing them off against eachother in a common scale. The elements of a good journey are not commensu-rable: adding more spectacular scenery cannot make up for bad food. (Ad-ding more salt, no matter how much, will not compensate for the cake’s lackof sugar.) We can readily quantify various features of urban life-cue rate,housing costs, park acreage per capita, and so on. But does that mean we cancombine such numbers into one single meaningful index of quality-of-life?

To think (as per the economists’ “utility”) of assessing the preferability ofgoods by a single number is every bit as sensible (or foolish) as to think thatwe can reflect the intelligence of people in a single number – or even thevalue of a human life. What is going on throughout is an indulgence innumber idolatry that rides roughshod over important differences and di-versities.

The commitment to convertibility at issue in the economist’s “utility”represents a harmless fiction in ist proper sphere of tradeable good whosevalue can be established in a common unit via a market exchange mecha-nism. But to pretend to have a more general and pervasive instrument for therations governance of human decisions is skating on very thin ice.

“The good” at large is something multi-dimensional and not homogene-ous. Enhancing it is a matter of optimizing a complex, not of maximizing adeterminable quantity. The evaluative aspects of the goal are not interchan-geable. We must harmonize rather than maximize. In general, when we haveto appraise a profile or complex of desiderata, preferability becomes a matterof a contextually determined structural harmonization rather than of mensu-rational maximization.

We come thus to the need for recognizing that even when we are dealingwith quantities that express meaningful measurements, the commensurabilityneeded for an integrated measurement to result may not be possible. In manysituations we may have to settle for quality-appreciative judgement wherequantity-oriented measurement is simply infeasible.

Our Cook’s Tour of quantificational fallacies is now completed. Theyrepresent principles of thought so deeply entrenched in our culture that it


will seem to many to be problematic and tendentious even to suggest thatthey may be incorrect. But seeing them as unwelcome does not, of course,make them any the less fallacious.

6. Larger vitas

In the aggregate, then, these deliberations indicate that quantification isneither necessary nor sufficient to obtain cognitively meaningful measure-ments. Accordingly, they indicate the need for recognizing that, even whenwe are dealing with a perfectly fine quantity, the conditions needed for thisto qualify as an authentic measurement may nevertheless not be satisfied Theimportance of science in modern life has engendered a quantitative prejudice.People incline to think that if something significant is to be said, then youcan say it with numbers and thereby transmute it into a meaningful measure-ment. They endorse Lord Kelvin’s dictum that “When you cannot express itin numbers, your knowledge is of a meager and unsatisfactory kind.”14 Butwhen one looks at the issue more clearly and critically, one finds that therejust is no convincing reason to think this is so on any universal and pervasivebasis.

Science has succeeded in mathematicizing the realm of our knowledge tosuch an extent that we tend to lose sight of the fact that the realm of ourexperience is not all that congenial to measurement. It is full of colors, odors,and tastes, of likes and dislikes, of apprehensions and expectations, etc., thatare not particularly amenable to measurement. We readily forget how veryspecial a situation actual measurability is – even in contexts of seemingprecision.

Moreover, reliance on numbers brings in ist wake a host of problems ofist own. For one dangerous thing about numbers is that small errors in theiruse can produce large – and very unfortunate – consequences. A minormistake in the number encoding of a prescription medication can provelethal. Again, for many years, spinach has enjoyed a great prestige as a valu-able source of iron because a misplaced decimal point credited this vegetablewith an iron content ten times ist actual value.15

A fetish for quantification seems to be astir among our contemporaries.We worship at the altar of statistics: the penchant for quantities is a salientcharacteristic of contemporary western culture. Everything we touch turns tonumbers: intelligence quotients, quality of life indices, feminine beauty(ranked on a scale from zero up to a “perfect 10”), and so on. It is thus easyto see why the prospect of meaningless quantities should cause unease. Forin this measurement-enchanted time of ours we constantly invoke on quanti-tative information as a basis for decision making and policy guidance. But


garbage in, garbage out. If those quantities that people throw about so readi-ly are in fact meaningless, then the decisions we so enthusiastically base uponthem are built on sand. In many situations we would do well to settle forrough-and-ready judgmental appraisals because meaningful quantitativemeasurement is simply infeasible.

After all, numbers do not always tell the story. The wise strategist realizesthat God is not always on the side of the big battalions. “How many divi-sions has the Pope?” Stalin asked. It was not a question that bemused Ge-neral Jaruzelski in Poland. By all quantitative yardsticks – body counts andall that – the U.S. was ahead throughout the Viet Nam conflict and duly wonall the battles; but it lost the war. One does not need to enroll oneself, withGoethe, as an opponent to measurement’s entry into the domain of humandoings and dealings to feel a deep disquiet regarding the particular ways inwhich people have sought to introduce measurement into the social sphere.The fact is that in everyday life, professional practice, and public affairsalike, stubborn reliance on numbers can sometimes prove more of an ob-stacle than an aid to critical and reflective thought.

The immense success of quantitative techniques in the mathematicizingsciences has misled people into thinking that quantification is the only viableroad to cogent information. But think – is it really so? Where is it writtenthat numbers alone yields genuine understanding – that judgment based onstructural analysis or qualitative harmonization is unhelpful and uninformati-ve, so that where numbers cannot enter, intelligibility flies away? (After all,modem mathematics itself is not all that quantitative, seeing that it is deeplyconcerned with issues such as those of topology and group theory that dealwith structures in a way that parts quantitative issues aside.)

It must be stressed, however, that to acknowledge the limits of measurabi-lity is not to downgrade the whole process, let alone to propose ist abandon-ment. It is precisely because we are well advised to push the cause of measu-rement as far as we legitimately can that we need to be mindful of the linebetween meaningful measurements and meaningless quantifications. That wecannot draw this line better than seems to be the case at present is – orshould be – a proper occasion for justified chagrin.

The hue and cry is audible in advance: “Only through quantification andmeasurement are we put on the high-road of a scientifically valid under-standing of how things work in the world”. But think – is it really so? Whereis it written that quantification alone yields genuine understanding – thatjudgement based on analogy or qualitative harmonization is unhelpful anduninformative, so that where numbers cannot enter, intelligibility flies away.Even to raise these questions is to be led towards a recognition that the


idolatry of numbers is a prejudice or preconception that is not only questio-nable but potentially badly misleading. In everyday life, professional activity,and public affairs alike, reliance on numbers is no substitute for reflectivethought.16

Notes 1 A collection of particularly fine articles on the subject is Harry Woolf (ed.),Quantification: AHistory of the Meaning of Measurement in the Natural and Social Sciences (Indianapolis, 1961). Seealso Brian Ellis, Basic Concepts of Measurement (Cambridge, 1966).2 See, for example, the Introduction to David R. Kranz et al, Foundations of Measurement, Vol. I(New York and London, 1971).3 S.S. Stevens, “Measurement, Psychophysics, and Utility,” in Measurement: Definition andTheories, ed. by C.W. Churchman and P. Ratoosh (New York, 1959), pp. 18-63 (see p. 19).4 M.R. Cohen and Ernest Nagel, An Introduction to Logic and Scientific Method (New York,1934), p. 294. Compare Norman R. Campbell: “Measurement is the process of assigning numbersto represent qualities,” Foundations of Science (New York, 1957).5 Perhaps one of the reasons for being of the fashionable idea of a “system” is to play just exactlythis role.6 Herbert Dingle, “A Theory of Measurement,” British Journal for the Philosophy of Science, vol.1(1950), pp. 5-26.7 In looking at the extent to which one quantity correlates with others one must do one’s scorekee-ping fairly. The number of noses in the cage correlates with the number of animals there. Well andgood. But it does not also get credit for correlating with the number of tails, or ears, of hooves, etc.8 For this distinction see N.R. Campbell, Physics: The Elements (Cambridge, 1920) and also Whatis Science? (Cambridge, 1921); rept’d. New York, 1952.9 Recent deliberations in the philosophy of science have done much towards showing that theattribution of observable features to the furnishings of nature is always theory ladenpart of aprocess in which our theoretical understanding of nature plays a significant role. But this is all themore so with respect to the attribution of measurable features, seeing that measurement is evenmore pronouncedly theory-involving than observation.10 The issues are closely parallel because a measured feature of something can be looked upon asconstituting a parametrized quality of it. As my Pittsburgh colleague Nuel Belnap has noted indiscussion, all of the seven factors singled out in the previous quantity-oriented discussion haveclose analogues in the qualitative case in relation to natural kind vs. random assemblage distinction.The difficulty of maintaining natural kindhood in the face of logical combinations (such as con-junction) exactly parallels the difficulty of maintaining actual measurementhood in the face ofmathematical combinations (such as multiplication).11 See Richard H. Shryock, “Quantification in Medical Science,” in Harry Woolf, (ed.), Quantifi-cation (Indianapolis, 1961). Note, incidentally, that “life expectancy will not do the trick here,seeing that a person may well expect a long life on whose course he often or generally “feelsmiserable.”12 The preceding discussion draws upon Chapter 7, of the author’s Satisfying Reason (Dordrecht:D. Reidel, 1995).13 Testimony of Allan J. McDonald as reported on The New York Times, February 26, 1986, p. 1614 Sir William Thomson, “Electrical Units of Measurement,” Popular Lectures and Addresses, 3vol’s [London, 1889-91], Vol. I, p. 73.15 See Peter Skrabanek and James McCormick, Follies and Fallacies in Medicine (New York,1990), p. 27.


16 Parts of this essay overlap with a discussion initially published in the author’s Satisfying Reason(Dordrecht: D. Reidel, 1995), pp. 71-83. And the concluding sections draw upon Chapter 7,“Number Ideology and Fallacies of Quantification” in the author’s Forbidden Knowledge (Dord-recht: D. Reidel, 1987).

258 David Resnik

RATIONALITY – METAPHORS – VALUES IN SCIENCE

David Resnik

Scientific Rationality and Epistemic Goals

In philosophy, it is often more important to properly formulate questionsthan to find answers. Nowhere is this more apparent than in current debatesabout the rationality of science (Siegel, 1985). Different sides in this contro-versy employ different interpretations of the statement “science is rational.”A quick survey of the literature on the rationality of science indicates thatthere are nearly as many interpretations of “scientific rationality” as there arewriters who explore this topic. Some of the different rationality assertionsmade on behalf of science are:

R1: Scientists are rational (Giere, 1988; Kantorovich, 1993; Hem-pel, 1979; Kitcher, 1993).

R2: Scientific communities are rational (Longino, 1990; Thagard,1993; Kuhn, 1970; Merton, 1973).

R3: Scientific methods are rational (Newton-Smith, 1978; Howsonand Urbach, 1990; Solomon, 1994; Popper, 1959; Merton, 1973).

R4: Scientific decisions are rational (Levi, 1990; Kyburg, 1990;Howson and Urbach, 1990).

R5: Scientific theories and hypotheses are rational (Howson andUrbach, 1990; Newton-Smith, 1978).

R6: Scientific progress is rational (Lakatos, 1978).

R7: Scientific consensus formation is rational (Laudan, 1984; Zi-man, 1968).

These are very different, though related conceptions of scientific rationality.The common link among these different conceptions of scientific rationalityis the widely held view that scientific rationality consists in the effectivepursuit of means to obtain various epistemic ends or goals (Newton-Smith,1978; Giere, 1988; Hempel, 1979; Kitcher, 1993). These goals can justify

Scientific Rationality and Epistemic Goals 259

and explain various scientific activities, according to many writers (Kitcher,1994; Solomon, 1994; Kantorovich, 1993; Laudan, 1984; Hempel, 1979).

But what becomes of this instrumentalist approach if we challenge thenotion that epistemic goals can explain or justify various scientific activities?Can science be rational without being epistemically “goal-directed”? If so,how should we understand the rationality of science? In this paper I willexplore the limitations of the instrumentalist model of scientific rationality(ISR) and discuss alternative models. I do not suggest that we abandon ISRsince I think it still has many useful applications. However, we need torecognize ISR’s limitations and be open to an alternative model of scientificrationality that can successfully account for the phenomena that ISR cannotaccommodate. The instrumentalist model most clearly applies to local deci-sions relating to specific epistemic goals and methods, but another modelshould be invoked in order to understand global decisions concerning generalepistemic goals and methods. I shall argue that a dynamic and naturalisticmodel of scientific rationality provides us with the most promising approachto understanding global decisions in science.

2. The Instrumentalist Model of Scientific Rationality

Since the notion of a “rational agent” plays a key role in the development ofvirtually all twentieth century ideas about rationality, we need to introducethis notion here (Brown, 1988; Kyburg, 1990; Levi, 1990). A rational agentis an agent who follows specific rules (or norms) for belief formation oraction, such as rules of deductive logic, Bayesian inference, decision theory,and so on. Since actual human beings do not always follow these rules, thenotion of a rational agent is an idealization we make for the purposes ofconstructing theories about rational belief or action (Kyburg, 1990; Jeffrey,1965; Hempel, 1979; Loui, 1993). We can use the notion of a rational agentto develop notions of “rational belief,” “rational decision,” “rational action,”and “rational methods.” Thus, a rational belief is a belief formed by a ra-tional agent; a rational decision is a decision made by a rational agent; arational action is an action carried out by a rational agent; a rational methodis one that would be employed by a rational agent (Brown, 1988). An actualhuman being is like a rational agent insofar as her decisions, beliefs, oractions result from her following norms of rationality or by being motivatedto act on those norms (Audi, 1993; Gibbard, 1990; Hempel, 1979; Kitcher,1993).

Having introduced the notions of “rational belief,” and “rational action,”we can now distinguish between different types of rationality. The firstdistinction is between theoretical rationality and practical rationality (Brown,

260 David Resnik

1988; Audi, 1993). Theoretical rationality focuses on rational belief formati-on; practical rationality addresses rational action. An agent who acts onnorms of theoretical rationality follows rules of belief formation, such asdeductive logic or Bayesianism (Howson and Urbach, 1990; Loui, 1993); anagent who acts on norms of practical rationality follows various rules formaking practical decisions, such as the rules of decision theory (Audi, 1993;Jeffrey, 1965).

A second important distinction is the difference between instrumental andcategorical rationality (Hill, 1973; Brown, 1988; Kantorovich, 1993; Nozick,1993). This distinction becomes clear when we reflect on the justification ofour various norms for rational belief or action and their motivational power(Hill, 1973). Rules of instrumental rationality are justified in that they areeffective means to goals and they can motivate human beings insofar aspeople desire to obtain those goals and believe that the rules prescribe effecti-ve means of obtaining them. On the other hand, rules of categorical ra-tionality can be justified without any reference to the goals they tend topromote and their motivational force is also goal-independent. People whoare motivated to follow norms of categorical rationality follow those rulesfor the sake of following the rules, not in order to obtain goals or satisfydesires. In Kantian terminology, rules of instrumental rationality are hypo-thetical imperatives; rules of categorical rationality are categorical imperati-ves (Hill, 1973; Resnik, 1992).

In rational choice theory (decision theory and game theory), rationalagents are characterized as utility or preference maximizers (Rosenberg,1988). As maximizers, rational agents follow rules that yield the greatestbalance of their own good/bad outcomes. If we view goals as good, valuable,or worthwhile for the agent, then this notion of utility maximization issimply another way of saying that rational agents effectively pursue theirends or goals (Jeffrey, 1965; Resnik, 1987; Loui, 1993). A human being islike an instrumentally rational agent, then, insofar as she is motivated tomaximize her utilities or preferences. Goals can motivate human action, onthis view, if we assume that people have desires to achieve those goals andthat they believe that certain actions (or beliefs) will enable them to achievethose goals (Myers, 1995). This account of human motivation is based on aHumean approach to rationality (Myers, 1995). Hume believed, according tomany writers, that desires are a necessary part of rational motivation; aperson will act on a “reason” only if they desire to obtain some outcome thatthey believe will result from an action. Davidson (1980) updates this view bydefending the idea that reasons (beliefs, desires, and related propositionalattitudes) can cause actions, and other writers adopt a similar perspective in


arguing that reasons can cause beliefs (Myers, 1995).1 What makes thiscausal approach Humean is the idea that desires are necessary conditions forthe explanation of actions (or some beliefs).

In light of these preparatory remarks, we can now define the instrumenta-list model of scientific rationality as a systematic attempt to apply notions ofinstrumental rationality to science (Newton-Smith, 1978; Solomon, 1994;Hempel, 1979; Kitcher, 1993; Giere, 1988; Resnik, 1993). In order to applythis model to science, one must posit ends or aims for science and means ofachieving those ends. These aims of science can motivate and perhaps justifythe actions of scientists. Great differences of opinion arise, however, whenwe try to decide which aspects of science are rational. The different inter-pretations of “scientific rationality” result from applying the notion of in-strumental rationality to different aspects of science, such as particularscientists, scientific communities, scientific methods, scientific decisions,scientific theories, etc.

Great differences of opinion also arise concerning the aims of science.Some frequently mentioned ones include, (a) truth acquisition, (b) erroravoidance, (c) explanation, (d) prediction, (e) knowledge, (f) problem-sol-ving, (g) technological development, (h) power, (i) mastery of nature, (j)health, (k) happiness (Longino, 1990; Stich, 1990). In order to help usunderstand discourse about the goals of science, I suggest we follow a stan-dard distinction in philosophy between epistemic goals and practical goals(Longino, 1990; Stich, 1990). Epistemic goals relate to belief formation,theory acceptance, and other knowledge-expanding activities in science;practical goals can be understood as those objectives that are pursued inorder to obtain non-epistemic aims. On my reading of the epistemic/practicaldistinction, goals (a)-(f) are epistemic; goals (g)-(k) are practical.2

I have omitted some important goals from this list, such as status, presti-ge, and money. These goals often play a role in our understanding of theconduct of individual scientists (Hull, 1988), but since science is a socialactivity, we need to distinguish between the aims of science and the aims ofindividual scientists (Kitcher, 1993; Merton, 1973). By “aims of science” Imean something more than an individual scientist’s aims, such as “collectiveaims of the scientific enterprise” or “goals of scientific institutions.” Indivi-dual scientists could conduct science in order to make money, gain prestige,and so forth, but these aims would not be science’s aims. Of course, indivi-dual scientists could also conduct science in order to achieve goals that are,by and large, scientific in nature, such as understanding the world, seekingtruth, etc...

262 David Resnik

Although it is not my intention to settle outstanding disputes within theinstrumentalist approach to scientific rationality, I will assume in this analy-sis that science’s primary goals are epistemic while admitting that sciencealso has secondary, practical goals (Giere, 1988; Laudan, 1984; Kitcher,1993). I make this assumption because we could not make sense of many ofthe activities of scientists without assuming that scientists are attempting toacquire knowledge, truth, or other epistemic objectives. Without this as-sumption, how could we understand highly impractical sciences, such asastronomy, or decisions to reject highly useful theories, such as Ptolemeicastronomy, in order to obtain the truth?

If we think of scientists as pursuing epistemic goals, there are two typesof instrumental rationality that might apply to science. Taking the notion ofa rational agent as our starting place, we can view scientific rationality aslike agent rationality. Since scientists are human beings, and human beingscan be rational agents (to a certain degree), science could be rational insofaras scientists (as individuals) are like rational agents. Thus, we have our firstconception of scientific rationality:

Individual Rationality (IR) Scientists, as individuals, act on norms of instrumental rationality inthe pursuit of epistemic goals.

For many years this was the dominant conception of scientific rationality inphilosophy (Hempel, 1979; Giere, 1988; Kitcher, 1993). However, theKuhnian revolution in the philosophy of science and the growth of sociologi-cal approaches to science have lead some writers to extend the notion ofagent rationality to scientific communities as well (Kuhn, 1970; Longino,1990; Solomon, 1994; Merton, 1973; Thagard, 1993; Goldman, 1992). Onthis social view of science, groups of scientists can make decisions, accept orreject theories, perform experiments, etc...A group can also act on norms ofrationality if we think of those norms as governing the behavior of membersof such groups and a group’s collective actions. Thus, by thinking of scienti-fic communities as like rational agents, we get a different slant on scientificrationality:

Group Rationality (GR)Scientists, as groups, act on norms of instrumental rationality in thepursuit of epistemic goals.

If we take these two conceptions of scientific rationality as our starting place,then we can derive other notions of scientific rationality from them, such asrational consensus formation, rational assessment of theories, rational deci-sions, rational methods, rational actions, and so forth. The notion of ra-tionality forms a hierarchy, with goals at the top (Laudan, 1984):


GoalsRules (or Norms)DecisionsBeliefs or Actions

Rational agents act on norms in making decisions, which lead to beliefs oractions. Beliefs, decisions, and actions are rational insofar as they result fromgovernance by norms, and norms are rational insofar as they promote thepursuit of scientific goals.

3. Methods of Supporting the ISR Model

Given this characterization of ISR, how might we support it? Although somewriters might view ISR as an article of faith, I do not. Indeed, since my maingoal is to assess ISR, then it is appropriate in this paper to look at evidencefor and against this model of scientific rationality. There seem to be two verydifferent ways of supporting ISR based on two different approaches to thephilosophy of science. If one adopts a normative approach to the philosophyof science, then ISR is a model that we can use to justify scientific methods,decisions, theories, actions, and so on (Hempel, 1979; Howson and Urbach,1990). The model prescribes conduct and provides us with standards thatscientists ought to follow in belief formation or action (Resnik, 1985). Forinstance, one might argue that scientific goals provide a sound justificationfor the peer review system (Goldman, 1992), for the decision to accept Dar-win’s theory of natural selection (Kitcher, 1993), and so on.

If ISR is viewed as normative, then we might provide support for thismodel in the same way that we support instrumentalistic, moral theories,such as utilitarianism. On the utilitarian approach to morality, we assumethat there are instrinsically worthwhile ends or goals, such as happiness, theavoidance of pain, the satisfaction of preferences, and so forth. Moral theo-ries, norms, decisions, and actions can be justified in so far as they effectivelypromote these morally worthwhile ends. This approach brings an empiricalelement to moral theorizing, since our knowledge concerning the connectionbetween means and ends is based on observation and experiment (Harman,1977). Similarly, one could justify scientific norms, actions, and decisions onthe grounds that they promote scientifically worthy goals. On this view, atheory of scientific rationality would also be based on some empirical eviden-ce, since our knowledge of the connections between scientific means andends would be based on observation and experiment (Goldman, 1992;Kitcher, 1993; Laudan, 1987),

264 David Resnik

(ISR could also be supported through the method’s of reflective equilibri-um, which is also used in moral theorizing, but I will return to this pointlater.)

If one adopts a descriptive approach to the philosophy of science, thenISR explains scientific decisions, beliefs, actions, methods, and so forth(Giere, 1988; Kitcher, 1993; Hempel, Newton-Smith, 1978; 1979; Laudan,1984). For instance, one might argue that we can appeal to scientific goals inexplaining why scientists abandoned the Phlogiston theory (Laudan, 1984),why Michaelson and Morley performed their famous experiment, and soforth. If ISR is viewed as descriptive, then we might support it in the sameway that we support other scientific theories, such as theories in psychology,economics, or social science. One might justify ISR through showing that ithas empirical support or by demonstrating that is has various theoreticalvirtues, such as explanatory power, simplicity, generality, and the like (Hem-pel, 1979; Kantorovich, 1993; Giere, 1988).

In pre-Kuhnian times, philosophy of science was viewed as a strictly nor-mative pursuit, and ISR would be employed only for justificatory purposes(Hempel, 1979). Thus, one might justify a particular approach to scientificconfirmation on the grounds that it promotes the goals of science withoutasserting that this approach also explains scientific activities (Hempel, 1979).However, post-Kuhnian philosophers of science tend to be much more opento descriptive and explanatory approaches. Indeed, some even suggest thatwe abandon normative philosophy of science in favor of descriptive phi-losophy of science (Quine, 1969; Barnes, 1974). Many writers also adopt anecumenical position and hold that the philosophy of science is both normati-ve and descriptive (Laudan, 1987; Kitcher, 1993; Giere, 1988; Goldman,1986, Kantorovich, 1993; Resnik, 1985). Those who hold this view takeseriously the Kuhnian Revolution in the philosophy of science yet do notwish to abandon philosophy’s traditional interests in normative questions.

While I do not have time to pursue this discussion much further here, Iwill assume that the instrumentalist approach to scientific rationality can beused for either explanatory or justificatory purposes, perhaps both. Normati-vists may use ISR to justify scientific activities and pursuits; descriptivistsmay use ISR to explain scientific activities and pursuits. Normativists cansupport ISR by appealing to the goals of science; descriptivists can supportISR by appealing to empirical evidence. This dual use of instrumental ra-tionality can be understood as very much like the appeal to rationalisticexplanations in psychology, economics, and the social sciences (Hempel,1979; Rosenberg, 1988). Thus, an individual agent’s goal might help toexplain or justify her actions, decisions, and beliefs, or one might appeal to


goals and beliefs in explaining or justifying the conduct of groups. My carry-ing an umbrella to work on a given day can be explained or justified byappeal to my goal to not get wet, my belief that it is likely to rain today, andso on. A bank’s decision to raise its interest rates could be explained (andperhaps justified) by appealing to its goal of profit maximizing and its vari-ous opinions about its shortage of cash, the continual demand for loans, andso forth. If we assume that it is possible for rationalistic explanations to bothexplain and justify human actions, then ISR could also serve both purposesin science. This approach makes the study of scientific rationality a sub-fieldof rational choice theory, a framework that has significant influence inpsychology, sociology, and economics (Rosenberg, 1988).

Based on this division between two different ways of supporting ISR andthe previous division between different conceptions of scientific rationality,we obtain four different types of applications of ISR to science:

Individual Rationality (IRE) ISR explains the conduct of individual scientists;

(IRJ) ISR justifies the conduct of individual scientists;

Group Rationality(GRE) ISR explains the activities of scientific communities;(GRJ) ISR justifies the activities of scientific communities.

I shall examine these four different claims in my critique of the instrumenta-list model of scientific rationality.

4. Critique of the Instrumentalist Model of Scientific Rationality

In critiquing ISR, I will divide my task into two parts. First, I will challengethe notion that ISR explains scientific conduct; second, I will challenge thenotion that ISR justifies scientific conduct.

4.1 Does ISR explain Scientific Conduct?

If ISR is to explain scientific conduct, then epistemic goals and norms ofinstrumentality rationality must play a non-trivial role in explaining eitherthe actions of individual scientists, groups of scientists, or both. I examineindividual scientists first, since many of the problems that occur at this levelalso arise at the group level. The claim that ISR explains an individual scien-tist’s actions is a psychological thesis that needs to be supported by exami-ning her beliefs, desires, background assumptions, her methodological ma-xims, cognitive and social resources, and goals (Kitcher, 1993). Given these

266 David Resnik

evidential sources, it seems quite possible that a good explanation of anindividual scientist’s conduct is that she is acting like an instrumentallyrational agent would act, given certain epistemic aims, i.e. that she is ra-tionally motivated. For instance, it is likely that Galileo accepted Copernicanastronomy because he was convinced by the evidence for this theory, that hebelieved it to be true, that he wanted to accept the true theory, and so forth.One might also explain Lavoisier’s rejection of Phlogiston theory as resultingfrom his desire to understand the truth and his belief that Phlogiston theorywas not true.

However, scientists do not always act like instrumentally rational agentswould act, given certain epistemic aims. Sometimes scientists accept or rejecttheories based on practical, not epistemic goals. Perhaps a particular scientistaccepts a theory because she wants to receive funding to do research, to earntenure or promotion, to get a paper published, because her mentor accepts it,or because it supports her moral or political views (Hull, 1988; Longino,1990; Kitcher, 1993). Thus, it might often be the case that scientists effecti-vely pursue practical rather than epistemic ends, and that they are instrumen-tally rational but not in any scientific sense of “rationality.”

But there is also a more significant threat to using ISR to explain theconduct of scientists, namely, the possibility that sometimes scientists are notclearly motivated by any particular epistemic goals at all. The problem is notthat scientists do not have goals; the problem is that a plurality of epistemicgoals may undermine rationalistic explanations of scientific conduct (Resnik,1992; 1993). The plurality of goals gives rise to two different problems, anunderdetermination problem, and an overdetermination problem (Davidson,1980). Underdetermination might occur when a scientist has a variety ofepistemic goals that do not determine or clearly favor any particular decisi-on, action, or belief (Laudan, 1984). For instance, a scientist might have tochoose between two theories that satisfy different epistemic goals, such asthe goal of providing parsimonious descriptions of the world, the goal ofexplaining a number of different facts about the world, and the goal ofdeveloping fruitful theories. Even though she makes a choice, we might stillwonder which of these goals (or combination thereof) motivated her to makeher decision (Kuhn, 1977). Overdetermination might occur when a widevariety of epistemic goals favor a particular decision that a scientist makes.For instance, one theory might be favored over its rivals because it has hasgreater empirical support, explanatory power, and because it offers a moreparsimonious description of the world. Overdetermination is a problem inthat it divides up explanatory power among different goals to the pointwhere any particular goal is explanatorily weak. Both overdetermination and


underdetermination are similar in that they demonstrate a weak connectionbetween goals, norms, decisions, beliefs, and actions. In order to act like arational agent, a scientist needs to be motivated by rational norms in pursuitof rational ends, but sometimes we will have very little evidence for this typeof motivation in scientists.3

To see these two problems a bit more clearly, think of rationalistic ex-planations of ordinary decisions, such as purchasing an automobile or goingto work. Suppose our shopper, Sheila, wants a car that is inexpensive, reli-able, safe, fuel efficient, stylish, and comfortable. Car A is more reliable,comfortable, and safe than Car B; Car B is more stylish, fuel efficient, andinexpensive than Car A. After seeing how these cars satisfy different goals,she chooses Car B. Since her decision resulted from weighing and comparingdifferent goals, it is not at all clear that she was motivated to act on anyparticular goal. She reached a decision, but her decisions and actions do notconform to the standard conception of instrumental rationality.

Suppose Sheila wakes up one morning and wonders whether she shouldgo to work. It is a rainy Monday, she is tired and simply does not feel likeworking. But then she thinks of some reasons why she should go to work:She is involved in a project that she wants to complete, she has an appoint-ment with her boss at 10:00 am that she wants to make, she would get boredat home and does not want to get bored, she would feel “worthless” if shedid not work and she does not want to feel worthless, and so on. Taking allof these wants (and their concomitant goals) into account, she decides to goto work. Since her decision resulted from many different goals (manfiested aswants), it is not at all clear how it was motivated by any particular goal.Since all of these reasons caused her to act, each one of them provided verylittle in the way of motivation. There are instrumentalist replies to thiscritique, of course. For the undertermination problem, the instrumentalistcould argue that people have some decision procedures that prioritize variousgoals in order to maximize their overall decision outcome. If people lacksuch a procedure, their goal might be to simply to make an acceptable (orsatisfactory) decision (Slote, 1989). People can be motivated to act accordingto a decision procedure or to simply make a satisfactory decision, the in-strumentalist might argue. For the overdetermination problem, the instru-mentalist could assert that all of these goals jointly cause a person to act. Aperson can be motivated by a “summation of goals” in acting just like asummation of inputs might cause a neuron to transmit a message or a sum-mation of forces might cause a tree to move.

However, I do not find these replies very convincing. First, although itmight be possible to develop decision procedures for rational agents to

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prioritize goals, I think it is highly unlikely that people actually have theseprocedures as part of their psychological make-up. I also think it is psycholo-gically unrealistic to assert that people are motivated by the goal of “maxi-mizing their decision outcomes.” Ideal, rational agents may “maximizedecision outcomes” but real people simply make decisions on a more or lesscase-by-case basis. Real people may often attempt to at least arrive at satis-factory decisions, i.e. they may be satisficers (Slote, 1989), not maximizers,but people are often not even good satisficers. Besides, even if we claim thatsomeone was motivated to make a satisfactory decision, this might not be avery good explanation if they could have made any number of decisions thatwould be satisfactory. If it would be satisfactory for Sheila to purchase eitherCar A or Car B, does this adequately explain her decision to purchase Car Ainstead of car B?4 Concerning the idea that people may be motivated by a“summation of goals,” this seems quite plausible, but it still does not give theinstrumental model much explanatory power. ISR has explanatory powerinsofar as particular goals explain decisions, actions, or beliefs; it loses itsexplanatory power when we start appealing to multitudes of goals. I couldprobably give 100 reasons why I am not going to commit suicide tonight. IfI don’t commit suicide, do any of these reasons (goals or norms) explain whyI did not kill myself?

Turning to the explanation of group conduct, ISR suffers from similarproblems if we think of groups of scientists as having different goals andadhering to different norms. Indeed, the underdetermination and overde-termination problems can be even worse at the group level, since the connec-tion between group goals, norms, decisions, beliefs, and actions is even morecomplex and less straightforward. Not only may individuals within groupshave different goals and accept different norms, but the group itself mayhave a plurality of goals and norms (Stich, 1990; Gibbard, 1990). Onceagain, I do not assert that ISR cannot explain group activities in science; Ionly claim that there may be types of cases where ISR does not provide uswith very good explanations. ISR may indeed work quite well in explainingscientific conduct when groups agree on ends and means; but ISR does notoffer very good explanations of group conduct when groups do not agree onends and means (Laudan, 1984). If we want to explain how scientific com-munities reach decisions, we need to make use of models of rationality thatcan make sense of axiological pluralism and value debates among scientists(Laudan, 1984). ISR, as I have presented it, does not perform this task verywell.

The instrumentalist might offer the same kinds of replies that could bemade against my critique of applying ISR to individual conduct. First, she


might claim that there are decision procedures for prioritizing group andindividual goals and that groups can adopt such procedures in order to arriveat decisions, carry out actions, and so on. Two decisions procedures forgroups come to mind, a corporate hierarchy or a voting procedure. A corpo-rate hierarchy would be a set of rules that regulate a group in its activities.The rules would promote the aims of the group and would assign rights andresponsibilities to different members of the group. Thus, one might explaina private corporation’s actions by appealing to its goal of profit maximizati-on and its corporate structure. Or suppose a group uses some type of votingprocedure to make decisions and that this voting procedure is adopted inorder to promote fair, effective decisions by the group. In a case like thisone, one might appeal to the goal of making fair, effective decisions and itsvoting procedure to explain the group’s conduct. Thus, one might explainthe decisions of a legislative body by appealing to its goals and its votingprocedures.

The problem with this instrumentalist reply is that it paints an unrealisticportrait of science. Science does not resemble a corporation or a democracy(Resnik, 1993). It is not a corporation because it lacks a corporate structureor hierarchy. Admittedly, some types of research, i.e. industrial or militaryresearch, have something like a corporate structure. But most science isacademic science and it lacks this formal, centralized structure. Science is nota democracy because group decisions in science are not settled by majorityrule or other voting procedures (Hull, 1988). How it is that scientists reachgroup decisions is a subject of great debate. Some would argue that scientificdecisions are based on reason and evidence, others would say they resultfrom appeals to authority, still others would claim that political or economicinterests cause group decisions. Despite these different perspectives on scien-ce, most writers would agree, I think, that science does not operate accordingto voting procedures. Perhaps it should adopt such procedures, but that is anormative issue, not a descriptive one.

A second reply the instrumentalist might make is that groups of scientistsreach decisions by simply trying to make satisfactory decisions. Groups aresatisficers, not maximizers. But this reply is also unconvincing since it leavesISR with little explanatory power. If either of two theories, T1 or T2, wouldbe satisfactory to a scientific community, does an appeal to the community’sgoal of reaching a “satisfactory decision” offer us much of an explanation asto why the community choose T1 instead of T2?

But the instrumentalist has one other reply that is different from hisreplies to problems with explaining the conduct of individual scientists. Theinstrumentalist might appeal to game theory in order to explain the actions

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of groups. Game theory is a part of decision theory that studies the inter-actions of rational agents with each other (Resnik, 1987). The conduct of agroup of rational agents could be explained, one might argue, by studyinghow these agents will behave toward each other, given certain goals, beliefs,norms, and so forth (Rosenberg, 1988). For example, one might argue thata group adopts a particular theory because individual scientists find it to bein their interests to adopt the theory. Group, theory-choice in science couldbe just a very complicated “prisoner’s dilemma” where individual scientistsinteract with one another and try to maximize their utilities or preferences.5

Although I cannot explore possible applications of game theory to scienti-fic rationality in adequate depth in this paper, let me mention some problemswith this possible approach. First, game theory does not seem to provideanything like an instrumentalist model of group rationality. Game theoryholds that individuals are instrumentally rational, but this does not implythat the resulting group conduct is rational. A group would be rational onlyif it makes sense to say that the group’s goals explain its conduct. But gametheory seems to explain group conduct not by appealing to the goals of thegroup but by appealing to the goals of members of the group (Rosenberg,1992). In short, a group of rational agents is not the same thing as a rationalgroup.

Second, there are some serious problems within game theory that maycarry over into its applications to science. The most serious problem seemsto be the problem of “free riders” in game theory, which shows that rationalagents will have reasons to not cooperate with other rational agents, if non-cooperation pays off in the long run (Rosenberg, 1992). In a sense, this is thesame problem that was introduced by Plato and has been discussed by Hob-bes and many other philosophers in the context of justifying morality and thestate. Since science demands a high degree of cooperation among scientists,the “free riders” problem also poses difficulties with applying game theory toscience.

I do not mean to imply, however, that game theory does not ever help usexplain scientific conduct. Indeed, writers such as Kitcher (1993) have shownthat game theory may have some useful applications in explaining the alloca-tion of intellectual authority in science. My main point is simply that gametheory has its limitations and that we need to pursue alternative explanationsof group conduct in science.

To summarize my critique of using ISR to explain the conduct of scien-tists, I do not deny that ISR can often explain the decisions, actions, andbeliefs of individual scientists or even groups of scientists. However, thereare some types of cases in science where the model breaks down and it does


not provide good explanations. These seem to be the types of cases wheremany different (often incompatible) goals could influence scientific conduct.ISR seems to work best when there is a straightforward connection betweengoals, norms, decisions, and actions or beliefs, when goals do not conflict,and when only a few goals seem to motivate action. ISR is not very useful inhelping us explain cases where there are many goals, where goals conflict, orwhere the connection between goals, norms, decisions, beliefs, and actionsconnection is not straightforward.

4.2 Does ISR justify Scientific Conduct?

If ISR often does not adequately explain scientific conduct, then perhaps itmight still justify scientific conduct. One might acknowledge that scientistsoften deviate from the instrumentalist model of rationality but still maintainthat they ought to conform to it. ISR could be well supported as a model ofidealized, scientific rationality. In this section I will challenge the notion thatISR can be supported as an approach to the justification of scientific conduct.

This first problem with the instrumentalist approach to justification isthat scientists and scientific communities have a wide variety of epistemicaims. In response to this axiological pluralism, the instrumentalist needs todevelop a decision procedure for prioritizing different aims and for adjudica-ting conflicts. As I noted earlier, one way of doing this is to assign different“values” or weights to different goals and to develop a method for calcula-ting an overall “decision value or utility.” An agent will be justified in perfor-ming the action (or holding the belief) that maximizes or satisfices her decisi-on value, on this view.

Earlier I argued that decision procedures for prioritizing goals are proba-bly often not very helpful in explaining scientific conduct. But could suchprocedures still be useful in justifying conduct? I think such procedures couldbe useful if they can be successfully developed and applied, but this is a big‘if’. One of the strongest defenders of applying rational choice theory toscience, Levi (1990), argues that there can be conflicts of epistemic goals thatno decision procedure can adequately solve. Stich (1990), Nozick (1993),and Resnik (1994a) echo this view. The same kind of problems can occur invoting procedures if we think of voting as a decision procedure for groups(Arrow, 1951). When we find axiological pluralism, it may sometimes beimpossible for individuals or groups to effectively pursue their goals. Even anideally rational agents may face choices that involve an “unsystematic”assessment of different goals analogous to the automobile buying examplediscussed earlier.

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While these questions are quite interesting, I will not pursue them furtherhere since they concern problems internal to rational choice theory and theconcept of rationality in general. Without a doubt, if the concept of ra-tionality in general cannot be purely instrumentalist, then any application ofthis concept to science will not be either. But since I am interested in theapplication of the instrumentalist approach to science, I will not stray too farfrom questions about scientific rationality, and in this section I am concernedabout questions of justification.

In returning to questions of justification in science, we encounter theAchilles heel of the instrumentalist model of scientific rationality, the pro-blem of justifying goals (Siegel, 1985). Some writers, such as Giere (1988)attempt to bypass this problem by arguing that ISR can explain scientificconduct even if we do not have an answer to questions about the justificationof scientific goals. Indeed, this problem really does not need to surface untilwe examine questions of justification, since even the most immoral or un-worthy goals can explain human conduct. Adolph Hitler ordered 6 millionJews killed because his goal was to eliminate the Jews. This goal (and itsconcomitant desire) may provide a good explanation of his conduct, thoughit certainly does not justify it.

What the Hitler case shows is that we have reasons to believe that norms,decisions, actions or beliefs cannot be justified if they derive their justificati-on from goals that are unjustified. We can think of the ISR model as provi-ding us with a justificatory hierarchy: goals justify methods, which justifydecisions, which justify beliefs or actions. If our goals lack justification, howcan anything else in this hierarchy be justified? If your goal is to die a horri-ble death, then maybe you could justify setting yourself on fire. But whyshould anyone have the goal of dying a horrible death? Isn’t this goal irra-tional? And if it is, then one’s conduct in pursuit of this goal must also beirrational, no matter how efficient it may be.

Rational choice theorists usually do not address questions about thejustification of goals. From their perspective, what makes an agent rationalis that she effectively pursues her ends, whatever those ends may be. We couldfind Hitler’s actions morally unconscionable yet still rational, given his aims.Here we enter a hotly disputed area in the study of rationality and I have nointention of solving these outstanding problems here. But I do not need toanswer these questions. I am concerned with the rationality of science, notwith rationality in general. And my main concern is whether scientific ra-tionality is the same thing as instrumental rationality.

Throughout this essay I have made the modest assumption that science isan activity carried out by human beings who are not ideal, rational agents.


Even if instrumentally rational agents do not seek justifications of epistemicaims, scientists do. Throughout the history of science, scientists have askedimportant questions about the aims of science and they have debated variousanswers (Laudan, 1977, 1984). For instance, the debate between Einsteinand Bohr was about much more than the EPR experiment and the results ofquantum mechanics; the debate was also about the aims of science (Fine,1986). Should science provide us with deterministic theories or statisticalones? Should science aim to uncover a “deeper” reality or should it simplydescribe to save the phenomena?

I think few people would deny that these debates take place in scienceand continue to do so. So, like it or not, scientists seek some justification forthe aims of science from time to time. How can the instrumentalist reply tothis fact about scientists? If she is to remain true to instrumentalism, then shemust claim that we cannot view debates about scientific aims as rationalsince rationality consists in the effective pursuit of aims. A debate aboutthose aims cannot be rational unless the debate itself promotes some other,more fundamental goals. But, ex hypothesi, such debates do not promotemore fundamental goals since the aims of science are taken to be science’smost fundamental goals. We can think of science as rational when scientistsmake decisions about how to effectively pursue their goals, but science ceasesto be rational when scientists examine their goals.

But this kind of reply reveals the absurdity of the instrumentalist’s positi-on. If “scientific rationality” applies only to ideal, rational agents who taketheir goals as given, then why bother calling this kind of rationality “scienti-fic?” If we are to understand science, we must be able to make sense ofdebates about the aims of science (Laudan, 1984) and we must find someway of understanding those debates that can allow such debates to (someti-mes) be rational. But if we admit this much, then we also have to admit thatthere are limits to ISR: the model may be useful when we do not questiongoals, but it cannot help us address questions about goals. To summarize thissection, the conclusion is similar to the previous one: ISR provides an ade-quate account of some but not all types of justification in science. If we wantto understand the justification of the aims of science, then we need to deve-lop an alternative model of scientific rationality (Laudan, 1984; Resnik,1993).

6.0 Categorial Rationality

The shortcomings of the instrumentalist model of scientific rationality indi-cate that we need to develop a different model of scientific rationality inorder to understand the kinds of questions, debates, arguments, and deci-

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sions that occur when scientists evaluate their basic goals and norms. Ofcourse, one might resist this suggestion, but this would require us to admitthat these debates about fundamental questions of science are simply notrational. One might claim that the only rationality in sciences is means/endsreasoning, and when science does not fit this model, it is simply not rational.But I think most philosophers and many other writers would find this viewextremely distressing, since it would indicate that some of the most impor-tant questions and debates in science go beyond the scope of rationality.Instead of accepting this troubling result, we should develop a differentmodel of scientific rationality. We should not abandon the instrumentalistmodel, since it can accommodate a great deal of scientific practice, but weshould have a different model that can apply to situations that the instru-mentalist model cannot accommodate. Some readers might object to thisview on the grounds that we should have one and only one model of scienti-fic rationality, but this is an unreasonable demand, especially given thediversity of the subject under investigation. In many scientific disciplines,such as meteorology, ecology, and evolutionary biology, scientists developdifferent models for the same phenomena. The models apply to differentaspects of the phenomena, make different assumptions and have differentparameters. It seems quite reasonable that we could take some lessons fromscientists and have different models of scientific rationality that would applyto different aspects of science, make different assumptions, and have diffe-rent parameters.

One possible model that we mentioned earlier is categorical rationality.On the categorical model of scientific rationality (CSR), some norms wouldbe justified without reference to goals (Doppelt, 1990). A scientist would berational in so far as he is motivated by norms of categorical rationality, anda group of scientists would be rational insofar as they are governed by normsof categorical rationality. On this view, certain norms of science couldexplain and justify scientific conduct without reference to any particular aimsof science (Doppelt, 1990). These categorical norms would themselves definethe aims that are worth pursuing (Doppelt, 1990). Kantian moral theoryprovides us with detailed account of categorical rationality in practicalmatters (Darwall, 1983), and one could presumably use this approach torationality to construct a categorical approach to scientific rationality. In-deed, one can read Kant’s Critique of Pure Reason (1965) as systematicdefense of a categorical approach to scientific rationality (Brown, 1988).Kant’s axioms of intuition, analogies of experience, postulates of empiricalthought, general logic, transcendental logic, and discipline of pure reasoncould be viewed as categorical rules of rationality.


There are some difficulties with applying this model of rationality toscience, however. The first problem has to do with its usefulness in explai-ning scientific conduct: can an appeal to categorical rationality ever explaintheory acceptance, experimentation, and other scientific activities? Any timewe appeal to a rule that we think is categorically rational, it seems that wecould also find some goal(s) that it serves (Resnik, 1992, 1993). If it is thecase that most rules do promote various epistemic aims, then how do weknow that any given rule’s real motivational power does not lie in the factthat it serves various goals? How do we know that any purported categoricalimperative is not really a hypothetical imperative? Consider the rules ofdeductive logic, thought by many writers to be good candidates for categori-cal rules of reason (Doppelt, 1990). If a scientist appears to be following arule of non-contradiction, we could explain her conduct by 1) appealing tothis rule only; or 2) by appealing to the rule and the goal it serves, such astruth acquisition. Does the scientist follow the rule for its own sake or doesshe follow it because she has a desire to obtain true beliefs about the world?This is not an easy question to answer and it may be the case that the twoopposing answers are strongly underdetermined by the data. Of course, thispoint does not show that scientists never follow rules of categorical rationali-ty but it shows that it may not be possible for us to ever know that they do.If we cannot know that someone is being categorically rational, then catego-rical rationality is of no use in explaining scientific conduct.

One other difficulty categorical rationality faces in explaining scientificconduct is the explanation of changes in scientific methodology. Manywriters have argued that the rules of scientific methodology have changedover time and that they are likely to undergo continual modification (Lau-dan, 1984). But categorical rules have been traditionally viewed as “absolu-te” in that they should not change over time (Brown, 1988). For example,one might argue that the principle of non-contradiction was held by theGreeks and that it will continue to be held for another 2500 years or more.Now it may be the case that some rules of scientific method have not chan-ged, but clearly many have (Laudan, 1977, 1984). If a rule that we oncethought was a categorical rule undergoes revision or is even rejected, does itcease to be a categorical rule or was it simply never a categorical rule in thefirst place? Answering “yes” to either part of this disjunctive question is toabandon the categorical approach to rationality and to admit, followingQuine and many others, that even rules of logic could be revised some day(Giere, 1985; Laudan, 1984)).

CSR also runs into some difficulties in the justification of scientific con-duct when we request justifications of the categorical rules. A long tradition

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in philosophy holds that some rules of rationality are self-justified and thatan attempt to try to justify them in terms of other rules or goals is mistaken.Again, consider the principle of non-contradiction, a prime candidate for acategorical rule. Following Aristotle, one might argue that anyone who doesnot accept such a rule cannot be rational. Or following Kant, one mightargue that a being that does not adhere to this principle cannot even think.Part of our conception of rationality involves accepting the principle of non-contradiction and forming beliefs on the basis of it and anyone who does notunderstand this simply does not understand what rationality requires orpresupposes (Blackburn, 1995).

But I think this line of argument is question-begging. A person who asksfor a justification of the principle of non-contradiction is questioning thenature of rationality itself, so the claim that the principle is self-justifiedsimply won’t do (Blackburn, 1995). One might argue that rationality someti-mes requires us to accept contradictions.6 It might be useful to accept con-tradictions from time to time in order to achieve a greater goal in the longrun. For example, a quantum physicist might argue that the concept of asuper-position of quantum states requires us to accept contradictions, e.g.Schrodinger’s cat, but she might also argue that accepting these contradic-tions will serve a greater good, e.g. the development of quantum theory.

The person who views the principle of non-contradiction as a categoricalrule cannot engage in this discussion about its justification in terms of itsusefulness for science. But these questions are legitimate and deserve somekind of answer beyond a question-begging one (Blackburn, 1995). We needto be able to justify the principle of non-contradiction and other naturalcandidates for categorical norms of rationality. Thus, if we should be able tojustify categorical rules, the question arises, “how can we justify them?” Wecannot appeal to other categorical rules without creating a regress or circleof rules (Resnik, 1992; Brown, 1988). Perhaps we can justify these rules byappealing to the aims of science, but if we do that, they cease to be categori-cal rules.

7.0 Dynamic Rationality

Although they differ in many respects, the categorical and instrumentalmodels of scientific rationality suffer from a common shortcoming: theyboth do not provide us with a very good account of decisions and debatesabout the most basic epistemic goals and norms in science. This is becauseboth models of scientific rationality take certain goals or norms as “fixed” or“given.” Scientific rationality consists in either effective pursuit of the aimsof science or governance by various norms of rationality. These accounts


work as far as they go, but they cannot make sense of episodes in sciencewhere scientists attempt to justify their basic goals and norms or wherescience undergoes fundamental changes in its goals and norms.

What we need, I suggest, is a model of scientific rationality that we canapply to debates about science’s basic goals and norms. The model shouldallow us to explain how changes in basic goals and norms can occur inscience and it should recommend procedures for evaluating basic, epistemicstandards in science. Of course, sophisticated versions of ISR or CSR canexplain or justify changes in science, but all change occurs within some kindof static structure provided by either the goals of science or the norms ofscience. In order to not be merely a sophisticated version of the instrumenta-lism or categoricalism, the alternative model should not take any aims ornorms as “fixed.” The model should give us a dynamic as opposed to staticaccount of rationality. ISR and CSR, on my view, are both static models evenif they allow for changes. The alternative model, call it dynamic rationality(DR) would be fully dynamic in that it would not take any epistemic goals,norms, or standards as fixed for all time.

What are the prospects for developing a fully dynamic model of scientificrationality? Laudan’s (1984) “reticulated model of scientific rationality” is afine attempt to develop a dynamic model of scientific rationality, but it fallsa bit short of being fully dynamic. According to the reticulated model, scien-tists can debate about goals, methods (or norms) and theories. Goals can bejustified by appealing to methods and theories; methods can be justified byappealing to goals and theories; and theories can be justified by appealing togoals and methods. The model allows for different levels of debate anddifferent types of consensus formation in science. The model is dynamic inthat it can explain and justify changes in goals, methods, and theories inscience. But the main weakness of the model is that it is not dynamic enoughbecause it defends several criteria for goal-assessment in science and givesthem a privileged status (Resnik, 1994b). A truly dynamic model wouldrecognize that even criteria of goal-assessment are not immune to revision.

Taking Laudan’s approach as a good start, I suggest that we consider amodel of scientific rationality that is thoroughly dynamic. All aspects ofscience – goals, norms, theories, beliefs, decisions – can be justified or ex-plained. No aspect of science is immune to revision or beyond the limits ofrational debate. This dynamic model of rationality would also take seriouslyQuine’s remarks about belief revision and empiricism without dogmas. Hereit is instructive to reexamine Quine’s famous (though highly cryptic) remarksfrom “Two Dogmas of Empiricism”:

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...no statement is immune to revision. Revision of even the logical law ofexcluded middle has been proposed as a means of simplifying quantummechanics; and what difference is there in principle between such a shiftand the shift whereby Kepler superseded Ptolemy, or Einstein Newton, orDarwin Aristotle? (Quine, 1980, p.43).

In this passage Quine has in mind the kind of global changes that can occurin science, which involve changes in basic assumptions, theories, aims, andnorms. I take seriously his assertion that “no statement is immune to revisi-on” and suggest that this recommendation applies not only to observationaland theoretical statements, but also to statements about logic, mathematics,and the basic norms and goals of science.7

But this commitment to “dynamic rationality” raises some problems forunderstanding changes in norms and goals. If changes can be so fundamentaland wide-ranging, how can they in any sense be “rational”? How can weview them as “rational?” Don’t these sweeping changes in science seem morelike the Kuhnian revolutions or conversion experiences than anything ra-tional?

This initial worry about a dynamic approach raises two questions, onepertaining to explanation, the other pertaining to justification. In order togenerate some sympathy for the dynamic approach, I will attempt to showhow it might be able to both explain and justify scientific conduct. Thegeneral idea I would like to develop is to view the process of fundamentalchange in science as rational insofar as it results from a reasoning process.Reasoning has logical, psychological and social dimensions (Harman, 1986;Resnik, 1985). Psychologically speaking, reasoning is a process wherebybeliefs, goals or other propositional attitudes cause changes in other beliefs,goals, or propositional attitudes in people (Harman, 1986). From a socialperspective, reasoning is process whereby a speaker defends a statement to anaudience by appealing to other statements for the purposes of changing theirbeliefs, goals or other propositional attitudes (Goldman, 1994). The similari-ty here is that in either case a “reasoning process” can be reconstructed interms of an argument. An argument can also be studied from a logical pointof view if we abstract away from its psychological and social dimensions andexamine its logical form (Resnik, 1985).

Since arguments could explain or justify radical changes in science, thereare two senses in which a fundamental change in science might be viewed as“rational.” When explaining scientific conduct, the change can be viewed asrational if it results from (is caused by) arguments. Arguments also play acrucial role in justification, since one might justify a fundamental change interms of arguments as well. Arguments can include statements about goals,norms, theories, and other aspects of science.


If we apply some of the notions discussed earlier to this dynamic modelof rationality, we can think of a rational agent as an agent who reachesdecisions, performs actions, or holds beliefs based on reasoning or argumen-tation. Scientists or scientific communities are dynamically rational insofar asthey reach decisions, perform actions, or hold beliefs based on reasoning orargumentation. If we think of means/end and categorical reasoning as typesof reasoning or argumentation, then the instrumental and categorical (orstatic) models of rationality are actually restricted versions of DR which takecertain premises used in argumentation as fixed, i.e. statements about episte-mic goals (instrumentalism,) or basic epistemic norms (categoricalism). If weapply the chart from section 3.0 to (DR), we obtain the following:

Individual Rationality (IRE) DR explains the conduct of individual scientists;(IRJ) DR justifies the conduct of individual scientists;

Group Rationality(GRE) DR explains the activities of scientific communities;(GRJ) DR justifies the activities of scientific communities.

Let us first consider a simple example to illustrate the model. Suppose thatJohn has recently undergone a fundamental change in his beliefs, goals, andoverall outlook on life. For most of his life he has been a “thrill-seeker.” Hehas participated in many high risk activities, such as rock climbing and skydiving. Thrill-seeking is the most important thing in his life and he viewsother things, such as family, career, money, and so forth, as secondary.However, John meets a women, Jane, they fall in love, and have a son. Henow starts to view thrill-seeking as not the most important thing in life andhis family becomes all-important. Many of his beliefs, goals, and wantschange as a result of this overall change in outlook. How might we explainthis change? Taken as a whole, this change seems non-rational but we canview it as rational if we can reconstruct and argument or series of argumentsthat influenced John’s attitudes as he changed from thrill-seeker to “familyman.”8 When asked, he (or we) might also use arguments to justify thisradical change. However, we should also realize that this change is notcompletely rational in that something besides argumentation probably playeda role in the change, such as meeting Jane, having a son, growing older, andso forth. The presence of these “non-rational” factors does not underminethe rationality of the radical change, however. Human conduct can be moreor less rational, depending on how much of an influence reasoning processesplay in explaining behavior or in justifying it.

To see how this model might be applied to science, let us consider aradical change in science, the change from Newtonian physics to relativistic

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physics and quantum mechanics. Here we have a change in theories, i.e.Newton’s theories of gravitation and motion vs. Einstein’s theory of gravita-tion and quantum mechanics; we have a change in basic assumptions aboutthe universe, i.e. absolute space and time vs. relative space and time; we havea change in methods, i.e. the use of simple experiments, geometry and calcu-lus vs. greater reliance on complex experiments and statistics; and we havea change in goals as well, i.e. the goal of discovering deterministic laws vs.the abandonment of determinism and the acceptance of statistical laws.When viewed as a whole, this change seems so radical that it would seem toinvolve an non-rational leap of faith or scientific revolution. But the shiftfrom Newtonian physics to modern physics might be viewed as rational if wecan explain (or justify) it in terms of various arguments leading from oneworld-view to another.

Admittedly, there are probably many “non-rational” factors that played arole in this change, and it would be a mistake to view the change as com-pletely rational, but it could be rational to a greater or lesser degree, depen-ding on how much reasoning played a role in explaining or justifying thechange. If arguments play no role in explaining a radical scientific change, ifit is explained by “external” social, psychological, political, or technologicalfactors, then the change is non-rational. If change cannot be justified byappealing to arguments, then it is also non-rational. This perspective leavesmost important questions about rationality in science open to debate. Ra-tional and non-rational factors could play a role in explaining the conduct ofindividual scientists or scientific communities, and it may not always bepossible to justify any given episode of scientific change.

This model of rationality, we should note, requires us to judge scientistsby their own standards, goals, beliefs, and theories. We might view aims ofscience, methods, or theories, or scientists as irrational given our currentunderstanding of science, yet we could still view them as rational given theirhistorical context. For example, many people would view alchemy as irra-tional but many of its goals, methods, and theories could still be rationalgiven its historical context. And of course the change from alchemy to mo-dern chemistry could be viewed as rational in so far is it resulted from reaso-ning processes. Given this dynamic approach to scientific rationality, what isrational today might not be rational tomorrow. The goals, methods, theories,and practices of 26th century science might bear little resemblance to ourcurrent science, but this radical change could be rational insofar as it resultsfrom reasoning processes.

Before wrapping up my presentation of this alternative model, let meanswer two objections. The first objection is that while the model appears to


be different from the categorical or instrumental approaches, it is in factnothing more than the same theories in a new package. The model takesspecific epistemic goals or norms as fixed. If some epistemic norms are fixed,then it is simply a version of the instrumental model; if norms are fixed, thenit is a version of the categorical model. For instance, one might argue thatthe model presupposes “reasoning,” “debate” or “argumentation” as the aimof science and therefore scientific rationality is still ultimately instrumental.Or perhaps it presupposes “attempt to persuade through reasoning” as a rulefor science and it is ultimately a categorical model.

In response to this objection, I will admit that the model might presuppo-se some very general and abstract goals or norms, such as “seek debate” or“attempt to persuade through reasoning.” But this hardly makes it just anot-her version of ISR or CSR. Since “reasoning” is understood in such a broadsense, the model allows for a great deal of diversity in the name of this goal,and a goal like “rational debate” imposes very little if any structure onscientific inquiry. The same point also applies to a rule like “attempt topersuade through reasoning.” If science is instrumentally or categoricallyrational in this very broad sense, then so be it. Indeed, the model would noteven be a model of rationality in science if it did not assume at least somebare notion of rationality. To abandon “reasoning” or “rational debate” asgoals or norms is to give up the idea of developing a model of scientificrationality.

The second objection is based on an outstanding problem in rationalchoice theory, i.e. the problem of rationally revising preferences, desires, orutilities. Many writers have argued that it is not possible to rationally revisepreferences, desires, or utilities (Levi, 1990). If it is impossible to rationallyrevise these propositional attitudes, then it would seem to be impossible torevise goals or basic aims. Although I cannot give a full response to thisobjection here, I should point out that we might make a distinction betweentypes of desires (preferences or utilities). We could distinguish between basicdesires (such as happiness) and derived desires (such as the desire for a car)and between practical desires and epistemic ones. With this distinction, wemight admit that certain basic practical desires cannot be rationally assessedwhile maintaining that epistemic desires and less basic practical ones can berationally assessed.

8.0 Types of Dynamic Rationality

Given the legitimacy of developing a fully dynamic approach to scientificrationality, we need to decide how we are to understand dynamic rationality.There seem to be several different ways of developing a dynamic model of

282 David Resnik

rationality and some might be better than others. Let us briefly examinethese alternatives

8.1 Conventionalism

One alternative worth considering is the conventionalist approach to scienti-fic goals and norms. On this approach, scientific goals and norms are nomore than linguistic conventions. As conventions, they can change over time.We can infer these from our use of the words ‘scientific,’ ‘rational,’ andrelated terms like ‘knowledge,’ ‘reason,’ ‘explanation,’ ‘evidence,’ and soforth. These and other words relating to scientific rationality presupposespecific linguistic conventions, one might argue. Scientific changes can beboth justified and explained in terms of changes in these conventions as well.So, many of the revolutions in science are at bottom little more than changesin the meaning or use of various words.

The attempt to arrive at epistemic ends or norms through linguisticanalysis should remind readers of Strawson’s (1952) ordinary languagedissolution of the problem of induction. Is induction rational? Strawsonanswered this question by claiming that a proper analysis of ‘rational’ and‘induction’ will show us that the statement “induction is rational” is a tauto-logy. To ask the question, “Is induction rational?” is like asking “Is the lawlegal?”

The trouble with this approach is that it still does not get us very fartoward a justification or explanation of our scientific aims or norms. It failsto justify aims or norms since one could still ask why we should follow alinguistic convention. If one could show that our concept of knowledgepresupposes truth as the aim of inquiry, then we could still ask why weshould use the term ‘knowledge’ in this fashion; perhaps we could use it in away that does not presuppose truth as an aim of inquiry and we might havegood reasons to use it this way (Resnik, 1994a). Returning to the analogywith Strawson’s dissolution of the problem of induction, Strawson’s ap-proach does not genuinely answer the key question raised by Hume, namely,why should we use inductive methods? After all, someone who does notaccept inductive methods will also not accept a usage of the words ‘rational’and ‘induction’ that makes the statement “induction is rational” a tautology.Thus, the appeal to linguistic conventions to answer questions about episte-mic aims and norms is not very helpful in justifying them (Kantorovich,1993).

Likewise, conventionalism also fails as a model of explanation in that itcannot adequately explain why we have adopted certain conventions (Giere,1988). Presumably, there are some “deeper” reasons why we view truth as an


aim of inquiry or why we accept inductive arguments. Perhaps truth-seekingand inductive methods have some biological basis beyond their status associal conventions (Kantorovich, 1993).

8.2 Reflective Equilibrium

Another approach to DR is to appeal to our intuitions about what is episte-mically worth pursuing and which norms seem to be justified. It is impossibleto debate about questions about ultimate aims and norms, one might argue,so all we can do is “come to see” or apprehend epistemic aims. The problemwith this intuitionist approach is that people may have different intuitions;I may believe that “truth” is the goal of science while you may believe that“explanatory coherence” is the goal. Our intuitions will also be “biased” inthat they will be shaped by our culture, politics, our current beliefs, and soforth. If all we can do is appeal to our intuitions, then we would seem tohave very little in the way of justification for ultimate, epistemic ends ornorms (Laudan, 1987).

As an improvement on this straightforward appeal to intuitions, onemight instead argue that we should apply the method of reflective equilibri-um to systematize our intuitions about epistemic standards (Goodman, 1965;Kantorovich, 1993). According to this method, we can take our consideredjudgments about the aims and basic norms of science as a “database” anddevelop theories to account for the data. Considered judgments are simplyintuitions the have been purged of social, political, and other biases. We canuse theories to revise our judgments, and then we can modify those theoriesin response to our “enlightened” intuitions. Eventually our intuitions andtheories reach a point of mutual adjustment known as reflective equilibrium(Rawls, 1971). The aims and norms of science on this view could be thosegoals and norms that we will endorse when our theories and intuitions are inreflective equilibrium (Kantorovich, 1993). One of the main advantages ofthis method is that it provides a way of developing a consensus (Rawls,1971). Reflective equilibrium is not my intuitions on the aims and norms ofscience or your intuitions; it is our intuitions. Reflective equilibrium alsoattempts to overcome the problem of bias in that biases should disappear asa result of criticism and reflection.

While the method of reflective equilibrium is an improvement over astraightforward appeal to intuitions, it still suffers from some difficulties.First, the method could result in biased outcomes. If we cannot completelyeliminate bias from our considered judgments, then our end results will bebiased as well. The computer science phrase “garbage in, garbage out” ap-plies here. The possibility of bias is a problem because it would seem to

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undercut the justification of aims and norms: if we have reasons to believethat a method could be biased, then why accept it results or even use it? Asecond problem is that reflective equilibrium makes no mention of whatscience and the history of science have to say about our epistemic norms andaims. Reflective equilibrium could be completely at odds with a scientificunderstanding of the human reasoning and empirical studies of science(Laudan, 1987). If this is the case, then it may not be very useful in explai-ning scientific conduct, since good explanations of science should at least besupported by empirical evidence (Giere, 1988).

8.3 Naturalism

The final dynamic account, which I think is superior to the other two ac-counts, is naturalism. According to the naturalist, we need to draw on evi-dence from psychology, biology, sociology, and the history of science toanswer questions about epistemic norms and aims (Laudan, 1984; 1987;Stich, 1990; Kitcher, 1993; Kantorovich, 1993; Kornblith, 1993). Thenaturalist can employ scientific theories, methods, facts, and hypotheses toanswer questions about the norms and aims of science. Our epistemic aimsand norms are simply those goals and norms that provide the best explanati-on of scientific activity and that have empirical support from psychology,sociology, biology, and other sciences. Naturalism is a scientific and phi-losophical approach to scientific rationality in that it attempts to both ex-plain and justify scientific practice (Kantorovich, 1993). Naturalism alsooffers us an inherently dynamic approach to scientific rationality because itis based on serious reflection on the growth of science: as science changes,grows, and expands, our explanations and justifications of science will alsochange in an continual conversation with scientific practice and progress.

However, naturalism has its own difficulties. One trouble with naturalismis that it would appear to be circular, since scientific theories and practiceswill be based on some of the aims and norms that may be in dispute. Thus,if we accept theories because we have reasons to believe that they are trueand we take truth to be the aim of inquiry, then we are caught in a circle ifwe appeal to these theories to justify truth as an aim of inquiry. Most na-turalists reply to this charge of circularity by admitting that their position isultimately circular (Giere, 1988). But they also remind us that this circlecould be very large and could continually expand as science changes and thatcircularity is unavoidable unless we accept some strong form of epistemicfoundationalism (Giere, 1985; Resnik, 1994b; Kitcher, 1992). Thus, thecircularity in the naturalistic approach need not be vicious or dogmatic.


The second problem with naturalism is one might claim that it commitsthe “naturalistic fallacy” by attempting to infer normative and justificatoryclaims about goals from the descriptive and explanatory claims of scienceand the history of science (Kitcher, 1992; Giere, 1985; Kantorovich, 1993).This is a difficult question for naturalism and I think it cannot be solvedunless we bring a normative perspective to naturalistic studies. Thus, thenaturalist would not simply “read off” goals from science and the history ofscience but she should develop an account of goals that is informed by herphilosophical and normative theories of those goals (Laudan, 1984; Stich,1990; Kantorovich, 1993). The “enlightened” naturalist realizes that weanswer epistemological questions about science through an ongoing dialecticinvolving philosophy, science, and the history of science. The “database” thatwe use in this study is not value-neutral since it includes our judgements ofgood and bad science (Kantorovich, 1993). Thus, there is indeed no chasmbetween normative and descriptive approaches to science since even the“descriptive” studies have normative content.

9.0 Conclusion: Global vs. Local Rationality

The following chart summarizes the distinctions draw in sections 7 and 8 ofthis paper:

Scientific Rationality1.Static a.Instrumentalism

b.Categoricalism

2.Dynamic a.Conventionalism

b.Reflective Equilibrium c.Naturalism

In this essay, I have characterized (1a) as the received view of scientificrationality. I have argued at length against this view and I have also criticized(1b), (2a), and (2b). I propose (2c), a fully dynamic and naturalistic accountof scientific rationality (DNR), as a worthwhile alternative to these othermodels. I think it is a plausible alternative because it provides the best ac-count of global scientific change, i.e. changes in science’s basic, epistemicgoals and norms, and global scientific debates, i.e. attempts to justify orevaluate science’s basic, epistemic goals and norms.9 I am also not suggestingthat we abandon the instrumentalist model of scientific rationality, since Ibelieve that it provides a fine account of localized scientific changes, i.e.changes that do not involve changes in basic, epistemic goals or norms, and

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localized scientific debates, i.e. debates where scientists do not evaluate orjustify basic, epistemic goals or norms. Local decisions might include thedecision to fund a project, reject an hypothesis, develop a new technique,referee a paper, and so on. In local decisions there is a straightforward con-nection between epistemic goals, norms, decisions, beliefs, and actions; inglobal decisions this connection, if there is one, is much more tenuous. I amarguing that ISR applies at the local level of scientific change and debate,while DNR applies at the global level. This outlook suggests that it might beuseful to make yet another distinction when it comes to scientific rationality,viz. local rationality vs. global rationality.10 On this view, the rationality ofscience looks quite different at different levels of scientific decision-making.If one focuses on local decisions, then scientific rationality may be bestviewed as instrumental rationality. But if one moves beyond this level andlooks at global decisions, scientific rationality resembles the dynamic modelI have articulated here.11

Notes1 In my discussion of the explanation of human actions I will assume that people have free willwhen it comes to making decisions that result in actions or beliefs. Not all beliefs are free, but atleast some are. Thus, we can be held not only morally responsible for our actions but also epistemi-cally responsible for some of our beliefs, i.e. those beliefs we can voluntarily control. See Miller(1995) for more on epistemic responsibility. 2 The distinction between practical and epistemic goals is not equivalent to the distinction betweenpractical and theoretical rationality, even within the instrumentalist approach, since one mightmaintain that norms of belief formation can be justified by appealing to practical goals, or thatnorms of action can be justified by appealing to epistemic goals. 3 These two problems, underdetermination and overdetermination are not unique to rationalisticexplanations of human actions because they can also occur in any type of theory that providescausal explanations. Underdetermination occurs when we do not have sufficient evidence tosupport any particular causes of an event; overdetermination occurs when we have evidence tosupport too many causes. Although I am construing these problems as epistemological, they canalso be construed as metaphysical problems. See Humphrey (1989). 4 The idea here is that all requests for explanation assume a contrast class to the statement des-cribing the fact to be explained (van Frassen, 1980). If we take “A” as a statement describing a fact(F) to be explained, and B,C,D are statements describing others facts (F1, F2, F3) that could haveobtained instead of F, then an explanation is an answer to the why-question, “Why A rather thanB, or C, or D?” 5 For more on game theory and the “prisoners dilemma” see Jeffrey (1965), Resnik (1987).6 The argument here involves the notion of the principle of non-contradiction as a rule for beliefassessment and belief change. This is not the same the principle of non-contradiction as an axiomin a system of formal logic. Formal logic can give us some guidance for the evaluation of beliefs butthe axioms and theorems of formal logic are not the same as rules for belief changes (Harman,1986; Cherniak, 1986). 7 I am assuming in this position that statements about goals and norms have the same cognitivestatus as scientific hypotheses, observational statements, and other statements in the body ofscience. If we take a cognitivist approach to descriptive statements in science, then I suggest that wealso take a cognitivist approach to normative statements in science. Thus, on my approach state-


ments about epistemic goals and norms in science should be viewed as being capable of having truthvalues. A statement like “Truth is the aim of scientific inquiry” should be treated in the samefashion as “The Earth is 3rd planet from the Sun.” If the latter can be true or false then so can theformer. 8 By “irrational” I mean “against reasoning”; by “non-rational” I mean “outside of or beyondreasoning.” 9 I have more or less assumed that there is a difference between basic and non-basic epistemic goalsand norms. To clarify matters, I will offer some examples but no definitions. “Seeking the Truth”is a basic goal; “Seeking the Truth about HIV infection” is a non-basic goal; “Appeal to expe-riemental results” is a basic norm; “Use double-blind experimental techniques to obtain results” isa non-basic norm. For more on the cognitive status of epistemic norms, see Gibbard (1990), Stich(1990). 10 This distinction bears some resemblance to the distinction between local vs. global justification,local vs. global epistemology and local vs. global logics made by some epistemologists and logicians.See Goldman (1986).11 I am not claiming that my model is entirely original but I do think the model brings up somenovel points and presents these current ideas in a convincing way. I find strong support for my viewand complimentary ideas in Laudan (1984), Giere (1988) Stich (1990), Kantorovich (1993), Nozick(1993), Kitcher (1993), Kornblith, (1993), Richardson (1994). I would also like to thank MichaelResnik and Ed Sherline for helpful questions and comments.

ReferencesArrow, K. 1951. Social Choice and Individual Values. New York: John Wiley and Sons.Audi, R. 1993. Action, Intention, and Reason. Ithica, NY: Cornell University Press.Barnes, B. 1974. Scientific Knowledge and Sociological Theory. London: Routledge and Kegan Paul.Blackburn, S. 1995. “Practical Tortoise Raising,” Mind 104: 695-711.Brown, H. 1988. Rationality. London: Routledge. Cherniak, C. 1986. Minimal Rationality. Cambridge, MA: M.I.T. Press.Darwall, S. 1983. Impartial Reason. Ithica, NY: Cornell University Press.Davidson, D. 1980. Essays on Actions and Events. Oxford: Clarendon Press.Doppelt, G. 1990. “The Naturalist Conception of Methodological Standards in Science: A Criti-que,” Philosophy of Science 57: 1-19.Fine, A. 1986. The Shaky Game. Chicago: University of Chicago Press.Gibbard, A. 1990. Wise Choices, Apt Feelings. Cambridge, MA: Harvard University Press.Giere, R. 1985. “Philosophy of Science Naturalized,” Philosophy of Science 52:331-56.Giere, R. 1988. Explaining Science. Chicago: University of Chicago Press.Goldman, A. 1986. Epistemology and Cognition. Cambridge, MA: Harvard University Press.Goldman, A. 1992. Liaisons. Cambridge, MA: M.I.T. Press.Goldman, A. 1994. “Argumentation and Social Epistemology,” The Journal of Philosophy 91: 27-49. Goodman, N. 1965. Fact, Fiction, and Forecast (2nd edition). Indianapolis: Bobbs-Merril.Harman, G. 1977. The Nature of Morality. New York: Oxford University Press.Harman, G. 1986. Change in View. Princeton: Princeton University Press.Hempel, C. 1979. “Scientific Rationality: Analytic vs. Pragmatic Perspectives,” in T. Gereats (ed.),Rationality To-Day. Ottowa: University of Ottowa Press, pp.46-58. Hill, T. 1973. “The Hypothetical Imperative,” The Philosophical Review 82: 429-50.Howson, C. and Urbach, P. 1990. Scientific Reasoning: The Bayesian Approach. La Salle, IL: OpenCourt.Hull, D. 1988. Science as a Process. Chicago: University of Chicago Press. Humphrey, P. 1989. The Chances of Explanation.Princeton, NJ: Princeton University Press.

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Jeffrey, R. 1965. The Logic of Decision. New York: McGraw-Hill. Kant. I. 1965. Critique of Pure Reason. Trans. by N. Smith. New York: St. Martin’s Press.Kantorovich, A. 1993. Scientific Discovery: Logic and Tinkering. Albany, NY: S.U.N.Y. Press.Kornblith, H. 1993. Inductive Inference and its Natural Ground. Cambridge, MA: M.I.T. Press.Kyburg, H. 1990. Science and Reason. New York: Oxford University Press.Kitcher, P. 1992. “The Naturalists Return,” The Philosophical Review,” 101: 43-114.Kitcher, P. 1993. The Advancement of Knowledge. New York: Oxford University Press.Kuhn, T. 1970. The Structure of Scientific Revolutions (2nd edition). Chicago: University ofChicago Press.Kuhn, T. 1977. The Essential Tension. Chicago: University of Chicago Press.Lakatos, I. 1978. The Methodology of Scientific Research Programmes. Cambridge: CambridgeUniversity Press.Laudan, 1977. Progress and its Problems. Berkeley, CA: University of California Press.Laudan, L. 1984. Science and Values. Berkeley, CA: University of California Press.Laudan, L. 1987. “Progress or Rationality? The Prospects for Normative Naturalism,” AmericanPhilosophical Quarterly 24: 19-31. Levi, I. 1990. Hard Choices: Decision Making Under Unresolved Conflict. Cambridge: CambridgeUniversity Press.Longino, H. 1990. Science as Social Knowledge. Princeton, NJ: Princeton University Press.Loui, R. 1993. “How a Formal Theory of Rationality Can be Normative,” The Journal of Phi-losophy 90: 137-143.Merton, R. 1973. The Sociology of Science. Chicago: University of Chicago Press.Miller, R. 1995. “The Norms of Reason,” The Philosophical Review,” 104: 205-245.Myers, R. 1995. “On the Explanation, the Justification, and the Interpretation of Action,” Nous29: 212-231.Newton-Smith, W. 1978. The Rationality of Science. London: Routledge and Kegan Paul.Nozick, R. 1993. The Nature of Rationality. Princeton, NJ: Princeton University Press. Popper, K. 1959. The Logic of Scientific Discovery. New York: Basic Books.Quine, W. 1969. Ontological Relativity and Other Essays.New York: Columbia University Press.Quine, W. 1980. From a Logical Point of View. Cambridge, MA: Harvard University Press.Rawls, J. 1971. A Theory of Justice. Cambridge, MA: Harvard University Press.Resnik, D. 1992. “Are Methodological Rules Hypothetical Imperatives?,” Philosophy of Science59: 498-507.Resnik, D. 1993. “Do Scientific Aims Justify Methodological Rules?,” Erkenntnis 38: 223-32.Resnik, D. 1994a. “Repairing the Reticulated Model of Scientific Rationality,” Erkenntnis 40: 343-55.Resnik, D. 1994b. “Epistemic Value: Truth or Explanation?,” Metaphilosophy 25: 348-61.Resnik, M. 1985. “Logic: Normative or Descriptive? The Ethics of Belief or a Branch or Psycholo-gy?” Philosophy of Science 52: 221-238.Resnik, M. 1987. Choices: An Introduction to Decision Theory. Minneapolis: University of Minne-sota Press.Richardson, H. 1994. Practical Reasoning About Final Ends. Cambridge: Cambridge UniversityPress.Rosenberg, A. 1988. Philosophy of Social Science. Boulder, CO: Westview Press.Siegel, H. 1985. “What is the Question Concerning the Rationality of Science?,” Philosophy ofScience 52: 517-37.Slote, M. 1989. Beyond Optimizing. Cambridge, MA: Harvard University Press.Solomon, M. 1994. “Social Empiricism,” Nous 28: 325-43.Stich, S. 1990. The Fragmentation of Reason. Cambridge, MA: M.I.T. Press.

Authors 333

Authors

Agassi, Joseph, Prof. Dr., York University, Faculty of Arts, 4700 Keele Street, NorthYork, Ontario M3J 1P3, CanadaBradie, Michael, Prof. Dr., Bowling Green State University, Department of Phi-losophy, Bowling Green, Ohio 43403-0222, USABrown, James R., Prof. Dr., University of Toronto, Department of Philosophy,Toronto Ontario M5S 1A1, CanadaEssler, Wilhelm K., Prof. Dr., J.W. Goethe-Universität, Institut für Philosophie,Dantestr. 4-6, 60325 Frankfurt am Main, RFAFoss, Jeffrey E., Prof. Dr., University of Victoria, Department of Philosophy, POBOX 3045, MS 7512, Victoria, BC, V8W 3P4Gruender, David, Prof. Dr., The Forida State University, Department of Philosophy,Tallahassee, Florida 32306-106, USAHarriott, Howard, H., Prof. Dr. The University of South Carolina, Department ofPhilosophy, Columbia, SC 29208, USAHughes, R.I.G., Prof. Dr., The University of South Carolina, Department of Phi-losophy, Columbia Campus, Columbia, SC 29208, USAJuhl, Cory, Prof. Dr., University of Texas, Department of Philosophy, Austin, USAKelly, Kevin T., Prof. Dr. Carnegie Mellon University, Department of Philosophy,Schenley Park, Pittsburgh, Pennsylvania 15213, USAMatheson, Carl, CARL A., Prof. Dr., University of Manitoba, Department of Phi-losophy, Winnipeg, Manitoba, Canada R3T 2M8Moulines, C. Ulises, Prof. Dr., Ludwig-Maximilians-Universität, Institut für Philoso-phie, Logik und Wissenschaftstheorie, Ludwigstr. 31, 80539 München, RFAPeter, Georg (Dr.), J.W. Goethe-Univesität, Protosociology, Brunnenstraße 5, D-35708 Haiger, RFAPreyer, Gerhard, PD. Dr., J.W. Goethe-Universität, Fachbereich: Gesellschafts-wissenschaften, Protosociology, 60325 Frankfurt am Main, RFARescher, Nicholas, Prof. Dr., University of Pittsburgh, Department of Philosophy,Pittsburgh, PA 15260, USAResnik, David, Prof. Dr., East Carolina University, Dept. of Medical Humanities, 2S-17 Brody, Greenville, NC 27858-4354, USASchlesinger, Georg N., Prof. Dr., The University of North Carolina at Chapel Hill,Department of Philosophy, Caldwell Hall 009 A, Chapel Hill, N.C. 27514, USASchwartz, Robert, Prof. Dr., University of Wisconsin Milwaukee, College of Lettersand Science, Department of Philosophy, PO Box 413, Milwaukee, WI 53201, USASkyrms, Brian, Prof. Dr., University of California, Department History and Phi-losophy of Science, Irvine, California 92717,USATang, Paul C.L., Prof. Dr., California State University, Department of Philosophy,Long Beach, 1250 Bellflower Boulevard, California 90840-4208 USAUlfig, Alexander Dr., J.W. Goethe-Universität, Fachbereich: Gesellschaftswissen-schaften, Protosociology, 60325 Frankfurt am Main, RFA

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