10. Ensemblistic-Identitary Logic (Ensidic Logic)
Jeff Klooger
Critiques of reason are as old as its veneration. For the
Enlightenment, reason was both the foundation and crowning
glory of the authentically human. Nonetheless, Kant’s
critiques investigated the limits of reason as well as its
power. Then, beginning with the Romantics, followed by
Schopenhauer and Nietzsche, and continuing in the twentieth
century with the Frankfurt School’s critique of instrumental
reason, phenomenology’s subsumption of logic within lived
experience, and Derrida’s deconstruction of logocentrism,
reason has been exposed as less and other than Western
thought has generally proclaimed it. Castoriadis’s critique
of what he at first calls ensemblistic-identitary logic and
later names ensidic logic for short – so named because it is
the basis of the logical operations involved in the
production and manipulation of ensembles or sets, operations
which themselves presume the fully determinable identity of
both ensembles and their components – may be read as part of
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this tradition. As such, its value may be assessed by how
well it completes the three tasks necessary for such a
critique: 1) to describe the nature and operation of reason;
2) to account for the effectiveness of reason; and 3) to
expose its limitations. If the critique is to be
comprehensive and satisfactory, all three of these need to
be achieved together, in a movement in which the responses
to the second and third tasks mesh organically with the
response to the first.
Key to Castoriadis’s version of the critique of reason is the
relationship between logic and ontology. Some recognition of
this relationship is implicit in all such critiques, but
Castoriadis makes it his explicit philosophical focus. The
link between logic and ontology is important for Castoriadis
because he comes to his critique of logic via a recognition of
the limitations of traditional ontology. Setting out to
elucidate the properties peculiar to society and history,
Castoriadis discovers that traditional ontology prejudices the
concept of ‘being’ in a way that excludes what is most
essential to phenomena in these realms: creation and self-
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creation, and the comparative indeterminacy which is the
essential precondition for these. Being is construed as
determined; indeed, as determinacy. ‘To be’ means ‘to be
determined’, and a thing exists precisely to the extent that
it is determined in itself or can be determined by thought.
Castoriadis contends that, despite passing realizations by the
greatest philosophers that this definition of being is
inadequate, the history of Western philosophy is dominated by
the equation of ‘being’ and ‘determinacy’. Having defined
‘being’ as ‘determinacy’, the tradition then proceeds to take
as models of ‘being’ only those beings which best conform to
this definition. Principally, this means purely physical and
logical objects. Phenomena which elude the definition of being
as determinacy, which resist being treated as determined or
determinable, are either ignored or reduced to second-class
status as mere appearances behind which true reality lies
concealed. This is commonly the case with social-historical
phenomena. Such phenomena are typically treated as though they
existed in the same manner and sense as physical and logical
objects as regards their identity, separateness and
interactions. Alternatively, social-historical phenomena are
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simply ignored, or reduced to something more ‘real’, meaning
something more amenable to being treated as a ‘properly’
determined being (Castoriadis, 1987, pp. 168-220; 1991, pp.
33-47).
The ubiquity and perniciousness of this equation of ‘being’
and ‘determinacy’ emerges for Castoriadis as he attempts to
get beyond deterministic models of society and history. His
critique of Marxism is prompted chiefly by his recognition of
its deterministic conception of history, and he criticises
other explanatory models of society and history, specifically
the functionalist and structuralist approaches, as being
similarly deterministic (Castoriadis, 1987, pp. 168-220). What
Castoriadis regards as most characteristic of the social-
historical is its comparative indeterminacy – in fact, an
interplay of indeterminacy and partial determinations, a
forming which excludes both pure formlessness and the sort of
fully determinate form which traditional ontology regards as
essential to ‘being’. This makes the social-historical alien
to the schema of determinacy assumed by the traditional
ontology. This comparative indeterminacy is both synchronic
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and diachronic. This means that social phenomena are
indeterminate both in and across time. (The distinction is
somewhat artificial from Castoriadis’s perspective, which
integrates the two into the notion of the social-historical, a
form of being which exists only as unfolding in a perpetual
movement of undetermined creation. Nevertheless, it is worth
noting that the indeterminacy of the social-historical is not
reducible to the fact that there is no determinacy across
time, and that even if it were possible to extract a social
phenomenon from the historical process, that phenomenon would
still evade attempts to fully determine it.) This linkage of
indeterminacy within and across time is mirrored in its
opposite, the linkage of ontological determinacy and
determinism. If beings understood as determined in themselves
are to be conceived as related to one another, these
relationships are bound to be conceived as deterministic. In
Kant, for example, one finds that, once one moves from the
nature of substance to the nature of succession and
coexistence, the principle of determinacy implies the complete
determination of all substances by all others with which they
coexist, either within or across time (Kant, 1933). Indeed, as
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Castoriadis argues, the difference between succession and
coexistence disappears when both amount to a universal
determinacy. The determinacy of each implies the determinacy
of all, and when it comes to temporality, that means
determinism, the determination of each succeeding state by the
preceding one, and underlying that, a determination of all
things by universal laws or principles which make the sequence
of succession inevitable because it is thoroughly
predetermined (Castoriadis, 1987, pp. 168-220).
Obviously this constitutes a problem for the understanding of
society and history. According to Castoriadis, if these are to
be understood adequately, we must get beyond the ontological
prejudice that equates ‘being’ with ‘determinacy’. We must
resist the temptation to model our understanding of being on
beings of one or two types conformable to our preferred
definition of being, and we must instead acknowledge the
possibility that ‘being’ may not mean the same thing in every
context, that a social institution or a psychical formation
may ‘be’ in a different manner and sense than chairs and
mathematical objects. Thus the move from ontological
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determinacy to comparative indeterminacy entails a move from a
single and universal meaning of ‘being’ to a polysemic
understanding of the term reflecting a recognition of real
ontological differences in ‘what is’ and ‘how’ it is
(Castoriadis, 1987, pp. 167-169). This leads Castoriadis
eventually to a model of the universe as ontologically
stratified, with different modes of being corresponding to
heterogeneous ontological realms (Castoriadis, 1997a, pp. 342-
373; 1984, pp. 145-226) (see the entries on Magma and the
Living Being).
One cannot hope to escape the grip of the traditional ontology
of determinacy merely by exposing it as flawed and partial,
because this traditional ontology is more than a mere error.
According to Castoriadis, it represents one (possible but not
inevitable) intellectual development of a fundamental
institutional dimension of the social-historical, a dimension
which is ineradicable and omnipresent. It is a measure of
Castoriadis’s profundity as a philosopher that he does not
dismiss the traditional ontology without attempting to trace
it to its deepest roots and to understand it at its deepest
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level. He recognizes first, that if this ontology is to be
transcended this can only be achieved on the basis of a deep
understanding; and second, that the phenomenon of this
ontology is worth understanding in and for itself, that it
reveals important aspects of what it is to be human, and
beyond that, important characteristics of what it is to ‘be’.
In this way Castoriadis recognizes that the third of the tasks
of a critique of reason enumerated above cannot be separated
from the first two.
For Castoriadis, the key to understanding the basis of the
traditional ontology was the discovery that the logic which
underlies this ontology, which presupposes it and is
presupposed by it, is the logic of sets (Castoriadis, 1987, pp.
221-227). He argues that this logic is best encapsulated by
the first or naive definition of the set presented by the
mathematician Cantor. This definition has been superseded by
more sophisticated versions which avoid some of the aporias the
naive definition leads to, but according to Castoriadis, the
naive definition better represents the innate logic in
question because the circularity it involves is essential to
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that logic in its native form. According to Cantor’s
definition, a set is ‘a collection into a whole of definite
and distinct objects of our intuition or of our thought. These
objects are called the elements of the set’ (Castoriadis,
1984, p. 208). In order to be an element of a set an object
must be distinct or definite; it must be assumed to be such
and treated accordingly. This encapsulates the ontology of
determinacy explored previously. The logic further proposes
that such elements may be collected together into wholes. In
order for this to be possible, the objects must be separable
from whatever may be their native or current context; in order
to be separable they must be discrete and fully
circumscribable – we must be able to determine precisely where
one object ends and another begins. We must therefore be able
to specify exactly what each object is in order to
differentiate it completely from other objects. In order to
separate objects and combine them into wholes, such objects
must be fully determinable. The possibility of assembly into
wholes presupposes not only separability of objects but the
potential for combining objects on the basis of properties
that are theoretically if not practically separable from other
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properties of these same objects. Thus objects are not only
separable, they are internally analysable into discrete
constituents.
The two sides of the definition – the possibility of assembly
and disassembly, and determinability – presuppose and refer to
one another. This is because, in Castoriadis’s terms, this
logic is ‘“an originary institution” – a true creation’
(Castoriadis, 1987, p. 223). The logic is not a reflection of
reality – though according to Castoriadis it does correspond
to a certain dimension of reality (we will explore this
shortly). Like all human representations and institutions, it
is a non-determined creation which is imposed on and
conditions our encounters with reality (see Institution and
Creation ex nihilo). Castoriadis calls this logic which set-
theoretical logic replicates and exemplifies ensemblistic-
identitary logic or ensidic logic for short. It is
ensemblistic in that it involves schemata for the assembly of
objects into wholes or ensembles; and it is identitary in that
it posits the full and complete self-identity or
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determinability of objects as the basis for their assembly and
disassembly (Castoriadis, 1987, pp. 221-228).
This logic operates in the history of philosophy, underpinning
the ontology of determinacy discussed already. It also
operates in all theoretical constructions informed by this
philosophical tradition: theories in the natural sciences, for
which the logic is better, though not always perfectly, suited
(for reasons we will explore), as well as theories of society
and history, for which the logic is quite ill-suited. But this
logic is not a philosophical artefact. As stated earlier, it
is, according to Castoriadis, an originary institution, and a
fundamental one, whose operation is evident in all social
institutions. All social institutions involve an ensidic
dimension, a dimension which presupposes the ability to
determine objects, and to separate and recombine elements.
Castoriadis identifies two aspects of this ensidic dimension
of the institution, which he calls legein and teukhein
(Castoriadis, 1987, pp. 221-272). Legein is distinguishing-
choosing-positing-assembling-counting-speaking; it operates
most conspicuously, though not exclusively, through language.
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Teukhein is assembling-adjusting-fabricating-constructing; it
operates through all social doing. These fundamental
dimensions of the institution, and of the activity of
instituting, will be explored in more detail in the entry
devoted to them (see Institution and Legein and Teukhein). The
important thing to note here is that ensidic logic is seen by
Castoriadis as embodied and operating through these (proto)
institutional dimensions, that it is a social creation which
emerges as these dimensions of the instituting and instituted
life of society. No social life is possible without the
ability to distinguish, choose, posit, assemble, count,
construct, and so on.
The ensidic dimension of the social institution is essential
and ubiquitous, but it is not the whole of the social. The
other dimension of the social is what Castoriadis identifies
as the imaginary element. This is the dimension of meaning and
meaning-creation. It requires the ensidic dimension and the
schemata of ensidic logic in order to realize its creations
and embody them in shareable forms. But these creations are
never reducible to that logic, just as meaning is irreducible
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to the manner of its formation and presentation. Each society
institutes itself and its world by bringing into being and
utilizing the ensidic logic of legein and teukhein in its own way
and to its own ends (Castoriadis, 1987, pp. 221-272).
With his analysis of the emergence of ensidic logic as a
social institution, Castoriadis fulfils the first of the three
tasks of a critique of reason identified at the start of this
entry. Only the second of these tasks remains to be addressed,
and in addressing this task Castoriadis also deepens his
understanding of the limits of ensidic logic, since the two go
hand in hand: an explication of the effectiveness of a logic
or form of reason and clarification of its limitations.
The ensidic logic which is only one dimension of the social
institution, and which is ill-suited to the elucidation and
explication of the social-historical as a whole, is
nevertheless quite effective in describing and permitting the
explanation of other types of phenomena, especially phenomena
within the natural world. Why is this so? Ensidic logic fails
in relation to the social-historical because in the social-
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historical the imaginary dimension is so important, and that
dimension does not conform to the postulates and ontological
assumptions of ensidic logic. Social-historical phenomena are
not determined in the way that this logic and its associated
ontology suppose; on the contrary, they exhibit a significant
degree of indeterminacy. As discussed in other entries, this
indeterminacy is so profound that it led Castoriadis to
propose an alternative mode of organization to that of the set
or ensemble as characteristic of human phenomena such as the
human psyche and the social-historical: the mode of being he
termed magma (Castoriadis, 1987, pp. 340-344; 1997b, pp. 290-
318). It follows from this that the effectiveness of ensidic
logic is dependent on the degree to which the objects to which
it is applied approach the mode of being of an ensemble. Where
they approach most nearly to ensembles or elements of
ensembles, ensidic logic is most effective; where the mode of
being of the objects is most magmatic, ensidic logic is least
effective. To the degree that such logic is effective in
relation to natural phenomena such phenomena must themselves
possess a greater degree of ensidic organization.
(Castoriadis, 1997a, pp. 342-373; 1984, pp. 145-226)
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There is an important point to be made here concerning
Castoriadis’s understanding of the relationship between logic
and objects. Castoriadis insists that human institutions, and
indeed all human representations, do not derive from a reality
exterior to them. They are instead non-determined creations.
However, if those creations are to permit the successful life
activity of human beings, they must to some degree correspond
to aspects of external reality. Castoriadis is a realist in
this sense: he presupposes forms of organization intrinsic to
reality which are independent of our construction of that
reality. There may therefore be a correspondence – or non-
correspondence – between our conceptual constructions and the
innate characteristics of any aspect of reality. This
‘correspondence’ is not to be understood as similitude, but
rather in terms of the effectiveness of our mental
constructions for guiding practical encounters with reality
and for permitting deduction of further facts and effective
theories concerning the reality. It is the latter point that
perhaps prevents one describing Castoriadis as a thoroughgoing
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pragmatist, though there is an element of pragmatism in his
epistemological approach.
Associated with this question of the intrinsic organization of
the object of knowledge is a shift in Castoriadis’s use of the
term ‘ensidic’. What is at first a description of a form of
logic becomes a description of an organizational
characteristic of reality conformable to that logic in the
sense that the reality can be understood and manipulated by
the logic. Henceforth Castoriadis talks about strata of
‘being’ which exhibit ensidic characteristics to a greater or
lesser degree, and which are to that degree more or less
amenable to ensidic logic. The natural world, particularly
that dimension of the natural world dealt with by classical
physics, is the stratum most ensidic in its organization. The
realm of quantum phenomena is less so, and the realm of the
living being dealt with by biological science is only
partially and imperfectly reducible to its ensidic
characteristics. The human realms of the psyche and the
social-historical are the least amenable to ensidic treatment
since they exhibit the least degree of ensidic organization in
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themselves. It is crucial to note, however, that this is only
ever a matter of degree. No realm of reality is ever
completely devoid of ensidic characteristics; and no realm of
reality is ever completely reducible to ensidic
characteristics. The world as a whole is not, according to
Castoriadis, an ‘ensemble of ensembles’, but a ‘magma of
magmas’ (Castoriadis, 1997b, pp. 290-318). Indeterminacy is
everywhere present, and determinacy is nowhere perfect and
complete. On the other hand, everything is to some degree
determinable, everything exhibits in itself an aspect which
makes it susceptible to an ensidic treatment. Everything is
ensemblizable (or ensidizable), everything can be treated
according to the logic of sets. What differs is the degree to
which such a treatment ignores or distorts dimensions of the
reality which exceed or deviate from the ensidic.
(Castoriadis, 1997a, pp. 342-373; 1984, pp. 145-226)
A core thesis for Castoriadis is thus that everything is a
magma, that everything exhibits a degree of indeterminacy
inconsistent with the nature of true ensembles. However,
Castoriadis sometimes speaks as though true ensembles did
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exist or could be created (Castoriadis, 1997b, p. 298). The
temptation to recognize the existence of true ensembles is
greatest in relation to mathematical and other purely logical
objects. Such objects are defined as completely determined or
determinable, and if it is supposed that this definition
determines their actual existence, one may imagine that they
constitute true ensembles. Another of Castoriadis’s theses,
however, is the impossibility of complete and perfect
partitioning of magmas (Castoriadis, 1997b, pp. 290-318).
Logical and mathematical objects may be supposed to be true
ensembles with nothing of the magmatic in them only as long as
they remain unaffected by the indeterminacy they exclude as a
matter of principle. But this indeterminacy haunts even
mathematics and logic, particularly where the question of
their foundations, and therefore the foundation of their core
ensidic postulates, intrudes. The cost of preserving the
effective ensidization of these objects is the deferral of an
interrogation of their underlying assumptions. Where these are
questioned, the appearance of their perfectly ensidic
character begins to dissolve. They too are revealed as magmas
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rather than true ensembles, albeit the most ensidic magmas
possible.
Finally, we should acknowledge that ensidic logic is not the
only form of reason Castoriadis identifies and discusses. The
other form is what might be termed dialectical or dialogical
reason. This is the form of reason essential to the
philosophical enterprise, the open-ended posing of questions
and the giving of reasons for one’s belief in the truth of any
answers to those questions – the latter Castoriadis often
refers to the Greek formulation logon didonai, meaning ‘to give
an account to others of what you are doing’ (Castoriadis, 1991,
pp. 3-32, 1997a, pp. 342-373). This movement of questioning and
argumentation is irreducible to any logic. On the contrary,
logic itself is open to interrogation, even though that
interrogation inevitably utilises logic in order to pose its
questions and propose answers. Though ubiquitous and
unavoidable, ensidic logic must not be allowed to prejudge
questions. Since one of the purposes of dialogical
interrogation is to decide what should count as a valid
reason, the answer to this question cannot be assumed to be
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given in logic itself. Castoriadis’s critique of ensidic logic
aims at exposing its limitations through a process of
interrogation that is itself an example of dialogical
reasoning, one which goes beyond ensidic logic not by throwing
that logic aside but by using it as a tool in its own
transcendence.
References
Castoriadis, C. (1984), Crossroads in the Labyrinth, K. Soper
and M. H. Ryle (trans and eds), Cambridge, Mass.: MIT Press.
Castoriadis, C. (1987), The Imaginary Institution of Society,
K. Blamey (trans). Oxford: Polity; and Cambridge, Mass: MIT
Press.
Castoriadis, C. (1991), Philosophy, Politics, Autonomy, D. A.
Curtis (ed), New York and Oxford: Oxford University Press.
Castoriadis, C. (1997a), World in Fragments, D. A. Curtis
(ed), Stanford: Stanford University Press.
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