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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Castoriadis, C. (1997b), The Castoriadis Reader, D. A. Curtis

(ed), Oxford and Cambridge, Mass.: Oxford University Press.

Kant, I. (1933), Critique of Pure Reason, N. Kemp Smith

(trans), London: MacMillan.

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