Concept and Form:
The Cahiers pour l'Analyse
and Contemporary French Thought

This project is funded by an Arts and Humanities Research Council (AHRC) research grant and is supported by the Centre for Research in Modern European Philosophy (CRMEP) and Kingston University's Faculty of Arts and Social Sciences.

François Regnault’s third and final article in the Cahiers pour l’Analyse (cf. CpA 6.2 and CpA 7.3) presents a dialectical approach to epistemology, considered as a theory of science. Taking up references made by Jean Cavaillès to Plato’s Parmenides as a source for reflection on the question of the unity of science, Regnault argues that Plato’s presentation of a series of Hypotheses about the status of the form of the One in the second half of the Parmenides can be given a dialectical interpretation, and that this helps bring to light a sequence of possible epistemological positions on the unity of science.¹

Drawing on an interpretation developed by Francis Cornford in his 1939 book Plato and Parmenides,² Regnault claims that the Parmenides is not (as has sometimes been suggested) a merely aporetic dialogue. Rather, in its second part it presents a series of well-regulated Deductions or Hypotheses that individual readers must make explicit for themselves. Regnault goes one step further than Cornford and suggests that the Hypotheses have a concealed dialectical order. He contends that if the concept of science is substituted for Plato’s ‘One’, every possible epistemological position regarding science can be correlated with a Hypothesis from the Parmenides. A ‘circular’ dialectic then comes to light that expresses all the possibilities with regard to the basic status of science - its existence or non-existence, and its unity or multiplicity - permitting an association with the various epistemological positions of absolute idealism, dogmatism, relative scepticism and absolute scepticism. By identifying the positions at issue in this dialectic, the epistemologist can help to clarify the relations at work between science and ideology, and the consequences of epistemological breaks in science.³

Regnault’s article is an essential text in the Cahiers pour l’Analyse, since it weaves together ideas from Plato, Cavaillès and Bachelardian epistemology with the Lacanian concepts of suture and foreclosure. Regnault provides the most sustained reflection in the Cahiers on the idea put forward by Lacan in the first article of the journal (‘La Science et la vérité’), that science ‘does-not-want-to-know’, or forecloses, the truth in its status as cause (CpA 1.1:25; E, 874). For Regnault, the relations between science, suture and foreclosure are complex. He claims, for instance, that in the case of a radically unified science that incorporated its own epistemology, the ‘foreclosure of a foreclosure’ would ‘amount to a suture’ (CpA 9.4:59). Regnault’s ‘Dialectique d’épistémologies’ stands as one of the most substantial and elaborate contributions to the general project pursued in the Cahiers pour l’Analyse.

At the outset of the article, Regnault justifies his oblique approach to the problem of the relation of epistemology to science with a reference to Cavaillès: ‘First of all we appeal to the authority of Cavaillès, who in his On Logic and the Theory of Science cites a passage from the second Hypothesis of the Parmenides (142d-143a) to exhibit the mechanism of a theory he claims is paradigmatic for science’ (CpA 9.4:46).⁴ Regnault adds that ‘it is true that he is more concerned with the specific object of a science than with its relations to its theory. Nevertheless, in the case considered, the former commands and envelops the second’ (CpA 9.4:46).⁵ For Cavaillès, the second Hypothesis of Plato’s Parmenides (the Hypothesis that the One cannot be conceived outside of its relation to Being, and can therefore only be relative, not absolute; see below for details of the different Hypotheses) is instructive for epistemology insofar as it reveals how ‘polymorphy in the single rational sequence [is] possible’.⁶ For Cornford, too, the second Hypothesis must be understood as the Hypothesis ‘really’ maintained by Plato himself; however, rather than expressing an epistemological position (as it does for Cavaillès), the Hypothesis mirrors the ontology Plato will go on to affirm in his Timaeus.⁷ Regnault will steer a path between Cavaillès and Cornford by identifying a ‘circular’ dialectic in Plato’s text that takes in and gives a place to all of the Hypotheses.

Regnault goes on to affirm Cornford’s identification of the nine Hypotheses in the dialogue. The basic matrix of the series of Hypotheses is determined, according to this reading, by the existence or non-existence of the One. Four elementary questions result. What follows if the One exists, for the One itself, and for that which is defined as not-One, i.e. ‘the Others’ (or ‘difference’, to heteron)? And what follows if the One does not exist, both for the One itself, and again for the Others or not-One? Since, according to Cornford, Plato proceeds to double the Hypotheses by taking the One in ‘absolute’ or ‘relative’ senses (and since in the process a supplementary Hypothesis is also generated), Regnault accepts that there are nine basic Hypotheses.

Most of Regnault’s article is devoted to a presentation of these different Hypotheses regarding the existence or non-existence of the One. For each of the Hypotheses, Regnault identifies an epistemological position appropriate to it, and amplifies its possible connections with ideas from the French epistemological tradition of Bachelard and Cavaillès on the one hand, and from Lacanian psychoanalysis on the other.

Before venturing down the path of the dialectic, Regnault presents three possible ways in which one might initially relate being and the One to epistemology and science.

In a first arrangement, based on the idea that Plato defines being in terms of the One (such that ‘the vector goes from the One to being’), we could allocate the form of One to science and being to epistemology (CpA 9.4:47). But ‘in this case, nothing is conserved of the meaning of the terms science and epistemology, which unproblematically translate the One and being, and the allegory is legitimate, but impoverished [...]. In order for science and epistemology to be involved (and not spoon and fork), it will be necessary to introduce their properties from elsewhere, in other words, from a place where they have already been defined and presupposed. So this matrix is not only impoverished, it is useless: what we thought we had won from it through its formalism is lost elsewhere by our having to import properties’ (CpA 9.4:47).

In the second arrangement, ‘taking account of the nature of the One and being, we could view these terms as so general that they could apply to any subject at all. In that case, it would hardly matter if the terms of science and epistemology were being substituted for them, since what would be involved would be every object about which it can be said that it is or that it is one’ (CpA 9.4:48). But this arrangement would occlude the asymmetry in the dialogue between the notions of being and the One. ‘In the Parmenides, since it is the One which has been chosen for the dialectical exercise, being finds itself receiving its status from the meaning given to the One’, and not vice versa (CpA 9.4:49).

Thus Regnault opts for a third arrangement, and abandons the attempt to find a direct correspondence between science and epistemology on the one hand, and being and the One on the other. ‘The functions of the One and being must no longer be delegated to science and epistemology, but to the unity and being of science or epistemology. So which of the two?’ (CpA 9.4:51). Regnault argues that if one starts from the basic postulate that the order of traversal must go from science towards epistemology, with epistemology as a discourse on science, ‘then the functions of the One and of being are henceforth obliged to be delegated to science alone’. Taking this route has two consequences:

The Platonic model, if it is complete, will permit the establishment of the numeration of all possible theories of the unity (or of non-unity) of the concept of science. If Plato produces the theory of the One, at the same time he produces the theory of the ‘one’ proper to science. [...] The status of epistemology follows from this: if it is a discourse on science (or the sciences), it must be explicitly held to be such. The existence or non-existence, unity or multiplicity of science radically commands all epistemological discourse. Roughly, there will be as many epistemologies as there will be different conceptions of this existence and of this unity (CpA 9.4:51).

According to this third arrangement, wherever there is a science, there will be a theory of science: an epistemology. In each case epistemology is dependent on the existence of science, and not vice versa. For Regnault, this assumption is precisely the condition for the emergence of a ‘combinatory’ capable of articulating all possible epistemologies. ‘To the objection that the nature of epistemology is already prejudged if its discourse is defined in terms of the hypotheses of the unity and the existence of science, we can respond that, if the model is well made and envisages all possible cases, we will have traversed, simply by means of the combinatorial mechanism [la combinatoire], the whole possible space of the problem, with the result that there is no epistemology outside the cases envisaged’ (CpA 9.4:52). Regnault’s driving claim will thus be that the Parmenides holds the key to a theory of the theory of science. Like Jacques-Alain Miller’s ideas for a theory of discourse (CpA 9.6) and Jean-Claude Milner’s own return to Plato in pursuit of the outlines of a logic of the signifier (CpA 3.5), the guiding purpose of Regnault’s reconstruction is to furnish materials for such a theory (cf. Doctrine of science).

The rest of Regnault’s article is taken up with an enumeration and analysis of the nine Hypotheses of the second part of the Parmenides. In the first part of the dialogue, Plato had presented Parmenides as bringing a series of objections against the theory of Forms or Ideas. These objections had allowed Plato to clarify his earlier version of the theory of Forms, as presented in the Republic. At the end of the first part of the dialogue, Parmenides is presented as recognising the necessity of the theory of Forms. In the second part, on Cornford’s account, Plato proceeds to carry out a ‘programme for dialectical exercise’.⁸ Cornford contends that in the second part Parmenides Parmenides is taking his own Hypothesis - that there is a One, that the One has being - as the basic matter for the subsequent Hypotheses.⁹ The method proposed for the dialectical exercise requires Socrates to ‘consider the consequences, not only of affirming, but of denying the Hypotheses’.¹⁰ By presenting through the character of Parmenides a series of Hypotheses about the consequences of affirming or denying the One, Plato in the process clarifies outstanding questions from the first part of the dialogue about the mutual relations of the Forms. (The problem of the mutual relations of the forms is pursued further in Plato’s Sophist, which is discussed in the Cahiers pour l’Analyse by Xavier Audouard in CpA 3.4 and Jean-Claude Milner in CpA 3.5).

Regnault acknowledges the long history of perplexity about the precise content of the Hypotheses, their number and their order. In the Hellenistic period, the Neoplatonist philosopher Proclus presented a ‘mystical’ and ‘esoteric’ interpretation of the Hypotheses in his Commentary on Plato’s Parmenides. Others have taken a different approach and claimed that the dialogue is ‘aporetic’ and even ‘ludic’ (CpA 9.4:53). Regnault affirms Cornford’s claim that the Parmenides is only aporetic to the ‘inattentive’ reader. If one elicits Plato’s true line of thought ‘between the lines’, the true relations between the concepts discussed come to light. The aporias are merely apparent, as Plato is writing for ‘the attentive reader [who] will have mapped the passage of the different possible readings of the One and being’ (CpA 9.4:54). For Regnault, ‘the Hypotheses of the Parmenides are not a “parody” of logic, destined to be mixed up in the irony of Zenonian arguments, nor a sequence of sophisms, nor an esoteric or mystical text, as some Neoplatonists supposed [...]. Both the ludic and the esoteric interpretation should be subordinated to a logical or dialectical interpretation’ (CpA 9.4:53).¹¹

For Cornford, ‘the key to the understanding of the second part [of the dialogue] must be sought in the unmistakable ambiguity of the Hypothesis, “If there is a One”’.¹² He takes the ambiguity of the One as the main topic of the dialogue, but as presented by Plato in such a manner as to perplex his students and then subject them to a dialectical exercise in order to clarify their sense of the Forms. This is the reason, Cornford notes, why the Parmenides contains more than double the amount of Hypotheses one might expect (if one takes the basic matrix of Hypotheses to concern the existence or non-existence, and unity or non-unity, of science). Cornford infers:

[T]here are in fact eight (or, as some think, nine) deductions. The reason is that the Hypothesis is taken in more than one sense; for instance, the One in Hypothesis I is not the same thing as the One in Hypothesis II. This has been obvious to all commentators, ancient and modern. In Hypothesis I, ‘the One’ is a bare unity which excludes all plurality and is not a whole of parts. The consequences deduced are purely negative: nothing whatever can be truly asserted of such a One. In Hypothesis II, the One is a One which, besides having unity, has being, and is a whole of parts.¹³

The ambiguity of the notion of the One was apparent even in antiquity. ‘The Neo-platonists already perceived the ambiguity of the notion of the One, and made it the basis for their interpretation of the dialogue’.¹⁴. Following Cornford’s interpretation, Regnault suggests that the aim of the programme of dialectical exercise was precisely to bring about the ‘disintrication’ of the various meanings of the term ‘one’.¹⁵ Plato in effect presents two sets of Hypotheses, one concerning an ‘absolute One’, and the other concerning a ‘relative One’ or whole in which the mutual interpenetration of forms such as being and unity is possible.

We have thus arrived at a basic series of eight Hypotheses. What follows if the Absolute One exists, both for it, and for others? And what follows if the Relative One exists, both for it, and for others? These are the four ‘positive’ Hypotheses. Then what follows if the Absolute One does not exist, both for it, and for the others? And if the Relative One does not exist, etc? These are the negative Hypotheses. The problem is that in the text, there appears to be a further Hypothesis (Parmenides, 155E-156B), increasing the total to nine. This is the Hypothesis of the interpenetration of the One and the many, or the Hypothesis of ‘pure becoming’. Cornford proposes that this further Hypothesis (the third in the sequence) should be read as the corollary of the second Hypothesis. According to Regnault, Cornford therefore ‘restrains its function’ (CpA 9.4:66) by numbering it as Hypothesis IIA. Cornford seems to hesitate between calling this Hypothesis a proper Hypothesis on the one hand, and the mere corollary of a Hypothesis on the other. Regnault suggests another possibility: the content of this third Hypothesis should be understood as the very form of ‘transition’ between Hypotheses. It appears then as the very vanishing or vacillation of the One itself. ‘Reduced to pure vacillation, it serves as a common place for all the Hypotheses (the One at the same time is not, is one and multiple, etc.); it is the multiple root of all equations, or the mediation of all instances.’ Regnault concludes that the dialectic of the Hypotheses ‘is therefore of a Hegelian order.’ (CpA 9.4:66).

Cornford’s original reconstruction of the nine Hypotheses is thus as follows:

• HYPOTHESIS I (Parmenides, 137c-d):

  IF THE ABSOLUTE ONE EXISTS, WHAT WOULD IT BE LIKE?

  If the One is defined as absolutely one, it is in no sense many or whole of parts.

• HYPOTHESIS II (142b-c):

  IF THE RELATIVE ONE EXISTS, WHAT WOULD IT BE LIKE?

  If the One has being, it is One Entity, with both unity and being.

• HYPOTHESIS III (155e-156b):

  IF THE ONE EXISTS, IT IS MULTIPLE AND THEREFORE CONTRADICTORY.

  A One Entity comes into existence and ceases to exist, is combined and separated, becomes like and unlike, and increases and diminishes.

• HYPOTHESIS IV (157b-158b):

  IF THE RELATIVE ONE EXISTS, WHAT ABOUT THE OTHERS?

  If the One is defined as One Entity which is both one and many or a whole of parts (as in Hypothesis II), the Others, as a plurality of other ones, form one whole, of which each part is one.

• HYPOTHESIS V (159b-d):

  IF THE ABSOLUTE ONE EXISTS, WHAT ABOUT THE OTHERS?

  If the One (unity) is defined as entirely separate from the Others and absolutely one (as in Hypothesis I), the Others can have no unity as whole or parts and cannot be a definite plurality of other ones.

• HYPOTHESIS VI (160b-d):

  IF THE RELATIVE ONE IS NOT, IN WHAT WAY IS IT NOT?

  If ‘a One is not’ means that there is a One Entity that does not exist, this Non-existent Entity can be known and distinguished from other things.

• HYPOTHESIS VII (163b-c):

  IF THE ABSOLUTE ONE IS NOT, IN WHAT WAY IS IT NOT?

  If ‘the One is not’ means that the One has no sort of being, the One will be a nonentity.

• HYPOTHESIS VIII (164b-c):

  IF THE RELATIVE ONE IS NOT, WHAT HAPPENS TO THE OTHERS?

  If ‘there is no One’ means ‘nothing that is “one thing” exists’, then the Others can only be other than each other.

• HYPOTHESIS IX (165e):

  IF THE ABSOLUTE ONE IS NOT, WHAT HAPPENS TO THE OTHERS?

  If ‘there is no One’ means ‘there is no such thing as an entity’, the Others will be neither one nor many, but nothing.

As mentioned, for Cornford the ultimate purpose of the Parmenides is to defend the validity of Hypothesis II, i.e. the Hypothesis of the Whole that Plato will elaborate in the Timaeus. Regnault defends another approach: rather than restraining the function of the third Hypothesis, it should be recognised as the mechanism that enables circulation among all the various Hypotheses. Regnault notes the paradox of Cornford’s refusal to give the third Hypothesis the function of a ‘synthesis in the Hegelian sense’ while nevertheless granting to Plato (with his idea of a developing world-whole) what he denies to Hegel.¹⁶ Regnault points out that Hegel himself refers to the Parmenides in his own account of the Doctrine of Being in the Science of Logic, and is in certain respects closer to the truth of the dialectic of the Parmenides than Cornford is. As evidence for the sophistication of Hegel’s view, Regnault cites the latter’s remarks on the Parmenides in the section of the Science of Logic on the idea of the ‘exclusion of the One’, and the generation of pure multiplicity.¹⁷ Hegelian dialectic can thus be turned back on Cornford’s affirmation of the second Hypothesis and his concomitant ‘restraint’ of the function of the third Hypothesis, on condition that the third Hypothesis is understood as having a special function as the form of transition between the Hypotheses themselves.

This allows Regnault to arrive at a new dialectical conception of the relations among the Hypotheses. First, he identifies the ‘partners’ among the Hypotheses. The partner of Hypothesis I (concerning the Absolute One) is Hypothesis V (what follows for the Others if everything is One?). Hypothesis II (concerning the Relative One) is paired with Hypothesis IV (what follows for the Others if the One exists in the form of the Whole?). Hypothesis VI (concerning the non-existence of the Relative One) is paired with Hypothesis VIII (what follows for the Others if the Whole does not exist?). Finally, Hypothesis VII (concerning the non-existence of the Absolute One) is paired with Hypothesis IX (what follows for the Others if unity does not exist at all). Hypothesis III occupies an exceptional, transitional position, between the first and second sets of pairs.

Thus Regnault arrives at the following sequence, which can be traced pair by pair. The first pair links Hypotheses I and V:

• HYPOTHESIS I (Parmenides, 137c-d):

  IF THE ABSOLUTE ONE EXISTS, WHAT WOULD IT BE LIKE?

  If the One is defined as absolutely one, it is in no sense many or whole of parts.

• HYPOTHESIS V (159b-d):

  IF THE ABSOLUTE ONE EXISTS, WHAT ABOUT THE OTHERS?

  If the One (unity) is defined as entirely separate from the Others and as absolutely one (following Hypothesis I), the Others can have no unity as whole or parts and cannot be a definite plurality of other ones.

Hypothesis I of the Parmenides concerns the supreme One that is indifferent to any relations to anything, including Being. On this model of an ideal, radically unified science, science itself must give rise to its own epistemology, without any intrinsic relation to the activities of knowledge or the subject. ‘If unity is posited in its absoluteness, without exterior, there is no place for the epistemological discourse that is correlative to it’, and so epistemology must either be ‘identified’ with science (as ‘the science of science’, as in Bolzano’s epistemology), or must be posited in an ‘exterior’ to the unity, without any assignable features other than that of being a language (as in logical positivism) (CpA 9.4:58). In the former case, and here Regnault again cites Cavaillès, ‘science, if it is, is completely demonstration, that is to say, logic’.¹⁸ However, the very assigning of metalinguistic status to epistemology involves making it relative to a particular science. According to Cavaillès, the problem with Bolzano’s version of the doctrine of science is that ‘scientific epistemology cannot directly constitute itself as primary, as was its ambition, but remains instead posterior to the analytic that provides the content of its object and to the ontology that accounts for its being’.¹⁹ In Bolzano’s ‘ideal science’ there is no space for an account of how sciences emerge at particular historical junctures, and then in turn submit their axioms to criticism in a sequence that, although ‘logical’ in retrospect, requires the criticism of ideology to proceed. ‘The difficulty immediately appears’, in the Bolzanian system, ‘not only of justifying and making precise these characteristics, but of situating the discipline that posits them.’²⁰

Hence the unavoidability of the separation between science and epistemology. Logical positivism goes beyond the paradox of Bolzano’s doctrine of science, but only in a relative and ‘external’ manner. The partner of Hypothesis I, Hypothesis V (If the Absolute One is, what follows for the Others?), expresses the fact that ‘others’, that is, anything other than the One, have no place under this ‘absolute’ kind of unity. The hallucinatory, evanescent appearance of the subject that emerges as a by-product of the unitary version of science in Hypothesis V - a ‘subject’ in some sense beyond and different to the ‘One’ in which it is said to be included - is the trigger for the dialectical move to the integral, holistic science implied by Hypothesis II.

Here Regnault pauses to consider the link between science and foreclosure proposed in the first volume of the Cahiers by Lacan, and subsequently developed in volumes 9 and 10 by Miller and Badiou. According to Regnault, the foreclosive nature of science emerges in a different guise in the four pairs of Hypotheses, each time through the medium of the partnered Hypothesis (the Hypothesis of what happens to the ‘Others’). What is the relation between foreclosure and the One of pure scientificity (Hypothesis I)? Referring to Miller’s account of science’s ‘lack of a lack’ (CpA 9.6:102-3) (and foreshadowing Badiou’s argument in CpA 10.8:158-61), Regnault contends that this Absolute One is beyond even a lack of a lack: it is rather a ‘lack of this lack of the lack, since beyond science taken in the sense of this first Hypothesis, there is nothing. Instead of excluding something at the exterior, science excludes the exterior itself’ (CpA 9.4:59). This primary ‘foreclosure of foreclosure’, by virtue of the repression of the Others it induces, turns into a ‘suture’ of the Others or ‘difference’, insofar as it does not even allow for a minimal epistemological position outside it.

Regnault’s second pairing links Hypotheses II and IV:

• HYPOTHESIS II (142b-c):

  IF THE RELATIVE ONE EXISTS, WHAT WOULD IT BE LIKE?

  If the One has being, it is One Entity, with both unity and being.

• HYPOTHESIS IV (157b-158b):

  IF THE RELATIVE ONE EXISTS, WHAT ABOUT THE OTHERS?

  If the One is defined as One Entity which is both one and many or a whole of parts (as in Hypothesis II), the Others, as a plurality of other ones, form one whole, of which each part is one.

Hypothesis II outlines an integration between the One and Being, a ‘science of the One-All’. A unified science exists, but it is a ‘dogmatic, participatory absolute’. It possesses its own kind of foreclosure in its partner, Hypothesis IV. Once the universe is organised into parts and wholes, epistemological breaks become unthinkable. But the occurrence of such a break conversely shatters the totality. After Einstein, the Newtonian sensorium Dei becomes just as ideological as the impetuses that characterised pre-Galilean physics (CpA 9.4:64).

In a footnote Regnault refers the reader to Miller’s ‘Action of the Structure’ (CpA 9.6:96), ‘where epistemology is defined as a discourse of overdetermination’ (CpA 9.4:59). For Regnault, one of the tasks of epistemology will be to detect the results of instances of foreclosure in science, in order to assign imaginary phenomena such as impetus and sensations of ‘force’ - the ‘Others’ of science - a place in relation to science. epistemology, as a theory of science, provides assistance to scientific subjectivity insofar as it permits the latter to break through the overdeterminations of experience necessarily generated by the progress of science).

At this point, in the middle of Regnault’s dialectic, the sequence is interrupted by a conversion or switch over, triggered by Plato’s third Hypothesis, the Hypothesis of the coexistence of the One and the Multiple:

• HYPOTHESIS III (155e-156b)

  IF THE ONE EXISTS, IT IS MULTIPLE AND THEREFORE CONTRADICTORY.

  A One Entity (being in Time) comes into existence and ceases to exist, is combined and separated, becomes like and unlike, and increases and diminishes.

This third Hypothesis stands in the middle of the four positive and negative Hypotheses. Regnault says that the third Hypothesis first appears in the form of scepticism: ‘it is the moment of the evil demon, the moment when Descartes charges every science and mathematical certitude with nullity in the name of a stronger Hypothesis’ (CpA 9.4:65). In the context of the Parmenides, however, this Hypothesis will really express the transition of each Hypothesis into another, and the ‘vacillation’ of the One (CpA 9.4:66).

Regnault proceeds to his third pairing, which links Hypotheses VI and VIII:

• HYPOTHESIS VI (160b-d):

  IF THE RELATIVE ONE IS NOT, IN WHAT WAY IS IT NOT?

  If ‘a One is not’ means that there is a One Entity that does not exist, this Non-existent Entity can be known and distinguished from other things.

• HYPOTHESIS VIII (164b-c):

  IF THE RELATIVE ONE IS NOT, WHAT HAPPENS TO THE OTHERS?

  If ‘there is no One’ means ‘nothing that is “one thing” exists’, then the Others can only be other than each other.

Here we enter the field of the negative Hypotheses, which concern the consequences of the non-existence of the One. Hypothesis VI imagines what it would be like if the relative One did not exist; what then would happen to the Others (Hypothesis VIII)? In this case, all epistemologies would be true as a matter of course, and none would have a privilege over any other (relative scepticism). This idealist negation of the Relative One implied by Hypothesis VI (as carried out, according to Regnault by philosophers such as Léon Brunschvicg) gives rise to a relativist scepticism, in which the Others find themselves ‘sutured to multiple discourses’ (Hypothesis VIII) (CpA 9.4:69).

The last pairing links the two remaining hypotheses:

• HYPOTHESIS VII (163b-c):

  IF THE ABSOLUTE ONE IS NOT, IN WHAT WAY IS IT NOT? If ‘the One is not’ means that the One has no sort of being, the One will be a nonentity.

• HYPOTHESIS IX (165e):

  IF THE ABSOLUTE ONE IS NOT, WHAT HAPPENS TO THE OTHERS?

  If ‘there is no One’ means ‘there is no such thing as an entity’, the Others will be neither one nor many, but nothing.

If Hypothesis VII (the non-existence of the Absolute One) were true, absolute scepticism would follow (Hypothesis IX). Where Hypotheses VI and VIII evoke a relativist negation of the unity of science, Hypotheses VII and IX perform an absolute negation of science tout court. The absolute non-existence of the unity of science (Hypothesis VII) results in the absolute meaninglessness of the existence of the Others (CpA 9.4:70).

Appealing to Hegel’s dialectic of Being and Nothingness at the outset of the science of Logic, Regnault claims that at the end of the dialectic, Hypothesis IX - the Hypothesis of what follows for the Others in the case of the absolute non-existence of science - leads full circle back to Hypothesis I (the indeterminate One). The One is reduced to nothing, reflecting the conversion of the One into indeterminacy at the outset of the dialectic. Hypothesis I and IX are dialectically identical with each other. In Hegel’s dialectic of Being and Nothingness,

[being] is pure indeterminateness and emptiness. There is nothing to be intuited in it, if one can speak here of intuiting; or, it is only this pure intuiting itself. Just as little is anything to be thought in it, or it is equally only this empty thinking. Being, the indeterminate immediate, is in fact nothing, and neither more nor less than nothing. [...] Pure being and pure nothing are, therefore, the same. What is the truth is neither being nor nothing, but that being - does not pass over but has passed over - into nothing, and nothing into being (cited in CpA 9.4:71).²¹

In Regnault’s dialectic, the identity is between the indeterminacy of the absolute One and that of the absolute non-existence of the One.

After this result, Regnault says, ‘there are no more possible Hypotheses, and therefore the circle is closed’ (CpA 9.4:71). The ‘matricial exercise’ [exercice matriciel] is finished (CpA 9.4:73). From Regnault’s perspective here, dovetailing with his 1968 presentation on the concept of the epistemological break in Althusser’s ‘Philosophy Course for Scientists’,²² the ‘dialectic of epistemologies’ is a formal cycle that can be attached to every science engaged in the process of making a break [coupure] with previous conceptions, as it pursues the reforging [refonte] of its concepts. ‘The matrix [matrice] is self-sufficient’ (71). There are no other positions available than those identified here: the ‘absolute idealism’ implied by Hypotheses I and V, the Platonism or ‘dogmatism of participation’ implied by II and IV, the ‘relative scepticism’ of VI and VIII, and the absolute scepticism of VII and IX, with Hypothesis III serving as ‘the name of the matricial exercise itself’. To engage in science is to occupy one of these positions, and to share it, happily or reluctantly, with its fellow occupants (72). By taking into account the cycle of different epistemological positions, we stand to gain some protection against ideological distortions of scientific claims, as well as an understanding of the mechanisms of foreclosure and suture at work in the course of the history of science

Notes

1. Benjamin Jowett’s translation of Plato’s Parmenides is online at http://classics.mit.edu/Plato/parmenides.1b.txt. The Parmenides is widely considered to be Plato’s most enigmatic dialogue, and it is worth quoting Samuel Rickless’ helpful summary of the text at some length: Plato’s Parmenides consists in a critical examination of the theory of forms, a set of metaphysical and epistemological doctrines articulated and defended by the character Socrates in the dialogues of Plato’s middle period (principally Phaedo, Republic II-X, Symposium). According to this theory, there is a single, eternal, unchanging, indivisible, and non-sensible form corresponding to every predicate or property. The theoretical function of these forms is to explain why things (particularly, sensible things) have the properties they do. Thus, it is by virtue of being in some way related to (i.e., by participating in, or partaking of) the form of beauty that beautiful things (other than beauty) are beautiful, it is by virtue of partaking of the form of largeness that large things are large, and so on. Fundamental to this theory is the claim that forms are separate from (at least in the sense of being not identical to) the things that partake of them. In the metaphysics of his middle period, Plato does not provide a theory of the nature of the partaking relation. But in the Parmenides, Plato considers two accounts of the partaking relation. According to the first ‘Pie Model’ account, for X to partake of Y is for the whole or a part of Y to be in X (as a part of X). According to the second ‘Paradigmatistic’ account, for X to partake of Y is for X to resemble Y. In the first part of the dialogue, Plato sets out reasons for thinking that, on either of these accounts of partaking, the theory of forms is internally inconsistent. Immediately following these criticisms, Plato describes a general method of training designed to save the forms. The method consists of a series of eight Deductions (with an Appendix to the first two) focusing on consequences that may be derived from positing the being of a particular form and consequences that may be derived from positing the non-being of that form. In the second part of the dialogue, Plato instantiates this method, taking the form, the one, as his example. Plato shows, in particular, that whether the one is or is not, the one (and also things other than the one: the others) have none of a series of pairs of contrary properties (whole/divided, in motion/at rest, same/different, like/unlike, equal/unequal, older/younger). Plato also shows that, whether the one is or is not, the one (and also the others) have (or, at least, appear to have) all of these contrary properties. Samuel Rickless, ‘Plato’s Parmenides’, The Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/plato-parmenides/. ↵

2. Francis Cornford was a leading figure in British classical studies between the wars; for more information, see ‘F.M. Cornford’, Wikipedia, http://en.wikipedia.org/wiki/F._M._Cornford. ↵

3. In a recent presentation on the Cahiers pour l’Analyse, Regnault explains the idea behind ‘Dialectique d’épistémologies’ as follows. ‘I took it upon myself, at the time, to develop an entire theory of epistemological rupture (for instance the birth of Galilean physics), and of the reforgings or remouldings [refontes] [...] which this same science might encounter in the course of its history – for instance, the science of physics brought by Newton to its classical perfection, followed by the remoulding of the concepts of physics of Einstein and the theory of relativity. I went as far as to turn this theory into a kind of formal system, of a somewhat scholastic kind, which could be applied to all the sciences, thereby establishing a sort of circle whereby what would qualify as sciences would be those disciplines or knowledges that conformed to this schema’ (François Regnault, ‘The Cahiers pour l’Analyse, or Of the God that Did Not Take Place’, Concept and Form: The Cahiers pour l’Analyse and Contemporary French Thought, Middlesex University, 21-22 May 2009). ↵

4. Jean Cavaillès, Sur la logique et la théorie de la science, 28/375. ↵

5. Cavaillès distinguishes between two operative functions in science: the paradigm, which is ‘longitudinal’, extending science forward in a sequence (i.e. the extension of form), and the ‘thematic’, which is the reflexive, or ‘vertical’, movement that establishes sense. Cavaillès takes the second Hypothesis of the Parmenides as an instance of the ‘paradigmatic’ function in science, i.e. of ‘paradigmatization’ as opposed to ‘thematization’. ↵

6. According to Cavaillès, the second Hypothesis tells us how ‘the being of the relation consists in what it adds to its origin and is therefore different from the necessity which makes it one’ (Cavaillès, Sur la logique et la théorie de la science, 28/375). ↵

7. Francis Cornford, Plato and Parmenides, 135-204. Most of Cornford’s interpretation of the Parmenides is devoted to the second Hypothesis. He writes: ‘Parmenides had disposed of the Pythagorean scheme precisely by asserting that a One Being has no parts and must be unique: it does not contain a manifold, and no other thing can ever come out of it. Plato now intends to deny this dogma and to restore the possibility of a (logical) evolution following the Pythagorean lines, with the refinements of his own more advanced thought’ (135). ↵

8. Francis Cornford, Plato and Parmenides, 109. ↵

9. Cornford, Plato and Parmenides, 106-7. ↵

10. Cornford, Plato and Parmenides, 106-7. ↵

11. On interpretations of the Parmenides as a ‘parody of logic’, cf. Cornford, Plato and Parmenides, 113-14. ↵

12. Cornford, Plato and Parmenides, 109. ↵

13. Cornford, Plato and Parmenides, 107. ↵

14. According to Proclus, who wrote a substantial treatise on the Parmenides, Plato’s use of the term ‘one’ was not just ambiguous but ‘trebly ambiguous’, since it referred to ‘a One which is superior to being, a One inferior to being, and a One of the same order as being’. Proclus also argued that ‘not-being’ was doubly ambiguous, ‘as between what in a way is and in a way is not, and what in no way is’. The result, for Proclus, was a scheme of nine Hypotheses, serially ordered, exhibiting the metaphysical foundations of Neoplatonism: ‘In the first, [Plato] inquires how the One which is superior to being is related to itself and to the others; in the second, about the one coordinate with being; in the third, how the One which is inferior to being is related to itself and to the others; in the fourth, how the others which partake of the One are related to themselves and to the One; in the fifth, how the others which do not partake of the One are related to themselves and to the One; in the sixth, how the One, if it is not as in a way being and in a way not being, is related to itself and to the others; in the seventh, how the One, if it is not as in no way being, is related to itself and to the others; in the eighth, how the others are related to themselves and to the One which is not, when it in a way is and in a way is not; in the ninth, how the others are related to themselves and to the One, when it in no way is’ (Proclus, Commentary on Plato’s Parmenides, 1040, 1-16). ↵

15. Cornford, Plato and Parmenides, 111. ↵

16. Cornford, Plato and Parmenides, 195, 202. ↵

17. Regnault cites Hegel’s Science of Logic, Introduction, I, 55, and Hegel’s ‘Remark on the Unity of the One and the Many’ in the ‘Doctrine of Being’, ‘Being-for-self’, section on ‘Exclusion of the One’, 172. ↵

18. Cavaillès, Sur la logique et la théorie et la science, 25. ↵

19. Ibid, 26. ↵

20. Ibid, 24 ↵

21. Hegel, Science of Logic. ‘Doctrine of Being’, Introductory section, 82-83. Regnault also cites Hegel’s Encyclopedia Logic, §§ 86-88. ↵

22. Regnault, ‘Qu’est-ce qu’une coupure épistémologique?’ (1968). ↵