If we needed to clarify the fundamental distinction between reason and intelligence, it’s because the three types of paradox (paracosmies, paralogies, paradoxies) seem to us to be distinctly addressed to these two instances of the mind, each providing a specific teaching.

Paradoxes of Reason: Paracosmies, Paralogies


As we have seen1, paracosmies correspond to irreproachable reasoning, but bring together two incompatible realities, facts and/or theories. These are essentially scientific paradoxes, constructed as such and, more often than not, delivered with their solution. Here we have an illustration of how discursive reason works, bringing its objects closer together – by resemblance or dissimilarity, identification or opposition – in order to construct ever more assured knowledge.

Obviously, it’s the bringing together by opposition that constitutes the paradox, and characterizes the crux of the gain in knowledge: if it’s not daylight at night, it’s because the stars are moving away (expansion of the universe, Olbers’ paradox*2; if matter is wave and corpuscle, it’s because it’s the corporeal and the physical that we now need to distinguish3; and so on.

On the other hand, if there is a rapprochement, we speak of analogy, and this mode of constructing knowledge is as old as mankind4 and widely treated in the philosophy of knowledge5 as, for that matter, by psychology6.

If there is opposition, we are at least familiar with the thesis-antithesis-synthesis treatment and, more generally, the analysis of each opposite in terms of category7, class, genus, species… or assimilated, then allowing their compatibility; such, typically, as the distinction of the corporeal and the physical making wave and corpuscle compatible (Wolfgang Smith). Whether reality is counterintuitive (the Birthday paradox*, the Alabama paradox*, Benford’s paradox*, etc.), or whether it hides behind a deceptive appearance (the optical illusion of the stick bending in water), this is the “simple” cognitive approach of natural science (probability, diffraction of light) and the simple description of an aspect of the discursive functioning of reason; there’s not much more to say about it, it seems:

Avoiding paradox is a basic rational requirement for any rational theory, because it’s simply a matter of avoiding contradiction.

Joseph Vidal-Rosset8

This is exactly what science illustrates with its fact-theory iterations based on paracosmies: scientific paradoxes par excellence. And if philosophy (rightly) seizes upon them, it can only do so by taking scientific solutions into account. Thus, when Bergson invokes the intuition of duration as any answer to the logical difficulties raised by Zeno, [he proposes only] a form of regression for philosophy [… and] this philosophical perspective has no more scientific value than Hegel’s dialectical logic9.


The poralogies seem to us to offer a crucial lesson. If the paracosmies were a reminder that reason is subject to its object10, paralogies remind it that reason is governed by logic. This is its chance to realize its limit, especially that of its discursive – and horizontal – functioning.

This indefinite horizontality is evident in the work of certain logicians on paralogies “which in fact affect only the grammar of our language, and not the relationship of our language to the world”11, i.e., which are, or are intended to be, like sophistical discourse, detached from any ontological mooring. Indeed, these logico-mathematical paradoxes (Cantor’s* or Russell’s* paradoxes, or the Barbier’s* variant, for example) and logico-semantic paradoxes12 (paradoxes of the Liar* or Grelling*), not only find varied and competing solutions13 (this is especially true of “ensemblist solutions”, where solutions and interpretations nevertheless diverge on the usual “hierarchy of expressions” scheme: ZFC theories14, NBG15 and NFU16, but can also lead to even greater enigmas:

by inventing NF, Quine gave the simplest and most elegant solution […] but, unintentionally, he offered the scientific community an even deeper enigma.

Joseph Vidal-Rosset17

If we’re dealing with the “circle of paradoxes” (de Rouilhan18), it’s because, without end, the mind can run on itself, or turn on itself: we call it the mental mill. The examples of work on the Liar* and Grelling* paradoxes illustrate this point once again, whether it’s scientific work by logicians or philosophical work19, Tarski’s, for example, being open to realistic interpretation and intuitionist criticism :

Independently of proof, truth value resides in the statement as a property. This is the meaning of what is known as “semantic realism”. Those who question this kind of realism will object that it’s hard to see what mathematical “facts” can be independent of thought or proof systems. Finally, we have no idea what the truth of a statement can mean if it is not at least justifiable in principle. This contradictory debate is far from over in philosophy today.

Joseph Vidal-Rosset20.

 It seems to us that the impossibility of concluding simply corresponds to the “pride and nothingness” of “the rage to want to conclude”, as denounced by Flaubert21. Here, with paralogies, reason speaks to reason – in a loop; and intelligence, having admitted with Kant that this reason would be the ultimate instance, is content to watch it imperturbably, subjugated by this mental power at work. A banal illustration of this phenomenon can be found in the frequent confusion between powerful intellectual capacities and intelligence; while many undeniably possess the former, they cruelly lack the latter22, it is, quite simply, the Kantian paradigm at work, with the resultant involuntary and unconscious abdication of intelligence.

This remark, of course, concerns philosophical interpretations of paralogies first and foremost, since science, as we’ve said, necessarily remains within its “voluntary epistemic confinement” and, more often than not, will derive practical and applicative benefit from its work. On the other hand, philosophically speaking, if we accept that the field of all sophistry is a discourse disconnected from any ontological attachment, we believe that paralogies constitute warnings against the permanent risk of sophistry.

For example, if Tarski demonstrates that truth cannot be completely defined within any language, even though he insists on the “philosophical neutrality” of his theorem of the indefiniteness of truth, it’s simply because truth is transcendent to any demonstration or verification. Otherwise, we’re back with the ancient sophist who claims that truth and falsity are indistinguishable, but necessarily refers to truth so that his discourse, however sophomoric, is simply intelligible.

If, against Tarski’s theorem, we recommend the included third as an alternative to the excluded third that we intend to refute? Again, a sophism, since we’re putting ourselves in a situation of excluded third parties: one and the other are in reciprocal exclusion!

So, in the face of the sophisms of reason: reason limiting itself (Kant), the rational affirmation of the non-existence of reason (Derrida), the belief that the only possible knowledge would be rational (Kant), paralogies are signposts for philosophers: one way or the other. Of course, it’s always possible to take a wrong turn, but it’s at your own risk; as for the dead end, you’ll never be able to do better than sink into it.

Paradoxes of Intelligence: Paradoxies

Insofar as paradoxies, or logical dilemmas, they are insoluble. They too, in the first instance, require us to recognize a limit to pure rationality; they are an easy marker for reason, that “infinity of things surpasses”23. Of course, we can stop here and believe, with Kant and his followers, that, the rest being unknowable, we can, at best, concern ourselves with it in the name of practical reason – but what then can found morality, and religion itself, if revelation is found within the limits of mere reason? (In Christian parlance: we may not believe in the Incarnation and Resurrection – many do not – but if we do, it’s because it makes sense to our intelligence, and thus in some way reflects an irrefutable reality).

Stopping dogmatically short of the limits of reason is what gives rise to Kantian sophisms24, when he intends to “expose the scenes of disorder and heartbreak engendered by this conflict of the laws (antinomy) of pure reason”25. It’s a pity that Kant saw that an antinomy can be a boundary – a “touchstone”, he writes – but he sees it as limiting knowledge, since reason – itself limited, as he clearly sees it – is for him, on the basis of experience, the only possible source of knowledge:

The antinomy that manifests itself in the application of laws is for our limited wisdom the best touchstone of nomotheticism, thanks to which reason, which in abstract speculation does not easily notice its missteps, is made more attentive to the moments of determination of its principles.26

Thus, when formulating his proof of the antithesis of a world without beginning, he writes: “Let us admit that the world has a beginning. Since the beginning is an existence preceded by a time when the thing is not, there must be an earlier time when the world was not, i.e., an empty time”27, without realizing that if there were a time before time, there would be no real beginning28; time does not limit time, any more than the sea would limit the sea29. Similarly, he writes: “if we first admit the opposite point of view, i.e. that the world is finite and limited, as for space, it lies in an empty space that is not limited” 30; but where does it follow that space (the world in its spaciality) would then be in an unlimited space? Space, too, cannot limit space!31. Thus, the fallacy is not between the terms of the antinomy, but within each of its terms.

This is why paradoxie frees reason from itself, opening it up to the intelligence that surpasses it, revealing the intellectual intuition capable of understanding – and illuminating – the convolutions of reason. For example, if the corollary of Gödel’s theorem proves that formal non-contradiction is indemonstrable, it is because this non-contradiction belongs in fine to the order of intuition32, that it is, as a principle, part of intelligence. From this perspective, paradox, in particular, makes “manifest the contradiction inherent in the scientific project of the epistemic closure of the concept”33.

Epimenides or the Test of the Semantic Principle

Even more than this, a particular paradox – the Liar’s Paradox* – can reveal to the attentive thinker the semanticity of being, or that being has meaning only for the intelligence. But first we must choose between the Liar’s paradox* per se, that of Eulubilus of Miletus, and that of Epimenides*. Admittedly, attributing the eponymous paradox to Epimenides poses a problem, since the formula reported by St. Paul about their prophet, “Cretans, always liars” (Tit I, 12), is not a paradox. Nevertheless, Clement of Alexandria and St. Jerome34. So, given the de facto unknown historical origin of this paradox, rather than seeing in Epimenides a later alteration to the Megaric argument (reduced, moreover, to the status of a mere sophism), it seems entirely appropriate to take into account what immemorial tradition indicates: Eubulides’ paradox as a sceptical vulgarization35 of Epimenides’ earlier esoteric teachings36. A number of factors support this thesis, in addition to the historical precedence established by Hermann Diels (1848-1922)37 from the disciple of Hesiod (8th c. BCE)38, in particular:

  • according to Diogenes Laërce (180-240), Epimenides is a “quasi-divine” being: a manifestation of Aeacus, judge of the Underworld, master of discrimination: of the “test” that distinguishes those who have the intelligence of signs39;
  • according to Plato, he is even the “divine Epimenides”40;
  • according to Plutarch and Diogenes Laërce, he was one of the Seven Wise Men of ancient Greece41;
  • according to Aristotle, “this prophet reveals the past rather than predicts the future”, indicating an orientation towards knowledge rather than action42;
  • Pythagoras himself venerated him43.

Furthermore, according to Enrico Castelli (1900-1977)44, three features of the character can be brought together; they help to support the consideration of a metaphysical teaching of this paradox, which reveals by veiling and, especially, attests to the principle of metaphysical intelligence: long withdrawal (sleep) in a cave on Mount Ida (that of the eponymous “myth”)45, fully tattooed body (but only known after his death46 and the paradox of the liar, who also “speaks without saying and says without speaking, for he conceals what he wishes to signify and denounces the signifier with the help of the signifier itself”47. Finally, “Epimenides realizes better than any other the contradiction constitutive of any paradox, because it concerns lies, i.e. the falsification of statements”48.

From a Socio-Psychological Point of View,

Epimenides is not a paradox. No one understands “the Spanish are proud”, “the French mock” or “Africans have rhythm in their skin” as anything other than a more or less characteristic trait of a population, more often a cliché.

From a Logical Point of View,

this paradox simply proposes a contradiction between the form and content of the proposition, so much so that we’re surprised it’s been the subject of so much ink:

How is it that simple sophisms that wouldn’t have embarrassed a disciple of Aristotle or a student at the Faculty of Arts from the University of Paris could be taken seriously by such eminent minds as Russell, Frege, etc.? We have no doubt as to the answer. The cause of this curious blindness lies in the formalism of logistical reasoning, and, above all, in the interpretation of judgment in extension”

Alexandre Koyré49.

This paradox, and others (Barbier*, Richard*, Russell*), marked a limit to set theory, precisely the limit of a purely extensivist definition reduced to membership of a set. The Barber* is a paradox only because the element “village barber” is considered to be entirely defined by the relation “to shave all men who do not shave themselves”. If he were also simply a man, there would be no contradiction in his shaving himself50. This concern for a closed definition, while certainly legitimate, is merely that of the “well-made tongue” or of the “radical closure of the concept”51: the wish for an absolute definition (of terms and the relations they support), i.e. where definiendum and definiens52 are identified, to the point where nothing of the definite overflows its definition – which is impossible in natural language53. This means that the discourse of the science of logic claims to be the origin of the term, of its meaning, of its sense; the definition claims to be the source of the defined54!

From a Philosophical Point of View,

notwithstanding Wittgenstein55 – or Quine’s attempt to equate science and philosophy – it is, on the contrary, the term that gives meaning to the discourse:

terms, concepts, ideas, thoughts, or whatever name we want to call them, insofar as they have a meaning that is their own, and with which, in a certain way, they identify, and therefore insofar as they do not receive this meaning from discourse itself, escape discourse, and find there only their formal translation. […] The semantic reality of a concept, which constitutes its linguistic beyond, is the point at which it is linked to being. It is the invisible of language to which only intelligence can gain access.

Jean Borella56

It is this openness of the concept to being – this “original openness” that gives it meaning and reality – that forever prevents it from being defined in language; we can only use it in language: “the use we make of it will never be more than an approximation and a limitation of its semantic reality, which in itself is informal and inexhaustible57.

The reduction – or impoverishment – necessary to logical language is, notably, the elimination of self-referential terms or phrases58, as the contra-diction comes from language speaking of itself. Appealing then to a metalanguage (of superior semantic power), the logician notes that there is irreflexivity between the formal system of language and that of the metalanguage – and so we find the limits of formalization59.

If, for his part, the linguist naturally spots the reflexivity of language 60, the better to denounce the supposed arbitrariness of the linguistic sign61 or, what amounts to the same thing, a supposed omnipotence of language62, which does not obscure the circle in which linguistics, originally, is constitutively situated, due to its inherent “epistemic reduction of the concept”63.

However, “it is not language that is metalinguistic, it is human thought that is reflexive by nature”:

The reflexivity of language merely reflects the essential reflexivity of thought, i.e. its capacity to take itself as an object, or to go beyond itself: there is no human thought outside the possibility of this ‘self-transcendence’ or ‘self-transitivity’

Jean Borella64

Admittedly, the linguistic sign provokes the mind’s awareness of the reflexivity of thought, but it does not denote itself: “it is thought that metalinguistically uses language”. The sign is “first and foremost a sign of itself”; first and foremost, it indicates that it is a sign, “and entry into signifiance is nothing other than that”65.

The contradiction only arises when this reflexivity of thought is prevented by its reduction to the “materiality of language”. This is the subversion of language, which, instead of expressing thought, seeks to produce it; but what is legitimate in logic and science in general, cannot be legitimate in philosophy. Intelligent thought can only contradict itself if we let words do the thinking for us: we can always say “the circle is square”, but we can’t really think it. If we can say it, it’s because words have lexical meaning, and, as such, “mediate between a signifying intention and a signified intention, and therefore continue to function and apparently produce meaning, even though they express no signifying intention”.

If words were not contractually bearers of meaning, the situation would be different: each signifying expression would be a unique event, indistinguishable from its meaning; in short, there would be no signs, i.e. distinct entities endowed with determinate meaning. In other words, the sign is a sign of itself, positing itself as a sign, and it is thanks to this metasemiotic property that it can precisely “act as if” its pure semiotic functioning was possible. In the proposition: “the circle is square”, we say nothing, and we mean nothing, or rather we only mean what we say (a statement), and not the real thing; we let the semiotic entities function “on their own”, but it’s an apparent, purely mimetic functioning. We take undue advantage of the lexical properties of language, we break the contract. And if we ask: but then, what are we thinking when we say: the circle is square? since we have to think it in order to say it, we’ll reply that we’re thinking words, not ideas, and this proves, irrefutably, that to really think is to think ideas, not words66.

Jean Borella

This is the first lesson of Epimenides: when reflexivity is both demanded and impossible, we are dealing with a discourse that claims that the meaning of discourse is produced by discourse itself, or, put another way, that “discourse claims to apply to itself the thesis that no discourse ever applies to anything”. The linguistic sign, which claims to produce signification itself, is no longer a linguistic sign, and produces nothing at all, for the principle of signs is to be traversed by the signifying intention, which is extralinguistic. The sign, which “intends to signify in reality that there are only apparent significations”, proposes the contradiction achieved by the permanent lie.

The second, complementary lesson lies in this signifying intention, associated here with a will to deceive (“all Cretans always lie”). It is in fact the free will that alone can “renounce its own will to say” and decide to let the being whose knowledge passes through the signifying intention speak. As we have seen, this intention passes through the sign, and is itself passed through by being: to “signify” is to let being make sense, to recognize the intelligibility of what is. Here, Epimenides recalls “the capacity of thought to allow itself to be informed by being [and] the freedom to acquiesce to it speculatively”.

Epimenides’ paradox thus constitutes the “test” of the semantic principle, whose two essential dimensions are “intellect and will, which are also the two poles of the human being”67. This is why contradiction is so precious: a language in which it is impossible could never become self-aware, and therefore could not be the place where thought discovers its own nature and the existence of the world68.


  1. See, in Metaphysics of Paradox, Chapter I, § A classification of paradoxes: paralogy, paracosmia, paradox.[]
  2. The * indicates that these paradoxes are listed and explained in a glossary at the end of each volume.[]
  3. Cf. Wolfgang Smith, The Quantum Enigma…, 4th ed., Philos-Sophia Initiative, 2023.[]
  4. Even if its inaugural philosophical implementation is due to Plato, who, “for the first time in the history of philosophical thought, expressly applies the notion of analogy to the resolution of the most fundamental questions of metaphysics”, Jean Borella, Penser l’analogie, p. 163.[]
  5. The most accomplished work we’ve read – including a metaphysics of analogy as such – is Jean Borella’s Penser l’analogie. See an overview in Bruno Bérard’s Jean Borella, La Révolution métaphysique..., op. cit. ch. 12. Métaphysique de l’analogie, pp. 249 sq.[]
  6. For example, in the same year: Emmanuel Sander, L’Analogie, du naïf au créatif. Analogie et catégorisation, Paris: L’Harmattan, 2000.[]
  7. Typically Aristotle’s critique of Zeno of Elea’s paradoxes for category confusion.[]
  8. Qu’est-ce qu’un paradoxe? op. cit., p. 10.[]
  9. Ibid., p. 46.[]
  10. Martin Heidegger, too, noted this submission (Unterwerfung = subjection) to being, leaving it to reveal itself, cf. Was ist Metaphysik? (conf. of 1929), Qu’est-ce que la métaphysique?, trans. Henry Corbin, Paris: Nathan, 1981. Summarized in Bruno Bérard (ed.), Qu’est-ce que la métaphysique? op. cit. pp. 19-24.[]
  11. Joseph Vidal-Rosset, Qu’est-ce qu’un paradoxe? p. 11.[]
  12. These paradoxes “do not directly concern mathematics; they have their roots in ordinary language”, Vidal-Rosset, ibid., p. 26, who specifies the equivalence between “semantic paradoxes” (Chwistec, 1937), “linguistic paradoxes” (Peano, 1906) and “epistemological paradoxes” (Ramsey, 1926).[]
  13. We summarize here, without detail, Joseph Vidal-Rosset, ibid., pp. 14-25, who emphasizes “the plurality of solutions and the fact that each of them entails important theoretical consequences that differ from rival solutions” (p. 21).[]
  14. Theory of Ernst Zermelo (1871-1953), modified by Abraham Fraenkel (1891-1965) and completed by the axiom of Choice (Peano). Synthesis to be read at Vidal-Rosset, op. cit.[]
  15. John von Neumann (1903-1957), Paul Bernays (1888-1977), Kurt Gödel (1906-1978).[]
  16. NF = New Foundation (Quine), U = Urelemente (simple elements).[]
  17. Ibid., p. 25.[]
  18. Cf. Philippe de Rouilhan (1943), Russell et le cercle des paradoxes, Paris: PUF, 1996.[]
  19. For example, the Philpapers site lists over 1,200 for semantic paradoxes alone (121 for so-called “epistemic paradoxes”, 1,100 on the Liar* alone.[]
  20. Ibid., p. 31.[]
  21. Here we can compare the idea that over-definition kills thought: “These models, which take on the appearance of science so well, seem to me to have been pushed too far to be useful. It’s as if it were better, sometimes, to accept the use of notions without their being too well defined, their lack of precision giving them a kind of safety valve in the right (relevant) approach to necessarily fuzzy domains”, Jacqueline Feldman, “Objectivité et subjectivité en science. Quelques aperçus”, op. cit, § 124. We could also quote Emmanuel Carrère: “It’s worrying, this sense of instability, of what we are, what we feel and what we think. It makes it very difficult to come to a conclusion. There’s no possible synthesis“, remarks collected by Sabine Audrerie and Bruno Bouvet, “Je ne crois pas, mais le christianisme est pour moi une boussole”, La Croix, 27/08/2014, emphasis added.[]
  22. It seems to us that this explains why some School, specialized in the sole selection of the best intellectual capacities, can put on the political and economic markets perfect imbeciles as well as patent asocials. Some recent changes in recruitment methods seem to have taken this into account.[]
  23. Pascal, Les Pensées, section V.[]
  24. Kant himself calls his antinomies sophisms: “When we apply our reason no longer simply for the use of the principles of understanding to objects of experience, but try to extend these principles beyond the limits of the latter, then sophistical propositions are produced which have neither confirmation to hope for, nor contradiction to fear in experience, and each of which is not only without contradiction with itself, but even finds in the nature of reason conditions of its necessity, and unfortunately the assertion of the contrary is on its side founded on equally valid and equally necessary reasons”; Critique of Pure Reason, trans. A. Tremesaygues & B. Pacaud, Paris: Alcan, 1905, p. 385.[]
  25. Critique de la raison pure, p. 377.[]
  26. Ibid., p. 387. Emphasis added.[]
  27. p. 389.[]
  28. See Appendix 13 in the book: The beginning is eternal.[]
  29. As Kant himself acknowledges a little further on – as we have seen: “because what limits must be different from what [it] serves to limit”, p. 444.[]
  30. Ibid.[]
  31. Admittedly, Kant didn’t have the idea of space-time – nor of the current cosmological model – but he would have had all the previous science and philosophy at his disposal (the evidence of a world without edges dates back to the 5th century B.C. with Archytas of Tarragona; the doctrine of creatio ex nihilo from the 2nd century A.D.), if he hadn’t gone out of his way to repudiate them, in order to lay down his own prolegomena. Above all, having placed space and time “inside” man, as categories of understanding, and the world being deemed unknowable, his discourse necessarily becomes sophistical.[]
  32. Jean Borella, Histoire et théorie du symbole (Le mystère du signe, 1989), 3rd ed., Paris: L’Harmattan, 2015, p. 99.[]
  33. Jean Borella, La crise du symbolisme religieux, op. cit., p. 303. From this point of view, the philosophy of logic does not escape this constitutive reductionism: “it seems to us [that it] still remains trapped in the circle in which Epimenides imprisons it” (p. 304).[]
  34. Stromates, I, 59, 2 and La sainte Bible de Pirot et Clamer, Paris: Letouzey et Ané, t. XII, p. 251; quoted by Jean Borella, La crise du symbolisme religieux, p. 297. We follow him in this section. He gives his interpretation of Epimenides’ paradox “the value of an initiatory test for entry onto the philosophical path” (ibid., p. 16).[]
  35. Greek scepticism is not necessarily to be understood in the modern sense of impossible access to truth, but can be interpreted as denouncing “the relative and contradictory character of formulations […] with a view to overcoming all form and to a direct grasp of the intelligence by Truth itself” (ibid. , p. 298, n. 709).[]
  36. “Pausanias, loc. cit., attests that the legends of Epimenides were still very much alive in the Ile siècle de notre ère”, Marie-Christine Leclerc, “Épiménide sans paradoxe”, Kernos [on line], 5 | 1992, URL : http://kernos., p. 223. As for historical research, “These uncertainties and distortions are the result of a positivist problematic” (ibid.).[]
  37. Epimenides is from the 6th c. AEC (Eubulides of Miletus from the 4th); E. R. Dodds, Les Grecs et l’irrationnel (1959), trans. Michael Gibson, Paris: Flammarion, 1977, pp. 146-147.[]
  38. According to Plutarch, Banquet of the Seven Sages, 158b. Influence noted by PLATO, Laws, 677d-e; Marie-Christine Leclerc, op. cit., p. 227.[]
  39. Vies et doctrines des philosophes illustres, Marie-Odile Goulet-Gazé (dir.), Paris: Le Livre de Poche (La Pochothèque), 1999, I, 114, p. 149 (Borella, ibid., p. 298.[]
  40. The Laws, I, 642 d-c; III, 677 e (ibid.).[]
  41. Plutarch, Banquet of the Seven Wise Men; Diogenes Laërce, l, 109-115; Marie-Christine Leclerc, op. cit., p. 221.[]
  42. Rhetoric, 1418 a 24 (ibid.).[]
  43. Francis Vian, “Grèce archaïque et classique”, Histoire des religions, Encyclopédie de la Pléiade, 1970, t. I, p. 560 (ibid., p. 300).[]
  44. Mythe et foi (coll.), Paris: Aubier, 1966, pp. 13-14 (ibid, p. 299).[]
  45. “Epimenides is well rooted in the cult tradition of the caves”, Marie-Christine Leclerc, op. cit., p. 222; referring to W. Burkert, Weisheit und Wissenschaft, Studien zu Pythagoras, Philolaos und Platon, Nuremberg, 1962, p. 127; R. F. Willetts, Cretan cults and festivals, London, 1962, pp. 216, 242).[]
  46. “Inscriptions apparues post mortem”, following Marie-Christine Leclerc, op. cit, p. 224.[]
  47. Jean Borella, ibid., p. 300.[]
  48. Jean Borella, ibid., p. 303.[]
  49. (1892-1964), Épiménide le Menteur (Ensemble et Catégorie), Paris: Hermann et Cie, 1947, p. 24; Jean Borella, ibid., p. 301.[]
  50. Jean Borella, ibid., p. 303.[]
  51. See ch. VII, § 3 of Metaphysique du Paraoxe.[]
  52. Formally, a definition puts in equivalence the defined term: the definiendum and a defining element: the definiens. Classically: “man” = “rational animal”.[]
  53. According to Tarski, only the impoverished language of logic can escape this; cf. Bertrand Saint-Sernin (1931), “Les paradoxes”, Revue de l’enseignement philosophique, 25e année, n°1, 1975, pp. 32 & 41-42; quoted by Jean Borella, ibid., p. 304 and n. 729.[]
  54. Outside logic, in other sciences, it has been observed that over-definition kills thought: “It’s as if it were better, sometimes, to accept the use of notions without their being too well defined, their lack of precision giving them a kind of safety buffer in the right (relevant) approach to necessarily fuzzy domains”, Jacqueline Feldman, “Objectivité et subjectivité en science. Quelques aperçus”, op. cit., § 124[]
  55. “The meaning of a word is its use in language”, Philosophische Untersuchungen, § 43, Frankfurt-am-Main: Suhrkamp Verlag, 1967, p. 35; trans. Jean Borella, ibid. p. 305. Underlined in the text.[]
  56. ibid., pp. 304-305.[]
  57. Jean Borella, ibid., p. 305. Emphasis added.[]
  58. “This word counts three letters” (the word “word” counts three letters); typically, a paradox will be the negation of a self-reference: “it is forbidden to forbid”, “is impermanence impermanent or permanent?”, “I’m lying”; see Grelling’s paradox*.[]
  59. “The limitations of formalizations derive from certain properties that are inherent in the notion of formal system […]; ultimately they are implicitly contained in the very project of formalization” (Ladrière, ibid., p. 324)”; quoted by René Amacker, Linguistique saussurienne, Geneva: Droz, 1975, p. 118.[]
  60. For example, in Saussure, whom it “haunted”: “There is no substratum whatsoever to linguistic entities; they have the property of existing by their difference, without the pronoun elles [in the sentence in question, which begins “elles ont la propriété” (RA)] managing anywhere to designate anything other than a difference itself” (N 24a = 3342. 2,1), quoted by René Amacker, “Saussure ‘heraclitean’: constructivist epistemology and the reflexivity of linguistic theory”, Linx, 7 1995 (pp. 17-28), n. 16.[]
  61. “Reflexivity is the property of every natural language to be its own metalanguage: we need language to speak of language, which means that the theoretical statements of the linguist are expressed by means of precisely what they are about. In other words, whatever property the linguist recognizes in language, that property belongs in principle to the statements that formulate the property in question. Thus, to affirm the radical arbitrariness of the linguistic sign is at the same time to affirm the radical arbitrariness of the radical arbitrary sign”, René Amacker, “Saussure ‘heraclitean’…”, § 4.[]
  62. “I would say that natural languages are omnipotent and reflexive, meaning not only that they can and must be able to speak legitimately of themselves (reflexivity), but also that they cover ‘the whole of the matter to be signified’ (omnipotence). Moreover, there is undoubtedly a link between these two attributes, which are like two sides of the same specific property of the linguistic system: language can speak of itself because it can say everything, and it can express everything, including itself, because it is omnipotent”, René Amacker, Linguistique saussurienne, Geneva: Droz, 1975, pp. 118-119.[]
  63. “If I have succeeded in getting across what I wanted to say, language should appear, insofar as it is reflexive, like a Moebius strip of the first type (such that whoever walks on it can change the face of the strip without changing the face of the strip) or, better still, like the mill in Escher’s painting, where the water that has just turned the wheel through its fall returns, quietly flowing in its channel, to turn the wheel through its fall. Everything happens, then, as if language were realizing perpetual motion”, René Amacker, “Saussure ‘Heraclitean’…”, § 6.[]
  64. Ibid., p. 305. See Jean Borella, Histoire et théorie du symbole, Paris: l’Harmattan, 2015 (3rd ed.), which sets this out in philosophical detail.[]
  65. Jean Borella, ibid., p. 306.[]
  66. Ibid., p. 307.[]
  67. Ibid., p. 308.[]
  68. Ibid., p.309.[]