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Quelques mots (essentiellement méta) sur l'intuitionnisme et les mathématiques constructives
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  2. This paper was originally published in French as “Borel et... Revue d’histoire des math´ematiques
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Il est difficile de trouver 10, 15, 20 personnes de confiance. Ceci afin de soit les blacklister, soit les cibler pour les compromettre. Pour cela, il est indispensable que chacun ait compris la technologie sous-jacente. Les experts se trompent, ne sont pas toujours objectifs, et sont parfois opaques. Il suffit de rajouter ces deux lignes dans votre fichier de configuration torrc :. Voter est-il immoral? Votre vote est-il secret?

Tous sont des outils, et comme tout outil, sont neutres. Des exemples? Can we then find on the final Page — that of the Septentrion — a sign that suggests a metrical count placed under the aegis of the 7? If we begin with the hypothesis that the 7 is the secret Meter of the poem, it is nevertheless necessary to determine what it counts. Now, this statement can be understood as saying that all thought is associated with an aleatory series comprising the Generally, such a series is stripped of all meaning — a mere throw of dice — but it is significant in the present case since it is a matter of associating a count with a text.

We can therefore suppose that our conclusion holds the metrical key that will allow us to work out what the constellatory 7 counts. Since the poem obviously includes many hundreds of words, the number will be three digits. We could therefore imagine a meter of , , or words.

If we were to arrive at one of these four counts, the hypothesis of a lexical meter based on 7 would become conceivable. But in order for this supposition to be convincing, we would have to discover that the number obtained by the count is furthermore effectively evoked, albeit in a willfully allusive manner, by the meaning of the poem. The central, double page of the poem — Page VI of the whirlpool — can precisely be read as staging the charade of a number with three figures. This passage clearly speaks of a whirlpool — the very same whirlpool in which the Master had no doubt drowned.

Yet, as we have already said, the whirlpool is perfectly symbolized by the 0, as much by its central void as by its circular form — a circularity on which the text insists via its own circumvolution. And they themselves are the enigma that is to be elucidated in order to discover the two other figures that frame the central 0 of the Number. Instead, we believe that these two segments do not constitute two incomplete hypothetical locutions, but rather propose a precise comparison, and therefore constitute two nominal phrases, which are syntactically complete.

Decapitation represents the recurrent symbol of spiritual purification in the literal form of a separation of the head from the body. The Noces even contain a song of John the Baptist at the very moment of his decapitation, the head leaving the body of the Saint as if in victory, launching itself towards the sky before falling back.

Decapitation, then, is a symbol of the spirit freed, for the time of its furtive projection, from the constraints of the body, before wisely embracing the declining trajectory of the sun, reconciled with the Earth and with no more hope for the beyond. Once again, there is therefore a diagonal of ifs, which reproduce the diagonal of the as if: If. Genuflection as if to the dazzling Nimbus out there very glorious dilating [arrondissant] In the absence of the saint with stiffened tongue Its and vacant conflagration Also perhaps without the mutual fusion Immobilized by an infelicitous clash Of divers worthless monsters whose dereliction ruins The dented ewer and the twisted candelabra Forever bequeathing no memory to the evening Other than this hereditary dresser piece Workaday heavy metal where the equivocation arranges With anxiety strange glory Who knows what fierce and bitter mask enlightened Triumphally and peremptorily if The trashed chimera of an illustrious dinner service.

Barely extinguished now is the one That beneath its miserly fires will not contain The longed-for delights of the nuptial meal This comparison of the Master to the Saint who prophesies the coming of Christ signifies that a decisive event will follow the decapitation staged by the shipwreck: no longer the coming of the one Messiah, but of the unique Number. Let us reprise this text segment by segment. It allows us to symbolize simultaneously the sonnet, the fixed form par excellence; rhyme, which demands that modern verse be dual, as opposed to the antique verse determining the superiority of the first over the second ;20 and the constellation that trembles like a mirage against the backdrop of a nocturnal void.

The unique Number is thus an homage to the old rule, the lexical metamorphosis of the Meter that allows it to conserve, by remembrance, the memory of rhyme and fixed form. For not only do the Noces reproduce this diagonal by separating the two si by two times 7 verses, but the text that is thus framed also invokes with insistence the void circularity of the Zero. The same procedure of encrypting the is stated in two ways in two texts written during the same period. We have seen that we could readily associate the 7 and the 0 — as well as the that joins them together — to a symbolics of the sonnet and of the constellation.

On the contrary, lexical meter appears to be even more arbitrary than traditional meter. Moreover, what good is it to encrypt such a count? How does the fact of writing a poem, which withholds the rules regarding the summation of its words, confer a necessity upon its number that it would not otherwise have had?

Only poetry produces Song as a music intrinsic to verse, and not as something added to it from an autonomous instance of non-meaning. At best, Wagner merely transfers to the German people what the tragedians had offered the Athenians: the possibility of seeing themselves through the dramatization of their mythology, and to undergo, by theatrical means, a reflexive test. The moderns have known an apparatus superior to tragedy: namely, Far from infusing a poetry that was to be the song of the here-below with an intimately Chris-.

To return to the moment before the Eucharist in order to understand the origin of its power is to interrupt its flow for the sake of following a new course that will be able to succeed it for having siphoned it off at its origin. To touch the source is not to repeat it: on the contrary, it is to interrupt the repetition of the same in favor of following a course that begins before what there already is.

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In this sense, Christianity produces the true form of the divine through its sole, celebratory moment that is perpetually repeated, with the help of a fictive past and future, conjured up in order to produce the spark of a ceremonial present split by the light of the false. The aestheticization of a mass can only produce a spectacle — and therefore, again, a representation.

Uninformed is he who would proclaim himself his own contemporary, deserting or usurping with equal imprudence, when the past seems to cease and the future to stall, in view of masking the gap. Before disclosing the principle of this solution, let us lay out, in chronological order, the principal stages of the poetic constitution and resolution of the two problems we have spoken of. The crisis of free verse crystallizes around the years — From to , the response to these two challenges is laid out in the Notes, taking the form of a description of a ceremony based on the Book a ceremony of the poem inspired by the mass, against that of the musical drama derived from the Greeks , and rife with symbolic numbers a.

The reason for this change of rhythm is also quite apparent in this succession of dates. After hav For the counts of these two sonnets and their variants , cf. The Number and the Siren, op. The failure of the Notes arose from two inadequacies: 1. The alternatives to the metrical count produced no effect of superior necessity; on the contrary, they produced the impression of an increased arbitrariness. The 12 can indeed be disseminated almost everywhere — price, pages, participants — yet this does nothing but increase the impression that the desire for a fixed number follows from a will that is, at root, political, as Kahn argued: this will consists in unifying the practice of verse with a view to its communitarian effect, and not for reasons of its internal exigencies.

Meter does not emerge strengthened from all this — quite the contrary. The ceremony does not succeed in extracting itself from the space of the stage, and it is therefore subject to the same reproach as Wagner. The episodes succeed one another and the drama remains the final form of what there is to read, hear, and see. How can poetry produce a fact, or at least the belief in this fact? By giving itself the means of effectively realizing its theme through the sole effect of writing. He describes himself hesitating, wondering throughout the composition of the poem if he will throw his stellar Number into the ocean of posterity; if he will cede to a gesture that risks never being discovered; and also if he will dismay his readers should his discovery be misunderstood and judged to be derisory.

But in itself this is of little interest. What matters instead is the following: these operations are articulated together by a procedure of encryption, which on this occasion gives them the following remarkable property: that of producing, by means of fiction, a fact that, through its reality, exceeds — and even undermines — the fiction that has engendered it. What must be underscored first here is that performativity is the property of a discourse that presents itself as fictional: that of a Master who, confronting a shipwreck, hesitates to throw the dice.

While the lure of the Evangels consists in offering, in the guise of something authen-. It presents itself falsely as the representation of a drama while it is, in fact, an authentic sacrifice. Fiction cancels itself out by redoubling itself: it reveals by the discovery of its code that its fictional being was itself fictive. The poetic fiction becomes the necessary moment of its effective selfabolition. What the Notes lacked, then, was not the count but rather the fact of making the count its principal subject, and to have willfully dissimulated this fact.

The Notes present us with a mass without a veritable sacrifice — without the risk of a meaning being lost. For nothing in the work allows us to guess this procedure, and only a chance-like attempt can, precisely, allow us to discover it. Everything was no doubt calculated so that randomness has the upper hand. Or more precisely: he takes the real risk of a death without the resurrection of meaning, for the lack of having missed the chance of an adequate deciphering.

The shroud of silence drawn around oneself by a silent reading and a text that has been purposefully constructed to be seen, by way of its typographical disposition, invites one to do just this, rather than be read for others is without doubt one of the final forms of reverence which, even today, each person can expect from one moment to another — a form that exceeds the simple idea of intellectual concentration.

In order to liberate Presence from its original Eucharistic mode, it is not enough to produce a real passion a sacrifice that has taken place. Far from announcing the principle of the failure of all literature insofar as it is submitted to the randomness of a dice throw that would render it vain, gratuitous, and ephemeral, the poem, on the contrary, says that it is henceforth possible to found literature upon the only thing that escapes the destructive force of Chance: namely, Chance itself. The Eternal is therefore Chance, our only Infinite. But in this case, in order that the Number not be the product of a contingent throw — in order, on the contrary, that it acquire a necessity — the Number must fuse with Chance rather than simply be the result of Chance.

Let us repeat: there is no way out. It was necessary for him to engender an effective sacrifice — the human part of the Passion — but one that had been renewed by the poetic act, to the point of taking on a more-than-human dimension. It was therefore necessary for him to put into play and in peril the project of his own decisive poem. But it was also necessary to discover a way of becoming the equivalent, in a manner consistent with the Nothingness of the modern era, of the man-God, and to produce the act that was to make him a man woven with the thread of chance via the mediation of fiction.

However, in this renewed inspiration for a previous endeavor, there is a paradoxical element that has not been sufficiently highlighted. What is essential is not that a text abandoned for thirty years seemed to suddenly resurface when some of its themes are reprised. In saying this, it is true that we are suggesting a hypothesis rather than noting a fact. The fact, in its neutrality, amounts to theoretical and notional borrowings: the throw of dice, Midnight, hesitation, and the infinite were already present in Igitur. From the perspective of the poem, the tale would only have been of value for certain elements that it included and that could be reused for themselves.

This paper was originally published in French as “Borel et... Revue d’histoire des math´ematiques

But what is interesting in this intimacy comes from the fact that it cannot be founded on the similarity between the two projects since, precisely, the first failed while the second transcends a long period of failure. Everything happens as if the inadequacy of Igitur appeared as the solution to the aporia of the Notes. If I complete it [my emphasis — Q. What is at stake is to show that a meter no longer opposed to Chance, but identical to it, is in the process of being constituted: a Chance-meter, and not a meter against Chance — and therefore,. But in what sense can Chance be said to be infinite?

And how can a meter a Number also be infinite? In particular, in what sense could a lexical meter be infinite, while its cardinal — — is, according to our hypothesis, finite? Here is the crucial passage: Midnight sounds — the Midnight when the dice must be cast. Tombsashes not feeling, nor mind dead center.

He recites the prediction and makes the gesture. Hissings on the stairs. The infinite emerges from chance, which you have denied. You mathematicians expired — I am projected absolute. I was to finish an Infinite. Simply word and gesture [ The family was right to deny it — its life — so that it stayed the absolute. This was to take place in the combinations of the Infinite face to face with the Absolute.

He seems to be the final representative of his lineage, and therefore incarnates by himself the absolute — the final custodian of its legacy. While he hears the hissing of his ancestors, who foresee the blasphemy that he is about to accomplish, Igitur retorts that the infinite always comes out of chance, and that its very denial was one of the combinatory possibilities that chance permitted. The following passage gives the meaning of the infinite that has caused them to expire: Briefly, in an act where chance is in play, chance always accomplishes its own Idea in affirming or negating itself.

Confronting its existence, negation and affirmation fail. It contains the Absurd — implies it, but in the latent state and prevents it from existing: which permits the Infinite to be. The old poets denied chance, but it was ultimately chance that produced the most perfect verses, non-meaning being at the source of the birth of poets as of their inspiration.

Igitur will, on the contrary, affirm chance, but this is meaningless since this affirmation originates in the same non-meaning. Chance contains within itself both its refusal and its acceptance, in the manner of a limitless contradiction, and above all — this is the nodal point of the Igiturian drama — it gives no more value to the gesture that lucidly recognizes it than to the illusion of those who were blind to it in their time.

Just as fortune can produce, in the course of a game, a throw whose luck gives it the appearance of a destiny, so can it produce a verse that seems to be inspired by a god. But it is the same non-meaning that produces both the throw without luck and the stanza without taste. In a sense, this hopelessness in the face of the abolition of ideal hierarchies has doubtless a rather banal allure, but its reformulation occurs in the terms of a more unexpected radicality once the lucidity regarding non-meaning, instead of being valorized, seems to be swept away by the equalization of all decisions.

For how, henceforth, can one act? What good is poetry if everything comes down to nothing? What if both verse and non-verse — both the splendor of verse and its randomness — are so many combinations of the infinite? How can one ground oneself in an Absolute that is identified with the Absurd? How can one guarantee verse with the maleficent power that accords no more grandeur to its recognition than to its rejection?

This is the question that Igitur fails to respond to. He fails to merge with the infinity of the Absolute that he had identified with the latent Absurd. Contrary to Hamlet, who is nevertheless the inspiration for this character, Igitur does not have the act by which he will be able to render homage to his lineage without giving up on the meaning of his own destiny. It indeed seems that chance, which renders all acts equivalent to one another, can no longer ground a specific poetic conduct. The writing of the interminable exhaustion of verse to lie down in the ashes of his ancestors , just as the writing of the perfect verse in defiance of nothingness and tradition to throw the dice under the hissings of his lineage — in the end, all this comes down to the same thing.

How could the failure of Igitur suddenly appear as the key to the solution that had been unsuccessfully sought after in the Notes? As we have seen, in Igitur, chance is infinite insofar as it contains opposed perspectives in a latent state, at least as far as appearances are concerned: both the manifest non-meaning the indifferent and the appearance of excessive meaning the perfect verse and the happy coincidence are equivalent with respect to chance, thus seeming to render vain any search for a gesture that would be its privileged bearer.

What is hesitation if not precisely this infinitizing capacity to hold the opposites in oneself in their latent state? In other words, what is hesitation if not the paradoxical gesture as a gesture that withholds all gestures by which a man participates in this new Absolute that is infinite Chance — an Absolute containing in itself all options in a state of potentiality, both meaning and non-meaning? To divinize oneself is to hesitate: to hold in oneself the equivalence of everything with everything else, and thus to incarnate chance, to include the absurd not by its own immobility, but by its active immobilization to immobilize oneself is a movement, a movement towards stopping movement.

However, this thesis seems to run counter to our preceding analysis of the code: if the Number is the result of the lexical count, then it seems that it is necessary to say, on the contrary, that the throw has indeed occurred, and that the indecision has been alleviated. We can remark, moreover, that it has been alleviated in favor 39 This is to say that the temptation that the Master initially resists does not consist, as we might expect, in refusing the wager, that is, the throw: on the contrary, the temptation would be to throw the dice, rather than to keep hold of them.

It is from this exigency — to keep his fist closed — that the Master first recoils, tempted as he is by the throw of dice. Why this inversion of the terms of his temptation? Because to hold the dice in his hand — just as Igitur shakes them in his fist — would at the very least be to keep their result latent, and therefore to move closer to the infinite than he would be were he to actualize a throw. How, then, can the infinity of Chance be made consistent with the determination of the result as a lexical count?

The principle of this final throw is in fact to apply the uncertainty of the gesture to the Number obtained. There is a throw, since the undecidability is now crystallized in the Number of the throw. It is therefore from this that the necessity of the Number results: this Number that cannot be.

It is the — demonstrating thus that there was a throw — but due to an indecision in the count that has been inserted into the poem it is not the , but perhaps another slightly larger or smaller number, whatever it might be — a number which demonstrates, on the contrary, that there never was a throw that is, a code. Above all, this relative irreality allows him to escape the constraints of choice, to which all flesh-bound individuals are subject he who does not choose still chooses to not choose.

Only now can we understand why it was necessary for the number to be encoded, for were it to be explicitly disclosed it would lose all of its power of uncertainty. It is not the , no more than any other number, which is infinite: it is the or any other chosen number insofar as it is affected by a marginally undecidable code — a code sufficiently fixed to convince us that there is probably a code, but insufficiently so to make us certain of it.

The final stage of our analysis must therefore unveil what this uncertainty of the count consists in, but must also show what in the poem can be interpreted as suggesting such a procedure. This seizing of the sum is indeed revealed to us in the poem in two deliberate ways. Among these words there are two that, at the time,. We are in possession of no unproblematic criteria for counting these words as being either two or four. The criteria of the count that gives now seems even more plausible: to count one word each time it is separated by a blank space from the word that follows it.

What remains is that other solutions that give other results are possible, thereby rendering undecidable, as we had wished, the correct count. Let us begin by remarking that these two prepositions occur in contexts that are both similar and decisive. But to conclude, we would like to present another clue, which was not sufficiently highlighted in The Number and the Siren, yet which also has the power to confirm the hypothesis we proposed. The most obvious confirmation of the procedure of the seizure of the count is thus present in the explanation the poem itself gives of the most profound meaning of its heritage: it bequeaths to us the possibility that nothing took place, by the final trembling of its supposed sum.

A man of flesh anointed by the nothing, a man who only just exists, and who, for all eternity, holds in his hand the destiny of poets on this vain earth. Hyperion is now expanding its language-base to include translations into French, German, Hungarian, Italian, Romanian, or Turkish and welcomes proposals for such. Hyperion is concerned with aesthetics, with the value of art and the ways in which it can be transformed and renewed.

We are looking for applied criticism — critical essays that are evaluative of specific artists and specific works of art. Write to us at info contramundum. Lui aussi doit parier. I, , t. II, Tel est en tout cas le pari de Quentin Meillassoux. Il avait trait au 12 selon Mitsou Ronat. Quentin Meillassoux y insiste : il aurait pu, tout aussi bien, ne pas trouver le code ; et, ne le trouvant que par hasard, il aurait pu, tout aussi bien, ne pas le comprendre.

Page X. He too must gamble. Additionally, the figure [chiffre] of the dice is invested with a particular symbolism in the representations of the Passion: with the death of the Man-God, his tunic is pulled at random — a sign of humanity abandoned to Nothingness —, also a sign of a 1. I, ; T. TN: All translations are my own. The hypothesis of encoded numbers in the poem is not new, as Meillassoux reminds us.

The Number therefore remained constitutive of the idea of Poetry; but, with the deconstruction of this idea, Number was also found to be implicated in the poem in a different way, disseminated in it, according to a new entanglement of the rule of numbers in the free play of language. For the numbering of the pages each Page equals a double page , we follow the numbering of Meillassoux, who reproduces the poem at the end of his book. III, Livres, textes, entretiens.

After all, a code is a puerile thing, and the search for a key is a ridiculous thing. Is not such reasoning too hasty, however? Igitur, in effect, does not throw the dice. He lies down on the tomb of his ancestors, shakes the dice in his closed fist, but does not toss them. The resulting Number is unique, even if haunted by all of the other numbers that could have been cast. An introductory course.

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Bibliothèque mathématique personnelle - PDF

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