badiou, godel, logic, mathematics, metamathematics, ontology

Badiou on Logic

Stellar cartographies has translated two different selections of course notes from Badiou’s lectures circa 1980-82 here and here. This translation is short, but extremely concise, so there’s a lot of material to absorb. In particular, the notes help to explain Godel’s achievement and his theorem and offers good insight into Badiou’s own mathematico-ontological project. Definitely check it out for a quick read on a slightly neglected aspect of this philosopher’s expanding corpus. Also be sure to check out his other posts on Deleuze/Meinong, Heidegger/Lucretius, and an extremely hilarious link to Simon Critchley’s musical side project.

being, event, face, gift, infinity, lacan, language, levinas, logic, machine, silence, turbulence, violence


Responsibility is what first enables one to catch sight of and conceive of value.
Levinas, Otherwise Than Being 123

Beyond the question of being and non-being, language is not the event — but rather a process of assembling unformed and unspecified elements, an abstract machinics which imagines new forms for itself by correlating the various distinct orders of reality with a plane of consistency in which a unified vision becomes possible — in short uncovering the infinite possibilities of the event. But this apparition of the event in its infinity would be only terror, the dark depth in which all mixtures are possible — and nothing is outlawed — were it not for the ambiguity of silence, the “not-yet” which the event, the “given” or gift, makes possible, and which makes possible the infinite time of cohumanity.

In speaking, reality opens itself up to an order without signification or concept, lost neither in the depths or heights but in the very shape of the world, the surface itself, a topological mode or order of being issuing neither in sound or light but in an idea given me by the other, the gift of language. In expression being can become free. Language is the discovery not only of novelty but justice itself; the enjoyment of discovery is essentially social. The event is not revelation but a secret apology, a map of the vortex. Turbulence is lucidity.

Black holes are everywhere, and this prohibited prohibition permits everything: the torsion of language disarticulates the tension of the soul. Beyond the face there is a paradoxical and two-sided barrier, an apparition which interrupts the symbolic order of discourse, as though by a lateral or diagonal movement between the signified and the non-signified. By an astounding finesse, speech uncovers the world as a lesson or donation.

Debt and faith are born simultaneously. Language is justice — a gift — only when it sheds its anonymity to become universal, not by inventing a world-beyond-the-world, but by reconciling us to one another. It calls us to hear a there-is rustling behind the void.

Hence the notion of event correlates at least three distinct orders of relationship between possibilities: a relative-absolute conjuncture uniting singular events and possible worlds; an absolute disjuncture prohibiting certain events from certain worlds; a trans-evental function sweeping up worlds and events.

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continuity, diachrony, evolution, institution, language, linearity, linguistics, logic, sign, synchrony, time

The Language Mechanism: Notes on de Saussure

A language thus has this curious and striking feature. It has no immediately perceptible entities. And yet one cannot doubt that they exist, or that the interplay of these units is what constitutes linguistic structure. That is undoubtedly a characteristic which distinguishes languages from all other semiological institutions.

Ferdinand de Saussure (Course in General Linguistics, 105)

After having investigated the physiological mechanisms of speech, Saussure turns to consider the nature of linguistic signs. In his analysis we find a clear formulation of the first principle of his “new” linguistics, namely that the sign is arbitrary.

At first glance this statement seems to suggest an argument for an evolutionary linguistics, but Saussure draws our attention to the fact that “this very same factor tends to protect a language from any attempt to change it.” (73) As a system of arbitrary signs, there is no rational basis for language; paradoxically this makes language itself “inaccessible” to reason.

There is no logical reason we should prefer “sister” over “hermana,” and thus no grounds for argument about change. The great number of signs necessary to constitute a language (and the complex character of the linguistic system itself) also contribute to the force of collective inertia resisting linguistic innovation:

“At any time a language belongs to all its users. It is a facility unreservedly available throughout a whole community… [it] is something in which everyone participates all the time, and that is why it is constantly open to the influence of all. This key fact is by itself sufficient explain why a linguistic revolution is impossible.” (74)

A community naturally exerts a restrictive, conservative influence upon a language. Nonetheless, the passage of time also allows linguistic signs to be changed with “some rapidity” — hence both variability (diachrony) and invariability (synchrony) are characteristic of the linguistic sign. These two characteristics are “intimately connected” — a sign is only subject to change because it “continues through time.”
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banquet, communication, epistemology, fractal, history, humanities, information, interruption, logic, matter, michel serres, narcissism, ontology, parasite, physics, power, relation, Science / Mathematics / Technology, Serres, symmetry, time, topology, turbulence

Science and Parasites: Michel Serres and the Unification of Human and Natural Sciences

Theorem: the history of science obeys the law of diminishing returns. The first attack on the narcissism of science…

Second: if we examine the set made of the problem and of the actions that transform it, there is no doubt that it is, at the beginning, more complex than the thing itself or the process. Clearer perhaps, yet more complicated. The question can then be reexamined in order to try to illuminate this new complexity and maybe, to transform it. Thus we form a set: the chain seems unending. The strategies of intervention, the interruption of the process or of the thing, observation that seeks to clarify, photon bombardment, the inseparable association of the knowers and the known–all make complexity increase, the price of which increases astronomically. A new obscurity accumulates in unexpected locations, spots that had tended towards clarity; we want to dislodge it but can only do so at ever-increasing prices and at the price of a new obscurity, blacker yet, with a deeper, darker shadow. Chase the parasite–he comes galloping back, accompanied, just like the demons of an exorcism, with a thousand like him, but more ferocious, hungrier, all bellowing, roaring, clamoring.

Have I described the elementary link of a system of knowledge or its pathology? I do not know. Anyway, it makes work, gives sustenance. One parasite drives out another. The second attack on the narcissism of scientists. The shadow brought by knowledge increases by one order of magnitude at every reflection.

Can we henceforth do without an epistemology of the parasite?

Michel Serres, The Parasite 17

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difference, flux, God, image, imaginary, individuation, insanity, logic, metaphysics, symmetry, void


Wild Magic of the Unbeliever (Dave Makin)

How much of our lives are caught up, inextricably, with the imaginary? A dangerous question only because it is silly, and stupid; why? Because it’s answer is both simple and impossible. For we know: none of it is imaginary, it is all real; and we also know: nothing is real, all of it is imaginary. A dangerous idea, a poisonous idea: there is contradiction at the origin. An unrest, a turbulence at the heart of being — not smooth immobility. There is origin only through explosion, individuation, hyperdifferentiation.
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