Four Accesses to the Infinite (Badiou)

Translation of: Alain Badiou, The Immanence of Truths, Section III, Chapter c11, parts 1-4 (out of 12)

Four accesses to the infinite

1. Objections concerning the set-theoretical concept of the infinite

I demonstrated previously that the ontology of every oppressive figure organizes itself based on an imperative of finitude. Now I launch into the counterpart of this negative observation: the aim is to establish that wherever human action liberates itself from the order that constraints it, it is a matter of an encounter with the infinite, in the figure of a work.

It is only natural to begin with what in any case we know about the infinite, a knowledge constitutive of mathematical thinking. This initial course will still be very approximative for two reasons. First, the dialectic finite/infinite is at the heart of the system [dispositif] of this entire book, and we will only see this clearly little by little. Second, the mathematical theory of the infinite is not only complex, but it is still today in the midst of evoltion.

For now it is only a matter of considering “in broad strokes” the challenge we are faced with, in its massiveness.

Objections concerning the infinite such as this book presents it – in the framework of set theory, the concept and the adequate formalisms – appear in two principle forms, instances of which we detailed in the first two sections but which deserve to be recalled here. Continue reading

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Bi-furcations of whatever sort – nature versus spirit, mind versus body, ultimate reality versus appearance, etc. – have their usage at the level of entrance into metaphysical ‘issues’ and as heuristics making it easier to investigate, discuss, and perhaps solve them, alone and together. Complication and nuance of the bifurcations, perhaps leading to zones of non-duality, come after contemplation of the basic dilemma, whereupon the either/or nature of the duality can be superseded.

Given how widespread these bi-furcation dilemmas are in human history, it is unlikely that they are just fabrications of this or that philosopher who happened to get stumped. When they receive canonical definition, for example by folks like Descartes and the mind-body problem, the drawback is that thought can then suffer from adherence to that definition as though it were an authority. Mental effort is then exerted to comprehend the canonical definition, rather than employing it for the sake of inner metaphysical discovery. Such definitions can provide coordinates to help orient in the conceptual territory, and so they can allow progress toward refutation, reformulation, and perhaps resolution of the dilemma, but only if enough time and contemplation is taken for them to become more than ‘intellectual’ exercises driven by the desire to be ‘right’.

In my experience, it is best to gain exposure to as many definitions of the dilemma as possible, both the canonical and the marginal, the obsessive and the dismissive, and to receive them all without bias, valuing whatever is unique about each model. That way contemplation avoids sticking to one specific model or definition and does not fall into the error of thinking that one specific model or conclusion – a merely external, discursive solution – will somehow resolve the issue. Rather, exposure to a multiplicity of models allows one to be experientially open to a creative transformation of the problem itself and especially its articulation. This can only happen once one feels in some way unbound from the dilemma as stated, once the original coordinates are well underway to reconfiguration. In other words, once a sort of non-discursive ‘resolution’ has been perceived or understood, through extended contemplation, thought can then freely enter back into the discourse without feeling detrimentally entangled by its many historical and conceptual referents. This is perhaps a resolution in ‘simplicity’; but it is also the grounding of thought in the non-temporal actuality that motivates the problem to begin with and which has been occluded by its contingent, imperfect articulation.

From such simplicity and grounding, a greater degree of conceptual and expressive innovation can take place; and one can do so playfully, perspicaciously, ‘indifferently’. This is not to detract from the importance of the operation, however, since those who earnestly undertake it often become innovators in the field, having transcended it enough towards actuality that they are able to play upon it differently and perhaps even rewrite the rules. It goes without saying that this ‘rewrite’ and its results are ever an invitation to future participants in the field to exert themselves similarly in the direction of inner metaphysical experience and simplicity in expressive freedom.

The emotion to such a procedure is, manifestly, joy: the pleasure of participating in the actuality of God. Such is not belabored by merely rationalist distinctions, by canonical grinding of gears, or by any need to reference tradition or gain authority from it. For now the articulation of the dilemma has gained the boldness to stand in the bifurcation without angst as a catalyst for novel future investigations. Its intention now derives not from the ‘imposition of view’, but from love: love of the contemplation and love for those who are still fruitfully animated by the bi-furcation dilemmas, those who have realized that these are necessary for the progression of speculative thought. This is the stance of a ‘loving circumstantialist’ who addresses each individual context of utterance with care, tied to none of them except to the extent that it is exactly those contexts which are to be worked with creatively, for the sake of being metaphysically unbound.

See more:
Descent to Higher Ground
Nihilism and the Absolute
Run-on Sentence

doig, peter - blotter-1993

Peter Doig, Blotter, 1993

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Agamben’s Philosophy

One of key statements of philosophy last century came through the mouth of Heidegger (though it was obviously not merely his statement): “Higher than actuality stands possibility.” The statement overturns a long-standing bias that favors of ‘what is there’, ‘what is actual’, what is present, for the sake of ‘the possible’, what ‘may be’. This bias is very much in line with common sense: generally, we value what is really there over what only might be there; what we can put our hands on over what seems mere thought and imagination. The blueprint is not as accomplished, not as real, as the completed building, etc. To say that possibility [Möglichkeit] stands higher than actuality [Wirklichkeit] marks a watershed moment where this bias – and the entire world based on it – enters into a crisis.

Another key statement of modern thought came through the mouth of Rimbaud: “Je est un autre,” I is an other. I view this as the motto for all the efforts to rethink individuality, subjectivity, selfhood, and so on, that have since been undertaken. It stands for how the self is not self-sufficient, not a being closed in on itself, not a substance; how it is in relation, at risk, constituted by forces beyond its conscious power; how perhaps the individual “is not” at all, is possibility, potentiality (and so on).

So, Agamben comes in highly situated within a philosophical and poetic tradition that he is very ambitiously trying to respond to in the entirety of its concerns. Among others, two of the primary axes of concern are “possibility is higher than actuality” and “the I is other” (taken to the extreme of “autrement qu’etre”). These two great over-turning and philosophically ‘revolutionary’ statements force a crisis to occur (as much as they register a crisis long prepared) in Western thought/society. Agamben’s big ambition is to bring these crises to bear on all the fundamental areas of Western thought – ontology, law, judgment, art, language, politics. With an eye to many others who also tried to deal with these consequences, he brings many threads together into a weave that is “uniquely his own.” I can only highly a few concepts: Continue reading

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