The Heideggers epistemic Ἀπορία and the Possibilities of its Dissolution by the Thinking of Alain Badiou

Heideggers philosophy has become unpopular, specially in Germany. But influence and the structure of his thought is more present than ever before. For a true critique of this omnipresent ideology, only a few thinkers can help us out – only a few took Heidegger serious and tried to confront him. In Alain Badiou there is an example of an innovative and modernist Marxist critique, that is, an dissolution of Heideggers Thought towards an Materialism in the tradition of Democrit, Epicur, Lukrez, Diderot, Holbach, Althusser.

I want to thank MaMuPhi and all the intersting people that came and took part on the discussion. The open questions of this presentation – concerning the mysterious nature of the philosophical or metaontological equation Ontology=Mathematics (O=M), the search for the „absolute“ ontology of sets V in the Immanence of truths will be answered here soon.

1. At minute 31: The reference to Heideggers reception of Karl Jaspers is to be found at page 398 und 399 (German Text) and states, that the „autentic cosciousness“ / „eigentliches Gewissen“ decides for the different „Weltanschauungen“ in Jaspers book on the Weltanschauunngen.
2. At minute 54 the question of the „intuitivity“ of continous and discrete infinities is in fact very intersting and would need a phenomenological investigation. Until know its just clear that the „discrete“ infinite like the totality of the natural numbers can not be intuitive in one instant.
3. At hour 1, minute 00: The „other extreme“ of an intuionist set theory that does not use V=L, the but also not the axiom of choice and foundation is avoided by Badiou by certain specific arguments of their „philosophical“ significance, but these are not very convincing and / or circular. Better ones are possible and can be given.
4. At hour 1, minute 46 I speak of „determinacy“ as a second aspect next to ontological maximility, but Badiou himselfs talks maybe of „immobility“ (in the english translation at page ?, in the french version at page 39) and means the same. Its clear, if we speak of mathematical universes, and our language is made for our physical world, its difficult to not use metaphors.
5. At hour 2:10 I speak of Badious critique of giving up the search of the „true“ set theory. This relates to page 63 f. of L’immanence des vérités. Badiou critizies other set theorists for giving up the idea of an „absolute“ ontology, based on different reasons: The indecidability of the hypothesis of the continuum, the axiom of choice and different logics seem to be arguments for that, but he tries to convince reader of his „platonist“ or „absolutist“ position.

After the presentation at MaMuPhi and the advice of Nicolas I read the interesting compilation: „THINKING THE INFINITE / PENSER L’INFINI“ of David Rabouin, Jana Ndiaye Berankova, Jelica Šumic Riha, https://fi2.zrc-sazu.si/en/publikacije/filozofski-vestnik-412 and can now relate to some of the articles there and the difficulties faced there:

1. First I would like to state that I defended always that „Ontology = Mathematics“, „Ontology = Set theory“ and „Ontology=ZFC“ and also their interelatedness is to understood with a lot of care; it is generally 1. a philosophical / metaontological statement, that has no significance for mathematicains but *in* philosophy it is a proper identity; 2. nonetheless, *in* mathematics are problems, concepts and proofs that point toward the thesis, like the dissolution of constructivity V=L that, as says also Berkanowa, the center of Badious work.
2. The problem of a plurality of ontologies and models, that Feltham is talking about in his article (and also Nicolas watching my presentation), is in fact a serious problem for Badiou. Badiou is opposed to a plurality of mathematics, as it is visible in his „Transitory Ontology“ in his attack on „aristotelian“ ways of thinking mathematics – in the English translation on page 104. In the Immanence of Truths he finds a proper method in that – in the metaprinciples and specially the maximalisation; similarly to Maddy in „Naturalism in Mathematics“. Another question au dela of Badiou is if this is actually a good idea for a ontology or foundation of mathematics – that would need more criteria; but it is certainly the „anti-heideggerian“ or „anti-postmodern“ aim of Badiou. There has to be a „true set theory“, that is „maximal“. Another, more interesting question is, if Badiou opens up the possibilites of different „object types“ and not just sets, but they would be in their possibilies also to be maximalized.
3. Ruda is right that Badiou searches an „absolute Ontology“ in Immanence of Truths; and its also the aim of alot of „platonic“ oriented set theorists to do so. If the continuum hypothesis will be necessarily refuted is not ultimately clear, but it seems *so far*, if we look at the Omega-Conjecture; but its not ultimately clear and it may be also otherwise.
4. Berankova Ndiay is right that all works of Badiou have the aim of surpassing constructivity with different methods; also *Logic of Worlds*, which shows indirectly boolean-valued model forcing and topos forcing. But is important to see, that this is in fact in the tradition of Althusser and his critique of idealism, as is the „atomist“, „democritian“ or „epicureist“ basic conviction of Badiou of which he talks about in his article in the compilation. But there is also a problem here: Badious utilisation of the maximalisation metaprinciple will bring him surely over V=L, but following that he would end up in the desert of choicless cardinals. So the main work of Badiou has to be „limited“ by a contrary force, or something else that lets him abandon V=L but keep also AC. This is a problem that Badiou doesn’t face sufficiently, even if I am inclined to think that I found a solution for that that Badiou didn’t mention.
5. Husseys article on the possibility of Ultimate-L is in fact one of the best articles there. But it has to be noted that the principle of maximalisation is strongly pointing towards the necessity to surpass Ultimate L, specially also with the „choiceless“ cardinals I am talking about; and here the trouble begins. To understand this, regard for example: Large Cardinals Beyond Choice from
Joan Bagaria, Peter Koellner, and W. Hugh Woodin, which I mentioned and used also during my presentation.

Extended by the small commentary on „Thinking the infinite“ on the 19. Mai 2026