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Set theory is a bridge between logic, which is traditionally considered a branch of philosophy, and mathematics. Thanks largely to the philosopher/mathematician/logician Bertrand Russell and his mentor, Alfred Whitehead, the idea that all mathematics could be reduced to logic was at one point in time a major topic of debate in philosophy, until Kurt Godel ...


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I think that the relevance of logic for philosophy is high if you are interested mainly in the so-called analytic philosophy (started with Frege and Russell). For me is difficult to think to the relevance of set theory for philosophy outside the branch of philosophy of mathematics. Of course, if you are interested into ontology or philosophy of language ...


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After the reconstruction of foundations of mathematics in 20 century, i.e. getting rid of the famous paradoxes (like Russell's paradox), the modern mathematics is based on the belief that no other paradoxes will appear again. Despite numerous efforts, logicians did not manage to prove that the systems of axioms of modern set theories are consistent (and at ...


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Yes and no (stack exchange is pretty horrible for philosophy eh?) Badiou is affirming that mathematics = ontology. The status of ontology (being or beings) is hereby sutured to the procedure of mathematics. While we can debate whether or not this is possible or if we like it, in Badiou's philosophy, the transcendental is divorced from its Kantian ...


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Regarding the statement Mathematics is rife with contradictions Most people would say that this is wrong. Certainly: this is not known to be true. Indeed, if you could show that this is true, you'd become world famous. For a decent first discussion of possible inconsistency "of mathematics" -- rather: one of its widely used foundations -- , see this ...


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Welcome, Jacob. The following extract from Christopher Norris might throw some light on where the foursome derive from and how they do not exclude philosophy. ... one can best summarize by saying that any such [full] treatment would involve consideration of the central role played in his thinking by four such subject-areas. These are mathematics (in ...


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It is the other way around. Falsification is just a statistical form of proof by contradiction. In proof by contradiction, you start off by assuming that a premise p is true. Then you show that such an assumption leads to a conclusion q, which has already been shown to be false. So long as we assume that our axiomatic system is logically consistent, this ...


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Of course it doesn't apply. It only applies to natural science. And even there, it doesn't apply everywhere. In a strict sense it applies only where you can conduct experiments in a controlled environment, i.e., test hypotheses. This, IMHO, excludes, for example, the theory of evolution. While this theory does a great job of explaining the development of ...


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Most of these answers seem to be pointing towards "continental" philosophers who have contributed to "analytic" discussions. Since I'm more familiar with the analytic segment, I'll point towards a philosopher or two who is analytically trained but does research on "continental" figures. First, there is Kris McDaniel, a younger philosopher at Syracuse ...


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An event for Badiou: has no objective or verifiable content. Its 'happening' cannot be proved, only affirmed and proclaimed. Event, subject, and truth are thus all aspects of a single process of affirmation: a truth comes into being through those subjects who maintain a resilient fidelity to the consequences of an event that took place in a situation but ...


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I might well be wrong, but what I understand, Badiou sees mathematics as our way of getting at things-in-themselves, as opposed to philosophy and the natural sciences, which have to deal with everything mediated by sense perception, with all the epistemic obstacles inherent to that (things-for-us). I'd also point out that that statement does not sum up ...


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It might be worth going back to when the term Event was first introduced by Derrida in his paper Structure, Sign, and Play in the Discourse of the Human Sciences presented at a conference in the US to investigate & ratify the idea of Structuralism, but was soon recognised as the beginning of post-structuralism primarily due to Derridas paper. He writes: ...


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Maybe that for Heidegger poetry is the peak of language. That is: poetry can say something other forms of language (for example theoretical statements) cannot. For example, it can designate, circumscribe, reveal, speak of what is not obvious or in plain view.


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although often called "The Language of Science", Mathematics is not the same as Science (or, more specifically, Natural Science). Mathematics is a specific application of philosophy and logic to the concept of quantity. whereas in Science that quantity of "stuff", whatever that stuff is, is salient, the techniques of mathematics is necessary to understand ...


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An important point to make is that, for a long time Mathematics was largely considered synonymous with Geometry--similar to how, today, there is a sense that Mathematics is essentially Algebra. Of course, professionals would deny this, but among the public there is certainly this sense; and among professionals, there is a feeling that, if a system doesn't ...


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About the question : Given this being said by one of the past masters of the subject [Paul Cohen], why is it taken by many people that a formalisation of logic has been fully achieved? I think that is not a "good practice" in science to ask about "fully completed" ... solutions, theories, and so on. History of science (mathematics included) shows us ...


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I really have no idea about Badiou, but I can say what I make of it, perhaps it will inspire someone to do better than me. There are some possible relationships that spring to mind. Music as a "rhetorical device". It can be to set a mood and provide hints as to the intent of a communication. A very direct form of communication. The converse of the above, ...


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I've tried - he's difficult; and I find his mathematical orientation obfuscatiry; still his prefaces read well; and someone said, I can't now recall who; that most of philosophy is reading prefaces... I'd suggest that it, in part, derives from what Unger calls the form of the encounter in (Modernist) literature; and what Badiou might call an event; it is a ...


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It seems that Badiou regarded religion as dogma and, as such, antithetical to philosophy. He took religion to be antithetical to "events", in his terminology, that is to truth. Therefore he found no place for religion among the four conditions of philosophy. Here is a relevant excerpt from a review of an interview with Badiou. It relates Badiou's disregard ...


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for Lacan, the foundation of truth-for-the-subject is the impossibility of unmediated encounter with the Real, whereas for Badiou, the foundation of truth-for-the-subject is its process of transcending its own limitations through fidelity to the "Event", which is some kind of an episode of unmediated encounter with the Real - for Lacan, there is no more ...


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From the perspective of these two philosophers there's not a debate about whether set theory or differential calculus are better, more important, more appropriate or anything in general terms. The discussion framing the book mentioned by DeLanda revolves around metaphysics and the specific claim made by Badiou that Set Theory was sufficient to found what ...


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The precise definition given for the Event evolves from Being & Event up to Logic of Worlds. So depending on what period one is reading of him, the presentation of this concept may be more or less complex. The most complete definition, given in Logic of Worlds presupposes different levels of "happenings" (my term not his) in a World (at a site): The ...


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Badiou wrote an essay specifically about music, which I'm afraid to say I can't locate at the moment. In it he argues that serial composition constitutes an event for music. As someone with a musical background, I completely disagree with this thesis, but there you go.


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You have the categories slightly wrong. Remove philosophy and add politics and you get Badiou's four truth procedures


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You may find this essay "Badiou and Music", written by a musician, helpful. The author emphasizes the revolutionary power of artistic creation, and indicates the autonomy of music from philosophical discourse (although philosophy may aid or inspire music): Let us recall foremost that for music properly speaking, philosophy has no use and can have no use: ...


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It's my understanding that Badiou uses ZFC explicitly to block the possibility of a transcendent center, or, in his words, the One. Whether ZFC then becomes the One or not is paradoxical, and points toward current debates among set theorists as to whether different models of set theory reduce to ZFC or rather to a multiverse of models.


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It's very hard for me to imagine how you could possibly theorize usefully about ontology or epistemology without testing your theories to see whether they say plausible things about mathematical entitities and our knowledge thereof. And it's very hard for me to imagine that you'd do a very good job of this unless you had a pretty clear understanding of the ...


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Set Theory is essential in the philosophy of mathematics -and perhaps Univalent foundations/category theory will be too one day when they are slightly more approachable to the untrained. The reason for this is that set theory offers an incredibly elegant and effective model for the whole of mathematics; in other words, all of mathematics, it seems, can be ...


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To some extent, the underlying problem here (and something that Cohen tacitly discusses in the linked paper) is one of Demarcation. Where does the mathematics of Set Theory end and the logic of mathematical truth begin? I really liked Cohen's description of the Lowenheim-Skolem theorem on p.1085 as the first nontrivial result of logic. To summarize, so ...


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