Read e-book online Badiou's Being and Event and the Mathematics of Set Theory PDF

By Burhanuddin Baki

ISBN-10: 1472524454

ISBN-13: 9781472524454

Alain Badiou's Being and Event maintains to affect philosophical investigations into the query of Being. through exploring the imperative function set conception performs during this influential paintings, Burhanuddin Baki offers the 1st prolonged learn of Badiou's use of arithmetic in Being and Event.

Adopting a transparent, basic technique, Baki gathers jointly and explains the technical information of the suitable high-level arithmetic in Being and occasion. He examines Badiou's philosophical framework in shut aspect, displaying precisely the way it is 'conditioned' via the technical arithmetic. Clarifying the appropriate information of Badiou's arithmetic, Baki appears on the 4 middle subject matters Badiou employs from set idea: the formal axiomatic procedure of ZFC; cardinal and ordinal numbers; Kurt Gödel's idea of constructability; and Cohen's means of forcing. Baki then rebuilds Badiou's philosophical meditations on the subject of their conditioning by means of the math, paying specific recognition to Cohen's forcing, which informs Badiou's research of the development.

Providing invaluable insights into Badiou's philosophy of arithmetic, Badiou's Being and occasion and the math of Set Theory bargains an outstanding observation and a brand new studying of Badiou's most complicated and significant work.

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Additional resources for Badiou's Being and Event and the Mathematics of Set Theory

Example text

The most famous counter-example to the proposition that every class is a set was given by Bertrand Russell when he had φ correspond to the self-referential predicate of ‘not being a member of oneself ’. The class X satisfies this predicate φ if X ∉ X. e. {x: x ≠ Alain Badiou}. Such a class includes everything, except for Alain Badiou. Since the class itself is obviously not Alain Badiou, it is therefore a member of itself. Now consider something a little bit more complex, the class of all ordinary sets: C = {X : X ∉ X}.

E. if at least one of x or y belong to a. 3. e. if both x and y belong to a. 4. P → Q is true if, when P is true, then Q is true. e. it is only false when x belongs to a but y does not. 5. e. if either both x and y belong to a or both x and y do not belong to a. Special care must be taken in explaining the symbols ‘∀’ and ‘∃’, which corres­ pond to the universal and existential quantifiers, respectively. Given some 42 Badiou’s Being and Event and the Mathematics of Set Theory proposition S(x) depending on the free variable x, the statement ∀x: S(x) says that the proposition is always true for all possibilities of x from the individuals that make the domain of discourse, while ∃x: S(x) says that there exists at least one possibility for x, one existing individual from the domain, where it is true.

When we say that a set fundamentally disregards order, this does not mean that we cannot somehow codify this order into the set, that we cannot make that order ‘count’ somehow in the language of specifying sets. An ordered set2 can be constructed in principle, but we omit here how it is done. For the moment, if we want to include order into the set, we simply replace the curly brackets with round brackets (some conventions use angular brackets instead). So one ordered analogue to the aforementioned set T would be: (Alain Badiou, Friedrich Hölderlin, ‘situation’, 35, May 1968).

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Badiou's Being and Event and the Mathematics of Set Theory by Burhanuddin Baki

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