Combining Texts

Ideas for 'Freedom to Act', 'Briefings on Existence' and 'Meno'

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2 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST

12337	There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou]
	Full Idea: 'Transitivity' signifies that all of the elements of the set are also parts of the set. If you have α∈Β, you also have α⊆Β. This correlation of membership and inclusion gives a stability which is the sets' natural being.
	From: Alain Badiou (Briefings on Existence [1998], 11)

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

12321	The axiom of choice must accept an indeterminate, indefinable, unconstructible set [Badiou]
	Full Idea: The axiom of choice actually amounts to admitting an absolutely indeterminate infinite set whose existence is asserted albeit remaining linguistically indefinable. On the other hand, as a process, it is unconstructible.
	From: Alain Badiou (Briefings on Existence [1998], 2)
	A reaction: If only constructible sets are admitted (see 'V = L') then there is a contradiction.