Combining Texts

Ideas for 'fragments/reports', 'Philosophy of Logic' and 'Which Logic is the Right Logic?'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

---

2 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set

18958	In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam]
	Full Idea: In the theory of types, 'x ∈ y' is well defined only if x and y are of the appropriate type, where individuals count as the zero type, sets of individuals as type one, sets of sets of individuals as type two.
	From: Hilary Putnam (Philosophy of Logic [1971], Ch.6)

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

10775	The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp]
	Full Idea: The main objection to the axiom of choice was that it had to be given by some law or definition, but since sets are arbitrary this seems irrelevant. Formalists consider it meaningless, but set-theorists consider it as true, and practically obvious.
	From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3)