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Ideas for 'Reportatio', 'Philosophy of Logic' and 'The iterative conception of Set'

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2 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL

9013	We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)' [Quine]
	Full Idea: The construction of 'alternation' (using 'or') is useful in practice, but superfluous in theory. It can be paraphrased using only negation and conjunction. We say that 'p or q' is paraphrased as 'not(not-p and not-q)'.
	From: Willard Quine (Philosophy of Logic [1970], Ch.2)
	A reaction: Quine treats 'not' and 'and' as the axiomatic logical connectives, and builds the others from those, presumably because that is the smallest number he could get it down to. I quite like it, because it seems to mesh with basic thought procedures.

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII

18192	Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy]
	Full Idea: For Boolos, the Replacement Axioms go beyond the iterative conception.
	From: report of George Boolos (The iterative conception of Set [1971]) by Penelope Maddy - Naturalism in Mathematics I.3