Single Idea 9013

[catalogued under 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL]

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)'.

Gist of Idea

We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)'

Source

Willard Quine (Philosophy of Logic [1970], Ch.2)

Book Reference

Quine,Willard: 'Philosophy of Logic' [Prentice-Hall 1970], p.24


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.