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Tractatus Logico-Philosophicus by Ludwig Wittgenstein + comments by Maarten Maartensz |
3.04 If a thought were correct a priori, it would be a thought whose possibility ensured its truth. I'd say that if a thought is correct "a priori", i.e. without needing to do an experiment or making an observation of how things are, this is so because it is interpreted by a system of interpretations that makes it true in any case. But this has nothing to do with "possibility ensured its truth". Now there are various
senses of "a priori", and perhaps W. was thinking of a Kantian conception - but
he doesn't say. What I am thinking of is "a priori" in the following sense: If
the rules of valuation for propositional logic are standard, and involve rules
for any propositions p and q like the following three (1) v(p)=1 or v(p)=0 (2) v(pVq)=1 iff v(p)=1
or v(q)=1 (3) v(~p)=1-v(p), then it follows, indeed again by logic (that here
may be called "metalogic" or "the logic of natural language") that v(pV~p)=1 in
any case, which accordingly is a priori true, regardless of whether p or ~p is
true, in any case - given the conventional rules of valuation. |