[FOM] Terminology
Aatu Koskensilta
Aatu.Koskensilta at uta.fi
Thu Nov 29 10:54:33 EST 2012
Quoting Alasdair Urquhart <urquhart at cs.toronto.edu>:
> In Section 15 of his Introduction to Mathematical
> Logic, Alonzo Church uses the word "contradiction"
> for a propositional formula that is false under
> all assignments to its variables. This terminology
> seems perfectly satisfactory to me.
In a wider context this terminology is not completely happy,
unfortunately. By a tautology is usually meant a sentence that is true
by virtue of its truth-functional structure, a substitution instance
of a validity in propositional logic. But there are contradictions
e.g. in first-order logic -- (x)(Ey)P(x,y) & (Ex)(y)~P(x,y) for
instance -- that are not (substitution instances of) logical
falsehoods in propositional logic, that are not false by virtue of
their truth-functional structure.
--
Aatu Koskensilta (aatu.koskensilta at uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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