[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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