[FOM] Terminology

T.Forster at dpmms.cam.ac.uk T.Forster at dpmms.cam.ac.uk
Thu Nov 29 13:12:58 EST 2012

I've also heard `self-contradiction'..

On Nov 29 2012, Aatu Koskensilta wrote:

>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.

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