[FOM] Regarding Terminology

Harvey Friedman hmflogic at gmail.com
Sat Dec 1 19:26:04 EST 2012

I use "negated tautology" for a proposition formula false under all
assignments. Of course

A and not A

is not, strictly speaking, a negated tautology But it is
propositionally equivalent to such, and presumably for many practical
situations, "negated tautology" will work just fine.

Harvey Friedman

On Thu, Nov 29, 2012 at 1:12 PM,  <T.Forster at dpmms.cam.ac.uk> wrote:
> 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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