Re: Tautologies Then and Now

From: Chris Menzel (cmenzel_at_remove-this.tamu.edu)
Date: 12/06/04 

Date: 6 Dec 2004 20:57:29 GMT

On Mon, 06 Dec 2004 19:43:18 GMT, robert j. kolker <nowhere@nowhere.com> said:
> George Cox wrote:
>
>> For me (am I alone?) a tautology (in the logical sense) is a formula of
>> propositional calculus which is true for all values of the truth values
>> of its constituent atomic letters.
>
> Theorems of first order logic are also tautologies.

In pretty much any logic text in existence, a tautology is a sentence in
the language of propositional logic that is true regardless of the
assignment of truth values to its atomic components. "Tautology" used
in any other way, in the context of mathematical logic, is, well, wrong.
The more general notion that covers both propositional logic and
first-order (and higher-order) logic is that of a logical truth, i.e., a
sentence of a given language that is true in all interpretations of the
language. So, alternatively, a tautology is a logical truth of
propositional logic.

Chris Menzel

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