I think there may be a terminological dispute. Part of the most recent sequence discusses the distinction between true and valid.
In brief, the colloquial word “true” is overloaded. Defining true as “corresponds with reality” we recognize that mathematics and first order logic are not true in that sense. Instead, we should use the word valid.
Under that definition, tautologies are never true, they are only valid. Essentially, resurrecting logical positivism. I think the resurrection fails, so I’m unimpressed. But usage of that terminology is the best steelman I can see for Petruchio’s post.
But usage of that terminology is the best steelman I can see for Petruchio’s post.
Fair enough. I also don’t think this use of ‘valid’ is a good idea (how do we distinguish between sound mathematical arguments and, at the extreme, arguments that validly take contradictions for premises?). Also, what happened to dear old Tarski?
I guess the answer to my original question is ‘yes, “tautology” is being used in a non-standard way’.
I think there may be a terminological dispute. Part of the most recent sequence discusses the distinction between true and valid.
In brief, the colloquial word “true” is overloaded. Defining true as “corresponds with reality” we recognize that mathematics and first order logic are not true in that sense. Instead, we should use the word valid.
Under that definition, tautologies are never true, they are only valid. Essentially, resurrecting logical positivism. I think the resurrection fails, so I’m unimpressed. But usage of that terminology is the best steelman I can see for Petruchio’s post.
Fair enough. I also don’t think this use of ‘valid’ is a good idea (how do we distinguish between sound mathematical arguments and, at the extreme, arguments that validly take contradictions for premises?). Also, what happened to dear old Tarski?
I guess the answer to my original question is ‘yes, “tautology” is being used in a non-standard way’.