Re: What isn't a tautology?

On 18 Jul 2005 17:13:49 -0700, Michael De <mikejde@xxxxxxxxx> said:
>
>
> Chris Menzel wrote:
>> On 18 Jul 2005 15:11:54 -0700, Michael De <mikejde@xxxxxxxxx> said:
>> >> Unless you redefine "valid", in which case you are just changing the
>> >> subject, the schema in question is invalid.
>> >
>> > Nobody denied that. But a proviso can still make an invalid schema
>> > valid without changing the definition of 'valid' (unless you call
>> > allowing the empty domain in interpretations a redefinition of
>> > validity).
>>
>> It is most definitely a redefinition of validity. You have altered the
>> class of models relative to which validity is defined and, even more to
>> the point, you've defined an *extensionally* different notion.
>>
>> I take it this is not the "proviso" you had in mind for rendering the
>> schema in question valid, though.
>
> Well, the definition of validity is the same insofar as it is stated,
> it's the definition of an interpretation that has changed.

If validity is defined in terms of the notion of an interpretation, and
the definition of "interpretation" has changed, the definition of
validity has changed, regardless of whether you are using the same
words.

> Anyway, I was not assuming specifically the definition of 'validity'
> for "standard" FOL--I was being vague about the underlying logic.

Well, ok.

.

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