I guess I don't understand your question. First order predicate logic applies to
propostions (or declarative sentences) which have values of 'true' and 'false'. The
rules of logical inference propagate 'true'. Now I imagine a different
universe...what elements of this differen universe does logic apply to? It applies to
propositions. Am I to imagine that 'propositions' are something different in this
different universe. If so, then I'm at a loss...I don't know what to imagine!?
Of course there are different logics that have been invented to apply to
sentences that are not simple declarative. But I don't see what they have to
do with other universes.
On 20-Sep-00, John Bailey wrote:
> Brent Meeker wrote:
>> Logic and number theory and in fact any mathematical theory are independent
>> of physical reality since they are simply sets of axioms and their
>> consequences according to some rule of inference.
>> Euclidean geometry didn't change in 1823; only the idea that it necessarily
>> applied to the physical world changed.
> That's exactly the point of departure. Before 1823 no one realized that there
> was a question of the applicability. After non-Euclidean geometry came to be
> recognized, the question arose. Paralleling that episode in the maturing of
> mind, I am asking whether it is conceivable that variations of logic could
> apply within different universes.
>> There are many physical entities that number theory does not apply to. It's
>> just that the the non-applicability is so obvious that one doesn't usually
>> think of number theory applying. For an example that sometimes trips up 4th
>> graders; consider that there are two school clubs, one with 15 members and
>> one with 20 members. They have picnic together. How many are at the picnic?
> This is sophistry. The question is, to the same logic which we would all
> agree applies to basic elements, is it conceivable that there are universes
> in which this logic, mapped to the same elements behaves differently?