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. Please explain. Brent Meeker 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? > > John > > Regards
