Copyright (C) 2019 Dennis Joe Darland
There was a time after the big bang, before there was any life and therefore before there were any minds or sentences. However there were facts then, which science is trying to discover more about. I suppose theists could argue against this.
Logic deals with facts, not wff’s, or sentences. Wff’s or sentences would need to be arbitrarily large as they can be arbitrarily compounded. Wff’s and sentences take up physical space. But the universe is physically finite. Facts do not take up any physical space. We use wff’s or sentences to talk about facts. But there are facts for which there are no wff’s or sentences.
It may be that logic itself is extensional, but that we only can know it with intensions. Considered as extensions all classes are equal. However, due to laws of nature, identifying some classes has survival value for humans. Therefore humans developed predicates in human language for only some classes. Those predicates allow us to identify regularities which help in our survival. The predicates developed as a result of regularities. Reasoning by induction is also a result of these regularities, although it is fallible. We identify regularities in terms of these (intensional) predicates. The actual regularities may be very complex mathematical equations (which we may eventually be able to discover), but there are fuzzy approximate rules humans discover that can be stated in terms of these (intensional) predicates. This seems to imply some difference in status of classes. If there were only extensional predicates it would seem impossible to learn them. Any class which was a superclass of how a predicate had been used so far, would be as good as any other for continuing the use of that predicate. (This is related to some of Kripke’s writing on Wittgenstein.) But logically all classes seem equal. However, by the Church-Turing Thesis, there are classes, for which there is no predicate.
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