Copyright (C) 2019 Dennis Joe Darland
I’ve been rereading some philosophy of logic. I have become convinced that it is often useful to assume extensionality. I suspect a lot of results depend on it. However, I think it would be clearer to just speak of classes or sets & not use predicates as extensional. I think (for purposes such as mine), it is useful to use predicates as intensional. Also, in Principia Mathematica, Russell showed how to contextually eliminate talk of [extensional] classes in terms of [intensional] predicates [propositional functions]. But this is only possible for cases where the sentences are describable. There are way too many classes [sets]. I think we must take classes [sets] as existing independently of language. But we must also take predicates as real and intensional in our actual world. There is no necessity for intensions to exist, but they are necessary in a world with mind and language. There will be many extensions for which there is no intension. Also two intensions may differ but still correspond to the same extension. In a world without intensions, there still might be universals – or natural kinds – in which there might be natural laws. Even so, I think it likely there would be more classes [sets] than universals – or natural kinds.
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