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I don't claim that this makes it inconsistent. Just that it admits meaningless concepts. You can attribute this, if you like, to the fact that I am a computer
by andrewla 8y ago
I don't claim that this makes it inconsistent. Just that it admits meaningless concepts. You can attribute this, if you like, to the fact that I am a computer scientist, and see things through that lens.
If you give me a statement saying "For two sets, A and B, is 'A union intersection B empty", the statement would not be well-formed, so you could just say that it is not a valid proposition without asserting anything about its truthiness. Similarly, a good foundation of mathematics should be able to reject a statement like "2 is a member of 4" as poorly formed, and make no statement about its truthiness.
I guess what I'm saying is that set theory is a bad basis for mathematics and should just be regarded as an interesting relic from previous attempts to formalize mathematics so that we can move on to more powerful systems.