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If you have to appeal to Platonism to make the "realness" of a concept less controversial, your claim will not be strong, as Platonism itself is controversial,
by bordercases 6y ago
If you have to appeal to Platonism to make the "realness" of a concept less controversial, your claim will not be strong, as Platonism itself is controversial, and by definition supposes the existence of things which cannot be perceived. This makes it more difficult to argue for the realness of a concept, not less, since any means of "observing" the existence of that concept must be indirect to a Platonist.
It is also inconsistent to claim that mathematics is a social construction, while agreeing with these Platonic mathematicians enough to use their view as evidence.
- myWindoonn 6y agoOkay, but like, every logic has a corresponding category, right? Please focus on the maths and stop struggling; you're only making things harder for yourself.
- bordercases 6y agoThat doesn't contradict the previous notion that category theory is "empty" or adds nothing to the original understanding of the logic. At best, you've just changed how you describe precisely the same elements of the system. And once you start using categories to talk about categories you lose concrete referents entirely, describing description. If the point was modelling linguistic syllogisms, or accounting for the stock of apples in your warehouse, why bother? These tasks are better served by analyzing the objects in question, rather than you, the describer. > Please focus on the maths and stop struggling; you're only making things harder for yourself. This is condescending – I could say the same thing and ask you to "stop struggling with philosophy". But neither of us should.