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I've been doing some introductory reading on the philosophy of mathematics in an attempt to find well expressed views similar to the following. I haven't been successful.

The view is that mathematical objects exist and the mathematicians are able to perceive their existence in some way. They then construct languages (axiom systems etc.) in an attempt to describe these objects and their properties. They can never know if their descriptions are accurate, but if several mathematicians independently make distinct languages for describing the same thing and they seem to express similar things, then at least some confidence in accuracy can be obtained.

It's certainly a kind of Platonism, but I haven't seen any "professional" treatment of a view that sees mathematics in this way. Any references would be appreciated. Thanks.

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James R. Brown is a philosopher at the University of Toronto who tends towards Platonism. His works are easy to read; you might want to check out his books "Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures" (1999/2008) and "Platonism, Naturalism, and Mathematical Knowledge" (2012).

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Check out Penrose's three worlds diagram, it appears in his book "shadows of the mind" if I recall correctly.

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