this is where Penrose disagrees: Penrose believes that the mind and by extension the universe are implemented in non constructive mathematics. (that should imply that he thinks that QM is the wrong foundation for physics, since it is a [slightly hyper]computational model)
It seems to me that there is an ideal way to do mathematics (I know that this is a crass oversimplification), and the customs of mathematicians are not cultural but pragmatic approximations of this. Deforming them into an idiosyncratic culture perverts mathematics.
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(I think that a set of policies and behaviors only counts as a culture if it involves a choice, and is not imposed by the rules of the game one has to play.)
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There are a few choices for mathematicians: 1. Which logic to use for their metalogic 2. What axioms should be made explicit: Most papers don't declare "we now use modus ponens" 3. What level of detail to present their arguments: what is acceptable as a pragmatic approximation
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