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sixes_and_sevens comments on Open thread, Dec. 8 - Dec. 15, 2014 - Less Wrong Discussion
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I might edit the OP. It's not about there being a right or wrong answer. The whole point of asking the question is to discriminate between "'what exactly is a number?' is a deep, nebulous, philosophical question we don't have a satisfactory answer for" and "'what exactly is a number?' is a trivial question I simply haven't asked myself yet".
It's also not necessarily about posing awkward questions to other people, but about mechanically assembling these questions for any given topic, which we can then ask ourselves.
A number is anything that acts numbery under certain operations.
Integers are very numbery. Reals are pretty numbery. Polynomials and matrices are still pretty numbery. Strings and graphs are somewhat less numbery. Rubber chickens are scarcely numbery at all.
"What is a mathematical operation?" is maybe a better question.
Inspired by this, I am going to come up with an amazing new philosophical theory of truth based on Perl.