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DanielLC comments on What are your contrarian views? - Less Wrong Discussion
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Just to clarify, you mean that there is a context in which "0 = 1" is a true statement, which is not tantamount to redefining "0", "=", or "1"? That is, in some alternate universe, "0 = 1" is consistent with the axioms of Peano arithmatic?
In most cases the numbers that normal humans use don't follow strictly the axioms of Peano. Most of the time the dates of a month follow Peano. Most of the time the day after September 2 is September 3. But not always.
On a computer you can't store every natural number as specified by Peano with common integers.
If you start counting apples and get really many apples you suddenly have a black hole and no apples anymore.
I don't know enough about the philosophy of math to get really deep by we had lately someone writing posts about constructivist math that also contained the notion that there are no absolute mathematical truths.
In that case, it sounds like you're just not a math realist. There are plenty of people who believe that Peano arithmetic somehow exists on its own. Or possibly people who have a different definition of "exist" from me. It's hard to tell the difference. But I don't think disagreeing with that is all that unusual.
I'm not good enough at math to confidently answer that question. I'm good enough at math that I think that people want to debate whether or not something like infinite small numbers exist.
I don't care primarily about math. I see math as a tool. I'm happy that there are some people who build useful math and I'm happy to use it when convenient but it's not central for me.