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 Originally Posted by Poopadoop
if tomorrow you had two items, added two more, and ended up with five, the statement 2+2=4 would be proven to be demonstrably false, as would all of mathematics.
These are 2 different things.
The premise is based on you observing items.
The conclusion is that counting is flawed.
The conclusion does not follow.
Review the fundamental assertions of math:
1) That identity is a meaningful thing. I.e. that an idea is separate from another idea, and it is meaningful to say 1 idea.
It's absurdly impossible to define the number one without being self-referential, which is generally bad form in defining. Nonetheless, the fundamental conceit of mathematics is that we can do this and it's all gravy.
2) There is an Increment Function, such that we assign an order of words/symbols/etc. to sets of 1's. E.g. 1, 2, 3...
Note that this is defining N + 1 = (N+1), for all N (whole numbers). I.e. this implicitly defines addition and equality.
These 2 ideas and the logic of algebra is all that is needed to derive subtraction, multiplication and division, exponents, logarithms, etc.
In summary:
I'm not sure your thought experiment "What if tomorrow 2+2=5?" is meaningful.
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