LizR wrote:
On 12 June 2015 at 17:40, Bruce Kellett <bhkell...@optusnet.com.auArithmetic is, after all, only an axiomatic system. We can make up an indefinite number of axiomatic systems whose theorems are every bit as 'independent of us' as those of arithmetic. Are these also to be accepted as 'really real!'? Standard arithmetic is only important to us because it is useful in the physical world. It is invented, not fundamental.So you say, and you may be right. Or you may not. The question is whether 2+2=4 independently of human beings (and aliens who may have invented, or discovered as the case may be, arithmetic).
It may well be independent of humans or other (alien) beings, but it has no meaning until you have defined what the symbols '2','4','+', and '=' mean. Then it is a tautology.
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