On 6/12/2015 6:29 PM, Bruce Kellett wrote:
LizR wrote:
On 12 June 2015 at 17:40, Bruce Kellett <bhkell...@optusnet.com.au
Arithmetic 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.
Bruce
It is commonly thought to be discovered and so to be "ought there" independent of human
beings or any cognition. But when considered more carefully what was discovered is that
one can group pairs to things together (at least in imagination) and have four things. So
two fathers grouped with two sons is four people. Except when it's three people. So we
said OK we'll *define* units to be things that obey the rules that 2+2=4. Then we
discovered that these rules implied a lot of things we hadn't thought of. But they aren't
"out there", they're in our language.
Brent
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