meekerdb wrote:
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
I agree. But I think that the attraction of Platonism lies in the fact
that if you abstract the notion of 'twoness' from all groups of two
things, such as fathers, sons, pebbles, and so on, then you get an
underlying perfect form that is independent of imperfections: such as
the possibility that two fathers plus two sons might be only three
people (or even only two people); or the unpleasant fact that two drops
of water plus two drops of water might make only one drop of water.
Platonism is a search for an escape from the 'ugliness' of reality.
Bruce
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