On 20/06/2016 3:10 am, Bruno Marchal wrote:
On 18 Jun 2016, at 02:25, Bruce Kellett wrote:
All these problem dissolve if you reject the notion of a platonic
realm for arithmetic and accept physicalism.
If you succeed in making me doubting that 2+2=4, I might doubt even
more on Hphi = Ephi. If you reject elementary arithmetic, you can
invoke directly the God of the Gap. (and I don't believe in a platonic
realm for arithmetic, I have no real clue what you mean by that).
I think you really do know what is meant by a 'platonic realm' -- you
know about Plato's theory of Forms that exist in a separate sphere
(world). Platonism in mathematics is just an formalization of the
feeling that mathematician's report that they seem to be exploring an
existing landscape rather than inventing things. Although this feeling
may be understandable, it is not a proof that mathematics and
mathematical objects are objective in any sense other than that they are
implied by the axioms and the rules of inference, and are thus
intersubjectively valid.
Knowing that 2+2=4 is just a matter of knowing the definitions or rules.
You know that in chess the King can only move at most one square a time
in any direction. The knowledge is just knowledge of rules and their
consequences -- no separate existence is implied. In Smolin's phrase,
mathematics is "evoked" rather than pre-existent in another realm.
It is really quite annoying that you keep suggesting that doubting that
2+2=4 involves the rejection of arithmetic and and an appeal to a
"God-of-the-Gaps". There is no suggestion of this in anything I have said.
Bruce
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