[FOM] Falsification of Platonism
dmehkeri at yahoo.ca
Sat Apr 24 15:45:55 EDT 2010
The example of a contradiction in PA is not a good one. There is no contradiction in PA, because it would already be a contradiction in Heyting arithmetic, and Heyting arithmetic is true. Or, if you prefer, a contradiction in PA would falsify all forms of constructivism, even those forms that accept principles that violate PA.
The example of a contradiction in ZFC is different, because there is no corresponding equiconsistent constructive system. So, until very recently, I thought that a contradiction in ZFC would be a falsification of Platonism that would not falsify constructivism.
Instead, I am surprised to hear that even a contradiction in PA would not falsify Platonism. So how does Platonism differ from formalism, in practice?
Yours in confusion,
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