On 1/20/2015 9:59 AM, Bruno Marchal wrote:
Ex(x+x=4) just means there is number
OK.
as defined by Peano's axioms that provably satisfies the expression.
Not at all. That means that PA believes Ex(x+x=4).
?? But you use []p to equally mean "provable p" and "believes p", so what does it mean "PA
believes Ex(x+x=4) other than it is provable?
Brent
Ex(x+x=4) means that N satisfies the idea that there is some number n having the
property that n + n = 4.
The meaning is in the semantics, not in the theory.
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