On 21 Jan 2015, at 01:33, meekerdb wrote:
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?
Yes, indeed. So "Ex(x+x=4) is provable by PA" is the same as []Ex(x
+x=4).
But "Ex(x+x=4)" means still only that there is a number n in N such
that n+n = 4.
Bruno
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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