On 5/17/2019 5:05 AM, Bruno Marchal wrote:
On 16 May 2019, at 01:28, 'Brent Meeker' via Everything List
<[email protected]> wrote:
On 5/15/2019 8:20 AM, Bruno Marchal wrote:
Mathematical logic distinguish well the name of a thing and the thing itself.
You confuse “0” and 0.
Also, when you say that something does not exist, you might give us your
metaphysical axioms. Taken literarily, what you say is like saying that the
equation x - 4 = 0 has no solution.
That's confusing "Satisfies a predicate." with "exists". Such a definition of
"exists" is only relative to a context. Compare, "There exists a physician companion of Sherlock
Holmes.”
In arithmetic, I use the expression “it exists x P(x)” with the meaning the
standard model of arithmetic satisfies “it exists x P(x)”. Which is the
logician way to describe the meaning of “it exists x such that x-1=0” in
high-school.
Since day one, we use the standard model of arithmetic. It is the one everyone
understand. The no standard model are sophisticated constructs in the mind of
logician, to prove that PA, and all sound machines, have limitation with
respect to the standard model, which can be defined online a richer theory.
And I use the standard model of Sherlock Holmes, the one everyone
understands. That doesn't make Watson exist.
Brent
The level of mathematical confidence is high up to ZFC, like in analysis and
physics.
Bruno
Brent
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