On 5/20/2019 2:50 AM, Bruno Marchal wrote:
On 17 May 2019, at 23:18, 'Brent Meeker' via Everything List
<[email protected]> wrote:
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.
Everyone agree on what what is the standard model of ZF, easily definable in
Analysis or Set theory.
I am not sure what could ever mean: "the standard model of Sherlock Holmes".
Give me your first order theory of Sherlock Holmes.
The stories written by Arthur Conan Doyle. Non-standard models are
produced by Hollywood studios.
If it is Turing Universal, and does not assume infinities, then I will be able
to have a standard interpretation of it, but your proposition will just be the
invention of a new formalism for “computable”, and as I said, you can use it as
your basic theory. I doubt that Conan Doyle will recognise its baby, though.
All physics theories use elementary arithmetic. You comparison between Sherlock
Holmes and Arithmetic does not make much sense. Or show me some application of
“Sherlock Holmes” in particle physics.
Sherlock Holmes is, by definition, a fictive person. Even if we discover
someone looking very much like him in the “real world”, it would not be
“Sherlock Holmes”, just a guy looking like him, because, by definition,
shellack Holmes do not exist: it is part of its definition, I would say. Same
for the unicorns.
Right. He doesn't exist in the real world, although real world
detectives may apply his ideas. Just like arithmetic doesn't exist in
the real world, but is useful.
Brent
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