On 8/27/2019 4:18 AM, Bruno Marchal wrote:
On 26 Aug 2019, at 21:04, 'Brent Meeker' via Everything List
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On 8/26/2019 4:19 AM, Bruno Marchal wrote:
On 26 Aug 2019, at 02:28, 'Brent Meeker' via Everything List
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On 8/25/2019 12:50 PM, Jason Resch wrote:
What's the difference between abstract and concrete? I think it's
only a matter of relative perspective. Other universes to us seem
abstract. While to people in other universes ours would seem
abstract. Do you agree?
No. The difference is one of completeness. A abstract something
is incomplete.
It is the finite construction, like a theory, which can be
incomplete. The arithmetical reality is complete. The theories are
incomplete.
That arithmetical reality is complete is a theory.
No, it is true by definition of the arithmetical reality, which here
has been defined by the set of all true sentences in the standard
model of PA.
Yes, I'm familiar with the fantasy that things can be true by
definition. Sadly it only works for fictional things, as "Watson was
Holmes companion...by definition."
Brent
I “model” it by the set of the Gödel’s number of those true sentences.
No theories can axiomatise that set, but by definition, that set is
complete. The definition of that set can be done informally, and does
not ask much that we we need to understand real number or analysis.
Bruno
Brent
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