On 10/23/2018 9:23 AM, Bruno Marchal wrote:
On 23 Oct 2018, at 04:30, Brent Meeker <[email protected]> wrote:
On 10/22/2018 6:54 AM, Bruno Marchal wrote:
The mathematical reality has noting to do with languages, except that languages
are needed if machine/people want to share the results of their exploration.
So how do you prove theorems without a language?
Of course, proving a theorem requires a theory, and a language. I was saying
(see the quote) that the *arithmetical reality* does not require a language.
The arithmetical reality does not require a language more than dinosaurs needed
the word “dinosaur” to exist. The prime character of 17 does not need a
mathematician to assert it, or to think about.
To prove a theorem requires a theory, which requires a language. We can only
ope that our theory is in relation with truth, but the truth of 17 is prime,
assuming it true, does not need a proof to be true. A proof is neither
necessary, nor sufficient. The arithmetical reality is independent of the
big-bang. It is more plausible than an event like the big-bang requires some
part of the arithmetical reality.
But you are basing our shared reality in what is provable, which is
therefore dependent on having language. Right?
Brent
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