> 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. 

Bruno






> 
> Brent
> 
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