> On 25 Oct 2018, at 20:05, Brent Meeker <meeke...@verizon.net> wrote:
> 
> 
> 
> On 10/25/2018 9:18 AM, Bruno Marchal wrote:
>>> On 24 Oct 2018, at 03:22, Brent Meeker <meeke...@verizon.net> wrote:
>>> 
>>> 
>>> 
>>> On 10/23/2018 9:23 AM, Bruno Marchal wrote:
>>>>> On 23 Oct 2018, at 04:30, Brent Meeker <meeke...@verizon.net> 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,
>> Absolutely not. I mean no more than any scientist, and I make clear my 
>> hypotheses.theory, without have ever claim any truth, like any sane 
>> scientist do. I am more exorcist: I base our shared reality on a mix of 
>> theory and experiences.
>> 
>> A theory is better identify with a being or a set of belief. I say that a 
>> machine believes A if the machine asserts A. I limit myself to what 
>> self-referentially correct machine can say, and not say, ...
> 
> But don't you identify "machine believes A" with "machine can prove A”?

Only because I am limiting myself to the theology of rational machine, which 
believe in some universal system. 




> 
>> 
>> 
>> 
>>> which is therefore dependent on having language.  Right?
>> The reality itself does not depends on the language, even if the language 
>> will be itself a part of the reality.
> 
> Not the reality, but the proof depends on language.

The proof depends on language, yes. No problem with that. Actually the proof 
depends accidentally on the language but depends in a more important way on the 
theory. If the axiom is the Riemann conjecture, the proof will be very easy.

I identify machine, theories, hypotheses, (personal) beings, numbers, finite 
things, etc. That is enough to get very interesting conclusions, and we can 
introduce the nuances when needed later. Likewise I identify semantic, meaning, 
model, reality, divine, god... The interesting things happen in the relation of 
machine and meaning/reality.

Bruno




> 
> Brent
> 
>> We need lanaguage to communicate about reality, including languages. We are 
>> ourselves words, written in the biochemical languages, and particles are 
>> words of some wort too. Now, the more a theory is lade independent of the 
>> language, or the even the theories,, the more is has a chance to be deep, 
>> and to help avoiding geographical prejudice on what is real or not.
>> 
>> Bruno
>> 
>> 
>> 
>> 
>> 
>> 
>>> Brent
>>> 
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