Bruno Marchal wrote:
> 
> 
>>>
>>>> and build our number system
>>>> around that. Like non-Euclidean arithmetic.
>>>
>>> That already exists, even when agreeing with the axioms, of, say,
>>> Peano Arithmetic. We can build model of arithmetic where we have the
>>> truth of "provable(0=1)", despite the falsity of it in the standard
>>> model, given that PA cannot prove the consistency of PA. This means
>>> that we have non standard models of PA, and thus of arithmetic. But  
>>> it
>>> can be shown that in such model the 'natural number' are very weird
>>> infinite objects, and they do not concern us directly.  But "17 is
>>> prime" is provable in PA and is thus true in ALL interpretations or
>>> models of PA. Likewise, the Universal Dovetailer is the same object  
>>> in
>>> ALL models of PA.
>>> All theorems of PA are true in all interpretations of PA (by Gödel's
>>> completeness theorem).
>>
>> I'm not saying that arithmetic isn't an internally consistent logic
>> with unexpected depths and qualities, I'm just saying it can't turn
>> blue or taste like broccoli.
> 
> Assuming non-comp.
There is no assumption needed for that. It is a category error to say
arithmetics turns into a taste. It is also a category error to say that
arithmetic has an internal view. It makes as much sense to say that a
concept has an internal view. Internal view just applies to the only thing
that can have/is a view, namely cosciousness. This is not a belief, this is
just the obvious reality right now. Can you find any number(s) flying around
that has any claim to an internal view right now? The only thing that you
can find is consciousness being conscious of itself (even an person that
consciousness belongs to is absent, the person is just an object in
consciousness).
You abstract so much that you miss the obvious.

benjayk
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