Bruno Marchal wrote:
> On 05 Oct 2011, at 17:33, benjayk wrote:
>> meekerdb wrote:
>>> On 10/4/2011 1:44 PM, benjayk wrote:
>>>> Bruno Marchal wrote:
>>>>>> Bruno Marchal wrote:
>>>>>>>> But then one 3-thing remains uncomputable, and undefined,
>>>>>>>> namely the very foundation of computations. We can define
>>>>>>>> computations in
>>>>>>>> terms of numbers relations, and we can define number relations  
>>>>>>>> in
>>>>>>>> terms of
>>>>>>>> +,*,N. But what is N? It is 0 and all it's successors. But  
>>>>>>>> what is
>>>>>>>> 0? What
>>>>>>>> are successors? They have to remain undefined. If we define 0  
>>>>>>>> as a
>>>>>>>> natural
>>>>>>>> number, natural number remains undefined. If we define 0 as  
>>>>>>>> having
>>>>>>>> no
>>>>>>>> successor, successor remains undefined.
>>>>>>> All theories are build on unprovable axioms. Just all theories.
>>>>>>> Most scientific theories assumes the numbers, also.
>>>>>>> But this makes not them undefinable. 0 can be defined as the  
>>>>>>> least
>>>>>>> natural numbers, and in all models this defines it precisely.
>>>>>> But natural *numbers* just make sense relative to 0 and it's
>>>>>> successors,
>>>>>> because just these are the *numbers*. If you define 0 in terms of
>>>>>> natural
>>>>>> numbers, and "least" (which just makes sense relative to  
>>>>>> numbers), you
>>>>>> defined them from something undefined.
>>>>>> So I ask you: What are natural numbers without presupposing 0  
>>>>>> and its
>>>>>> successors?
>>>>> This is a bit a technical question, which involves logic. With  
>>>>> enough
>>>>> logic, 0 and s can be defined from the laws of addition and
>>>>> multiplication. It is not really easy.
>>>> It is not technical at all. If you can't even explain to me what the
>>>> fundamental object of your theory is, your whole theory is  
>>>> meaningless to
>>>> me.
>>>> I'd be very interested in you attempt to explain addition and
>>>> multplication
>>>> without using numbers, though.
>>> It's easy.  It's the way you explain it to children:  Take those red
>>> blocks over there and
>>> ad them to the green blocks in this box.  That's addition.  Now  
>>> make all
>>> possible
>>> different pairs of one green block and one red block. That's
>>> multiplication.
>> OK. We don't have to use numbers per se, but notions of more and  
>> less of
>> something.
>> Anyway, we get the same problem in explaining what addition and
>> multiplication are in the absence of any concrete thing of which  
>> there can
>> be more or less, or measurements that can be compared in terms of  
>> more and
>> less.
>> meekerdb wrote:
>>>> Bruno Marchal wrote:
>>>>> But to get the comp point, you don't need to decide what numbers  
>>>>> are,
>>>>> you need only to agree with or just assume some principle, like 0  
>>>>> is
>>>>> not a successor of any natural numbers, if x ≠ y then s(x) ≠  
>>>>> s(y),
>>>>> things like that.
>>>> I agree that it is sometimes useful to assume this principle, just  
>>>> as it
>>>> sometimes useful to assume that Harry Potter uses a wand. Just  
>>>> because we
>>>> can usefully assume some things in some contexts, do not make them
>>>> universal
>>>> truth.
>>>> So if you want it this way, 1+1=2 is not always true, because  
>>>> there might
>>>> be
>>>> other definition of natural numbers, were 1+1=&.
>>> It's always "true" in Platonia, where "true" just means satisfying  
>>> the
>>> axioms.  In real
>>> life it's not always true because of things like: This business is so
>>> small we just have
>>> one owner and one employee and 1+1=1.
>> Yeah, but it remains to be shown that platonia is more than just an  
>> idea. I
>> haven't yet seen any evidence of that.
>> Bruno seems to justify that by reductio ad absurdum of 1+1=2 being  
>> dependent
>> on ourselves, so 1+1=2 has to be true objectively in Platonia. I  
>> don't buy
>> that argument. If our mind (or an equivalent mind, say of another  
>> species
>> with the same intellectual capbilites) isn't there isn't even any  
>> meaning to
>> 1+1=2, because there is no way to interpret the meaning in it.
> Would you say that if the big bang is not observed then there is no  
> big bang?
> Why would it be different for "1+1 = 2"?
Right, the big bang is the infinite power of observing itself, so without
observing,... Well, there is no without observing.

Bruno Marchal wrote:
>> It only seems
>> to us to be true independently because we defined it without explicit
>> reference to anything outside of it. But this doesn't prove that it  
>> is true
>> independently anymore than the fact that Harry Potter doesn't  
>> mention he is
>> just a creation of the mind makes him exist independently of us  
>> eternally in
>> Harry-Potter-land.
> This does not logically follows, and beyond this, it is obvious that  
> Harry-Potter land does exist in any "everything" type of theories.  
> Indeed with comp, or with other everything type of theories, the  
> problem is that such fantasy worlds might be too much probable,  
> contradicting the observations. The mere existence of them cannot be  
> used in a reductio ad absurdum.
My point is just that AR is not plausible just because we have rigid
definitions that we claim to be unchangeable.

Bruno Marchal wrote:
> We don't know what reality is. We are searching.
I don't think reality is primarily a "what". It is an "that". "What"s arise
is reality.

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