Le 27-nov.-07, à 05:47, marc.geddes.domain.name.hidden a écrit :
> Geometric properties cannot be derived from
> informational properties.
I don't see why. Above all, this would make the computationalist wrong,
or at least some step in the UDA wrong (but then which one?).
I recall that there is an argument (UDA) showing that if comp is true,
then not only geometry, but physics, has to be derived exclusively from
numbers and from what numbers can prove (and know, and observe, and
bet, ...) about themselves, that is from both extensional and
intensional number theory.
The UDA shows *why* physics *has to* be derived from numbers (assuming
CT + "yes doctor").
The Lobian interview explains (or should explain, if you have not yet
grasp the point) *how* to do that.
Bruno
>
>
>
> On Nov 27, 3:54 am, Bruno Marchal <marc....domain.name.hidden> wrote:
>
>>
>>> Besides which, mathematics and physics are dealing with quite
>>> different distinctions. It is a 'type error' it try to reduce or
>>> identity one with the other.
>>
>> I don't see why.
>
> Physics deals with symmetries, forces and fields.
> Mathematics deals with data types, relations and sets/categories.
>
> The mathemtical entities are informational. The physical properties
> are geometric. Geometric properties cannot be derived from
> informational properties.
>
>
>
>>
>>
>>
>>> Mathematics deals with logical properties,
>>
>> I guess you mean "mathematical properties". Since the filure of
>> logicism, we know that math is not really related to logic in any way.
>> It just happens that a big part of logic appears to be a branch of
>> mathemetics, among many other branches.
>
> I would classify logic as part of applied math - logic is a
> description of informational systems from the point of view of
> observers inside time and space.
>
>>
>>> physics deals with spatial
>>> (geometric) properties. Although geometry is thought of as math, it
>>> is actually a branch of physics,
>>
>> Actually I do think so. but physics, with comp, has to be the science
>> of what the observer can observe, and the observer is a mathematical
>> object, and observation is a mathematical object too (with comp).
>
>
>>
>>> since in addition to pure logical
>>> axioms, all geometry involves 'extra' assumptions or axioms which are
>>> actually *physical* in nature (not purely mathematical) .
>>
>> Here I disagree (so I agree with your preceding post where you agree
>> that we agree a lot but for not always for identical reasons).
>> Arithmetic too need extra (non logical) axioms, and it is a matter of
>> taste (eventually) to put them in the branch of physics or math.
>>
>> Bruno
>>
>
> I don't think it's a matter of taste. I think geoemtry is clearly
> physics, arithmetic is clearly pure math. See above. Geometry is
> about fields, arithmetic (in the most general sense) is about
> categories/sets.
>
>
> >
>
http://iridia.ulb.ac.be/~marchal/
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Received on Tue Nov 27 2007 - 09:17:36 PST