Bruno Marchal wrote:
> > You could at least state them.
>
> I do it in all paper on this subject, and I have done it at nauseam in
> this list. It is computationalism: the doctrine according to which
> there is a level of substitution such that I survive a digital graft
> made correctly at that level. (+ CT + AR for giving univocal sense to
> word like "number" and (discrete) computation"). Just go there:
> http://iridia.ulb.ac.be/~marchal/publications/
> SANE2004MARCHALAbstract.html
>
> (I recall having already given to you this reference).
3) Arithmetical Realism (AR). This is the assumption that arithmetical
proposition, like
''1+1=2,'' or Goldbach conjecture, or the inexistence of a
bigger prime, or the statement
that some digital machine will stop, or any Boolean formula bearing on
numbers, are
true independently of me, you, humanity, the physical universe (if that
exists), etc. It is
a version of Platonism limited at least to arithmetical truth."
Platonism isn't about truth, it is about existence.
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http://www.maa.org/reviews/whatis.html
There were three major points of view in the debate about the nature of
mathematics. The formalists argued (roughly: the short
summaries that follow are really caricatures) that mathematics was
really simply the formal manipulation of symbols based on
arbitrarily-chosen axioms. The Platonists saw mathematics as almost an
experimental science, studying objects that really exist
(in some sense), though they clearly don't exist in a physical or
material sense. The intuitionists had the most radical point of
view; essentially, they saw all mathematics as a human creation and
therefore as essentially finite.
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http://plato.stanford.edu/entries/platonism/#1
Platonism is the view that there exist abstract objects, and again, an
object is abstract just in case it is non-spatiotemporal, i.e.,
does not exist in space or time. [ ... ] Three examples of things that
are often taken to be abstract are (a) mathematical objects
(most notably, numbers), (b) properties, and (c) propositions.
Platonists about mathematical objects claim that the theorems of our
mathematical theories - sentences like '3 is prime'
(a theorem of arithmetic) and 'There are infinitely many transfinite
cardinal numbers' (a theorem of set theory) -
are literally true and that the only plausible view of such sentences
is that they are about abstract objects
(i.e., that their singular terms denote abstract objects and their
existential quantifiers range over abstract objects).
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The philosophy of Plato, or an approach to philosophy resembling his.
For example, someone who asserts that numbers exist
independently of the things they number could be called a Platonist.
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http://www.fortunecity.com/emachines/e11/86/enm3.html#
The view that mathematical concepts could exist in such a
timeless,ethereal sense was put forward in ancient times
(c.360 BC) by the great Greek philosopher Plato.Consequently,this view
is frequently referred to as mathematical Platonism
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Received on Wed Jul 12 2006 - 18:04:45 PDT