Bruno Marchal wrote:

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> > 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. -------------------------------------------------------------------------------------------- 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. -------------------------------------------------------------------------------------------------------- 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). -------------------------------------------------------------------------------------------------------- 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. -------------------------------------------------------------------------------------------------------- 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 --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---