Le 02-sept.-06, à 17:26, 1Z a écrit :

## Advertising

> Things don't become necessarily true just > because someone says so. The truths > of mathematics may be necessarily true, but > that does not make AR a s aclaim about > existence necessarily true. AR as a claim > about existence is metaphysics, and highly debatable. Yes. So let us never do it. > Necessary truth doesn't entail necessary existence unless > the claims in question are claims about existence. Exactly. > Whether mathematical truths are about existence is debatable > and not "necessary". Existential mathematical statement are about existence. > Not if AR is only a claim about truth. AR is about the truth of arithmetical statements, and among arithmetical statements, many are existential, so AR makes claim about the independent truth of existential statements. No need to add metaphysics at this stage (nor at any other stage by the way, except the yes doctor, which I prefer to range in "theology" than in "metaphysics"). > Necessary truth > can exist in a world of contingent existence -- providing > all necessary truths in such a world are ontologically non-commital. I don't understand. > As non-Platonists indded take mathematical statements to be. AR does not ask you for believing in some metaphysical (still less physical) existence of numbers. It ask you to agree that a proposition of the type ExP(x) is true or false independently of any cognitive faculty. Cognitive abilities are needed to believe or know that ExP(x) is true (or false), but that's all. > That's what White Rabbits are all about. > > There is also an apriori argument against Pythagoreanism (=everything > is numbers). If it is a *contingent* fact that non-mathematical > entities > don't exist, It is not even a fact. It is an assumption. Nobody has proved that something non mathematical exists, although comp is quite close in proving this. Indeed comp shows that no first person can be described mathematically by herself. So *relatively* to a machine first person, many things will *appear* non mathematical. It is a consequence of incompleteness + the theaetetical-plotinian definition of knowledge. > Pythagoreanism cannot be justified by rationalism (=- > all truths are necessary and apriori). Therefore the > Pythagorean-ratioanlist > must believe matter is *impossible*. Not impossible. Just useless. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---