Bruno Marchal wrote: > Le 02-sept.-06, à 17:26, 1Z a écrit : > > > > 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.

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Debate is what we are here for. > > 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. And Sherlock Holmes lives because Sherlock Holmes lives at 221b Baker Street. > > 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. Arithmetical statements use the word "exists", or the symbolic euivalen thereof. However, it is not to be taken literally in all contexts. > No need to add > metaphysics at this stage Yes there is. You need metaphysics to answer the question of whether the existence-claims of mathematics shouldbe takne literally. > (nor at any other stage by the way, except > the yes doctor, which I prefer to range in "theology" than in > "metaphysics"). Is theology better-foudned as a discipline ? > > 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. If necessary truths don't refer to contingently existing things, they cannot be "infected" by their contingency. > > 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. Then it does not show the UD exist, and it cannot follow that I part of its output. > It ask you to agree that a proposition > of the type ExP(x) is true or false independently of any cognitive > faculty. It may well be true. It may well mean nothing more than "P(x) is non-contradictory" > Cognitive abilities are needed to believe or know that ExP(x) > is true (or false), but that's all. Quite. So nothing in the argument can tell me about the nature of my existence. > > 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. I already said "if"... > Nobody has proved that > something non mathematical exists, although comp is quite close in > proving this. That isn't the point. The point is the consistency Pythagorean rationalism as a hypothesis. > 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. The Pythagorean rationalist *must* believe mater is impossible -- the argument becomes inconsistent otherwise. The argument that matter is "useless" is more akin to empiricism than rationalism. > 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 -~----------~----~----~----~------~----~------~--~---