"1Z" <[EMAIL PROTECTED]> wrote on August 29 > The version of AR that is supported by comp > only makes a commitment about mind-independent *truth*. The idea > that the mind-independent truth of mathematical propositions > entails the mind-independent *existence* of mathematical objects is > a very contentious and substantive claim.
I'm very late in reading this thread. I assume AR is "Arithmetical Realism" and that *truth* in this thread implies alethic qualification of some sort. To me, a statement like "only use batteries with the same rated voltage" would seem only to be qualifiable as true or otherwise if related to factual content. Such a statement would not be meaningless and would contain information which could be worth preserving or using. I am wondering how much semantic loading Bruno's ideas of quantification are obliged to carry here. Quantifiers always worry me as they often seem to come up at a very early stage and they do always seem to carry with them a similar pattern to "only use batteries with the same rated voltage" and their meaning if any is never absolutely clear or clarifiable. Perhaps they cannot entail the aforementioned "mind-independent *existence* of mathematical objects". Or, at least, not without further qualification, rendering his theory possibly incomplete as theories tend to be. This is not the same as people saying "in spite of all we know about electricity, we do not know what electricity is", because of course we do know what electricity is, in context if not in metaphysics. [Bruno's defintiion of Arithmetic Realism I understand to be " Arithmetical Realism. All proposition pertaining on natural numbers with the form Qx Qy Qz Qt Qr ... Qu P(x,y,z,t,r, ...,u) are true independently of me. Q represents a universal or existential quantifier, and P represents a decidable (recursive) predicate. That is, proposition like the Fermat-Wiles theorem, or Goldbach conjecture, or Euclide's infinity of primes theorem are either true or false, and this independently of the proposition "Bruno Marchal exists". It amounts to accept, for the sake of my argument, that classical logic is correct in the realm of positive integers. Nothing more."] --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to firstname.lastname@example.org To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---