> On 1 Jun 2019, at 11:27, Tomas Pales <[email protected]> wrote: > > > > On Saturday, June 1, 2019 at 10:06:31 AM UTC+2, Bruno Marchal wrote: > >> On 31 May 2019, at 22:27, Tomas Pales <[email protected] <javascript:>> >> wrote: >> >> Existence is just the principle of logical consistency or identity. > > Almost. Peano arithmetic is consistent with the proposition that Peano > arithmetic is inconsistent. Consistency is shown rather cheap, and far away > from Truth, which is the key notion, but of course not a very obvious one. > > > If PA is consistent, it exists. If PA is not consistent, it doesn't exist.
If PA is consistent, a Model of PA exists. Most people believe that PA is consistent, because they have learned the standard model (N, 0, +, x) at school. > But since PA is subject to Godel's second incompleteness theorem, we may > never know, right? Even PA knows it. What Gödel’s show is that not theory/machine can prove its own consistency. If PA would inconsistent, it would still exist. Inconsistent people, machine and numbers exists already in the model of RA (which is much weaker than PA). > > > Here I disagree. 17 is very concrete. It the successor of 16, which is very > concrete, etc. With mechanism, 0, 1, 2, 3, … are taken as the most concrete > “really existing” object. The moon, and yourself are extremely abstract type, > having only phenomenological existence. > > This is what I mean by "abstract" and "concrete": > > abstract: has instances/examples (is a property) > > concrete: has no instances/examples (is not a property) > > Number 17 has instances/examples in any collection of 17 objects (is a > property of any collection of 17 objects). Therefore number 17 is an abstract > object. > > Our moon has no instances/examples (is not a property of any object, just as > Bruno Marchal is not a property of any object). Therefore our moon is a > concrete object. I can accept such definition. Then 0, 1, 2, … are concrete. Prime becomes a property and is abstract in that setting, but then computers are even more abstract and physical computer still even more, and the moon can be said to instantiate the theory of the moon, unless you postulate that there is “really” a moon out there, which is incoherent with the mechanist hypothesis, where the numbers (or Turing equivalent). (If you are aware that mechanism and materialism oppose each other logically (see my papers if not, it is still rather ignored). Bruno > > > > > >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected] <javascript:>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/everything-list/2470590b-373e-4595-970c-40409ee19907%40googlegroups.com >> >> <https://groups.google.com/d/msgid/everything-list/2470590b-373e-4595-970c-40409ee19907%40googlegroups.com?utm_medium=email&utm_source=footer>. > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/30ae74e7-66d0-47f9-baa2-230001d10843%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/30ae74e7-66d0-47f9-baa2-230001d10843%40googlegroups.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/4AE65D92-D9E3-4AE9-B686-6D58397BB194%40ulb.ac.be.
