> On 16 May 2019, at 01:25, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 5/15/2019 8:15 AM, Jason Resch wrote: >> Nothing is wrong, except that you are using a different notion of "real". >> Integers are invented by humans, even though there is intersubjective >> agreement about them. >> >> >> I would say we invented theories (axioms) to study them, but that the >> properties of integers were always there waiting to be discovered. Prove me >> wrong. > > Were there always infinitely many of them? > > Prove you're right.
In science, we can never prove that we were right. But for the arithmetical reality, nobody serious doubt that all undecidable arithmetical sentences of PA, ZF and there effective sound extensions are true. That is why we believe in the propositional axiom (A or not A) in arithmetic. Even intuitionist believes this, albeit formulate it differently. The difficulties comes always from the infinity axiom, but there is none in the mechanist ontology description. Their use remains confines in the phenomenology of the numbers. Bruno > > Brent > > -- > 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/4ad589d2-17f7-e2c9-c464-36d95c81d985%40verizon.net > > <https://groups.google.com/d/msgid/everything-list/4ad589d2-17f7-e2c9-c464-36d95c81d985%40verizon.net?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/419BD192-115C-4E3A-BBE5-DE23740262FB%40ulb.ac.be.
