On Monday, July 22, 2019 at 12:01:31 AM UTC-5, Bruce wrote: > > On Sat, Jul 20, 2019 at 8:16 PM Bruno Marchal <[email protected] > <javascript:>> wrote: > >> On 19 Jul 2019, at 22:47, Dan Sonik <[email protected] <javascript:>> >> wrote: >> > >I think the main "leap of faith" that you make (and many others simply >> can't, because it >appears absurd) is somehow thinking that the completed >> computations are already "out >there,” >> >> If you agree that 2+2=4 implies Ex(x+2 = 4), or more simply that the >> equation x+2=0 has a solution in the integers, then you have to believe >> that the computations all exists in arithmetic. Peano Arithmetical proves >> the existence of those computations, like it proves the existence of the >> prime number. >> >> > This is your standard conflation of the Existential Quantifier over a > domain with an ontology, Bruno. Or, equivalently, your oft-repeated > assertion that people confuse "2+2=4" with 2+2=4. What you refer to here > is the fact that the word "dog" is not actually a dog, namely a 4-legged > mamal that barks and greets you affectionately at the door. That is, the > name is not the same as the physical object. But that distinction does not > exist for arithmetic -- given nominalism (the fact that the integers are > not independently existing objects), the name "2+2=4" is the same thing as > 2+2=4. There is no object that differs from the name of the relationship > expressed in 2+2=4. The claim "that all computations exist in arithmetic" > has no content. Peano arithmetic no more "proves" the existence of these > computations than it proves the existence of the moon. > > in some sort of Platonic superspace. >> >> >> Not at all? Realism in arithmetic is only the statement that you have no >> objection to what is taught in primary school. >> > > There you go again, Bruno: re-defining terms so that you are always right. > "Realism", or more particularly, "arithmetical realism" means no such > thing, Students are taught elementary calculations and multiplication > tables in primary school, they are not taught philosophical platonism,. > > Bruce >
*Peano arithmetic no more "proves" the existence of these computations than it proves the existence of the moon.* Of course the moon is a numerical entity, the result of some (numerical) computation. :) Once one posits numerical reality as producing (computing) things, then one is saying arithmetic is a programming language, and then the issue is what sort of semantics it has, e.g. The operational semantics for a programming language describes how a valid program is interpreted as sequences of computational steps. These sequences then *are* the meaning of the program. - https://en.wikipedia.org/wiki/Operational_semantics The semantics of a program leads down to some sort of machinery, which in numerical reality are platonic machines - which basically have all the properties of the material machines that PLT operational semantics addresses (no pun intended). *they are not taught philosophical platonism* Of course they are. When students are told numbers exist, that is the beginning of their brainwashing by platonism. @philipthrift -- 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/593b3158-9127-44ab-9fb2-913aa23710fe%40googlegroups.com.
