On Sat, Jul 20, 2019 at 8:16 PM Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 19 Jul 2019, at 22:47, Dan Sonik <danialso...@gmail.com> 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 > -- 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRsLk6y3xtR65U4MSjL8qHWf86Ak%3DVPruB_CKWL_MgLcQ%40mail.gmail.com.
