> On 22 Jul 2019, at 07:01, Bruce Kellett <[email protected]> wrote: > > On Sat, Jul 20, 2019 at 8:16 PM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > On 19 Jul 2019, at 22:47, Dan Sonik <[email protected] > <mailto:[email protected]>> 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.
It is not a conflation. It is a necessary conclusion. > Or, equivalently, your oft-repeated assertion that people confuse "2+2=4" > with 2+2=4. ? (Yes, some people just did it many times just recently, but I don’t see the relation with the ontological existence). > 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. The name of an object is not the same as the object (physical or not). > But that distinction does not exist for arithmetic -- given nominalism (the > fact that the integers are not independently existing objects), But that is not among my assumption. My assumption is (at the meta-level) only YD and CT. Then, from this we show that the TOE is “only” elementary arithmetic, or combinators, or any first order specification of a universal machinery, or universal machine. > the name "2+2=4" is the same thing as 2+2=4. That is a huge mistake (even for a nominalist). It is beyond ridiculous. > 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. Hmm… I *can* agree. It is a shortcut for the model (N, 0, +, *, s) satisfies all the condition for the computations to be relatively run. > Peano arithmetic no more "proves" the existence of these computations than it > proves the existence of the moon. In the Aristotelian metaphysics, that might be given some sense, but you cannot invoke your metaphysics in a work in metaphysics. That is the same, in metaphysics, as saying that the structure (N, +) refutes group theory, in mathematics. > >> 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. Ad hominem + I only show how weak the realist assumption is. > "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,. Of course. But we do metaphysics, and it is important to understand that the metaphysics is in CT and “yes doctor”, not in the arithmetical realism, which is used only to make sense of CT (needed to make mathematical precise sense of “digital”). Bruno > > 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 [email protected] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAFxXSLRsLk6y3xtR65U4MSjL8qHWf86Ak%3DVPruB_CKWL_MgLcQ%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAFxXSLRsLk6y3xtR65U4MSjL8qHWf86Ak%3DVPruB_CKWL_MgLcQ%40mail.gmail.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/482F9F70-E1AC-40AD-A636-7204475FC7F2%40ulb.ac.be.
