On Mon, Jul 22, 2019 at 7:28 PM Bruno Marchal <[email protected]> wrote:
> 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]> wrote: > >> On 19 Jul 2019, at 22:47, Dan Sonik <[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. > It is a clear conflation - necessay for no one. > 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). > Don't you, now. Maybe that explains quite a lot of what you are missing. > > What you refer to here is the fact that the word "dog" is not actually a > dog, namely a 4-legged mammal 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. > Who said it was among your assumptions? I state it as a fact that must be taken into account. > 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. > But that "proof" requires exactly the conflation of an existential quantifier with an ontology. The difference between "2+2=4" and 2+2=4 is that one is the name for the other. But the name is all that exists, so these are identical. > 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. > That is your mistake, not mine. > 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. > The theory consisting of (N, 0, +, *, s) is sufficiently rich for one to write down all arithmetical computations. But that does not bring these computations into existence -- you require pen and paper and intelligence, or something equivalent, to do that. The computations do not exist in the abstract. 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. > Oh dear. So all your work is a futile waste of time, then, is it? You invoke your metaphysics all the time. I reject your metaphysics in order to criticize it, by adopting a more reasonable metaphysical attitude. > That is the same, in metaphysics, as saying that the structure (N, +) > refutes group theory, in mathematics. > No, it is not. Sarcasm is not your strong point, Bruno. > 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 > Bullying yet again, Bruno. That only goes to show that you have no reasonable rebuttal of my point. > + 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”). > Without arithmetical realism (defined in the usual way, not as in Brunospeak), you cannot get all computations as existing in arithmetic, and the dovetailer does not ever get off the ground. So your metaphysics is strongly built in from the start. So don't you dare criticize me for my metaphysics. 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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLSf%2B4MFa0HGj3VwXYSyQLvDGB_fgxJKD-uW_2o3j9DA5Q%40mail.gmail.com.
