> On 7 May 2020, at 23:00, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 5/7/2020 9:30 AM, Bruno Marchal wrote: >> I can imagine a materialist psychologist claiming that the natural numbers >> are not primitive but explainable by a cultural anthropo-evolutionary >> genetic, say. But 1) he is confusing the human natural number theories with >> arithmetic, and 2) he is cheating, as his explanation will make only sense >> by an implicit acceptance of some universal machinery equivalent to the >> belief in RA, so, he is just confusing level of explanation. > > It's not confusion when you explain something in terms of what you > understand. Confusion is to say things must be explained in terms of > something infinite and incomprhensible…
Not with mechanism. The assumption are just that Kxy = x, and Sxyz = xz(yz). In fact, with mechanism, we can explain why the axiom of infinity has to be false. Even, the induction axioms are possibly false ontologically. Mechanism, contrary of what I said a long time ago, is consistent with utltrafinithsm. > and then claim it's incomprehensibility proves it's primitive because is > can't have an explanation. That is provably the case for “simple" things like natural numbers and combinators, but is false for the appearance of matter as they are explained by the mechanist consciousness flux in arithmetic (itself explained by G and G* and their difference). Evidences for a physical reality are not the same as evidence for a primitive physical reality. That is the Aristotelian prejudice, which I think comes from a misunderstanding of Plato, or a lack of reasoning. There are tuns of evidences for a physical reality, and I understand the elegance and appeal the idea that such reality is primitive. Yet, I am rationalist and an empiricist. The close observation of the physical universe confirms that it cannot be primitive, like digital mechanism predicts. Bruno > > Brent > >> Yes, the human number theory is a fascinating subject, and it sustains the >> idea that 2+2=4 is “really absolutely” true, as all humans agree on this, >> and even many other mammals, actually. But that is a different subject >> matter than the one number theory is build for. This one avoid the >> philosophy of numbers by using the axiomatic method. It should be obvious >> that with mechanism, the discovery of the numbers by the numbers is part of >> the meta-arithmetic that Gödel’s showed embeddable in arithmetic. The real >> bomb is still Gödel’s 1931, even if it is the two theorems of Solovay which >> sums it all in G, and G*. > > > -- > 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/27aed6d9-b0f1-80e1-93ca-29ed04d4257a%40verizon.net. -- 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/00BDDFB5-7BCE-4273-B36A-E2AF6767FA5D%40ulb.ac.be.
