> On 11 Mar 2021, at 20:58, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 3/11/2021 3:51 AM, Bruno Marchal wrote: >> When doing theology (aka metaphysics) with the scientific method, it is >> better to not commit oneself in any ontological assumption at the start > > That's pretty funny coming from a guy who assumes all of arithmetic exists as > a starting point.
The staring point is the Mechanist assumption, and not more than Darwin. Then the reasoning shows that very elementary arithmetic is not only enough, but cannot be completed, so I assume less than basically all scientists. But your way to express this is misleading, as “all of arithmetic” is not an arithmetical notion, and it would need a much more string theory like set theory to be made precise, and this, typically is not part of my assumption. So I assume only, beyond classical logic the non-logical usual axioms: 1) 0 ≠ s(x) 2) x ≠ y -> s(x) ≠ s(y) 3) x ≠ 0 -> Ey(x = s(y)) 4) x+0 = x 5) x+s(y) = s(x+y) 6) x*0=0 7) x*s(y)=(x*y)+x This is the minimal amount of things that we have to assume to make sense of “Digital Mechanism”. I have no doubt you do believe in them, as they are used in all physical theories. I called that theory RA (Robinson Arithmetic), but his standard name in the literature is Q. It is a sub theory of practically any conceivable theory. It is even believed by formalist, as the definition of what is a formalism is as powerful as Q. I can even be dispensed of classical logic, and use the (entirely given) following theory (of combinators): 1) If x = y and x = z, then y = z 2) If x = y then xz = yz 3) If x = y then zx = zy 4) Kxy = x 5) Sxyz = xz(yz) I can use even weaker theory, but then they are no more finitely axiomatisable, and requires (like PA and ZF and most Löbian machines) some scheme of axioms. I might come back on the someday. Bruno > > Brent > > -- > 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/d57757bd-0cbe-e57e-3173-983bb2506bba%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/2E50A6D6-A97D-40A3-8D62-07D8CBD6A528%40ulb.ac.be.
