Re: Within Proof Theoretic Semantics Gödel's G h as no meaning in PA
André G. Isaak <[email protected]>
| Newsgroups | sci.logic,comp.theory,comp.ai.philosophy,sci.math |
|---|---|
| Organization | Christians and Atheists United Against Creeping Agnosticism |
| Message-ID | <[email protected]> |
On 2026-07-06 12:12, olcott wrote: > On 7/6/2026 12:56 PM, André G. Isaak wrote: >> On 2026-07-06 11:45, olcott wrote: >>> On 7/6/2026 12:27 PM, André G. Isaak wrote: >>>> On 2026-07-06 10:58, olcott wrote: >>>>> On 7/6/2026 11:07 AM, André G. Isaak wrote: >>>>>> On 2026-07-06 09:47, olcott wrote: >>>>>>> On 7/6/2026 4:17 AM, Mikko wrote: >>>>>>>> On 04/07/2026 20:07, olcott wrote: >>>>>> >>>>>>>>> Q that cannot resolve (∀x, S(x) ≠ x) is complete >>>>>>>>> according to its definition. >>>>>>>> >>>>>>>> By the defintion of "incomplete" Q is incomplete. The theory >>>>>>>> Q + (∀x, S(x) ≠ x) is more complete but still incomplete. >>>>>>> >>>>>>> It fully meets its design spec thus calling it >>>>>>> any kind of incomplete is a damned lie. >>>>>> >>>>>> What exactly do you think the 'design spec' of Q is? >>>>> >>>>> Make sure that Q has less capability than PA is its design >>>>> spec by its designer. >>>> >>>> And you presumably have a reference to back that up? >>>> >>> >>> It is common knowledge that was Robinson's purpose >>> >>> In mathematics, Robinson arithmetic is a finitely >>> axiomatized fragment of first-order Peano arithmetic >>> (PA), first set out by Raphael M. Robinson in 1950. >>> It is usually denoted Q. >>> >>> https://en.wikipedia.org/wiki/Robinson_arithmetic >>> >>>> But it doesn't matter either way since the mathematical definition >>>> of incomplete makes no reference to the 'spec' of a system. >>>> >>> >>> Within the natural preexisting order of the body >>> of knowledge saying that incomplete(math) inherits >>> part of its meaning from incomplete(base) semantic >>> parent node is simply a lie. >> >> Yes, I agree that it is a lie. >> >> For starters, there's no such thing as the 'natural preexisting order >> of the body of knowlege'. >> > > Sure there is. There is a minimal sized knowledge ontology. > Anything less than minimal wastes RAM and CPU cycles. Saying something is preexisting means it has always been around; before there was RAM or CPU cycles; before there were people to know things. A specific computer model might implement a knowledge ontology, but that's hardly 'preexisting'. And if it implements something where the mathematical meaning of 'incomplete' inherits from some other definition of 'incomplete' then that model does not correspond to reality. André >> And incomplete(math) doesn't inherit from anything so claiming it >> inherits from incomplete(base) (whatever that may be) is of course a lie. >> >> André >> > > -- To email remove 'invalid' & replace 'gm' with well known Google mail service.