> On 23 Sep 2019, at 19:41, Philip Thrift <cloudver...@gmail.com> wrote: > > > > On Monday, September 23, 2019 at 8:43:05 AM UTC-5, Bruno Marchal wrote: > > > On 20 Sep 2019, at 01:25, 'Brent Meeker' via Everything List > > <everyth...@googlegroups.com <javascript:>> wrote: > > > > Consciousness being algorimthic or Mechanism? and what notion of truth > > does it rely on? (not the one conditional on Mechanism being true, I > > hope). > > Not it relies on the arithmetical truth, which we cannot define, but > everybody agrees on it. > > > > There is no "arithmetical truth" that "everybody agrees on" because there is > no agreement on the things the variables refer to.
I am not sure why you say that. That could make some sense for set theory, or function theory, but for arithmetic, we have a pretty good idea what the variable refers to, as we can get them from 0 and a simple operation s(0) (1), s(s(0)) (2), etc. It is like consciousness and time, we cannot define them, but we do know what we are talking about. In fact, concerning the natural numbers, it takes a lot of study to understand that we cannot genuinely define them. > > (An ontology that only has a finite set of numbers 1, 2, ..., #thatsallfolks > leads to a different arithmetical truth.) No. It leads to different notion of numbers, unrelated with the arithmetical truth. We have accepted the following axioms: 0 ≠ s(x) s(x) = s(y) -> x = y x = 0 v Ey(x = s(y)) x+0 = x x+s(y) = s(x+y) x*0=0 x*s(y)=(x*y)+x There is no model of this with only finitely many numbers or, you are using “finite” in a non standard sense. We can’t define “finite” and “infinite” either, except by using stronger logics or axioms, leading to further ambiguities, like in analysis (second order arithmetic) or in set theory. The natural numbers is the domain where all humans have no problems, other that the problem in cognitive science related to how we can understand the numbers. A nice paper is McCulloch paper: “what is a number that a man can understand, and what is a man that can understand the number”. You have cited numerous paper which are based on our understanding of the natural numbers and their laws. Bruno > > @philipthrift > > -- > 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/6ead3c59-2d5e-4b5b-87bc-d569a3977bb5%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/6ead3c59-2d5e-4b5b-87bc-d569a3977bb5%40googlegroups.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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/BD30F9DD-D3B3-42F4-BB17-CD530ABE7279%40ulb.ac.be.
