On 15 Jan 2014, at 15:05, Edgar L. Owen wrote:

## Advertising

If the fundamental axioms of arithmetic are the fundamental axiomsof your UDA then where do those come from?

`Russell and Whitehead suggested that they could be derived from logic`

`alone, but that has been refuted, and today, we know that we cannot`

`derive arithmetic from anything less than the first order logic`

`specification of a universal Turing system.`

`For the TOE I could use another Turing-complete theory, like the`

`combinators, with the two axioms`

Kxy = x

`Sxyz = xz(yz) (the precise meaning of this being not relevant`

`right now)`

From those two axioms, I can derive the arithmetic axioms. From the arithmetic axioms, I can derive the two combinator axioms.

`But from anything less than a Turing-complete theory, I can't derive`

`the existence of arithmetic or any other Turing-complete theory.`

`I guess you need to study some math to see what happens. I try to`

`explain the matter with enough detail from times to times, so that you`

`might grasp (independently of believing it or not).`

Unless you can answer that question you have a gap in your theorythat mine doesn't have.....

?

`Your theory is fuzzy, and seem to assume quantum mechanics, which`

`assumes arithmetic. The very notion of computations assumes arithmetic`

`too. Your theory assumes also a physical or psychological reality`

`(your present time).`

`Can you justify the numbers and prove addition and multiplication from`

`less than another choice of universal machine/number/system/language?`

`Our conscious understanding of {0, 1, 2, 3, ...} is a mystery, but`

`comp illustrates that it might be:`

1) necessarily mysterious, 2) and, with the laws of addition and multiplication, the only mystery.

`Comp explains, I think, why our understanding of {0, 1, 2, 3, ...} can`

`seem and even *be* obvious, *from* the first person point of view. But`

`that point of view is not communicable, and the (Löbian) machines`

`already know that (in precise rather standard sense).`

`In mathematics, that "obviousness" is more or less captured by either`

`a much less "obvious" theory (like set theory, or category`

`theory, ...), or by second order logic, which gives non effective`

`theories (proofs are no more checkable).`

`Once you assume comp, it is just a matter of work to understand that`

`the arithmetical reality is full of life and mysteries, when seen from`

`inside.`

`I don't know if comp is true, but the point is that by its relation`

`with computer science and mathematical logic, comp, well classical`

`comp if you prefer, is made testable/refutable.`

Bruno

Edgar On Wednesday, January 15, 2014 8:50:44 AM UTC-5, Bruno Marchal wrote: On 15 Jan 2014, at 13:41, Edgar L. Owen wrote:Bruno, Of course it is circular - but it is meaningful.Without further ado, circular statements are *to much* meaningful.The fundamental axiom MUST be circular,Is that anew meta-axiom? Again, that is not obvious at all.but it must be so in a meaningful way. I already noted that when Isaid it was 'self-necessitating'."self-necessitating" contains two hot complex notions: "self" and"necessitate".We want to explain the complex from the simple, not the other wayround.So far as I know my Existence Axiom is the most meaningfulfundamental axiom.If that was true, you would not need to say so.What is YOUR fundamental axiom? 'Arithmetic exists becausearithmetic exists' perhaps? Sounds like a similarly circular axiomto me....You should also never put statements in the mouth of others,especially when they are completely ridiculous, like if I would havesaid that "arithmetic exists because arithmetic exists".I am working at two levels: an intuitive meta-level, where theassumption is a precise version of Milinda-Descartes old mechanistassumption. To put it shortly it says that not only I can survivewith an artificial heart, kidney, skin, but that the brain is notexcluded from that list. It means that my body functions, at somelevel, like some sort of machine. As far as I understand you, itis implied by your "computational stance".So my assumption, at that level, is a tiny part of your assumption.By reasoning at that meta-level (UDA), we get as "meta-theorem" thatthe TOE does not need to assume more than the usual elementaryaxioms of arithmetic. One precise theory is classical logic + theaxioms, where you can read s(x) by "the successor of the number x".0 ≠ s(x) s(x) = s(y) -> x = y x+0 = x x+s(y) = s(x+y) x*0=0 x*s(y)=(x*y)+xThen, in that theory, all the terms I need are defined. It is inthat theory that we define the observers and derive physics (andmore). That's AUDA, or "the machine's interview" (in the sane2004paper). Comp makes the whole thing both mathematical andexperimentally testable.BrunoEdgar On Wednesday, January 15, 2014 3:10:30 AM UTC-5, Bruno Marchal wrote: On 14 Jan 2014, at 19:05, Edgar L. Owen wrote: > Bruno, > > 'Non-existence cannot exist', obviously refers to the existence of > reality itself, Then it is circular. > not to milk in your refrigerator! Existence must exist means > something must exist, whether it's milk or whatever. Individual> things have individual localized existences, but existence(reality)> itself is everywhere because it defines the logical space ofreality> by its existence. That is not intelligible. > > The Axiom of Existence means there was never a nothingness out of > which somethingness (the universe) was created. Assuming that there is a "universe". But then you do not explain why there is something. You just assume this. You axiom is "something exists". > > Milk is created by female mammals in case you had some doubt? > :-) > > Next question: Reality IS a computational MACHINE in the general > sense of machine. That is digital physics, which is refuted. > Thus of course consistency applies to it. That does not follow. Machines can be inconsistent. Bruno http://iridia.ulb.ac.be/~marchal/ --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To unsubscribe from this group and stop receiving emails from it,send an email to everything-li...@googlegroups.com.To post to this group, send email to everyth...@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.http://iridia.ulb.ac.be/~marchal/ --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To unsubscribe from this group and stop receiving emails from it,send an email to everything-list+unsubscr...@googlegroups.com.To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.

http://iridia.ulb.ac.be/~marchal/ -- 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 post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.