> On 11 Jul 2019, at 19:48, 'Brent Meeker' via Everything List
> <everything-list@googlegroups.com> wrote:
>
>
>
> On 7/11/2019 3:40 AM, Bruno Marchal wrote:
>>> On 10 Jul 2019, at 23:04, 'Brent Meeker' via Everything List
>>> <everything-list@googlegroups.com> wrote:
>>>
>>>
>>>
>>> On 7/10/2019 7:59 AM, Bruno Marchal wrote:
>>>> The machine define by the two following equations Kxy = x and Sxyz =
>>>> xz(yz) + S ≠ K, and with the combinator induction axiom (that I gave some
>>>> posts ago) is already as much conscious than you and me.
>>> Which in it self is a reductio of your theory.
>> Why? If you agree with the definition of consciousness that I have given
>> (true, knowable, non provable, non definable without invoking truth) then
>> SK+induction *is* provably conscious, and indeed has the G/G* theology
>> applicable to it.
>
> But I don't agree that your definition defines consciousness. And part of
> the reason for that it doesn't include being conscious of something. And I
> don't even know what "non-definable without invoking truth" means. Since
> "truth" is, according to you, undefinable that would seem to say your
> definition of consciousness says it's undefinable.
But we do have a good intuition of what is truth for simple Löbian machine,
like we have a good intuition of the arithmetical truth. Indeed without that
intuition, there is no second order arithmetic, that is there is no Analysis,
no “limits”, no topology on the reals. And all this can be formed in super-rich
theory, like set theory.
I know it is subtle matter. But with mechanism, consciousness is shown non
definable in exactly the sense of Tarski theorem on the non definability of the
arithmetical truth, and consciousness becomes “meta-definable” in analysis or
second order logic.
Consciousness is “<>t” (consistency) but as seen from the first person
perspective (which is more close to <>t < t, making it trivial in that
perspective, like we feel it to be).
Now, consciousness of something is given by just <>p < p.
>
> Elsewhere you rely on the common sense idea that everybody you're
> communicating with knows consciousness "from the inside", which is
> independent of your definition.
?
No it is part. It is the “indubitable” part, and in the “immediately knowable”
part.
> And for your definition to work you would need to show that it not only
> describes the first person experience of consciousness,
OK. That is the knowledge part. Glad you see this.
> but also that it doesn't describe anything else.
Why should I?
As I explained to Bruce, this is just impossible. Not just for consciousness,
but already for the simple natural numbers. Nobody can give a definition of the
natural numbers which would be true only for the natural numbers and not
something else. We cannot eliminate the non standard models.
Some would say: "- come on, we can define the natural numbers in ZF set
theory", but that would be true if they were non non standard model of set
theory.
By definition, a standard model of ZF is a model where the least infinite
ordinal is supremum (borne supérieur) of the finite ordinal as defined by von
Neumann induction (0 = { }, n+1 = n U {n}).
With mechanism, we can “prove" in (ZF + some large cardinal) that to define
consciousness is equivalent to define the natural numbers, and that this is
just totally impossible for any (standard) machine. I put “prove” in quote,
because that large cardinal has to be *very* large, and we can’t exclude that
it is so large that it makes make set theory inconsistent. I am working on this
since sometimes (formalising the whole Mechanist philosophy in some model of
ZF).
> Yet you're saying it also describes the consequences of two equations.
It is not a description. It is just that in the theory RA or SK, we get all
computations, and so we get consciousness by computationalism, intuitively
*and* in the sense that we get the machines which are confronted to some true,
immediately knowable, indubitable, yet non definable and non provable
proposition.
It looks like “time” when addressed by St-Augustin. He was taking about
subjective time, to be sure, and describe it as what he knows the most, yet get
utterly confused when attempting to describe or define it. Consciousness is
like that: it is what we know the best, yet we are incapable to define it, and
indeed, like the numbers, we need it to describe it. In a sense consciousness
is the virtuous irreducible circle. Then with mechanism, it can be shown to be
a fixed point of a transformation of the machine, that the machine cannot named
or described.
Consciousness is far simpler than matter, but not that simple!
Bruno
>
> Brent
>
>>
>> Bruno
>>
>>
>>
>>
>>> Brent
>>>
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