> On 12 Jul 2019, at 21:10, 'Brent Meeker' via Everything List
> <[email protected]> wrote:
>
>
>
> On 7/12/2019 2:28 AM, Bruno Marchal wrote:
>>> On 11 Jul 2019, at 19:48, 'Brent Meeker' via Everything List
>>> <[email protected]> wrote:
>>>
>>>
>>>
>>> On 7/11/2019 3:40 AM, Bruno Marchal wrote:
>>>>> On 10 Jul 2019, at 23:04, 'Brent Meeker' via Everything List
>>>>> <[email protected]> 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.
>
> And we have an even better intuition of what is consciousness.
Natural number is conceptually clearer and simpler than consciousness (on which
the human fight since day one). When I was young the term “consciousness” was
said to be prohibited in science. Some scientists still believe so.
> And it doesn't comport with your definition.
I am intersted in knowing why you say that. Which part doesn’t comport ?
>
>> 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.
>
> But that's my complaint that you have not defined consciousness. You have
> defined computations. But not all computations are consciousness. It's like
> saying "A country in Europe" is a definition of Belgium.
I don’t see the relation with my definition. I recall it:
A conscious person is someone for which there is something:
-true,
-immediately knowable,
-indubitable,
-non provable,
-non definable without invoking the notion of truth
Another definition is that consciousness is the belief (in a weaker sense than
“[]”) in at least one reality. I don’t use it due to the difficulty to define
that weak notion of belief. The one above is simpler, and entail that all
(Löbian) universal machine are (self) conscious.
It provides a role to consciousness: accelerate the computation with respect to
the probable universal number/environments which execute the computations
supporting that consciousness. All this is detailed in some of may papers.
That does not make all computation conscious, only the universal or Löbian one.
>
>>
>> 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,
>
> Then why pretend you have defined it?
Because I meta-define it. With mechanism, the seemingly paradoxical state of
affair is solved in the same way that with Traski notion of truth. The machine
or theories cannot define a truth encompassing themselves, but can do that for
simpler machine that they can prove consistent.
The axiomatic tools have been invented to allow those kind of apparent
paradoxes.
>
>> 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.
>
> That's like saying you've found a country in Europe; therefore it is Belgium.
See above.
> That's the problem with the axiomatic method, you can't get out more than you
> assume at the start.
The contrary is true. The problem with the (first order logical) axiomatic
method is that we always get more than what we assume. We get the non standard
models. But the advantage is that we get rigour and precise statement, whose
clarity comes from the independence from metaphysical baggage (already lost
with second order logic).
Bruno
>
> Brent
>
>
>
>>
>> Consciousness is far simpler than matter, but not that simple!
>>
>> Bruno
>>
>>
>>
>>> Brent
>>>
>>>> Bruno
>>>>
>>>>
>>>>
>>>>
>>>>> Brent
>>>>>
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