> On 16 Apr 2019, at 15:10, Telmo Menezes <[email protected]> wrote:
>
>
>
> On Tue, Apr 16, 2019, at 03:44, 'Brent Meeker' via Everything List wrote:
>> You seem to make self-reference into something esoteric. Every Mars Rover
>> knows where it is, the state of its batteries, its instruments, its
>> communications link, what time it is, what its mission plan is.
>
> I don't agree that the Mars Rover checking "it's own" battery levels is an
> example of what is meant by self-reference in this type of discussion.
It is a correct third person self-reference, like when someone says I have two
legs is correct in the case ha has two legs.
> The entity "Mars Rover" exists in your mind and mine, but there is no "Mars
> Rover mind" where it also exists.
I would say that there is surely a tiny one, but not something like what we get
from the second recursion theorem, which make a machine able to compute any
function applies to its own code.
Third person self-reference is the base of the whole recursion theory, and the
trick which makes this definable is Kleene’s theorem, as I have sometimes
explained.
More difficult is to capture the first person self, but we got it by the
“meta”-invocation of the notion of truth.
Rover is conscious, but still dissociated from ‘rover”. But that is just
because it has no strong induction axiom, and no way to build approximation of
models of itself. It lack a re-entring neural system rich enough to manage the
gap between its first person apprehension, and the third person apparent
reality around it.
> The entity "Telmo" exists in your mind and mine, and I happen to be an entity
> "Telmo" in whose mind the entity "Telmo" also exists. This is real
> self-reference.
I agree. It is unclear for me if Mars Rover has it, or not, as I have not seen
the code, and even seeing it, it could ba a Helle of a difficulty to prove it
has not that ability. I doubt it has it, because Naza does not want a free
exploratory on Mars, but a docile slave.
>
> Or, allow me to invent a programming language where something like this could
> me made more explicit. Let's say that, in this language, you can define a
> program P like this:
>
> program P:
> x = 1
> if x == 1:
> print('My variable x s holding the value 1')
>
> The above is the weak form of self-reference that you allude to.
Yes, but it can work for Rover’s task, and I agree it is less sophisticated
compared to genuine “second recursion”.
> It would be like me measuring my arm and noting the result. Oh, my arm is x
> cm long. But let me show what could me meant instead by real self-reference:
>
> program P:
> if length(P) > 1000:
> print('I am a complicated program')
> else:
> print('I am a simple program')
>
> Do you accept there is a fundamental difference here?
OK. Perfect. That one is definable by using Kleene second recursion theorem.
But it is still “this person self-)reference”, the first person experience
needs to involve the concept of truth (making the first person non definable by
the first person, but still mathematically precise for anyone assuming the
entity is sound (which indeed the entity itself cannot justify rationally).
Bruno
>
> Telmo
>
>>
>> Whether it is "formalizable" or not would seem to depend on choosing the
>> right formalization to describe what engineers already create.
>>
>> Brent
>>
>>
>> On 4/15/2019 11:28 AM, za_wishy via Everything List wrote:
>>> Hmm... the thing is that what I'm arguing for in the book is that
>>> self-reference is unformalizable, so there can be no mathematics of
>>> self-reference. More than this, self-reference is not some concept in a
>>> theory, but it is us, each and everyone of us is a form of manifestation of
>>> self-reference. Self-reference is an eternal logical structure that
>>> eternally looks-back-at-itself. And this looking-back-at-itself
>>> automatically generates a subjective ontology, an "I am". In other words,
>>> the very definition of the concept of "existence" is the
>>> looking-back-at-itself of self-reference. So, existence can only be
>>> subjective, so all that can exists is consciousness. I talk in the book how
>>> the looking-back-at-itself implies 3 properties: identity (self-reference
>>> is itself, x=x), inclusion (self-reference is included in itself, x<x) and
>>> transcendence (self-reference is more than itself, x>x). And all these
>>> apparently contradictory properties are happening all at the same time. So,
>>> x=x, x<x, x>x all at the same time. But there is no actual contradiction
>>> here, because self-reference is unformalizable. The reason why I get to
>>> such weird conclusions is explored throughout the book where a
>>> phenomenological analysis of consciousness is done and it is shown how it
>>> is structured on an emergent holarchy of levels, a holarchy meaning that a
>>> higher level includes the lower levels, and I conclude that this can only
>>> happen if there is an entity called "self-reference" which has the above
>>> mentioned properties. So as you can see, there pretty much cannot be a
>>> mathematics of self-reference.
>>>
>>> I will also present about self-reference at The Science of Consciousness
>>> conference this year at Interlaken, Switzerland, so if you are there we can
>>> talk more about these issues.
>>>
>>> On Thursday, 11 April 2019 02:55:55 UTC+3, Bruno Marchal wrote:
>>> Hi Cosmin,
>>>
>>> It seems your conclusion fits well with the conclusion already given by the
>>> universal machine (the Gödel-Löbian one which are those who already knows
>>> that they are Turing universal, like ZF, PA, or the combinators + some
>>> induction principle).
>>>
>>> Self-reference is capital indeed, but you seem to miss the mathematical
>>> theory of self-reference, brought by the work of Gödel and Löb, and Solovay
>>> ultimate formalisation of it at the first order logic level. You cite
>>> Penrose, which is deadly wrong on this.
>>>
>>> In fact incompleteness is a chance for mechanism, as it provides almost
>>> directly a theory of consciousness, if you are willing to agree that
>>> consciousness is true, indubitable, immediately knowable, non provable and
>>> non definable, as each Löbian machine is confronted to such proposition all
>>> the “time”. But this enforces also, as I have shown, that the whole of
>>> physics has to be justified by some of the modes of self-reference, making
>>> physics into a subbranch of elementary arithmetic. This works in the sense
>>> that at the three places where physics should appear we get a quantum
>>> logic, and this with the advantage of a transparent clear-cut between the
>>> qualia (not sharable) and the quanta (sharable in the first person plural
>>> sense).
>>>
>>> You seem to have a good (I mean correct with respect to Mechanism) insight
>>> on consciousness, but you seem to have wrong information on the theory of
>>> the digital machines/numbers and the role of Gödel. Gödel’s theorem is
>>> really a chance for the Mechanist theory, as it explains that the digital
>>> machine are non predictable, full of non communicable subjective knowledge
>>> and beliefs, and capable of defeating all reductionist theory that we can
>>> made of them. Indeed, they are literally universal dissident, and they are
>>> born with a conflict between 8 modes of self-apprehension. In my last
>>> paper(*) I argue that they can be enlightened, and this shows also that
>>> enlightenment and blasphemy are very close, and that religion leads easily
>>> to a theological trap making the machine inconsistent, except by staying
>>> mute, or referring to Mechanism (which is itself highly unprovable by the
>>> consistent machine).
>>>
>>> Bruno
>>>
>>>
>>>
>>>>
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