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 > > > > > -- > 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 [email protected] <javascript:>. > To post to this group, send email to [email protected] > <javascript:>. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
