Sentience, the ontology of experience by Cristinel Stoica

Rayan, Rastin,

I couldn't disagree with you more as I've openly disagreed with Cristi also.

First, if you analyse carefully this his statement you quoted : "But even if we would know with what mathematical structure our world is isomorphic, it wouldn't mean we would know everything, because our knowledge can only be expressed in a finite number of axioms, and our proofs can only have finite length. Our knowledge will always be limited by G ̈odel incompleteness (G ̈odel, 1931) and Turing's noncomputability result (Turing, 1937) you could right away notice many anomalies:

1. It's not even grammatically correct ( "But even if we knew everything...it wouldn't mean... " is the correct syntax in English but Cristi is grammatically thinking in his mother tongue so I can understand and overlook the root of his error.

2. It's logically inconsistent since Gödel's results express exactly the opposite, namely, the even in mathematics there can never be a complete and self-sufficient system of knowledge grounded on a finite set of axioms, therefore mathematics is inexhaustible in itself. Chaitin, for instance, went even further to assert that mathematics as such, after Gödel, is ruled by uncertainty and randomness just like the one discovered in QM. He could be right in the sense that whenever and wherever actual infinity pops up(especially since Cantor open the way in set theory)so does uncertainty and randomness, so in a way, the so-called hidden order that science strives to discover in the Universe, seems paradoxically to be both opposed to randomness/chaos/disorder and necessary to it!...

3. Finally, it's semantically meaningless because it's a speculative and arbitrary hypothesis about an isomorphism of 'nothing concrete' with something abstract, that is, a clearly defined concept of a mathematical structure such as a topological or metric space for instance that are not only rigorously defined axiomatically.

Dear Mihai Panoschi Panoschi,

Thank you for your response!

Since you disagree with Professor Cristinel Stocia, you should direct your disagreements to them.

Grammar errors and such are something I can look over. I am also failing to see how the statement goes against Godel's Incompleteness Theorems and its computational analogue, Turing Machine.

To quote you, "It's logically inconsistent since Gödel's results express exactly the opposite, namely, the even in mathematics there can never be a complete and self-sufficient system of knowledge grounded on a finite set of axioms, therefore mathematics is inexhaustible in itself."

Actually, Godel merely says if a formal system can express or encode arithmetic then it cannot prove its self consistency with a finite set of axioms. So if a finite set of axioms strong enough to encode or interpret arithmetic is incomplete in the sense we will have statements which we cannot decide it is true of false with the statements we have. Which is what Professor Cristinel Stocia's clearly states; if there exists a mathematical structure isomorphic to our physical reality, we cannot prove its self consistency. The implicit assumption is that such a structure much include formal systems strong enough to encode or interpret facts about arithmetic. They state, " Our knowledge will always be limited by Godel incompleteness (Godel, 1931) and Turing's noncomputability result (Turing, 1937)". It is very clear to those familiar with Godel and Turing's results. The limitations are we cannot verify the consistency of the mathematical structure.

As for the hypothesis being unfalsifiable, that itself is not true. Read Principle 2, "The collection of all true propositions about our physical world admits a mathematical model"

Thus, if have a mathematical model ( which we can derive from the said mathematical structure), that produces all the true propositions as verified through observation, measurement, and experiments we have a way of connecting the mathematical structure to the physical world. Whether or not they are the mathematical structure itself is a useful abstraction or actually exists is a separate question.

Professor Stocia cites Tegmark, and I think if you refer his work you would fine a more detailed explanation of a mathematical structure, how it is corresponds to our physical world ( by doing a set of mathematical operations deriving physical symmetries) and such.

Again, I am no expert here, but the extend Professor Stocia detailed her work, and from what I know I see and understand I cannot detect any "anamoly", and grammar errors while unfortunate is something I have no interest in penalizing someone for.

Kind Regards,

Raiyan Reza

Raiyan,

Wittgenstein warns and teaches us that grammar/syntax plays an important role within the semantic universe of a given language. The "If Clause" in English has a very precise and well defined temporal structure that we need to pay attention to when we write something of (supposedly) importance such as a scientific essay. For instance, I again fail to comprehend what you're trying to say in this sentence: "Thus, if have a mathematical model ( which we can derive from the said mathematical structure), that produces all the true propositions as verified through observation, measurement, and experiments we have a way of connecting the mathematical structure to the physical world. Whether or not they are the mathematical structure itself is a useful abstraction or actually exists is a separate question." and what type of "If Clause" you're trying to use...

Since it is not a clear cut of a cause/effect type 0 relationship like in "if it rains, the ground gets wet", and it's something more hypothetical and problematic, I think what you're trying to say is that " Thus, if we had a mathematical model....then we would have a way..." which for me resembles more of a wishful naïve thinking rather than serious logical argumentation with its further implications.

But maybe you're trying to say something else in which case I may be wrong but we'll both agree that in both cases correct grammar plays an important role for our understanding to have a common starting ground and thus make the transfer of ideas between two minds possible. So, it's not necessarily about penalising but about comprehension and communication of our thoughts mostly.

Dear Cristi,

I am very glad to see that your essay is doing well.

I really enjoyed it!

The consciousness question is both difficult and fascinating. And I think that the fact that we have so much of ourselves invested in the solution does not help us to attain an honest understanding.

I have long thought that consciousness arises from the brain modeling (describing ) itself, which is inherently self-referential. If so, we should expect some element of strangeness or surprise. What precisely that would be, I am not in the position to say. That by itself would be an interesting question. What predictions could this hypothesis (that the brain describes itself) make? Certainly, answering this is necessary for falsifiability.

I would agree that science focuses on relations and not things.

This really is the essence of my work on Influence Theory, which has shown greater promise than I had originally expected.

In that work (Influence Theory), we make it clear that the only properties that one can know about are those properties that affect how an object influences others. Despite the validity or invalidity of Influence Theory as a foundational theory, I still believe that this idea is correct.

So what does this say about Consciousness in terms of it being a result of relations or substance?

Well, if consciousness is a property that arises from properties of a substance, then we can only know about this property consciousness because it affects how objects influence one another. In fact, further thought reveals that the characteristics of that property are defined (operationally) by the affect it has on such influence. Since influence is a relation, and that is the only means we have to know about or describe properties, then consciousness cannot really be the result of a property of a subtance, because it would be indistinguishable from the property of any other substance that affected influence in an identical manner.

So, I would have to conclude that consciousness must arise from relations, like most everything else.

I'd like to hear your thoughts on that.

As for me, I still think that consciousness arises from the brain modeling itself.

Thoughts??

Thank you, again, Cristi, for your enjoyable and thought-provoking essay!

Sincerely,

Kevin

Dear Cristi,

I really enjoyed reading your essay to cover several academic fields.

In Section 5, you discussed the relationship between thermodynamic context and information theory or computational viewpoint. In the past essay contest, I wrote the specific part of this fundamental question as seen in my past essay. Your point is reductionism. Is this related to the operationalism?

Best wishes,

Yutaka

Dear Cristi,

Thanks for replying and sharing the longer version of your work, we will read it with great interest!

We wish you all the for this essay contest and research!

Raiyan and Rastin

Dear Professor Mihai Panoschi Panoschi,

I apologize for missing an honorific in my first response.

Thanks for replying and your thought provoking comments!

That said, yes I fully agree grammar and syntax play an important part in semantics of sentences and indeed cited Wittgenstein in my own work to advocate my stance, though I by no means claim your level of expertise or depth.

Having said that, in day to day conversation we rely on "informal" systems to communicate.

Unless you propose to reduce everything we have said to a formal system ( which is time consuming) than some degree of leniency on regards to grammar, and syntax is warranted, even in scholarly works.

That said, I am confused you attribute cause/effect to the sentence, "If it rains, the ground gets wet". Implication is not causation, something I remember being from my Discrete mathematics course. Let us attribute false value to the proposition p," it rains", and truth to the proposition ," the ground gets wet", the truth value for p implies q would still be true. However, a causal understanding would tell us a different scenario.

Again, thanks for your detailed critique and replying here!

All the best for this essay contest and researches! And, I suppose apologies for semantic ambiguity and resembling "naive wishful thinking".

Best Wishes,

Raiyan Reza

This paper was fun to read Cristi...

I'm grinning right now like someone who looked in the back of the book in the section called 'solutions to problems.' Or maybe I've just been actively exploring the other side of the coin from what you set out. If Science is only in the realm of relations and theory arises only in the form you describe; what I have been doing is not Science nor theoretical Physics.

Instead; I discovered something in pure Maths that boggles the mind, almost by accident while trying to find something else, and as with Haldane struggled for years to understand what I had discovered and to learn its relevance. I spent 33 years grappling with questions like "Why does it explain so much?" and more recently with "How do I avoid getting scooped again?" when someone comes out with a theory proposing something I'd learned years ago.

For the record; I do think consciousness is primal, or essential. I think the evolution of consciousness is possible to express mathematically, however, or resides naturally in the octonions as the vehicle for projective geometry, the geometry of perspective and hence of observation. I have just published a collection of "Octonion Poetry" (link below) with a section explaining how that algebra explicates the dynamic of involution and evolution, leading to a specific syntax and yielding sentences that sound like aphorisms or poetry.

"One, open, as multiplicity and formless nothingness, finds peace in true relation, and knows all as self." - J. Dickau

So if true; this means that consciousness cannot arise by its local relations alone, but only in relation to the whole, or global relations. One can think about this in terms of Misner, Thorne, and Wheeler, chap 44 sec 5, talking about pregeometry as the calculus of propositions. Oneness --> openness --> postulation --> repetition, and so on. The same words can serve as a formula for quantum gravity or for the evolution of consciousness. It's kind of a personal credo for me, but it is suitable for scientists. Proceeding as if we are a multiplicity of things and a sea of nothingness between them acknowledges reality as it is.

Anyhow; you get high marks from me, and you leave me with about 144 more pages of comments to make. So I'll leave off here for now.

Regards,

Jonathan

Unity, Oneness & Numbers: Octonion Poetry

Cristi, I seem to recall mentioning that the concept of mathematical structure came out of the set theoretical approach only in modern times, especially with Bourbaki in the 50s. What I've said earlier was that if a certain concept or structure is rigorously axiomatised, like the example you picked with the set of natural numbers N, then the additional structure you wish to add to it, e.g. operations of addition, multiplication, ordering etc. the respective functions or relations will still be still based on

the fundamental axioms system, Peano-Dedekind in this case or ZFC if you want to prove other theorems unprovable in Peano-Dedekind. Therefore I'm not mistaking mathematical structure for an axiomatization of it but rather I take it as the ground of it and I'm also quite sure that Plato wouldn't disagree either, since it is since Plato that we've been thinking in terms of noumena/ essences as the ground or root of phenomena/ appearances and our mental representations of them.

Therefore rigorously speaking, addition as a function on NxN -> N is based recursively on the 'successor' injective function S and the '0' number as defined axiomatically by Peano- Dedekind. Therefore you need '0' and the 'successor' injective function S first as primitive concepts to build up other simple relations or structures on N or richer algebraic structures such as that of group, ideal, module, ring or field. Having said that, an interesting question in the context of your essay however will be 'where do you get the intuition of successor or the number '0' or '1' from?' Do we get them from the ontology ( Being) of experience as it enfolds in Time or from the phenomenology of Mind ( (thinking, self-consciousness). If one reflects properly, I'd say that absolutely all beings ( things, concepts, relations, structures, systems, processes, etc) presupposes a 'thought' or 'consciousness' having that entity as its object and consequently 'being-thinking' are two terms of a disjunction and for this reason oneness is not to be found in one or the other but in the connection of both!!...

This question will take us back to the very same problem posed by the Greek philosophers, namely, to the relation between Being and Thinking as to which one is more fundamental but, with few exceptions, not many people actually cared to understand deeper their connection as Truth and Certainty which is why probably we have more to learn from Lao Tzu (as Bohr once remarked), Parmenides, Plato, Hegel, Heidegger's or Noica's treatises of ontology etc. than from a modern text book on symbolic logic.

Christi,

Congratulations on winning the community scoring. I gave you a ten on the last day to help put you there, but I see that fqxi has knocked you below someone with only two scores. I was the winner of the community scoring last year, but fqxi then changed the scoring so that I ended up number two.

These contests are valuable for presentation and exchange of ideas, but once fqxi enters the picture, the fix appears to be in for conformity with the academy. Congratulations again on your winning the other authors' approval.

Edwin Eugene Klingman

Dear Cristi,

I would appreciate to learn if you happened to read my last response. No, reading is not a requirement, just the information.

Rajiv

Dear Cristi,

congratulations to a wonderful essay! I've finally found the time to read it, and I enjoyed it a lot.

I agree with many of your arguments. This I found great: "For example, call the nature of things `matter´. Once we get used to the words, we can have the illusion of understanding, and forget that we know so little". And you make a very good point for the "hard problem".

I'm not sure I fully agree with the way quantum theory enters at the end of the essay, because I believe that we could be part of a fully "classical" word, be conscious, and wonder about the very same questions. But this would be a topic for a longer discussion I guess. :)

All the best,

Markus