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

Dear Raiyan and Rastin,

Please call me Cristi.

>I found your line of reasoning demonstrating the hard problem of consciousness in fact exists, and its centrality to our conception of reality using arguments grounded in mathematics both ingenious and beautiful.

Thank you very much for reading my essay and for your insightful remarks.

>I will keep a copy of your work for further reading, and references ( if any circumstances arise).

I would recommend the longer one, The negative way to sentience, in case you are interested.

>What also pleases me is that I sense in between your work and ours [...] We hope you have time to read our work!

You definitely made me interested to hear more about your essay!

Thanks again for the visit, and I wish you good luck in the contest!

Cheers,

Cristi

Mihai,

Thank you for the lesson in English grammar, dully noted! I am also flattered by your attention with the second part of your comment. May I remind you that I defined what a mathematical structure is in my essay, and I also even gave you a link in replies to some of your comments, where you mistook it for "a mere representation of our minds" (which is not what I mean). Now you are mistaking mathematical structure for an axiomatization of it (which, again, is not what I mean, and I'm pretty sure Plato didn't mean this either!). As an example, think of the set of natural numbers, along with the operations of addition and multiplication defined as subsets of NxNxN. This is an example of a known mathematical structure. Now think at some axiomatization of it, and Gödel's incompleteness theorem, and see why the structure can be known, yet not everything about natural numbers can be known.

Cheers,

Cristi

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

        Dear Kevin,

        Thank you for visiting and reading my essay, and for the excellent question.

        > "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?"

        As my argument aims to prove, if consciousness is 100% reducible to relations, then one must also admit that a rule 110 cellular automaton with suitably chosen first row can have consciousness. This despite being a flat timeless tapestry. There are certainly people who think this, and even I take this view as true about anything that ignores sentient experience. And there are people who don't accept this, because they know that they are in a way beyond the mere relations, roles in society, processes, computation etc. Relations are about the "easy problems". And, while I agree that the behavior of consciousness, and all of its relations, including the causal relation that makes Descartes say "I am", are, of course, 100% reducible to relations, like the structures P and S mentioned in my essay, my whole claim is that this is not what makes experience possible. This is what makes conscious-like behavior possible. By sentience I understand what makes experience possible, its nature, its ontology. So consciousness is 100% relations by any objective and independently verifiable means, yet it's 100% sentience by its ontology, which is not accessible by the objective and independently verifiable means. Incidentally, while this position is usually associated to an epiphenomenalist position, I think that it can make testable predictions, so it's falsifiable. And in my longer essay The negative way to sentience I explain what variants of the relations between P and S correlate to what interpretations of Quantum Mechanics, and that some of them make testable predictions. If you are interested in this issue, I'd very much appreciate some comments to that longer essay, especially since you take the position that you take. No rush with this. And who knows, maybe you'll find the more elaborate arguments more compelling ;-) Or maybe you'll change my mind (just kidding about the latter, I doubt everything I think, except for the fact that I am sentient).

        Thanks again for the insightful comments!

        Cheers,

        Cristi

        Dear Yutaka,

        Thank you for reading my essay and for the interesting comments. You mention a past essay of yours, I read it at that time and commented. I look forward to read your current one.

        > "Your point is reductionism. Is this related to the operationalism?"

        I am not sure that my point is reductionism per se. I am fully for trying to push reductionism to its natural limits as much as possible. I discussed these limits in a previous essay. As for the relations with operationalism, there must definitely be such relations. And I take here the position that science cleaned of all of its assumptions is about relations only, which is close to operationalism. I am not an adept of operationalism in my work though. And particularly when talking about sentience, I think sentience (stripped of all form and relations) is what's beyond relations.

        Cheers,

        Cristi

        Dear Jonathan,

        I appreciate your visit and comments!

        Take my detour through "science as the study of relations but not relata" as a way to remove assumptions from science. Because without this purification, people would project, due to their mirror neurons, sentient-like properties on whatever models they make for consciousness, when in fact they are about the "easy problems" only. To see the naked truth that "consciousness is primal, or essential", as you well say, within the framework of science, one needs first to go through this process of austerization of science.

        >"I think the evolution of consciousness is possible to express mathematically, however"

        Evolution of consciousness probably corresponds to what I call the system S. If this is the case, it is possible to express mathematically. Octonions may play a role here, I have to look in your essay to see what you mean, and I look forward to do this.

        I like very much your remarks in the second part of your comment, and you made me curious. I was going to read your essay, but time ran too quickly. But I will read it in time.

        Cheers,

        Cristi

        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 Edwin,

          Thank you, and also thanks for the news, it was because of the notification about your comment that I know the result. This edition was again a great opportunity to exchange ideas, a lot of interesting essays here. Also the chosen theme was good.

          Cheers,

          Cristi

          6 days later

          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

          7 days later

          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

            Dear Markus,

            Thank you very much for reading and for the reply, and congratulations for your essay too!

            > "I believe that we could be part of a fully "classical" word, be conscious, and wonder about the very same questions."

            I believe this too, we have various relations between S and P, which are possible in both quantum and classical worlds. There are two reasons for me to focus on quantum theories here. The first one is that it is more easier to find relations in which sentience is causally active, as opposed to merely epiphenomenal, in quantum theories. Being causally active allows for testable predictions, while being epiphenomenal doesn't. It is logically possible that sentience is an epiphenomenon, but this would make irrelevant reasonings of the form "I know I am sentient because I experience it, and I know I experience it because I think about this experience and talk about it, and I know that others are sentient because they talk about being sentient". If we want such inferences to really be due to sentience and not to some whatever mindless evolutionary reasons that make us talk as if we are sentient as opposed to really being, I think philosophical zombies should not be taken seriously. I mean, I think sentience must be causally active, rather than a mere epiphenomenon. And I think most classical theories, at least the known ones, only support this kind of relation between S and P. In them, talking about sentience is still possible, but it's a zombie talk. Not all classical ones, I think that at least the known classical theories in physics allow only epiphenomenal sentience, and can't be tested empirically for sentience. By contrast, a causally active type of sentience is in my opinion more easier to accommodate in quantum theories, and in my longer essay I discuss various options, and it seems that most types of interpretations of QM allow it. This is interesting, because each type of interpretation of QM comes with a different answer to the question "what is the difference between the quantum and the classical", which means that classical theories that have certain features that quantum theories have, and by this allow for causally active sentience, are possible. I think something forces this possibility of causally active elements of a theory, and it may be a common denominator to all quantum interpretations: the existence of a quantum micro level and a quasi-classical macro level. The macro level is described in terms of the quantum level as a very small, zero-measure subset of the set of all possible quantum states. This is unlike in classical theories, where the macro states are well defined for any possible micro state. So this was my main reason to focus on quantum theories. And the second one is that the world is quantum.

            But I also agree with you that "this would be a topic for a longer discussion" :), which I hope we'll have someday, because I am very interested to hear what you specifically have in mind about this.

            Thanks again, and good luck with the contest!

            Cheers,

            Cristi

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