Cristi, any domain of knowledge that is able to turn from a domain dealing with (supposedly)real objects, magnitudes and relations found in the outer 'outer world', into an autonomous discipline that is able to take care of its own foundations by thinking itself and using key concepts produced 'from within' could therefore be considered a 'think in it self' in Kant's sense or as something that reaches the essence or strikes into the heart of the that domain, enabling us to understand reality in a much deeper way. Mathematics for instance started out as the 'science of magnitudes' but it has undergone repeated and gradual reconstructions of its basic and most fundamental concepts and ideas, and which eventually finished in the belief all mathematical theories can be considered extensions of set theory and hence a thing that's worth studying in itself and for itself ( as Hegel would say).Modern physics, or rather its foundations, is heading in the same direction so I guess one could say that physics in itself is mathematics, but that of course will be a gross underestimation of other powerful unifying concepts in physics such as field, symmetry, conservation law, etc

Dear Cristi Stoica!

We reviewed your work. The text contains many important and original ideas. We share the initial assumptions made in the article. Yes, science is studying relationships. But there is an ontology - a philosophical theory of being. You correctly noted that there is Time - a strange entity. But in the world there is something called GENESIS - this is an expression of Time. Therefore, we believe that the very principles of mathematics need a deeper clarification. For example, Hegel tried to see the genesis in logic. We think it makes sense to look for the genesis in mathematical structures.

We wish you a successful scientific work!

Truly yours,

Pavel Poluian and Dmitry Lichargin,

Siberian Federal University.

    Dear Pavel and Dmitry,

    Thank you for the review and the very interesting comments. I'll read your essay in time.

    Cheers,

    Cristi

    Dear Cristi,

    Thank you indeed for re-opening the discussion, I thought you had closed it. And I must say, I liked the intensity and forthrightness of your later response as truly heart warming. I am sure, you must be socially and professionally successful for keeping such fierceness within, and presenting only the kind of response you offered me first. I have not learned this trick.

    I respond only to one point you mentioned that includes several contentious issues between us. Let me apologize upfront for this being long, yet non-comprehensive, I do trust in your acute abilities to discern and see things beyond what is presented. For detail, please refer to Fundamentals of Natural Representation . I would request you to be kind first to give a serious consideration, then to be exceedingly critical.

    >> You make a profound observation, "science deals with relations only, not with the nature of things", and yet you let that slip out of hand.

    > Well, thank you, but you could point out where I let it slip out of hand. Or perhaps it just went in a direction you disagree with?

    Most of us have not seen yet that the relations are all that we can observe, not the underlying reality, which may not be deterministic. Every observation is relative to some configuration of instrument, every deduction is relative to a reference, every description is an expression of relations, and every information is constructed of relations only. It troubles most that how can one create a definition or a description of an object in terms that are not in themselves absolute; that is, a description is not complete without a firm basis. But the absolute basis does not exist. Even the definition of an electron is based on constancy of certain relative causal state descriptions, (rest mass 0.511 MeV, 1 negative electronic charge, and one half spin) that remain preserved under transformations; the accountable constancy of causal states gives it an identity.

    Fundamental primitive (elemental semantics) of all descriptions is the causal power of physical systems, so let me define the limits of natural causation first. Natural universe, as observed from within, undergoes change. Changes exhibit certain uniformity and regularity (constancy), such that an observable state S of a physical system P bears dependence on certain other states {S_i} within limits, where {S_i} may include relative static or dynamic values (rates of change). That is, if {S_i} were not to form a part of contextual reality within the limits, the state S of P could not have an existential reality either. Therefore, if a state C bore a dependence on B, and B on A, then it is possible to define an order on the sequence of dependence. A mutual dependence indicates conjugate state variables evolving together. It is ascertainable then that A is a precursor to B, while A and B are to C. It is noteworthy that A is not said to cause B, but rather B depends on A; B may depend on other factors in conjunction or disjunction. This relation of `precursor to the consequence' is referred to here as `natural causation'. It is referred to as `natural' to imply the independence of this relation from any model or interpretation, to mean what really exists, an ontological connotation.

    From the first principles of constancy of causal relation in the nature of change, if an interaction among physical systems results in an observable state S of a physical system P, then S of P must remain congruent with, or correlate with the information of the causal context effecting the change. Otherwise, measurements do not have an interpretation relating to the cause. Let me be forthright and ask, can we deny this? One must take a moment to either except or deny this for this is critical. If not, then we have an ontological basis to existential reality of information of causal correlation, independent of an interpreter.

    Causal context includes precursor state descriptions of interacting systems. For example, mass of a physical system Q denotes its causal power in an interaction, which constitutes Q's function or the basis of its relation with other systems. If a system P interacts with Q and gains a state S due to this causal function of Q, then S of P is said to correlate with this information; `mass' is mere label for the causal power of Q. Causal power of Q (mass) forms a semantic primitive from which higher level structured semantics can be constructed. This is how semantics gets grounded in physical function. The information of causal correlation of state S is referred to here as semantic value represented by the state S; this statement connects the term `semantics' to the physical function while also defining `representation'. That is, the term semantics is used only to refer to what value (relation) an information expresses.

    For the same reasons of natural causal dependence, S of P also must correlate with what the observed precursor states of interacting systems correlate with. This is a second order correlation which inductively takes into account all causal descriptions responsible for S of P. Can we deny this either? It is the second order correlation that allows construction of all structured and abstract semantics as shown in the cited publication above.

    A few more definitions:

    Object: An object has a specification in terms of functional relations with other objects, or in terms of a structural relation among its components, it is always expressed in relative terms; therefore, an object description or definition is equivalent to a semantic value. Structural and functional relations suffice to construct specification.

    State: A description of causal quality associable to a physical entity having an observable consequence defines an element of state.

    Relation: A relation among objects is an expression (description) of constancy that holds over the objects even when objects undergo change or transformation. The term `constancy of relation' refers to this description. Therefore, a relation functions as a constraint over objects related.

    Interaction: An interaction is defined by the `observable transitions in the states of physical entities' that are accountably interdependent on the description of causal powers (qualities) of the states.

    From the perspective of a transition to an observable resultant state S of a physical system P, an interaction is equivalent to a specific transition from a priori configuration of precursor states of accountable interacting systems to the state S of P. An interaction is describable as a disjunction of specific conjunctions (configuration) of precursor state descriptions of respective interacting systems that result in the observable state S of P. That is, information processing occurs at each interaction by this expression. Furthermore, this expression forms a constructor of all expressible semantics. Please refer to the cited publication above.

    Abstract and abstraction: The term `abstract' as an adjective is used as a qualifier to refer to a definite class of objects or instances, or to a relation that describes the class. `Abstraction' refers to the process of forming a class, or the emergence of a class from its instances. Therfore, a reference to an enumerable set of instances, or to a range of values is a reference to a class descriptor, an abstract entity, which is describable as disjunction of discrete values, or overlapping range of values.

    As promised earlier, a proposed definition of consciousness is as follows:

    Consciousness is a phenomenon of representation of structured information that specifies objects and their inter-relations, where one of the objects refers to the very system of representation at a level of abstraction that includes the system as an observer, and effector of change. The generic term object includes all that is referable. Every term used in this definition has already been related to causal function, thereby avoiding any intermediate hidden miracles. This definition is stated to be minimal, which only requires a representation of an observing self relating with other objects to control action. A stronger definition is one where a step higher abstraction of structured self is required that includes specific references to self as an observer of observing and controlling self.

    Though I had not planned to enlist what you let slip out of hand, even though you captured the most critical element about the role of relations in science, but since you asked, let me state.

    1. The most fundamental causal qualities (states) that give rise to all observable changes can have only relative description. That is, observations are limited to relations, and we can never have direct access to physical reality of causal states.

    2. All information is only expressions of explicit or implicit relations. This recognition takes the discussion away from Shannon's measure of information to the semantics of information, and to semantic processing.

    3. The reality of information is associated with the observable states of physical systems as given by causal relation among precursor states, not with the system itself. Whereas, among several other considerations of information in physics today, one is the information content of a physical system is a description of its own (model) state such that a measurement in specific context conforms to it. If it were to be so, then no matter what information processing occurs via physical interaction, information can never be anything but a state description, never the kind what a brain represents and processes. That is how we have created an artificial barrier. That is why universe appears to compute its own evolution. Funny thing is, even in the domain of computing, artificial semantic values (information) are associated with (assigned to) the states of registers rather than to the registers themselves. In the natural context, the relation of causal dependence forms the ontological reality of information.

    4. If information processing occurs at logic gates in computing devices, so it must take place at all interactions in natural context; all that one requires is to found a generic expression of relation that holds true at each interaction. The constructor expression stated above serves this purpose. Now, all that is required is processing in modular hierarchy to construct higher level semantics as neurons do. No coding or decoding is required, a neural state correlates with specifics of information intrinsically, and given by disjunction of conjunctions of semantics represented by pre-synaptic neurons. This is only mechanism suggested so far on how information processing occurs in neural system. Neurons representing contextual elements in coarse coding method share synchrony, which can then be used to activate other neurons in hierarchy. A preliminary simulation is presented in the cited work.

    5. Since, information cannot be separated from observable states, the only knowable reality is information, even though not directly measurable, everything else is interpretation. And, as defined above consciousness is constructed of specific information, that includes a semantic description of self as an observer, as an actor, as a controller, and so on, along with its relation to all other represented objects, even the phenomena of consciousness has a basis in relation, and information. Please note that objects are created by relations, they have no absolute correspondence to external reality.

    First para from my essay: If we look around, we observe objects and their inter-relations embedded in 4.pi steradian (sr) space; consider relations as objects too. We particularly note that all of the observable descriptions are constructed of information. For instance, the paper or the computer right in front, is constructed of shape, size, color, texture, brightness, distance from us, material it is made of, and its placement relative to the table which in turn has a description made up of similar information, and so on. Next we notice is the ontological realism of all this information. Here, we are not concerned with whether or not the computer and the table exist, not even with the consciousness that relates this information to the observing self, merely with the descriptive information. Are we in a position to deny the existential reality of this information? Observe carefully! One may draw an immediate inference that all elements of consciousness, including the self and its relation with other objects, are constructed of information based on natural causation.

    Sir, you read my essay, but did not offer any comments, for you may have determined the futility of such an exercise. Sometimes, one observes the strength of an argument, when one tries to critique it. Of course, I am at loss to understand why. Yet, it may make sense to visit the above cited work, which does not deal with consciousness, only with physics of information, where every inference is drawn from established experiments in physics.

    We have a choice to make, either we observe every detail in our consciousness as information, representation of which can be shown to arise from second order causal correlation alone, or we continue to consider that as mystical. Indeed, the hardness of the hard problem arises when we consider the feel as ontologically fundamental, rather than the feel being a representable semantics of feel related to representable self; naturally, the feel is as real and as concrete as the self. One often asks how can a represented information feel like any thing, but they forget to see that the self is also the represented semantics in the same domain of reality with causal power of control. Hardness also arises when we refuse to see and evaluate consciousness as emerging from ontological reality of information. It is the correlation of physical state with causal information that connects the physically observable state with the non-measurable information bridging the gap between material universe to consciousness.

    We have no problems now accepting that the sense of pain in a phantom limb is an attribution of pain to a non-existent limb, or even the dreams do not need a reality to be present, just the semantic representation of objects constructed merely via relations, but we have tremendous problem in accepting that the sense of consciousness is yet another representable semantics attributable to semantics of self as a sensor, an observer, and an actor. If the object descriptions were not based on relations, requiring presence of absolute objects (absolute feels in absolute limbs), one cannot have phantom limb and dream experiences.

    Rajiv

    Cristi,

    Glad I got to your essay. Well up to the expected standard. I agree about relationships of course, indeed I've long argued that also finding ways to explore the 'what is' will be the only way to escape our present poor understanding (the other 99 thousandths of 1%!). You seemed to agree, if in a diffuse way!

    I also agreed much of your thinking on consciousness, very much in line with my own in my essay 2yrs ago, though I did actually describe a 'what is' ontological layered feedback mechanism which could replicate it. Speculative of course but its architecture is similar to the latest advanced AI.

    Nicely written, but I was left wondering about the connection with the topic, which seemed to be rather obtuse. None the less good on all other scoring criteria and nothing I feel the need to take issue with.

    I hope you may get to mine, very fundamental in allowing is 'what is' approach, identifying sound evidence for a simple physical mechanism for uncertainty at 'measurement' momentum exchange!

    Very best

    Peter

      Christi,

      at the end I had the chance to read your essay. Sorry to be late but this year everything is totally different.

      Thanks for the wonderful essay which I gave my highest possibel vote.

      I'm glad that we agree that relations are more important, also relations between relations (as often used to define a mathematical structure).

      You wrote also about onsciousness and its reducability. I also analyzed onsciousness from a math point of view. Here, onsciousness is also purely relational and I'm not sure that the fact that it consists of matter is important.

      See the paper

      Best wishes Torsten

        Very nice essay! Clearly written and interestingly argued. Aesthetically the prettiest-looking essay I've seen. I like the use of blue for various headings/citations, and the figures you produced are all very beautiful and clear.

        The point about Wolfram's Rule 110 cellular automaton was strikingly mind-boggling. I can't even object on the grounds that there is some infinity-related trick being used, because the set of all sequences of conscious thoughts (given finitely many brain states and finite human lifetimes) is finite...

        I agree that science is all about relations. The idea of a particle's mass, for example, is only meaningful insofar as it helps us predict how a particle will behave when interacting with other particles. But on the other hand, this makes me worried when it comes to consciousness. I feel like the hard problem of consciousness is deliberately posed to exclude all scientific investigation (experimental, modeling, etc)---like you said, if you can measure it, it's not part of the 'hard' problem anymore.

        Maybe I did not read carefully enough, but I am not sure I understand the consequences of your argument. How can the collection of all true propositions about the world, and the collection of facts about sentient experience, be equal? Does that mean the world may be one big collective dream?

        John

          Dear Cristinel,

          Glad to read your work again.

          I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

          "Interested especially in the geometric aspects of the physical laws".

          It is necessary to understand that all elements of matter from the micro- to macroscales have a quantum and fractal structure of their geometry. This is given and experimentally confirmed in my work.

          While the discussion lasted, I wrote an article: "Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus", due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 "Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability".

          I hope that my modest results of work will provide you with information for thought.

          Warm Regards, `

          Vladimir

            Peter,

            Thanks for visiting my page and reading the essay and for leaving interesting comments.

            > "I also agreed much of your thinking on consciousness, very much in line with my own in my essay 2yrs ago, though I did actually describe a 'what is' ontological layered feedback mechanism which could replicate it. Speculative of course but its architecture is similar to the latest advanced AI."

            This sounds impressive.

            > "Nicely written, but I was left wondering about the connection with the topic, which seemed to be rather obtuse. None the less good on all other scoring criteria and nothing I feel the need to take issue with."

            The central starting point of my essay is that, since science can only deal with relations,

            1. The nature of things is undecidable from within science, which is only about relations.

            2. The nature of experience is undecidable from within science, which is only about objectively and independently verifiable.

            So it's very topical I think.

            Despite this undecidability, I take the hypothesis that sentience is fundamental and show that some of its variants make empirically falsifiable predictions.

            > "I hope you may get to mine, very fundamental in allowing is 'what is' approach, identifying sound evidence for a simple physical mechanism for uncertainty at 'measurement' momentum exchange!"

            This sounds very appealing!

            Cheers,

            Cristi

            Dear Torsten,

            Thank you for reading my essay and for the comments!

            > "I'm glad that we agree that relations are more important, also relations between relations (as often used to define a mathematical structure)."

            Yes, both what we can talk about and what can be made into a mathematical structure are relations of various arity and including between relations.

            > "You wrote also about onsciousness and its reducability. I also analyzed onsciousness from a math point of view. Here, onsciousness is also purely relational and I'm not sure that the fact that it consists of matter is important."

            If something is reducible to relations only, its material substrate shouldn't matter. My point is that, when it comes to consciousness, reducibility to relations corresponds to the "easy problems". Thank you for the link to your article!

            Thanks again for the comments, and good luck in the contest!

            Cheers,

            Cristi

            Dear John,

            Thank you for the comments and for reading my essay!

            > "The point about Wolfram's Rule 110 cellular automaton was strikingly mind-boggling. I can't even object on the grounds that there is some infinity-related trick being used, because the set of all sequences of conscious thoughts (given finitely many brain states and finite human lifetimes) is finite..."

            I agree with you.

            > "I agree that science is all about relations. The idea of a particle's mass, for example, is only meaningful insofar as it helps us predict how a particle will behave when interacting with other particles. But on the other hand, this makes me worried when it comes to consciousness. I feel like the hard problem of consciousness is deliberately posed to exclude all scientific investigation (experimental, modeling, etc)---like you said, if you can measure it, it's not part of the 'hard' problem anymore."

            Part of the reason I constructed this argument was to explain the fact that there is a hard problem, and it's not just some way to move some cherished belief in a gap where science momentarily didn't arrive yet. Nothing has changed in the definitions of sentience as a result of the advance of science. I mean, people always identified it with something unreachable by objective means. But, what I also try to bring with this essay, is that some variants of the hypothesis that sentience is fundamental make empirically falsifiable predictions. More details in my longer essay.

            > "Maybe I did not read carefully enough, but I am not sure I understand the consequences of your argument. How can the collection of all true propositions about the world, and the collection of facts about sentient experience, be equal? Does that mean the world may be one big collective dream?"

            In my longer essay I analyze more possible relations between P and S. Here I mention one of them, which is the simplest that solves Problem 2, of unifying the ontologies of P and S. One way to interpret it would be the one of a big collective dream that you mention, but I think this metaphor wouldn't do justice to the proposal that P=S. First, as we explore deeper the physical world P, we realize that at finer grained levels things are not how they seem at the coarse grained level, and in fact are very different from what we used to think. I expect nothing less from exploring S. So in this case, "dream" is just some manifestation at the coarse graining of S. And even so, "just a dream" assumes that we have any clue what dreams are, but we don't really know. We hallucinate even when we are awake, but we do it in a consistent way in tune with the others, and our brains create representations that we describe to others and since we all use them, we think reality is like this. But this is what we think it is, see endnote 5 of my essay. A distinguishing characteristic of dreams is that they are unstable and inconsistent, while the world P seems rather consistent and persistent. P=S would not break this persistence and consistency, it would just provide it with an ontology, one able to endow it with experience, rather than a cold dead ontology.

            Thanks again for your excellent observations, and good luck with your essay!

            Cheers,

            Cristi

            Dear Vladimir,

            Thank you for reading my essay and for the interesting observations.

            > "I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

            I'm just a neural network, with all the inherent biases and training-dependency features, that work well in some setting but fail in other settings. At least from the point of view of P. So what may seem abstract or concrete in my thinking depends on the context and the interlocutor, of course.

            > "It is necessary to understand that all elements of matter from the micro- to macroscales have a quantum and fractal structure of their geometry. This is given and experimentally confirmed in my work."

            This seems very interesting to hear more about it.

            > "While the discussion lasted, I wrote an article: "Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus", due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 "Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability"."

            Thank you for sharing this here!

            Best luck with your essay and with fighting the pandemics!

            Cheers,

            Cristi

            Dear Professor Cristinel Stoica,

            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.

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

            What also pleases me is that I sense in between your work and ours ( link: https://fqxi.org/community/forum/topic/3563) we share mutual ground, and we conclude indeed limitations of mathematics are equivalent to limitations of natural science along very similar lines of reasoning; something which you nicely summarize as:

            "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)."

            Indeed we share a similar stance to what you have said, "Science

            is a way to decode the book. It proceeds by identifying various words in various contexts, and

            the result is a dictionary, along with some grammar rules. Each word in the dictionary is defined

            in terms of other words, but there are no primary words whose meaning we understand. All the

            definitions in the dictionary are eventually circular. And the grammar rules, which correspond in

            this metaphor to the laws and principles we propose to describe the world, are purely syntactical.", and propose a grand lexicographic project for constructing a complete dictionary for Nature.

            We hope you have time to read our work!

            And thank you for your marvelous entry and the joy and insight we found in your work is reflected in our rating!

            Kind Regards,

            Raiyan Reza, and Rastin Reza

              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

              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