Essay Abstract

This article presents a three-part analysis on revealing possible descriptive requirements for a math of intention. Part one, titled Philosophical Reduction, presents reductive reasoning for arriving at three possible problems that ultimately one of which a mathematics of intentionality must satisfy. Part two, titled Scientific Modelling, considers the potential resolution of these problems in light of current scientific theory, allowing the selection of a most probable problem from part one. Part three, titled Computational, Mathematical and Physical Description, considers what descriptions, and the nature of their relations, are required to satisfy the most probable problem. It is proposed in Part 3 that a threefold equivalence of description at a specific level is a necessary requirement to illustrate the formation of intention. In exposing the requirement there emerge two significant consequences for the nature of our current descriptions: a) David Chalmers 'Hard Problem of Consciousness' specifically results from the absence of the requirement, and similarly b) Kurt Godel's incompleteness proofs exist as true only in an operational conception of mathematics that exists post non-inclusion of the requirement. Finally, there is reason to suggest that even if the requirement is revealed and a math of intention realised, a math of consciousness likely cannot follow from it premise - a claim very much counter-intuitive.

Author Bio

Jack is in his final months of writing his PhD in philosophy at The University of New England in Australia. His research interests include moral philosophy and psychology, environmental ethics, the philosophy of science (sociobiology), metaphysics, and decision theory.

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Dear Prospective Dr. James,

Please excuse me for I do not wish to be too critical of your fine essay.

Only nature could produce a reality so simple, a single cell amoeba could deal with it.

One real visible Universe must have only one reality. Simple natural reality has nothing to do with any abstract complex musings such as your "reductive philosophy" comment describes.

The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

A more detailed explanation of natural reality can be found in my essay, SCORE ONE FOR SIMPLICITY. I do hope that you will read my essay and comment on its merit.

Joe Fisher, Realist

Thankyou Joe,

I, like I presume all other entries, agree there is only one reality.

In reply to your point about my complex musings, well they are descriptive insights, and such description must be a part of that one reality. The challenge is not to realise one reality but present a description that reflects as much in the limited ways it can. So such complex musings are a necessary path to that end, esp. given there is so much to deal with that we know in only some ways, and so much we dont know.

Kind regards,

Jack

While mathematics is a historical product or civilizational tool of human consciousness, intentions are more a part of human subconsciousness or deep psychology. Several experiments have shown that the human heart anticipates faster than the brain; a maths of intention would consequently aim to formulate these physiological processes of human psychology. Otherwise, it would be a pure academic artifact. These are the thoughts that came into my mind, after reading your interesting essay, Mr. James.

    Thankyou Stephen Ternyik (and Lee Bloomquist) for your alternative perspective of what was meant by intention.

    When I assessed Brendan Fosters outline I found it to be very broad. I find consciousness, or intention in deep psychology as you suggest, to be insurmountable without advanced technology that is able to reveal the workings of the brain more effectively than fRMI. So the reduction of complex human intention, to the theoretically simpler intention found in basic life itself, as opposed to non-life, seemed quite appropriate, and indeed interesting. For it seems to me that describing this property should be a simpler task than describing an intention like ours. But we still haven't achieved even this - and perhaps worse I argued that even if this is possible it seems unlikely we will be able to utilise it to the end of explaining consciousness and human intention.

    Best,

    Jack

    "... Ecorithms are nature's (evolution's) algorithms . This is the idea of computational theorist Leslie Valiant (4), but none have been discovered yet. ...

    (4) Valiant L, "Probably Approximately Correct: Nature's Algorithms for Learning and Prospering in a Complex World" ..." (typo in original at time of this communication)

    According to Leslie Valiant, "... the goal of learning is to perform well in a world that isn't precisely modeled ahead of time. A learning algorithm takes observations of the world, and given that information, it decides what to do and is evaluated on its decision. A point made in my book is that all the knowledge an individual has must have been acquired either through learning or through the evolutionary process. And if this is so, then individual learning and evolutionary processes should have a unified theory to explain them."

    https://www.quantamagazine.org/20160128-ecorithm-computers-and-life/ "Searching for the Algorithms Underlying Life" by John Pavlus (interviewing Leslie Valiant), 28 January 2016

    It seems to me that there are serious problems with the scientific definitions of "goal", "learning", and what it means to "perform well". Does an oak tree learn? Is there learning in the system consisting of acorns and oak trees within a Northern hardwood forest? Does Valiant's concept of "ecorithm" involve deep problems in the foundations of quantum theory? How relevant is what Francis Crick called "molecular psychology" to the theory of machine learning?

      An algorithm is about existing knowledge, the heuristic method applies to learning. Ecorithms may apply to the animal and human mind, plants are not capable of moving. The molecular Aufbau (construction) of living matter does not apply to technical automata, automated information cannot 'die'. Consequently, algorithms of life and death are surely existent and can be formulated in a unified mathematical theory.

      Dear Jack,

      Natural reality cannot be described by abstract linguistic concoctions.

      Joe Fisher, Realist

      Dear Jack,

      Dr. Brendan Foster's supplemental notes for the theme of this essay contest were quite explicit. Meandering mathematical musings have failed to produce a satisfactory explanation of the real observable Universe. All Dr. Foster suggested we do am either to confirm a mathematical explanatory proof, or furnish a more reliable one.

      Joe Fisher, Realist

      Thanks for the thread commentary. Stephen's comment here is what fascinates about ecorithms, because if life arises from the physical as Tegmark argues (and life has this property of intention in its mere movement) then there must be some kind of mathematical theory of 'transference', where such life algorithms are generated by non-physical interactions.

      "The molecular Aufbau (construction) of living matter does not apply to technical automata, automated information cannot 'die'. Consequently, algorithms of life and death are surely existent and can be formulated in a unified mathematical theory."

      My initial philosophical thoughts on ecorithms as the 'gap filler' deterministically explaining the success of evolution at the organism level can be found [link:philosopher.io/Ecorithms-within-Evolution ]your link text[/here.]

      Best,

      Jack

      Dear author,

      Clearly the length limits imposed by the contest have constrained you to develop your proposal almost as an algorithm, which makes it quite difficult to read.

      Nevertheless I gather that you are discussing the requisites for an eventual formal mathematical description of how life evolved from matter.

      You conclude the following at the end: "We are descriptively stranded, and so whilst we may reveal a math of intention I doubt that it will provide a math of consciousness." I have to say that I disagree with your conclusion, because I unequivocally show in my essay the mathematical elements belying both consciousness and intentionality. There is one other essay here among the ones I have seen that does offer as well some mathematical elements to "meaningful information" as a prelude to intentionality and consciousness.

      There is always a danger in setting limits a-priori or from a metaphysical viewpoint to what is feasible, although the effort to frame the solution elements to a problem cannot be overstated.

      I suspect that your essay would have been more interesting and perhaps more eloquent if presented in a more natural language and structure, with less use of shortcuts.

      Good luck.

      Joseph

      __________________

      Thankyou Joseph.

      I did try and keep it very short and to the point and your comment 'almost as an algorithm' is quite on point.

      I appreciate your disagreement. I wish to be wrong in this and I didnt expect it from my initial reasoning on the subject. Yes, I made comments on Carlo Rovelli's entry today as I thought he attempted to show what you have said. This idea of yours and his (will read your paper shortly) reminds me very much of John Locke. See what I mean from this summary here:

      "For Newton the world of matter was to be described in terms of uniform particles, and the laws of its behaviour are the laws of the interactions of these particles. Locke applies this conception directly to the mind, which is treated as a box containing the mental equivalents of Newton's particles. These particles are called ideas, and these ideas are distinct and separate entities which are simple or atomic in that they have no parts into which they can be split."

      Now the issue I have with this is abstraction, which is really what I have tried to get at demonstrating through description and actual reality rather than any mental quality.

      Thanks again for your comments, and I look forward to reading your essay.

      Best,

      Jack

      Ecorithms within evolution (?) makes sense, a very good article. The Tegmark-Valiant argument of computational evolution is a decisive one; however, a clear disntinction between maths (tool) and computation (evolution) must be elaborated. Human technological (tech-know-logical) is most probably an extension of natural evolution; with the help of mathematical tools, the human mind could rise over the animal mind while advanced computation makes the algorithms of life and death more accessible, in terms of scientific models. The heuristic part of this research quest is for me the most exciting, i.e. how does a living and learning organism like a human being detect algorithms ?

      Hello Jack.

      You write: "Locke applies this conception directly to the mind, which is treated as a box containing the mental equivalents of Newton's particles. These particles are called ideas, and these ideas are distinct and separate entities which are simple or atomic in that they have no parts into which they can be split."

      I am not familiar with John Locke's philosophy. However with this view, he was right on the money! Interesting that you bring that up, because my essay precisely tries to show that cognition is based on atomic or root thoughts, which I call eigenthoughts because in their many different classes they all derive from an overarching mathematical Eigenfunction.

      Henceforth, you should not have a problem with that abstraction because it is widely mathematically substantiated as you will see.

      Thank you for your feedback.

      Joseph

      ________________

      Thanks Joseph,

      You might enjoy the full article that quote was taken from. Its an outline of Locke's ideas: Link

      Best,

      Jack

      Hello Jack.

      Have read it all.

      Now I can claim I am no longer unfamiliar with John Locke's philosophy! More versed as I am in the French philosophical tradition...

      Thank you.

      Joseph