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Beyond Math/Matter/Mind: a search for objective knowledge

Recently I entered into a debate with a fellow on Sabine Hossenfelder’s Backreaction blog [1] about the objectivity of mathematics; he takes the position that mathematics is demonstrably objective, a position I find fallacious. This is an interesting subject to which I have been giving considerable attention ever since reading a couple of papers from Piet Hut’s website, one in which Hut, Max Tegmark, and Mark Alford discuss the Math/Matter/Mind trilogy of Roger Penrose [2] and the other a transcript in which His Holiness the Dalai Lama and Thupten Jinpa discuss, momentarily, the origins of logic [3].

As I stated in another recent blog post of Sabine’s [4], mathematics as an exercise really begins with transcription, proceeds through logic, and concludes with pattern; mathematics is, in a very literal sense, a language, optimized to suppress as much ambiguity as possible while maintaining as much expressivity as possible, which is used to study natural language itself. Due to the optimization process, mathematics is constrained to declarative statements or those sentences in natural language which contain declarative propositions. This is what enables proof. The rules of inference are all tautologies or identities and these rules, when properly applied to a consistent set of premises, lead to logically valid conclusions.

Now someone could say that if you limit yourself to first-order logic, which only allows declarative propositions, and you use the rules of inference, a set of tautologies and identities, to make natural deductions about those declarative propositions, in the pure sense, then, mathematics is an objective art. But hidden in the above conditional is the assumption that pure deductions are sterile, by which I mean devoid of sematic content, and it would seem to me that the Lakoff/Nunez book, “Where Mathematics Comes From” [5], provides a counter-example to this assumption. By this I mean that, while pure math is devoid of explicit semantic content, it is completely saturated with implicit semantic content and this implicit content is a reflection of how our subjective minds work.

The key point Lakoff and Nunez make is that mathematics primarily arises due to the application of a primary cognitive schema known in the science as metaphorical mapping, and it is known that these metaphorical mappings preserve inferential structure! Even the tautologies we use to transform premises into conclusions are a reflection of how our subjective minds work simply because they are defined on truth functional connectives which are themselves, quite obviously, the result of metaphorical mapping. With one possible exception, there is, in my way of thinking, no possible way to obtain objective knowledge. Everything we know about the real world out there, to use Lee Smolin’s term, is filtered through our sensory-perceptual system, hence, subjective and our natural languages are grounded in these sensory perceptions; is that not what we mean when we say we make sense of something? And our mathematics begins with a transcription of natural language.

Of course one could point to Wigner’s observation about the “unreasonable effectiveness” [6], but is this effectiveness really so unreasonable? We start with a sense perception (an experimental result); we use natural language, a language which evolved as an extremely useful tool relative to the specific environment under study, to describe that sense perception; we transcribe that natural description; we make natural deductions which logically (logically here defined by minds which are themselves products of that evolutionary environment) extend our description beyond the original sense percept; we validate or invalidate that extension with subsequent sense perceptions. There is nothing unreasonable about the effectiveness of that algorithm that I can see.

Perhaps what Wigner found unreasonable is the frequency of which those logical extensions are found to be valid, but is this so surprising? We and our logic are a product of the very environment under investigation; all of our tools and technologies are products of that environment modified by that logic; further experiments simply reflect previous experiments logically extended; the only real mitigating factor is the inductive assumptions which start the whole process off or mitigate contradictions between effective theories, erroneous assumptions lead to erroneous results. It seems mysterious to some that our environment is comprehensible but comprehensibility itself is defined by that environment! We make sense of things! Of course a key element to admit here is that those logical extensions are NOT demonstrated valid 100% of the time, we don’t make perfect assumptions. This should exclude any consideration of a “Post-empirical Science” [7]; post-empirical science is not science, rather, it is mathematics.

Since natural languages are grounded in sensory perception, it would seem clear that they and their derivatives are all subjective, or, to be more precise, inter-subjective – by convention. From this it follows that truly objective knowledge cannot be communicated via language, since any attempt to constrain the knowledge with language would necessarily reduce that knowledge to the subjective. So objective knowledge, if attainable, can only be directly apprehended and this apprehension requires, by definition, the transcendence of the subject – the self. In other words, truly objective knowledge is only attainable by the dis-embodied mind, i.e. through meditative equipoise or its close relative, near-death experience. Of course all materialists and most neuro-scientists will scoff and insist that meditative equipoise and near-death experiences are nothing more than brain states but what makes them so certain? Prior to Maxwell’s natural deduction which extended our perception of the electromagnetic spectrum well beyond the visible, we had no idea such an extension was even possible.

What I find most telling, when yogis and yoginis speak of the Samadhi bardo, the state experienced during meditative equipoise, they use negatives: not one/not two; not emptiness/not form; not simply this/not simply that. They use negatives because negatives are inclusive; when one attains the state of Samadhi all distinction between this and that, self and other, is transcended and the knowledge obtained is total, complete, and necessarily uncommunicable; anything said about it is both true and false – paradoxical. And this, in the words of Barwise and Etchemendy [8], is the lesson of the Liar: propositions cannot be made about the totality of what can be known. Does not this experience, which cannot be reduced in any way, represent the only possible attainment of objective knowledge? Objective knowledge is, by its very nature, total knowledge, since the very idea of partial knowledge involves a distinction between that and other, and any kind of distinction represents a perspective, a relative reference frame, in short, subjectivity.

Math/Matter/Embodied Mind is a continuous tapestry, a beautiful tapestry emerging from constraints, and the way to transcend that tapestry, those constraints, leads to Dis-Embodied Mind: pure primordial awareness [9].

1) http://backreaction.blogspot.com/2016/05/the-holy-grail-of-crackpot-filtering.html

2) https://arxiv.org/abs/physics/0510188

3)http://prof.usb.ve/rescal/The%20New%20Physics%20and%20Cosmology%20Dialogues%20with%20the%20Dalai%20Lama.pdf

4) http://backreaction.blogspot.com/2016/08/math-blind.html

5) http://www.cogsci.ucsd.edu/~nunez/web/FM.PDF

6)http://www.maths.ed.ac.uk/~aar/papers/wigner.pdf

7) http://backreaction.blogspot.com/2014/07/post-empirical-science-is-oxymoron.html

8) http://www.ams.org/journals/bull/1989-20-02/S0273-0979-1989-15770-4/S0273-0979-1989-15770-4.pdf

9) http://vajranatha.com/excerpts/self-liberation.html?start=1

Recently I entered into a debate with a fellow on Sabine Hossenfelder’s Backreaction blog [1] about the objectivity of mathematics; he takes the position that mathematics is demonstrably objective, a position I find fallacious. This is an interesting subject to which I have been giving considerable attention ever since reading a couple of papers from Piet Hut’s website, one in which Hut, Max Tegmark, and Mark Alford discuss the Math/Matter/Mind trilogy of Roger Penrose [2] and the other a transcript in which His Holiness the Dalai Lama and Thupten Jinpa discuss, momentarily, the origins of logic [3].

As I stated in another recent blog post of Sabine’s [4], mathematics as an exercise really begins with transcription, proceeds through logic, and concludes with pattern; mathematics is, in a very literal sense, a language, optimized to suppress as much ambiguity as possible while maintaining as much expressivity as possible, which is used to study natural language itself. Due to the optimization process, mathematics is constrained to declarative statements or those sentences in natural language which contain declarative propositions. This is what enables proof. The rules of inference are all tautologies or identities and these rules, when properly applied to a consistent set of premises, lead to logically valid conclusions.

Now someone could say that if you limit yourself to first-order logic, which only allows declarative propositions, and you use the rules of inference, a set of tautologies and identities, to make natural deductions about those declarative propositions, in the pure sense, then, mathematics is an objective art. But hidden in the above conditional is the assumption that pure deductions are sterile, by which I mean devoid of sematic content, and it would seem to me that the Lakoff/Nunez book, “Where Mathematics Comes From” [5], provides a counter-example to this assumption. By this I mean that, while pure math is devoid of explicit semantic content, it is completely saturated with implicit semantic content and this implicit content is a reflection of how our subjective minds work.

The key point Lakoff and Nunez make is that mathematics primarily arises due to the application of a primary cognitive schema known in the science as metaphorical mapping, and it is known that these metaphorical mappings preserve inferential structure! Even the tautologies we use to transform premises into conclusions are a reflection of how our subjective minds work simply because they are defined on truth functional connectives which are themselves, quite obviously, the result of metaphorical mapping. With one possible exception, there is, in my way of thinking, no possible way to obtain objective knowledge. Everything we know about the real world out there, to use Lee Smolin’s term, is filtered through our sensory-perceptual system, hence, subjective and our natural languages are grounded in these sensory perceptions; is that not what we mean when we say we make sense of something? And our mathematics begins with a transcription of natural language.

Of course one could point to Wigner’s observation about the “unreasonable effectiveness” [6], but is this effectiveness really so unreasonable? We start with a sense perception (an experimental result); we use natural language, a language which evolved as an extremely useful tool relative to the specific environment under study, to describe that sense perception; we transcribe that natural description; we make natural deductions which logically (logically here defined by minds which are themselves products of that evolutionary environment) extend our description beyond the original sense percept; we validate or invalidate that extension with subsequent sense perceptions. There is nothing unreasonable about the effectiveness of that algorithm that I can see.

Perhaps what Wigner found unreasonable is the frequency of which those logical extensions are found to be valid, but is this so surprising? We and our logic are a product of the very environment under investigation; all of our tools and technologies are products of that environment modified by that logic; further experiments simply reflect previous experiments logically extended; the only real mitigating factor is the inductive assumptions which start the whole process off or mitigate contradictions between effective theories, erroneous assumptions lead to erroneous results. It seems mysterious to some that our environment is comprehensible but comprehensibility itself is defined by that environment! We make sense of things! Of course a key element to admit here is that those logical extensions are NOT demonstrated valid 100% of the time, we don’t make perfect assumptions. This should exclude any consideration of a “Post-empirical Science” [7]; post-empirical science is not science, rather, it is mathematics.

Since natural languages are grounded in sensory perception, it would seem clear that they and their derivatives are all subjective, or, to be more precise, inter-subjective – by convention. From this it follows that truly objective knowledge cannot be communicated via language, since any attempt to constrain the knowledge with language would necessarily reduce that knowledge to the subjective. So objective knowledge, if attainable, can only be directly apprehended and this apprehension requires, by definition, the transcendence of the subject – the self. In other words, truly objective knowledge is only attainable by the dis-embodied mind, i.e. through meditative equipoise or its close relative, near-death experience. Of course all materialists and most neuro-scientists will scoff and insist that meditative equipoise and near-death experiences are nothing more than brain states but what makes them so certain? Prior to Maxwell’s natural deduction which extended our perception of the electromagnetic spectrum well beyond the visible, we had no idea such an extension was even possible.

What I find most telling, when yogis and yoginis speak of the Samadhi bardo, the state experienced during meditative equipoise, they use negatives: not one/not two; not emptiness/not form; not simply this/not simply that. They use negatives because negatives are inclusive; when one attains the state of Samadhi all distinction between this and that, self and other, is transcended and the knowledge obtained is total, complete, and necessarily uncommunicable; anything said about it is both true and false – paradoxical. And this, in the words of Barwise and Etchemendy [8], is the lesson of the Liar: propositions cannot be made about the totality of what can be known. Does not this experience, which cannot be reduced in any way, represent the only possible attainment of objective knowledge? Objective knowledge is, by its very nature, total knowledge, since the very idea of partial knowledge involves a distinction between that and other, and any kind of distinction represents a perspective, a relative reference frame, in short, subjectivity.

Math/Matter/Embodied Mind is a continuous tapestry, a beautiful tapestry emerging from constraints, and the way to transcend that tapestry, those constraints, leads to Dis-Embodied Mind: pure primordial awareness [9].

1) http://backreaction.blogspot.com/2016/05/the-holy-grail-of-crackpot-filtering.html

2) https://arxiv.org/abs/physics/0510188

3)http://prof.usb.ve/rescal/The%20New%20Physics%20and%20Cosmology%20Dialogues%20with%20the%20Dalai%20Lama.pdf

4) http://backreaction.blogspot.com/2016/08/math-blind.html

5) http://www.cogsci.ucsd.edu/~nunez/web/FM.PDF

6)http://www.maths.ed.ac.uk/~aar/papers/wigner.pdf

7) http://backreaction.blogspot.com/2014/07/post-empirical-science-is-oxymoron.html

8) http://www.ams.org/journals/bull/1989-20-02/S0273-0979-1989-15770-4/S0273-0979-1989-15770-4.pdf

9) http://vajranatha.com/excerpts/self-liberation.html?start=1

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The following link is to an interesting debate between Bryan Van Norden and Nicholas Tampio carried out almost entirely on twitter! The debate regards multi-culturalism in Philosophy and I like to think that Van Norden, arguing for the multi-cultural position, gets the best of Tampio . . . oh, alright, he pummels him!

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I recently finished a couple of Prismacolor pencil drawings and uploaded them to the studio.

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