Essay Abstract

In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this existential crisis may appear to be new, we develop the view that it has a long history and that, in fact, providing closure to undecidable questions is a defining feature of scientific practice and development. We support our claim with historical and contemporary examples and suggest that the crux of many instances of undecidability in science is a form of invalid induction. Finally, we use our thesis to discuss the place of mathematics in the sciences, and to assess whether or not certain perspectives in the philosophy of mind might provide us with closure.

Author Bio

Fabien Paillusson is a senior lecturer in the School of Mathematics and Physics at the University of Lincoln, UK. His interests range from soft matter computational modelling to foundational issues in physics. Matthew Booth is a lecturer in the School of Mathematics and Physics at the University of Lincoln, UK. His interests range from photophysics of semiconductor nanomaterials to the philosophy of science.

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Dear Fabien Paillusson,

I loved your: "When Chuck Norris makes an inductive inference, it becomes deductive"

which I elsewhere framed as:

Science is about giving answers making scientists flush red about the questions they have previously been trying to answer.

Nevertheless, I have not succeeded to find this (the 'Chuck-Norris-discontinuous-continuity') clarified in your essay. You say there are scientific and philosophical questions, but I don't manage to find out from the text what the precise difference is. Do philosophers simply take over from scientists when the latter got stuck, do scientists turn into philosophers under such conditions, or is the subject of philosophy radically different from the subject of science?

good luck,

Heinz

    Dear Heinz,

    Thank you for your comment.

    With regards to your question, our thesis is that philosophical questions are undecidable. This does not mean that an answer has not yet been proposed, but rather that no method has been proposed by which people may agree on an answer. The reference to the Chuck Norris quote is meant to suggest that most of the time the undecidable character of these philosophical questions pertains to a form of induction. We claim that a scientific question is the conjunction of a philosophical question with a method that makes it decidable. What substituting a philosophical question for a scientific one does in effect is turn an inductive inference into a deductive one.

    One example we gave in the essay has to do with the philosophical question "Does the Earth revolve around the Sun or is it the other way around?". Stated as is, this question is subject to underdetermination and has no definite answer. In antiquity, sense-data and additional aesthetic principles were used to devise corresponding scientific questions such as "do we feel the Earth moving?", while the more modern mechanistic view from Newton relied on the concept of inertial frames and additional rules of reasoning to formulate scientific questions such as "Can the geocentric frame be inertial if there is only the Solar System in the Universe?".

    Now, with regards to communities such as 'philosophers' or 'scientists', as far as our essay is concerned, they are only defined by the kind of questions they are trying to answer. In principle, scientists may turn into philosophers (and vice versa) and we give historical examples to support this view in the essay.

    The set of ampliative principles which can turn some philosophical questions into scientific ones may also lead to undecidable questions within the new framework. As long as these undecidable questions remain, they will be considered philosophical questions as far as our taxonomy goes.

    Also, since we argue that philosophical questions always survive their 'scientification', some paradigm change may also emerge from philosophical reasons alone. The kind of discussions occurring on the foundations of quantum mechanics nowadays is a good example of a theory that works very well in practice, yet has various alternative formulations which are mostly motivated by different philosophical views.

    I hope this answers your query.

    Best,

    Fabien and Matt

    Fabian and Matthew. I liked your essay and I think my essay would be interesting for you to read and compare to your thoughts. I introduce a new level of fundamentals that unifies the fundamentals of all of the sciences, mathematics, computability, philosophy and religion. Those fundamentals are the basis of a Successful Self Creation process that has its own "halting" solution and creates finite results. In its processing it creates Quantum Mechanics, Planck Actions and the variables/ relationships of time, space, mass, speed and direction that are the basis for the Relativity theories. This combination is the basis for a complete theory of physical reality. SSC is also is the basis for the creation of intelligence and its incorporation into the SSC realm of existence. Consciousness is a component of this intelligence. I believe the SSC and the new level of creation is the something that has been missing from a comprehensive overall (framework) understanding of ordered existence. I would appreciate your comments on how my essay fits with your thoughts. John Crowell

      Dear Fabien,

      it's the nature of every age to think its problems unique, and the role of history to point out they aren't. Taking a historical stance towards the problems of undecidability (etc.) is thus, I think, a necessary and welcome addition to this essay contest.

      Furthermore, there tends to be a kind of intellectual chauvinism directed towards past generations---they back then were just the unenlightened rubes that didn't yet have the benefit of our advanced scientific understanding. So, what could they conceivably have to tell us that could help with our present-day issues?

      I read your essay as, in part, questioning these intuitions. The example of heliocentric versus geocentric models is a striking one---data itself does not adjudicate between these views; what does, then, is extra-theoretical constraints, such as e. g. a principle of parsimony. But in what sense is swapping one such constraint for another tantamount to 'scientific progress'?

      I'm reminded of the oft-related exchange between Ludwig Wittgenstein and Elizabeth Anscombe---as relayed by her: "He once greeted me with the question: 'Why do people say that it was natural to think that the sun went round the earth rather than that the earth turned on its axis? I replied: 'I suppose, because it looked as if the sun went round the earth.' 'Well,' he asked, 'what would it have looked like if it had聽looked聽as if the earth turned on its axis?'"

      You also touch on Hume's problem of induction. This has, in fact, a closer tie to the present contest's theme, in that a straightforward algorithmic formulation of induction, incorporating a principle of parsimony in the form that more simple hypotheses should be given higher weight, ends up being formally uncomputable---this is the theory of Solomonoff induction. Thus, if one is prepared to accept that an algorithmic formalization with a requirement of parsimony is a sufficient characterization of the notion of induction (and one may well not be), then it turns out Hume's problem is exactly equivalent to the unsolvability of the halting problem. Thus, given this formulation, it seems that your notion that "the problem of induction is a point of contact between different notions of undecidability" might be pretty spot on.

      You propose an interesting interface between science and philosophy, with the open-ended questions of the latter being brought under a certain formalizable framework by the former. If this is true, then it seems a straightforward corollary is that we'll also never run out of either: for it will always be possible, given a question having transitioned from philosophy to science in this way, to ask the meta-question of wether this transition was truly appropriate---whether, in your words, the ampliative assumptions needed to give form to a given question are actually apt.

      It seems to me that this process can also fail badly---for instance, take the question 'Why is there something rather than nothing?', that some physicists take to be answered by phenomena such as vacuum fluctuations, or quantum tunneling between different vacuum states. To me, this 'solves' the question by essentially substituting a radically different one---one about how a certain kind of state matching what we observe today can emerge from a different kind of state that can be thought of as a vacuum state. I think this essentially loses the point of the question---and moreover, I'm not convinced that it's not systematically the case that certain questions don't really survive the spawning of 'daughter' questions to be attacked by the sciences. Perhaps you gain an answer, but only at the expense of the original question.

      Regarding the completeness of quantum mechanics, I have a few things to say in my own entry into this contest that might be of interest to you.

      Finally, as for the question of consciousness, I have recently put forward a proposal---'The Abstraction/Representation Account of Computation and Subjective Experience', Minds & Machines (2020), https://doi.org/10.1007/s11023-020-09522-x---to the effect that a 'consistent set of principles or hypotheses, possibly new ones, which would allow one to conclude the existence of consciousness (or lack thereof) in a given system' does not exist; at least not in the sense that there could be a chain of rational deductions, or equivalently, a computation, that decides the presence of consciousness within a physical system. Still, I view this as a thoroughly physicalist position---there's a distinction to be made between physics, the science, and physical stuff. This, I believe, is the origin of the hardness of the hard problem.

      Anyway, as you can see from the length of my comment (brevity never has been my strong suit), I found much of interest in your article, and lots of food for thought. I think the perspective you present on this contest's topic is an original and necessary one, and therefore hope your article will do well in it.

      Cheers

      Jochen

        Dear John,

        Thank you for your comment. As for your essay, I will read it and come back to you in the corresponding thread.

        Best,

        Fabien

        Dear Jochen,

        Thank you very much for your very insightful comment!

        I am happy you seemed to have enjoyed our essay.

        Just to follow up on some of your comments:

        - I must say that I was unaware of Solomonoff's induction programme. Thank you very much for mentioning it that will be a valuable thing to look into.

        - Yes, as you say, as far as we describe it in the essay there is no end to the process of generating daughter questions from philosophical ones. Although we did not have the space to go further, it is often the case as well that philosophical questions can emerge from specific set of principles which were used to transform another philosophical question into a scientific one.

        - With regards to questions like "Why is there something rather than nothing?" whose substance could essentially be lost by being substituted with scientific ones, I totally agree that this could happen and, in fact, wonder if this has not happened may times in the past and we are simply oblivious to it now. For example, the very deep questioning of Parmenides and Zeno on change have been replaced, in my opinion, by empty mathematical questions on the convergence of geometric series (answers to these questions are obviously mathematically rich but by stripping off all the philosophical content, it is difficult to evaluate how such mathematical answers do actually provide closure to the initial philosophical questions). That is the reason why, as you say, historians, scientists and philosophers alike should keep track of these things. Ernst Mach in fact was already calling upon the apparent arrogance of his contemporaries in the first pages of his critics of mechanics.

        - I look forward to reading your essay and commenting on it in the corresponding thread.

        - With regards to consciousness, I will have a look at your paper and possibly continue the discussion here or elsewhere :) .

        Many thanks.

        Fabien

        I think I get your point. But, let me add some history.

        At Newton's time, the Ptolemaic model was more accurate than the Copernican model (Copernicus still had circular orbits) AND the Copernican model had a falsifier. The falsifier was that Galileo attempted to find parallax in the stars and failed. The parallax waited until the 1830s to be found and the size of the universe accordingly increased.

        The Ptolemaic model was essentially a Fourier series. That is, it was more accurate for any periodic orbit by just adding terms. This is a similar condition to modern use of Fourier.

        Thanks for your good points.

          Dear John,

          Thank you for having read the essay and for your comment.

          Yes indeed the Copernicus model was less accurate than the Ptolemaic one and it could be refuted on various empirical grounds (like absence of parallax). That is the reason why we said in 1st paragraph on page 3 that "despite having no empirical evidence" Copernicus still insisted his view was correct; and many followed him in the following centuries.

          As for the parallax, as far as my understanding is concerned, it was certainly considered as a silver bullet by people opposed to a Copernican view but Copernicus himself had an argument to explain the absence of observed parallax with respect to the background of the fixed stars (which can be found in his book On the Revolutions of the Celestial Spheres) which was that the stars of the background of the fixed stars were so distant that a parallax was simply not observable. The absence of parallax was then used to infer the size of the universe. That's what I would call turning the tables!

          As you may know this lead to further major problems with regards to the size of each individual star within the background of the fixed stars. Namely, a single star was then expected to be larger than the Solar System. This compelled Tycho Brahe to propose an alternative geo-hello-centric view in which such problems would not occur.

          In any case, since as you say the parallax was only observed in 1830, the absence of parallax did not prevent many scholars, including Newton, to adopt a heliocentric view. The way it was done was precisely by overhauling the way to infer the laws of Nature.

          Now, if your comment implied that the presence/absence of parallax constituted an absolute observational means to assert who is moving, I would disagree. For the parallax argument to make sense, one still needs to assume that the background of the fixed stars is actually fixed. If this assumption is lifted and this background has no special property then nothing can be derived from observing a displacement of one of the stars.

          Best,

          Fabien

          Dear Fabien

          Nice and well thought essay. You deal with several important topics; particularly the topic of consciousness. I disagree with the statement that science leaves some problems to philosophy. I think it is the opposite way, for the last 5 centuries science has taken from philosophy many unresolved problems and have solved some of them. I conceived science as an evolved philosophy, after all philosophy also have tried to understand the world. I have a couple of books that deal with the most important problems in philosophy (authored by George Moore and Russell, respectively) and most of these problems have not been solved. For instance the problem of space and time, have been led by physics in the last 3 or 4 centuries, philosophers have contributed almost nothing to these concepts. Unfortunately, in my opinion, philosophy is nowadays more a reviewer of science than an author of science.

          You deal with the topic of geocentrism and heliocentrism which is very interesting. In my essay I give a short discussion on absolutism and relativism; perhaps you may be interested in taking a look at my essay. I would be glad to see some comments from you.

          Good luck in the contest!

          Israel

            Dear Fabian and Matthew,

            I like your title: "...taking a stance about undecidable issues. I treat essentially that issue in my essay Deciding on the nature of time and space where I deal with the issue, "which world view is real?". I invite you to read it and welcome comments.

            I think it's appropriate that you apply these ideas to the problem of consciousness. You discuss various concepts and note that some strong forms of panpsychism suggest that electrons have some degree of consciousness. To my way of thinking panpsychism is more of a field phenomenon, and the primordial field is gravity, whose nonlinear self-interactions can be thought of as implying a minimal 'self-awareness'. Any moving mass density, such as the extremely dense electron, will induce local gravitomagnetic circulation in the field, thus 'coupling' the matter to the consciousness field and at the same time providing a deBroglie-like wave associated with the particle. This posits a Wheeler-like universe in which consciousness exists at the creation and evolves to the present.

            One can only hint at this in a comment, but the idea answers some of Chalmers 'hard' problems. I address similar issues in The Nature of Mind, which had the top community rating in the 2016-2017 contest.

            Good luck in the contest, you're off to a good start.

            Edwin Eugene Klingman

              Dear Israel,

              Thank you for having taken the time to read our essay.

              With regards to your comment on science versus philosophy. Would you have an example in the last 5 centuries where science has brought definitive closure to a philosophical question?

              Many thanks.

              Best,

              Fabien

              Dear Edwin,

              Thank you for having taken the time to read our essay. I hope you did find some propositions in there insightful.

              With regards to your field view of panpsychism where gravity would relate to consciousness, would you agree to see this as a form of functionalism as we describe at the end of our essay with IIT or Tegrmark's pattern of communication channel ideas for example?

              That is to say, a given pattern of the gravitational field will correspond to a certain degree of consciousness.

              Or am I missing something?

              As a personal side note, I am quite sympathetic to the idea of a field of consciousness. The point is whether this field is already described by our physical theories or whether one needs to add a new one.

              Many thanks for your insights.

              Best,

              Fabien

              Thanks.

              Apologies, I was addressing your "empirically undecidable" issue. Between the 2 models, it eventually became observationally decidable.

              RE: EPR

              Another conclusion is EPR is true with ALL interactions occurring at speeds >> c (non-local). Newton's planet model works if the gravity speed >>c as van Flandern and others measured.

              Thanks for you insights. I wish you had said a bit more on the crisis in physics (GR vs QM - which or neither or both as part of a larger model). For example, Newton had his gravity in Principia but followed it with an aether model which suggested the same cause of gravity (big) and diffraction of light (small) with corpuscles warping the aether and the aether directing corpuscles in Opticks.

                John,

                Unless I made a mistake in my last observation I do not believe this is the case. It is not absolutely decidable on the sole observational basis. One needs to assume the background of the fixed stars to be fixed for the parallax evidence to actually make the problem decidable from astronomical observations.

                If the stars in the background are not fixed, the reality of their observed motion from the Earth becomes as undecidable as that of other planets and the Sun.

                So, you are right that it did support a non-geocentric view but this was not for free.

                Best,

                Fabien

                John,

                Thank you for suggesting further ideas.The GR vs QM would fit within the problem of contrastive underdetermination and we can interpret the current programme of find a theory that combines the two as the belief that there is "better" theory, in some sense, than the existing alternative of having GR and QM kind of separate. The request for unification appears to me as an aesthetic constraint.

                I have read Optiks some time ago and light as being made of particles is only addressed in the last book from what I remember. I do not recall the aether argument. Would you have a link to suggest where these ideas are explored further?

                Thank you.

                Best,

                Fabien

                Newton "Opticks" 1730 edition, book number: 0-486-60205-2 (Dover Publications, Inc., New York, 1979) (careful - different editions have different Query numbering)

                Qu. 1 Masses bend passing light and amount inverse to distance.

                Qu. 3 Light passing close to edges are diffracted in fringes.

                Qu. 4 Light path begins to bend BEFORE reaching body or slit.

                Qu. 5 Light heats mass.

                Qu. 6 Black bodies absorb all light.

                Qu. 8 Black body radiation.

                Qu. 11 Sun and stars are black body radiators.

                Qu. 17 suggested the corpuscles are pushed around (divergence of the aether's density) by waves that "overtake" the rays of light - Because this aether also causes the gravity effect, the waves in the aether travel faster than light - its not a big stretch to say MUCH faster than light.

                Qu. 18 suggests a Medium that refracts and reflects light that allows light to heat effect bodies.

                Qu. 19 suggest the refraction of light implies differing densities of the Medium.

                Calls it "...this aether Medium..". Density of the aether GREATER in "...free and open spaces void of air and other grosser bodies...".

                Qu. 20 the density increase (ie divergence) refract light.

                Qu. 21 Aether rarer within dense bodies and increase with distance and "...thereby cause the gravity of those great bodies; every body endeavoring to go from the denser parts of the medium towards the rarer?". Also suggests light travel faster in the void (denser parts of the aether). Hence today we see the Shapiro delay. Also suggests the aether is so rare as to not impede the planets revolution (no aether wind).

                Also, video showing diffraction using a toy computer simulation following Newton's queries:

                https://www.youtube.com/watch?v=OMAjKk6k6-k&t=18s

                  Dear Fabien and Matthew

                  Traditionally, philosophy has tried to give a description of the universe, understand it in all aspects: economic, natural, social, cultural, abstract, etc. However, since the enlightenment, science started replacing many branches of philosophy. Science can be understood today as an evolved philosophy. In other words, philosophy is just a primitive way of doing science. Besides the methods used by philosophers, scientists also used math and experimentation. For this reason science has been more successful than philosophy in understanding the world.

                  Philosophy started "dying" in 1686 when Newton taught us how theories have to be done. Before Newton people did just philosophy. Newton put philosophy in mathematical formulations and carried out experiments to quantitatively verify theoretical predictions. Thanks to this, we have made great progress in our endeavor to understand how the universe works. Topics that were discussed in philosophical circles were later addressed in scientific terms, that is, formulated in mathematical terms and measured with precision. For instance the concepts of space and time were advanced by relativity, we now know that they depend on speed and gravity. Achieving this level of knowledge was the result of studying electromagnetic effects in systems in motion. This understanding would not be possible by mere philosophical methods. The nature of matter is another traditional philosophical problem that has been largely advanced by science in the last 3 centuries. Other topics include the essence of life and consciousness, just to mention the most relevant.

                  Regards

                  Israel

                  Dear Fabien,

                  Probably I would say that the complexity density of a given pattern will correspond to a certain 'degree' of consciousness. The most 'dense' or complex patterns exist in the brain where we find the highest degree of consciousness.

                  You agree that a consciousness field is not unreasonable and ask whether this field is already described by our physical theories or whether one needs to add a new one. Charmers thought that we needed a new one and thought that physics 'left no room' for a new field.

                  In 2006, when I was lead to the idea of a new field, I asked myself how this field could interact with matter. If I thought 'raise my arm' I wondered how the thought actually exerted any force on matter to start the bio-chemical-mechanical process. It took less than an hour to derive a formula for the force of a consciousness field on matter, based on a change in the local field, that was analogous to the electromagnetic force on charge. Similarly, the motion of mass induced a change in the local field, thus inciting awareness of the moving matter. We don't really want to be made aware of matter that isn't changing with respect to us.

                  It actually took a while for me to realize that the equation I had worked out thinking the problem through in all it it's aspects was actually written down in 1885 by Oliver Heaviside based on his formulation of gravitational theory in analogy with Maxwell's electrodynamics. The more I analyzed the situation, the more every aspect fit together.

                  In other words, I did not sit down one day and think, "maybe gravity is the consciousness field'. Instead I worked out the simplest equation that exhibited all the properties the consciousness that I thought consciousness must have and then found out that the equations described the gravito-magnetic field of Heaviside that also are the 'weak field' equations derived from Einstein's general relativistic field equations. In other words, I was dragged kicking and screaming to the realization that gravitomagnetism fills the bill perfectly.

                  Also in 2006 Martin Tajmar measured this C-field in the lab and then 2011 Gravity Probe B detected this field. Eventually, after everything fit perfectly in place, I accepted this ideas, and it has provided the most comprehensive understanding of consciousness that I have come across.

                  Along the way I realized that physicists, always projecting structure on the world and thinking that this actually describes the world, had misunderstood the 'weak field' equations of relativity. To simplify the non-linear field equations they simply linearized the equations to describe the 'weak field'. Since the equations are no longer self-interactive, they believed the field is no longer self-interacting. This is foolishness. Changing the equations to simplify the calculations does not change the nature of the field. A self-interactive field remains self-interactive. It only means that one must iterate to restore self-interaction to the calculations. Also significant is that it is not mass in the equations but mass density. Physicists again foolishly think that the gravitational field is only significant for large masses. False -- it is density that drives the gravitomagnetic field circulation, hence electrons and atoms induce changes in the local field.

                  The book I wrote describing this theory of consciousness is "Geneman's World", ISBN-13: 978-0-9791765-5-5, in 2008. My first FQXi essay in 2009 was on the Physics of Consciousness but only ten years ago it was not cool to talk about consciousness in physics. I am quite pleased to see that this topic is now 'respectable'. Believe me, it wasn't.

                  Warmest regards,

                  Edwin Eugene Klingman