Hi Fabien,
Thank you for the essay, I enjoyed it very much!
Do you think it would ever be possible to reach an end to science? To answer in a satisfactory way all or most questions that are able to be answered? And How do you you feel Godel's undecidability and Turing's uncomputibility fit into science, if you feel they do at all? Would love to hear your opinions on these topics.
Best regards,
Ernesto
Dear Ernesto,
Thank you for your comments. We do hope you found some aspects insightful.
With regards to the "End of Science", with the thesis we defend in our essay, it is possible to reach a state where scientists believe that "they have got the whole picture right" and maybe what remains to be done is just getting better and better quantitative agreement between theory and observations. It is unclear whether the remaining quest driven by quantitative agreement can ever reach an end though. That being said, even if most scientists believe that the "End of science" is reached, it does not follow that philosophers agree and nor does it follow that future scientists are going to agree either. There are at least two situations that come to mind where scholars thought that "we have got the whole picture right" and yet that was not the end of it. The end of the 19th Century and the pre-Renaissance period. Copernicus is a very interesting example because, although he motivates to some extent his theory based on disagreement between observation and the Ptolemaic model, his main drive was reportedly the antiquity texts of the Pythagoras school that had been translated from Greek and Arabic (leading up to Renaissance movement) and lead him to look at the world from a unique vantage point with respect to his contemporaries.
Although this is much more complicated than what I am going to say here, one cannot dismiss the influence that Eastern philosophy has played on the development of Quantum Mechanics in the 1920s, in particular when it comes to the development of the Copenhagen school.
With regards to Turing's uncomputability, we think it plays a very practical role in many problems of physics where one wants to infer the infinite time and/or infinite size limit of a system; which is relevant to computer simulations but also to experimental works as well. Alongside Goedel's incompleteness theorem it also gives trouble for answering fundamental questions on the spectral gap. Note that for the latter example, extrapolating to infinity is not the only issue. The point is that it is undecidable to know which finite system size can actually reproduce the real system the model is trying to characterise (https://www.nature.com/news/paradox-at-the-heart-of-mathematics-makes-physics-problem-unanswerable-1.18983).
Beyond the above detailed example, what has come from Goedel's proof of his incompleteness theorem and from other examples such as the Barber's paradox etc.. is whether some self-referential questions can put physics in some problematic situations. A somewhat recent article claims that indeed QM runs into problems when we try to "apply it to itself" so to speak (https://www.nature.com/articles/s41467-018-05739-8).
Hope that answers in part some of your questions.
Best,
Fabien
Dear Fabien,
thanks for your reply. I'm desperately trying to juggle different conversational threads in this contest, so I apologize if I might sometimes take a while to respond.
I think that the issue of losing the substance of a question due to a 'translation' into the scientific realm is an important one---and incidentally, I agree (and have made the point a few times myself) with your example of Zeno's paradoxes. In a sense, the mathematical 'answer' doesn't really tell us anything at all about how motion is possible; it gives a description, but does not really dispel the mystery. That description, of course, can also be had by simply moving to the other side of the room, or overtaking tortoises (I tried it, it's possible---how's that for empirical philosophy?).
That said, the questions spawned in the scientific realm are in themselves important ones---not least because answering them allows us to build nice things, like computers and rockets. So I think, we must find a way to keep both in view---not in the competitive sense that's often on display in the present discourse, with scientists belittling philosophers as having nothing to say with many words, and philosophers deriding scientism (both of which are, incidentally, sometimes also valid complaints), but rather, in a mutually reinforcing way.
The German physicist and philosopher Carl Friedrich von Weizsäcker coined the term 'Kreisgang', literally something like 'circle-walk' or 'circumnavigation'---we return to the same topics, with a deepened understanding, and lift them again onto a higher level of appreciation. This is something that, I think, we should strive the interaction between philosophy and science to further---the philosophical questions spawning scientific investigations, which in turn help us to rephrase the philosophical issues, and so on.
Perhaps there's some way of expressing this more clearly; I shall think about that.
Cheers
Jochen
Dear Jochen,
Yes I totally agree with your view here. I do believe scientific questions are important, first because they allow a given perspective to be followed through and through for a relatively long time. Second because, from them, may emerge new philosophical questions too. And third, because ultimately they strongly participate to enrich our understanding of a topic.
Reading on the history of science, scientists in the first half of the 20th century were, for the most part, all versed in literary subjects and very much so in philosophy. Later on, Carl Friedrich von Weizsäcker (whose writings I do enjoy very much) did try to bring closer philosophy and the sciences and was somehow disappointed at the lack of literary culture of the new scientists he saw emerging in his time.
That philosophy appears to be entirely separated from the sciences and possibly "dead" appears to me as a somewhat recent (post-war) phenomenon that has been further fuelled by events like the "science wars" in the 1990s and by the two-culture paradigm. Whether this schism will survive the various challenges that we have to face nowadays, which call upon moderation, humility and collaboration from all sides, we will see.
That being said FQXi does manage to bring like-minded people from philosophy and the sciences by making them interact on questions where there is still much contention or where an apparent consensus can be looked at with a more critical outlook. That is an opportunity that should not be missed indeed.
Best,
Fabien
Dear Fabien,
You said above that your are quite sympathetic to a field of consciousness. Some new information became available 3 days after your comment, and I have included it in my re-written essay. It is now the last 3 pages of my essay. I do think that you would find it worthwhile to read these 3 pages.
Best regards,
Edwin Eugene Klingman
Dear Fabien,
I very much agree with your observation that there are many undecidable problems in science and the art of doing science is to focus on the what is possible to solve.
I do realise that you are using the evolution of our understanding of the solar system as an illustration of how under-determination works in science. However, I always found it intriguing that Aristarchos came up with a heliocentric system two millenia ago and I would dearly have loved to know just what kind of debates were raging then about that particular theory.
I've also always suspected the influence of Eastern philosophy on quantum mechanics, especially given Wigners notion that consciousness causes collapse, though he leaves unexplained in his paper just how collapse is going to occur when no-one is actually around - which would have been the case - to play on the safe side - before the earth was actually formed (I also recently discovered that Schrodinger was well read in Vedanta, via Schopenhauer). One possibility of course is that reality, in some manner, has mental attributes. This of course is a flavour of idealism and so far out of the epistemology and methodology of mainstream science that its hard to know just how they could possibly conceive it. Perhaps this means philosophy can be safely left to philosophers, especially those of the idealist stripe - still I find it worthwhile thinking on these topics and take encouragement from the fact that this didn't stop scientists of the calibre of Schrodinger or Wigner from doing so.
I wish you all the best in the competition.
Warm wishes
Mozibur Ullah
Dear Mozibur,
Thank you very much for having taken the time to read our essay. I am happy to read that our thesis seems to resonate with some of your views.
With regards to your first question on Aristarchus, I must confess that I knew that he, and others before like Pythagoras, had proposed heliocentric models which somehow did not "take off" so to speak, but I do not know the exact details.
I personally believe that sense data is a very difficult argument to overcome. Now, I am not an expert in antiquity and some much more knowledgeable than I am on the matter have discussed your question here (https://hsm.stackexchange.com/questions/1979/why-didnt-aristarchus-theory-of-heliocentrism-stick) for example. I found the discussion therein particularly illuminating.
As for the influence that Eastern Philosophy has probably had on the development of quantum mechanics, I totally agree with you. Most physicists of then were versed in their classics of Western philosophy and many appeared to think that physics and Western thought had reached a stalled state and were looking for ideas in Eastern philosophy. While you mention Wigners and Schrodinger (I would have to read more about them), interestingly I would have directly mentioned Bohr (who famously designed his coat of arms with the Yin-Yang symbol at its centre and strongly advocated for a universal form of his Complementarity Principle) or Pauli (who developed a theory with Jung on the I Ching and thought that there were there principles that would enable physics to move forward).
This is not to say that the development of quantum mechanics was not also driven by experimental results, but the inconceivability of these results within the inherited Western philosophical and scientific tradition of the time compelled these people to turn Eastward to find different ways of thinking.
Best wishes,
Fabien
Dear Fabien,
Sorry for the late reply, this has been a hectic couple of weeks for me.
Thank you for your detailed reply, it has been very insightful. I agree with you, what you say about not everybody agreeing with when the "end of science" would occur. The examples you provided are a helpful way to think about that type of situation, though I am not too familiar with what you are speaking about with Copernicus, so I will have to look that one up a little more. Thank you again.
Sincerely,
Ernesto
You wrote: "The title of this essay implies there is an 'art' involved in taking a stance."
Generally, when statements like that are made what follows is a series of speculative assumptions that have nothing to support them other than personal conviction (and lots of hand-waving!). Your essay did not follow that path. What followed was a very intelligent and well-reasoned argument for the necessity of creativity in science. Should I go so far as to say it is an argument that science (and mathematics) is, at least to some extent, invented?
I certainly agree with your contention that "the problems of uncertainty and undecidability" represent an opportunity. I attempted to hint at that in my own essay. However, the problem of consciousness, even "the easy one", is much too big. I would guess that, like the "the long-standing philosophical question of whether matter is discrete or continuous" that you mentioned, this problem will not be resolved or, if it is, the resolution will be short-lived.
You wrote: "... the creative frameworks proposed to address undecidable problems are in fact a defining feature of science, whereby what we called philosophical questions give birth to scientific questions that are decidable."
Very well said. My only complaint is that more was not said. I wish you well in the contest.
Dear Fabien and Matthew,
Thank you for the interesting philosophical essay. I think your section towards the end 'crisis or the new normal?' is particularly interesting. I think Kuhn was right when he proposed that we go through cycles of revolutionary and normal science. As a consequence, it appears we become stuck in an 'undecidable' trap when we are doing normal science and don't know how we could possible answer particular philosophical questions.
The current dominant trend in much of modern science is reductionism where we try to build up a global understanding of the laws of nature by studying them independently then bolting them onto one another. Do you think the undecidable philosophical problems could also be a result of this? If we were to consider more globalised theories, could this resolve the undecidable tension arising in many philosophical problems.
I can't help but think of dualism as a reductionist approach to consciousness---we separate our self out as a separate part of the universe---which forces us into the Hard Problem.
In any case, I touched on this theme a little but from the perspective of indeterministic vs deterministic theories. I would love to get your feedback.
Thanks again, and well done on a very interesting essay!
Michael
Dear Jason,
Thank you for your comment and for the positive feedback.
With regards to your comment "Should I go so far as to say it is an argument that science (and mathematics) is, at least to some extent, invented?" I would say that there is some degree (or maybe a lot) of invention but the corresponding creative freedom is bound by rules which compel the invented narrative (or its consequences) to match some agreed-upon aspects of reality (where the minimum required tends to be a form of consistency). Contemporary sciences use as matching tools essentially mathematical tools.
I will make sure to look at your essay.
Best wishes and good luck for the contest.
Fabien
Thank you for having read our essay and for the further thoughts about it.
You said "I think Kuhn was right when he proposed that we go through cycles of revolutionary and normal science.As a consequence, it appears we become stuck in an 'undecidable' trap when we are doing normal science and don't know how we could possible answer particular philosophical questions. ".
Yes, in a way, a philosophical question that cannot be answered by science could be considered as an example of what Kuhn would call an anomaly. Given our definitions of philosophical and scientific questions, we would claim is that this is tautological; of course philosophical questions cannot be answered by science.
I think Kuhn was thinking more about scientific theories failing to answer scientific questions. In this event, we might say the unanswered scientific questions must be 'recoded' as philosophical ones?
You said "The current dominant trend in much of modern science is reductionism where we try to build up a global understanding of the laws of nature by studying them independently then bolting them onto one another. Do you think the undecidable philosophical problems could also be a result of this?"
Yes reductionism is a prominent philosophical doctrine in contemporary scientific circles and it does come with its set of issues. Anderson was already pointing this out in 1972 in his famous paper "More is Different" (https://science.sciencemag.org/content/177/4047/393). Incidentally he did not formulate it in term of undecidability but it is tempting to imagine that in todays terms he may have phrased in that way. In fact some people have done it https://arxiv.org/abs/0809.0151 . This was also already mentioned in one of S. Wolfram's last scientific publication in PRL in 1985 (https://www.stephenwolfram.com/publications/academic/undecidability-intractability-theoretical-physics.pdf ). So in the end yes reductionism brings along with it some undecidable questions which could be decidable if a different doctrine was adopted.
With regards to your comment on dualism and reductionism, would you mind specifying what you meant? I would think that dualism refers to a necessary difference in kind, as philosophers call it, whereas reductionism simply focuses on the premise that a whole is made of parts and if the purported parts do not confer an alleged phenomenon then the said phenomenon is, sometime, deemed illusory.
Many thanks and best of luck in the contest.
Fabien and Matt
Dear Drs. Paillusson and Booth,
I read your essay with great interest. You address a number of important issues in the history and philosophy of science, including reviewing various theories for the basis of consciousness. These seem to be of two classes; consciousness is either difficult and mysterious or entirely illusory.
In my own essay, "The Uncertain Future of Physics and Computing", I take the quite different view that consciousness is due to specific computational architectures in the brain, and that the internal sense of consciousness provides direct clues to the structure of these architectures. I further argue that these can be emulated by artificial neural networks of the not-too-distant future.
Alan Kadin
Dear Fabien Paillusson,
I agree "there is an 'art' involved in taking a stance" but isn't science less about the individual opinion and more about the scientifically proven consensus?
cc walters