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This is Tegmark's short formulation of the "mathematical universe" (paraphrased by detractors as "reality made of math"), and he goes out of his way to stress that he means the "is" literally:"Whereas the customary terminology in physics textbooks is that the external reality is described by mathematics, the MUH [mathematical universe hypothesis] states that it is mathematics (more specifically, a mathematical structure)". Deutsche gives a related physical Church-Turing thesis, roughly "every physical process is realizable on a Turing machine", although he is a bit more cautious.

This rings all sorts of Kantian alarm bells for me. The reason for "described by" in textbooks is that "mathematical structure" is a representation, while "physical world" is not, so one can not literally "be" the other for conceptual reasons. Representation by itself is not a representation of anything, it can only represent something else through a correspondence scheme, just like a book without a 'reader' (possibly inanimate) is only an object combining ink and paper. In the case of correspondence to something physical the scheme itself would normally consist of some physical procedures that relate "forces" to forces, "masses" to masses, "motion" to motion, etc. This is how "such and such is described by mathematics" is usually interpreted.

Tegmark's expansive formulation though seems to leave no room for such an interpretation. It would not help to say that the physical procedures involved are themselves mathematical structures, or realizable on a Turing machine, because what we are trying to understand is exactly what it means for the physical to be so structured, or so realizable. We'd be back to the same question, only now asked for the physical procedures that do the corresponding. It would not help to say that in place of "mathematical structure" it means some physical realization of it either, for the same reason, both set off infinite regress.

So what does it mean? If we put "described" back in, then "physical world is described by an abstract mathematical structure" makes sense, but I think that Tegmark wants more, like "fully described". I do not see how to make sense of anything like that though, how does one "animate" idealities without recourse to physical, or to supernatural? Philosophers of old invoked God's powers (sub specie aeternitatis?), but that would hardly work for Tegmark, and it does not explain.

Conifold
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    At first glance, it looks like Tegmark has simply committed a gross category mistake here. I'll read the paper more carefully and report back. –  Feb 19 '16 at 19:40
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    To paraphrase the old joke: Biologists think they are chemists, chemists think they are physicists, physicists think they are God, and God thinks he is a Turing Machine. – Alexander S King Feb 19 '16 at 19:44
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    http://www.closertotruth.com/series/what-are-possible-worlds#video-2729 – Thomas Klimpel Feb 20 '16 at 10:54
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    If horses had gods, Xenophanes observed, they would look like horses. The same goes for mathematicians, it seems. But I don't see why Tegmark's position excludes the physical correspondence. It only reverses the "description" relation to "prescription." A mathematical ontology grants existence to all that is mathematically definable or "not impossible." The physical just becomes a reduction of all mathematical possibilities to something like Kant's space-time "form of sensible intuition," which is already a "representation." Isn't this just Kant with "categorical" mathematics? – Nelson Alexander Feb 20 '16 at 21:20
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    @nelson Alexander: doesn't mind-stuff, for Kant, come beforehand; as well as the noumenal? – Mozibur Ullah Feb 21 '16 at 01:21
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    If one thinks of mind-stuff as having some essential link with the noumenal; this makes it sound rather like atman and Brahman; but I might be make links where none actually are; it would be interesting to have some insight into how Indian philosophy affected German philosophy, in Kants day. – Mozibur Ullah Feb 21 '16 at 01:24
  • Is Tegmark not simply expressing a structuralist point of view here, or more precisely an in re structuralist / Aristotelean realist point of view here, whereby the objectification of a mathematical structure comes by its real world instantiation. I posted an answer to this effect but I deleted it since it seems entirely impossible that you would not be aware of this point of view. However, it would be helpful for me to know why you would not consider this an answer. – nwr May 14 '18 at 04:34
  • @NickR Well, it would have to be Platonist rather than Aristotelian since under hylomorphism the "structure" is undetachable from the "matter". And both Aristotle and Plato have "knowers" to either connect ideas to sensible things or to strip forms from their physical matter, which is exactly the piece ostensibly missing from Tegmark's "mathematical universe". Hence my puzzlement. – Conifold May 14 '18 at 20:15
  • @Conifold Note to self: review the classics - long overdue. I've only just started reading about structuralism. I guess my understanding is still pretty ill-formed. – nwr May 14 '18 at 21:19
  • I've spent some time thinking about this and try as I might cannot make sense of what Tegmark is suggesting. Yet something about it seems right. You say you have 'Kantian' concerns, but as a mathematical structure (as a thing, not a description) can only exist in the mind this seems a rather Kantian idea. But I can't make sense of it as it is. I suppose one could call the Matrix a mathematical structure, but the minds that instantiate it are not part of the mathematical system. . –  May 15 '18 at 10:00
  • *"mathematical structure" is a representation, while "physical world" is not* Isn't this an argument against mathematical platonism in general? Or do you think one can be a mathematical platonist and still think all mathematical forms are representations? If so what would the form of the Mandelbrot set, or of a cellular automaton like the Conway's Game of Life, be representations of? Anyway, for those who don't reject mathematical platonism out of hand, I gave an answer showing one way to understand Tegmark's proposal philosophically [here](https://philosophy.stackexchange.com/a/72799/10780). – Hypnosifl May 06 '20 at 22:04
  • @Hypnosifl Plato's forms are not mathemtical structures in the modern sense. They are almost alive and act on sensibles through partaking, in neo-Platonism this is done through the powers of God's mind, which they are parts of. If Tegmark endorsed such a thing there would be no problem, but I doubt he'd get much traction with his colleagues. The problem is that he wants it both ways, have platonic forms with awesome powers and eat them up with a physicist's respectability too. Modern mathematical platonism does not require any physical action, so it doesn't help Tegmark at all. – Conifold May 06 '20 at 22:11
  • When you refer to "modern mathematical platonism" in your last sentence, that's what I was thinking about as well when I made my comment, I wasn't referring to Plato's specific ideas. But I don't understand what you mean by "require any physical action" in that sentence. If you look at my linked answer on the other thread about interpreting Tegmark's proposal in terms of the idea of psychophysical laws (or 'psychomathematical laws', perhaps) that cause conscoius experience to arise in any mathematical form with the right structure, would you say there's any "physical action" there? – Hypnosifl May 06 '20 at 22:37
  • @Hypnosifl It is very long and I do not have time to read it closely now, but identifying abstract with mental, invoking psychophysical laws, consciousness, subjective experience, etc., is not very attractive to most mathematicians (because of psychologism) and physicists (because of idealism), who are Tegmark's target audience. Reactions to Penrose are telling in this regard. And Tegmark steers clear of this sort of thing in his MUH expositions. He tries to leave the impression that thin modern platonism is enough, but that only endorses causally inert abstractions, so it isn't. – Conifold May 06 '20 at 22:55
  • I don't think the reaction to Penrose tells us about scientists' receptivity to psychophysical laws because he is proposing that explaining human *behavior* requires new laws of physics. Anecdotally I think you can find a lot of scientists who act like hardnosed materialists in their understanding of behavior but who are sympathetic to Chalmers/Nagel style arguments about there being some further mystery to subjective experience. For ex. T.H. Huxley, Darwin's colleague who was Darwinism's main defender in debates, [seems to have been an epiphenomenalist](https://www.iep.utm.edu/epipheno/#H2). – Hypnosifl May 06 '20 at 23:21
  • For some more recent examples, see comments by cognitive scientist Steven Pinker [here](https://web.archive.org/web/20120329092117/http://www.lse.ac.uk/CPNSS/projects/darwin/publications/evolutionist/pinker.aspx), or the article by neuroscientist Christof Koch [here](https://www.scientificamerican.com/article/is-consciousness-universal/). Koch is one of the advocates of "integrated information theory" which has been proposed as a type of psychophysical law that would determine the "degree of consciousness" of physical systems, and Tegmark also advocates this as I discussed in the other thread. – Hypnosifl May 06 '20 at 23:24

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Douglas Hofstadter would call this a strange loop. If one believes mathematics can "fully describe" reality, one can make a pitch to claim that reality is a subset of mathematics. Empirically, these two would look identical. Tegmark is arguing that you can choose to put reality inside mathematics instead of putting mathematics inside reality. Like all ontologies, it is very hard to challenge. If you say that reality is not mathematics, and he says reality is mathematics, how can we really decide which one is "right?"

His theory does include some interesting threads to tug on. In CUH (his Computable Universe Hypothesis), he argues that the entire world is computable. Non-deciable things, such as the issue with band gaps being non-decidable are resolved by stating that only the description of things must be computable, not the actual time evolution of it. This implies that he considers reality and the description of reality to be one and the same. He also readily admits that this means that our universe can contain questions which cannot be answered within the universe. Whether this is acceptable in one's ontology or not is one's own business. However, it does give insight into how he would view things. If something in reality existed which was not fully made from a mathematical structure, he would be able to treat it as though it is something which can be described using mathematics but which is not decidable. You would be unable to come up with a logical process to disprove his claim, because his claim is that one cannot prove nor disprove his claim within this universe.

Also, paradoxically, you wouldn't be able to point our that non-mathematical real thing either. If you could successfully point it out to him in terms he would recognize as identifying an object, you would have to do so in a formal language (he would not accept anything else). By doing so, you provide a mathematical description for the thing (you used a formal language to do it), and he would be able to stand on his claim that it is merely an undecidable time-evolution, literally until the end of time.

In the end, I'd call his theory testable but not falsifiable. He makes the argument that he provides testable hypotheses that we will find more mathematical structures, but there's nothing in the theory which permits Popperian falsification. This puts it in a category alongside many Asian concepts such as Traditional Chinese Medicine, which permit testing but not falisification. Thus, his theory must find its use the same way TCM does. It gets picked up by people who feel their lives are improved by picking it up, but it is rejected by science because it does not conform to the strict rules science uses today.

Cort Ammon
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    I think Tegmark's CUH is stronger than that: He argues [that all computable structures exist](http://arxiv.org/abs/0704.0646). An odd, if plausible, combination of Everett's multiverse and Computational Platonism. – Alexander S King Feb 20 '16 at 16:12
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    My issue is not disbelief, if I said "truth is an organ" I'd be asked what I mean by "is" before it even gets to that, and answering that I embed truth into body won't cut it. This is different from disbelieving in God say, where the meaning is clear. I also suspect that spelling out "is" might make MUH incoherent for the same reasons that "world" of rational metaphysics was incoherent, as Kant showed in the first antinomy. – Conifold Feb 21 '16 at 01:33
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    Mathematical universes were proposed before, e.g. by Plato, Leibniz or recently Penrose, but they had extras, fantastic ones, to make them work. Replacing extras with unintelligible "is" is not a solution. If all MUH amounts to is that we will discover more structure it is not testable, almost every classical epistemology "predicts" that, including Kant's. These are legitimate concerns, arguments and difference of opinion can only happen after opinions are made intelligible, coherent (or paraconsistent at least, if one wants to go there), and non-vacuous. – Conifold Feb 21 '16 at 01:34
  • "This puts it in a category alongside many Asian concepts such as Traditional Chinese Medicine, which permit testing but not falisification." AFAICT TCM HAS been tested AND proven false, so this claim is also false. Whether its practitioners want to accept the falsification or not is another matter. – The_Sympathizer Apr 09 '17 at 10:31
  • On a tangent, I'm also curious about something else: If the universe contains non-computable elements, are they _harnessable_ to do any sort of "non-algorithmic computation", e.g. to build a non-computer "computer" that can solve the halting problem? (E.g. we can't build a computer to decide the phenomenon, but we could use the _phenomenon itself_ as an "engine" of computation beyond finite Turing computers' capabilities?) – The_Sympathizer Apr 09 '17 at 10:34
  • Furthermore, looking again at this it seems these are not "non-decidable _phenomena_", i.e. like if we found a physical process that was outputting the bits of Chaitin's omega, but rather "non-decidable _questions_ we can pose about phenomena coming from dynamical laws that might still be executable on a standard computer". For example, Conway's game of life is a simple, entirely mathematically-describable (even to a child!) "universe" whose dynamical laws can be executed to perfect fidelity on any Turing-style computer. _However_, there are (cont'd) – The_Sympathizer Apr 09 '17 at 10:44
  • (cont'd) questions _about_ it which cannot be so decided, e.g. there is no algorithm that will decide if a given pattern eventually stops growing or grows forever. Having nondecidable questions one can _ask about it_ doesn't make the _fundamental laws_ then nonmathematical or noncomputable. On the other hand, if there is a physical process which, say, outputs the digits of a Chaitin omega indefinitely, then the universe definitely IS based on noncomputable laws. (cont'd) – The_Sympathizer Apr 09 '17 at 10:44
  • (cont'd) On the third hand though, of course, how would we know? It could be that after 10^1000 years, say, then the process stops pumping out digits of Chaitin omega or starts repeating itself, thus only producing a (rational in the second case) approximation. But we could never falsify it empirically; matter itself is likely to decay before ~10^200 years and humans will almost certainly be extinct long before that time even. Thus the conclusion is not changed; the computability or "mathematicalness" of the universe is not a question solvable by empirical science. – The_Sympathizer Apr 09 '17 at 10:47
  • (Interestingly though if the process DID produce Chaitin omega for 10^1000 years and then veered off (we could never run it, but if we deduced it through other means), that would tell us that we would probably have no hope of writing down the exact laws of the computable universe, if it is so, for the digits of Chaitin omega are algorithmically random and thus it would require a set of "laws" on the order of needing 10^1000 years to write them all down, or a formula of similar length to calculate a particular constant therein from first principles.) – The_Sympathizer Apr 09 '17 at 10:49
  • @mike3 That is the interesting thing about non-algorithmic computation: there's no known reason it can't be done, but it can be terribly hard to harness. We, in the modern world, are so used to computable things that it can be awkward to think about what can and cannot be done in a ream which is not computable. Then again, it's also worth remembering that we have never built a Turing machine, and most likely never will. Something about that infinite tape always makes things tricky. – Cort Ammon Apr 09 '17 at 16:47
  • @mike3 And as for falisifying TCM, I think that situation points out an incredibly important thing that is key to understanding science: falsification is relative to the person making the judgement -- always has and always will. If we forget this, then the world starts making less sense. For example, we start to get confused at how anyone could possibly disbelieve global warming. It doesn't make any sense, until you consider that their definition of what qualifies as falsification is different than yours. Then we have to figure out what to do about that, which is another topic entierly. – Cort Ammon Apr 09 '17 at 16:50
  • @Cort Ammon: Yes, which means that essentially we cannot actually compute every Turing computation either (some will require too much "tape" to fit in the entire universe. To see this, just note the set of all Turing computable problems is countably infinite, but the number of bits we can store in the accessible universe (e.g. Bekenstein-Hawking entropy) is finite, thus the exponential of that (number of strings we can store) is finite too.). Thus meaning we only have an "island" of Turing computable problems accessible to us. (cont'd) – The_Sympathizer Apr 09 '17 at 23:00
  • (cont'd) Nonetheless, the question could exist as to whether the Universe doesn't also permit us an "island" of _non_-Turing-computable problems as well. (Although perhaps may you could say it could, because we will only again, by the same rationale, be able to solve a finite amount of instances, and in theory that could also be done with a Turing machine, if nothing else by just imagining the finite Turing program that brute codes every answer. So maybe this is not distinctive, but we could still ask whether it permits an "elegant" solution meaning one much more compact than that.) – The_Sympathizer Apr 09 '17 at 23:00
  • Also, I want to point out that as mentioned I'm not sure that the "band gap non decidability" makes the universe not mathematical. Because you can ask non-algorithmically-decidable questions about an algorithmic system (e.g. even a Turing Machine, that's what the whole "halting problem" business is.). Yet Turing Machines are definitely mathematical and algorithmic. – The_Sympathizer Apr 09 '17 at 23:03
  • Also, regarding TCM, yes, the falsifiability is "in the observer", but then it's not a property of "concepts". – The_Sympathizer Apr 09 '17 at 23:04
  • Mathematical systems are finite and closed, with the definitions made from 'outside' them. Strange Loops account for this, giving a role for the emergence of meaning from information through subjective experiences https://philosophy.stackexchange.com/questions/51633/how-does-gödels-incompleteness-theorem-apply-to-materialism-and-the-mind/52169#52169 – CriglCragl May 15 '18 at 00:13
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If mathematics is the repository of what all humans can intuitively conceive, then whatever lies behind the material world may or may not be a mathematical structure, but the entirety of what we can ever understand about the external world would be.

Given that theory of what mathematics is, the question then becomes, in stages of progressive aggressiveness:

  1. why we assume there is a remainder,
  2. whether we can even know of the existence of a remainder, and
  3. whether, if we are sure we can't know, it is more logical to just assume there is none.

As I see it Tegmark is just proposing the exact opposite of the Kantian notion of noumena in an indirect form. Kind of by definition, even for Kant, the nature of noumena is an unresolvable question. If we relied logically upon noumena for any real purpose other than inspiration, our inability to access them would contradict the idea that we are fully capable of becoming intelligences and doing things like acting morally.

The only real way out that leaves noumena intact at all seems to be the Hegelian response is that we perpetually 'move toward' them. But math itself does not work that way: what is entailed is resolved, even if you are not a Platonist. So a mathematical model of dialectic would be a single mathematical structure, whether or not it allows for everything to be resolved with a single pass through any given evolutionary process, or requires infinitely many reversals, or whether it can even be navigated by any possible mind. It is still the closure of some set of entailments that we cannot, by our given nature, question. (Presumably more than countably many basic notions are involved, since otherwise the nature of language keeps us from getting to closure.) The terminal point of the whole of dialectic has to be part of the model. Whether or not anyone can get there, Hegel's endpoint where "We, as God, know God," is in the model.

Math has gotten beyond topology, and limit points don't make us worry anymore. So we can't avoid the question by ledger-de-main. Noumena either are or are not part of our model. But if we have them, we still can't know anything about them -- even whether or not they are really there.

In that case, what is the difference? Whatever transcends those forms is lost to us, and we will not be able to understand, much less prove, anything about it. Either side of a proposition independent of your system is open for adoption into truth with no loss.

So Tegmark's is, at the very least, an un-disprovable assertion, and one that sets the very frame of Occam's razor. To doubt it not only requires we create unnecessary entities, but that we acknowledge that those entities are utterly unhelpful to us, since they are necessarily unknowable and beyond consideration.

What is the risk in presuming it is true, since we can never know anything about why it might be false?

The extension by Deutsche is unwarranted and almost unrelated. No Turing Machine can compute randomness. There are only so many states, and we will be drawn back into them. So ideas like those behind classical Quantum Theory, etc. are not consistent with Deutsch. In effect, Deutsch is making the same error Nietzsche makes in deducing the Eternal Recurrence, only about non-computability rather than chaotic dynamics. Being arbitrarily close is not being right, and in endless time, eventually the gap with show some effect.

  • But "all we can understand" and "all there is" have very different semantic and logical properties, not the least because of indeterminacy about expressive means. There is no "shared reality" as a finished thing. Ignoring the difference, in Kantian or some other form, leads to exercises in lack of imagination, about both reality and understanding, and makes it harder to recognize limitations of existing means, and develop new ones. Most of what we know in biology, psychology, history is non-mathematical for a reason. But subtlety aside, Tegmark explicitly rules out your interpretation. – Conifold Feb 25 '16 at 01:31
  • I am stuck in dialectical land. So, take it from there. From an evolutionary perspective, we should reach a point where 'We, as God, know God.' Where we have addressed every fact and taken the proper perspective on it. So there should be no individual thing that we can in fact not know (even if we cannot know contrasting things at the same time). Also, what is non-mathematical? From the point of view of the opening sentence, noting. Modern mathematics contains all of those forms -- relations, degrees, processes, structures... –  Feb 25 '16 at 13:13
  • I am not sure Tegmark rules this out, it is not 'representation' or 'interpretation' it is 'embodiment'. –  Feb 25 '16 at 13:14
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    Evolution is not teleological, there is multiple branching and no Omega point, so there is no back projected "proper perspective" on anything. Multiple ones are "proper" for different purposes even in physics, let alone in biology. Today's concepts, like "individual things", do not work even for some existing physical theories, and are likely to grow more useless in the future ones. Attempts to construct mathematical semantics of even natural language did not go far due to inherent pluralism and ambiguities, mathematics does not mix well with ambiguity. – Conifold Feb 25 '16 at 23:30
  • The whole Everett universe of possible worlds is a properly mathematical structure, and so are paraconsistent logics. Math does not need a classical structure, nor does history predict future potential. Time can be parameterized in as complex a way as is necessary. All those branches are dialectical paths. You give symbolism short shrift if you consider those genuine limitations of mathematical models. You are talking, so far, about the limitations of mathematicians and of classical logic, and not about the limitations of mathematics. –  Feb 26 '16 at 00:04
  • Everett's multiverse does not consist of "possible worlds", that would contradict conservation laws, "possible world talk" suffers from the lack of access problem in itself, and incompleteness implies that "dialectical paths" can not be stuffed into a single structure anyway. "Mathematics" may have no limitations, but we do not know what such "mathematics" means, we can only talk in terms understandable today, or we do not understand what we are talking about. I am not concerned about verbal formalities, projecting familiar backyard onto the world is not a source of great insights. – Conifold Feb 26 '16 at 01:19
  • You are asking a question about what can possibly be a mathematical structure. Presuming you already know what mathematical structures you are going to allow, there was no point in asking the question. If you insist math can't handle known aspects of reality, why consider Tegmark's hypothesis at all? –  Feb 26 '16 at 04:18
  • Incompleteness says nothing useful at all about structures like Everetts that have more than continuously-many symbols, and that is only the simplest way of trying to model possible dialectical paths, so it surely says nothing useful about all possible explanatory paths. Vocabulary aside, you seem to simply want to foreclose the options and throw away the question without considering any options not already covered before we were born. –  Feb 26 '16 at 04:27
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    I am not asking what can possibly be a "mathematical" structure, or prescribing what "mathematics" (of the future) can or can not handle, neither I nor Tegmark know what it will "allow". But he is advancing his hypothesis today, and it is fair to ask what it is beyond empty words. Possible world talk and Platonist completions often blow up known bubble to the size of "all there is", on the contrary I am asking for more options, insight *how* mathematics can be made more real, not pronouncements. Incompleteness enters because it tells us how not to do it, given that we have no Platonic access. – Conifold Feb 28 '16 at 00:21
  • This strikes me as evasion via nitpicking. You need some pretty stark dualism to make any difference between the two questions "What are the bounds on what can be mathematical?" and "Can all of (physical) reality be mathematical?". As I see it, Tegmark is really just proposing the opposite of Kant -- that phenomena (which are mathematical, if you accept the definition of math from the first line of the answer) do not require noumena to back them up. If you just reject the opening premise, you don't have to be abrasively condescending about the rest of the post. –  Feb 29 '16 at 16:57
  • I have edited my defense into the post itself, since these comments are getting kind of bulky. –  Feb 29 '16 at 17:26
  • Maybe I was not clear enough, both questions are moot because answers to them are meaningless. A meaningful proposal would be to take unmathematized aspects of reality, analyze what the obstructions are, and sketch ideas for overcoming them. The analogy would be Michelson pontificating in 1902 about "*single compact body of scientific knowledge*" where "*all the phenomena of the physical universe are... manifestations of the various modes of motion of one all-pervading substance — the ether*" vs. Einstein actually working (under Kantian influences btw) on a synthesis beyond such projections. – Conifold Feb 29 '16 at 23:06
  • If you consider the latter question meaningless, why ask about it? I thought you were trying to make sense out of it, not just ravage it pointlessly. And given the definition of math I am using (which has to be an immediate corollary of the MUH if not a precondition of it making any sense at all), you cannot "take unmathematized aspects" of anything. By the time you "take" it, and proceed to treat it as an object, you have reduced it to symbols, if only fuzzy ones, whether that was your intention, or not. –  Mar 01 '16 at 18:49
  • I am trying to see if Tegmark actually has something non-trivial in mind, even if he is expressing it awkwardly. But I thought through the usual Platonist moves you suggested, they do not work without a God like add on. Your definition of "mathematics" is unintelligible to me, and probably incoherent because "all that..." is badly self-referential, I was referring to the colloquial one. For instance, trouble with mathematizing biological evolution is likely due to current lack of mathematical concepts for indeterministic dynamical systems that are not probabilistic in the simple way of QM. – Conifold Mar 03 '16 at 01:27
  • To my mind the only thing here that is not Platonist is that the semantics of the realm is not necessarily classical, he has avoided the reference to perfect logic by renaming it mathematics. All 'computational structures' exist, and we cannot depend on more than that because we, ourselves, are trapped in a world of symbols. So the world is ideas but the rules of the ideal realm may be something like Russian Constructivism. He seems to take Wittgenstein's 'final dictum' seriously and to consign 'What whereof we cannot speak' not just to silence, but to nonexistence. –  Mar 03 '16 at 12:37
  • This statement caused me dissonance. " Kind of by definition, even for Kant, the nature of noumena is an unresolvable question". This is not the case. Those who study consciousness reach a different conclusion from Kant. For a start, Kant's idea that there is more than one noumenon is logically incoherent since they must always be defined as being identical. Let's just say that many people would disagree with the idea that we cannot know the facts about these things. Kant proposes we cannot know but does not prove it. –  May 15 '18 at 10:13
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    @PeterJ Your individual dissonance is not a concern of philosophy. I would need proof that these "many people' actually exist, and are not crackpots. –  May 19 '18 at 18:19
  • @jobermark - Sounds like time for some research. –  May 22 '18 at 13:30
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Don't you agree with Alexander's nice joke?

Mathematical universe means that our "real" world is a "virtual" reality, designed and executed by mathematical algorithms.

It is difficult to find arguments against this view. A possible counter argument: We should register more anomalies due to rounding errors of the computation with finite precision.

Jo Wehler
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    Universe as a simulation may work for Deutsche but not for Tegmark, the problem simply shifts to what it means for the simulator to be a structure, there's no need to refute it. I like the joke but I have a different interpretation of it: what they all think of is a "reduction", which upon reflection is either unintelligible or incoherent :) Similar to naive realism and "rational metaphysics" that Kant dismantled in the antinomies. – Conifold Feb 21 '16 at 01:33
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In Tegmark's MUH, it claims there's really a single ontological world originated from math entities, like a computer stack, final screen outputs are ultimately originated by its CPU instructions. MUH is a form of classic Platonism's "ideal forms world" while focusing on abstract math structures instead of old more concrete Platonic "form of goodness" ethics. MUH must conceive of Math structures like space/time as real substance so that it's possible the physical can be born from the ideal. He's a good theoretical physicist, so like many other modern physicists' metaphysical philosophy, QM String-theoretic world is increasingly becoming an application of Algebraic Geometry which is hoped to contain the final Theory of Everything.

However, a much more important and interesting question from my perspective is how either MUH or classic Platonism can explain and deduce "consciousness". For me no matter how clever in MUH math can be employed to construct some "integrated information" metric borrowed from neuroscience (Tononi, et al), ultimately it's just a notion only understood in a conscious rational mind. So MUH essentially claims Math creates consciousness while traditional idealists claim vice versa, like the egg-chicken trap. Similar to Searle's Chinese Room Argument or Leibniz's Mill Argument, a computer or any entity processing math has no true understanding of math itself. So I personally favor traditional idealist view that mind is the ultimate real ontological existence. As Renaissance Cardinal and philosopher Nicholas of Cusa put it, the ontological world is nothing but the perfect Oneness conceives with the supervenience of all its images reflecting with actions...

Double Knot
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I have always understood consciousness to do a lot of the heavy lifting in his saying the universe is mathematical, and reality being very far removed from the pictures our senses provide us.

His chapter on the conscious illusion of the flow of time provides a template for how large of a role conscious experiences play. And because there is such a large gap to understanding conscious experience, a lot can be stuffed in there for later scientists. He routinely writes most of the work left will be for psychologists and biologists.

It is only in this near unfathomable gap between external reality and subjective awareness that Tegmark's phrasing makes sense. What bestows these mental properties of pain or time flowing? Presumably they supervene on something. Is it onto the computational structure of the brain? Unto unknown physical processes or objects? Or could it even be onto mathematical structures? Since the explanatory gap for something giving rise to mental states is so great ("How pulses of water in pipes might give rise to toothaches is indeed entirely incomprehensible, but no less so than how electro-chemical impulses along neurons can." -- Tim Mauldin https://doi.org/10.2307/2026650 ), we should not be so quick to dispel of a mathematical structural origin for them.

From within these mental states we have to probe the outside world. And since we can't absolutely trust the ontologies they have presented us until now are the "true" ontologies, Tegmark can say a tree really is mathematical. That is my thesis here, and I believe what Tegmark had in mind. We have to really take seriously we may be experiencing a heavily transduced perspective of reality. What we think of a tree existing classically is actually closer to something like Mario thinking he really exists in Mushroom Kingdom, and thinking it really exists on some fundamental level. That is the level of delusion we must be living under for Tegmark's remarks to make sense.

Somehow a mathematical structure can give rise to something believing it is experiencing time flow, colors, and trees existing. If you think circuits can lead to an AI experiencing, I think this argument is not hard to swallow. If the flow of time is not fundamental, likewise it shares similar logic. You just have to trust that you should distrust your own senses more than you probably do.

J Kusin
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  • "It is only in this near unfathomable gap between external reality and subjective awareness that Tegmark's phrasing makes sense." To me that is exactly where Tegmark's theory makes no sense at all. We have enough trouble bridging the gap between physics and consciousness. (And that is a huge understatement!!!) There is no imaginable way to bridge the gap between mathematics and consciousness. – Daniel Asimov Sep 03 '21 at 17:22
  • @DanielAsimov But see the Maudlin quote. He thinks there is no imaginable way to bridge the gap between physicalism and consciousness either. For scientists and philosophers who likewise see the gap as "huge", why not pick the most global, universal theory (math) and build up from that. Rather than from computation or physicalism, which are more assumptive and require an equally long bridge to join the gap – J Kusin Sep 03 '21 at 17:39
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Our physical world, is not an abstract mathematical structure. It existed for a long time before mathematics was ever invented! It just so happens that mathematics can be used by us (humans) to understand (make sense of) some portions of it. Mathematics is only a "tool" created by (inside) our imagination. How can something inside our brain (thoughts) "create" physical matter? There's no way!

Guill
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    1. You're bringing too much preconceived notion into this. Philosophy is about suspending disbelief and exploring other people's ideas, not saying "THERE'S NO WAY!" Without providing reasoning as to why this is. Given your previous points, it seems you have some strong preconceived notions about the nature of mathematics as well. 2. Tegmark argues that math is not "invented" or "a tool" but is actually the fundamental building block or conduit of reality. – Derek Janni Feb 26 '16 at 17:33
  • It may appear that mathematics was "invented" but many people (including me) believe that in fact mathematics is *discovered*, not invented. Any true theorem is true independent of time and space and anything else. – Daniel Asimov Sep 03 '21 at 17:27
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Tegmark makes a distinction between mathematical notation and mathematical structures. Model theory makes exactly the same distinction between the concepts of a theory and a model of that theory. A mathematical structure is not a representation but more like a Platonic Form.

Ron Inbar
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