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I'm coming at this from the POV of a physicist. Physics demonstrates that the universe does not feel any obligation to follow a humans naive idea of what makes sense. This idea of what "makes sense" was developed for surviving in a Newtonian world, and understanding the behaviour of an electron passing through two slits with dimensions proportional to their wavelength is not included in that kind of common sense. But if we allow for things to be unexpected, they do appear to be logical and internally consistent. Requiring that the universe be logical and internally consistent seems to be a requirement for doing physics.

I struggle to come up with an experiment that could detect evidence that this universe exhibits behaviour that is not internally consistent. Perhaps someone with more imagination than me could write one down. Having read stories that lacked internal consistency, I know that there are signs of it, so an experiment ought to be possible.

My question is less practical though. Is there an argument that our universe should be possible to describe with internally consistent rules?

I'm not asking about the possibility of actually deriving these rules. There are an abundance of ways that a reality can have rules that are not possible to obtain. Nor do I place any constraint on the structure of these rules. But does the reality itself have to behave in a way that does not require contradictions in those rules?

NotThatGuy
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Clumsy cat
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  • Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/133154/discussion-on-question-by-clumsy-cat-is-there-a-reason-to-believe-that-our-unive). – Geoffrey Thomas Jan 13 '22 at 09:23
  • Consider Black Holes. Is their existence inconsistent or merely incomprehensible (to us at this stage of cosmology and physics understanding)? – Carl Witthoft Jan 13 '22 at 16:09
  • why not "yes and no"? sorry, just complaining about that move –  Jan 17 '22 at 19:35

14 Answers14

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If it's not consistent, you can't usefully make predictions. Since we so far are pretty good at predictions based on the physical laws we have discovered, it is a good working hypothesis that the universe is consistent, even if there is no way to prove it.

Once you encounter something that is in contradiction to current models, either you improve the models (by formulating rules that capture what you have observed) and continue to be able to predict. Or you hypothesize that the universe isn't consistent, throw up your hands in confusion, and stop being able to make useful predictions. One is clearly more useful than the other, and has been more successfull in the past.

kutschkem
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  • You first sentence seems like a good argument for making the assumption that it should be internally consistent, but not much of an argument that it is internally consistent. I would not be able to agree with the rest of your first paragraph, we have constructed some beautiful theories (e.g. MSSM) which were ultimately not found in reality, and out best theories have some pretty big holes in (gravity, dark matter, etc.). We have some good predictions and some bad ones, there is no general rule. – Clumsy cat Jan 10 '22 at 11:47
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    @Clumsycat The answer explicitly states “there is no way to prove it,” because there isn’t. The only evidence for the universe’s internal consistency is the success of hypotheses that build off of that axiom. That evidence is, necessarily, circumstantial, not proof—as an axiom, it _can’t_ be proven. That’s the answer to this question. – KRyan Jan 10 '22 at 20:15
  • "If it's not consistent, you can't usefully make predictions." Until you define what it means for the universe to be "consistent", this is a meaningless sentence. There is no standard sense of the word "consistent" that applies to the universe. I don't even know of any non-standard sense of the word that applies to the universe. – David Gudeman Jan 10 '22 at 23:03
  • @DavidGudeman For example, there are domains where Special Relativity, which is a well-tested theory, and Quantum Mechanics, which is also a well-tested theory, clash and are inconsistent. That means in these domains we can't properly predict what happens due to singularities in the equations. The general assumption here would be it's our theories that are incomplete. If both theories were already the Truth and it was actually the Universe that is inconsistent, then you can just give up, you have reached the boundaries of knowledge and a place where you can only confusedly give up. Not useful. – kutschkem Jan 11 '22 at 07:53
  • @KRyan That seems like a sound conclusion. And thanks, I understand this answer better now. – Clumsy cat Jan 11 '22 at 08:45
  • @kutschkem "If both theories were already the Truth and it was actually the Universe that is inconsistent" – What does this mean? How can theories be "true" about an inconsistent universe? And what is the universe doing inconsistently in this example? It seems that our theories do not properly bridge between two areas, but I'm not sure how we could ever point a finger at the universe for that. – TheRubberDuck Jan 11 '22 at 15:22
  • "one is clearly more useful than the other" is entirely subjective. It is not more likely the universe is consistent because a stackexchange user thinks one mindset is more useful than the other – Tvde1 Jan 11 '22 at 16:36
  • @kutschkem, you are equivocating between the universe and a theory about the universe. Theories can be inconsistent. The universe cannot. – David Gudeman Jan 11 '22 at 18:07
  • Unfortunately, there's a hole in this logic: We know that we are good at making predictions, because our predictions have always worked out in the past. But that is inductive reasoning, which is exactly what we are trying to justify in the first place! (Don't blame me for this observation, it's all David Hume's fault.) – Kevin Jan 12 '22 at 06:56
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You state a form of Hume's 'problem of induction': do we have any reason except the regularity of regularities in the past, to think the future will resemble the past?

Then you frame a version of Hilbert's 6th problem, can physics be axiomatised? That is, a set of rules given with a minimum of assumptions, and those self-evident, or compelling. Godel Incompleteness & Turing's Halting Problem basically ended thus project. And I would relate that to the nature of the universe being that rules emerge, and are not 'foundational' - except maybe the uncertainty principle.

The universe in a very real sense is unpredictable, random, chaotic. The quantum foam of virtual particles. Sensitivity to initial conditions. Stochastic processes. Limits imposed by the uncertainty principle.

What seems to happen is that large scale order emerges from this disorder. Continuous symmetries, conservation laws, emergent regularities and consistencies.

Time seems to emerge in two ways. As an asymmetrical dimension, where travel is only possible in one direction (Relativity). And as the thermodynamic arrow of time, the tendency of ordered systems to become disordered. We have good reasons from the search for quantum-gravity, to think the dimensions, including time, emerge from something else, eg a spin lattice network. I would say this points to the idea all laws are emergent, and to say a law is 'inviolable' is only to say, what we've seen so far strongly obeys a given symmetry. CPT violation shows how even strong patterns can have exceptions based on higher symmetries.

The expectation of consistency is deeply related to everything in the universe having once been in the same place at the same time, or very, very close to it, at the Big Bang. Which the asymmetry in the time dimension seems to have started from, beginning causality.

Dark matter shows we don't have the full picture, but we know it's there because it's part of the story, part of explaining the structure we see. All kinds of other universes and materials and behaviours of things could be out there, but if they don't interact with our universe we can't evidence them. The order and consistency relates to telling the story of what was 'one thing'. New rules can always emerge, because they are only the observation of patterns.

CriglCragl
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  • I'm glad that you have given me proper names for Hume's problem of induction and Hilbert's 6th problem. Possibly Hume's problem is closer to the crux of the question, if we decide there is no fundamental requirement for consistency. Your comments on the distinction between behaviour at different scales also nicely illustrates why fundamental truth doesn't come out of observation. We only get probabilistic comparisons by observing things. In the end, you sort of dodge the question, but the impression is that you feel that consistency is a necessary assumption, and not possible to determine? – Clumsy cat Jan 11 '22 at 13:28
  • Popper claimed the idea science is based on induction is a myth, that it's about falsifying incorrect or incomplete models. If you look at Bayesian reasoning, which closely follows how we do things intuitively, guessing reasoning and experience all go into generating our prior probabilities. I don't think consistency is a necessary assumption, I think everything can be generated via uncertainty principle +Anthropic principle – CriglCragl Jan 11 '22 at 13:59
  • yes, I think most people would agree that even falsification is not perfectly achievable from observations. We get confidence intervals, and we pick a level to call "proof". So no absolute conclusion can stem from observation (pardon the pun). The remaining question is; do we know anything about our universes internal consistency without making observations? – Clumsy cat Jan 11 '22 at 14:07
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I suspect you won't like this answer — physicists tend to like concepts that are neat and contained while philosophers deal with scruffy, unruly ideas — but it's worth considering a quote from Wittgenstein:

1.1 The world is the totality of facts, not of things.

Facts are things that we have use for (or have to overcome); they are mental constructs, not physical. It's a 'fact' that an object has mass because 'mass' is something we can use (or have to overcome as a problem). If we want to hurt an enemy, we throw a heavy stone, then we systematically improve — impose order on — our use of mass so that we can hurt enemies more. But through all of this, we have no real idea what 'mass' is; we just know how we can use it.

What the world is, the world of things... [shrug].

The functional regularity of physics tends to infer that there is ontological regularity in the universe. But that itself is just another mental conception: something we humans find useful in or lives and work. Many mystical traditions hold the intuition that there is a higher-order regularity in the universe — karma, dao, the will of God, etc. — but again, that is nothing more than a useful human conception. Humans like order and regularity. We find order where we can, and ignore (or fear) what cannot be organized and structured. We are ineluctably biased towards consistency, so that the 'facts' which constitute our world are only those things that we can find order, structure, and use for. The more we dig for the essence of the universe, the more we find reflections of ourselves.

Ted Wrigley
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  • Can we not come upon a fact we did not wish to learn? For example the muon was broadly perceived as inconvenient and messy; "Who ordered that?" - I.I.Rabi. This would indicate that the facts of our universe may be more than just the nice neat symmetric ones we would like to find. – Clumsy cat Jan 10 '22 at 16:00
  • @Clumsycat: The only reason we have the conception of muons is that the (nice, orderly) standard model needed something with those characteristics to make it complete. If muons are considered inconvenient and messy, then eventually someone will revise the standard model to make them more convenient and orderly. And let's be clear: we still have little idea what muons ***are***; they are a label that defines a particular effect from which we infer the existence of some ostensible 'thing'. It's all a bit crazy-making, really... – Ted Wrigley Jan 10 '22 at 16:16
  • " If muons are considered inconvenient and messy, then eventually someone will revise the standard model to make them more convenient and orderly." this is exactly what physics aspires to do, and operates on the assumption that it can, and with the muon we succeeded. But I don't follow your argument for why we should always succeed? And actually, this is a stronger requirement than what I ask. I'm asking if there must exist a consistent set of rules, not if we will be able to keep finding them. – Clumsy cat Jan 10 '22 at 16:23
  • Also, I would note that the muon was observed before it was predicted. – Clumsy cat Jan 10 '22 at 16:25
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    this is the point that's soooo hard to get across. Rules are a product of human cognition. The universe doesn't have 'rules'; the universe merely *is* what it *is*. Humans formulate rules based on what they can see and know. It's like asking whether ducks have bills. Humans think ducks have bills; ducks (and the rest of the universe) don't make the distinction. – Ted Wrigley Jan 10 '22 at 17:22
  • I don't disagree with that bit, but we don't make up just any physical theories, we pick try to out rules that have correspondences to observations. At present, our rules do have holes (don't match observation) and problems (anomalies and inconsonant limiting behaviour). Normally we assume that both the holes and problems are a result of our incomplete understanding, and a set of rules that match all observations and have no holes could exists, I am questioning that assumption. – Clumsy cat Jan 11 '22 at 08:15
  • @TedWrigley "*The world is the totality of facts, not of things.*" No. We don't think of the world as the totality of facts. What we mean when we say "the world" is the totality of existing things. So the only question is whether there exists such a **thing** as the world as we think of it. If there isn't, then the world is still not the totality of facts. If there is, then the world exists as we think of it, that is, as the totality of existing things. What matters here is what we mean when we say "the world". It is not for Wittgenstein or anyone to redact the definition of the words we use. – Speakpigeon Jan 13 '22 at 18:00
  • @Speakpigeon: I think you missed W's point. Only those things which can be expressed in language — the 'facts' of the world — have any meaningful existence for us. Anything beyond that is (at best) a mystical intuition. W doesn't deny that the 'mystical' exists. It merely has no representation in our language, and thus no meaningful *human* existence. – Ted Wrigley Jan 13 '22 at 22:39
  • @TedWrigley "*Only those things which can be expressed in language — the 'facts' of the world*" Facts are not things that can be expressed in language. 2. "*have any meaningful existence for us*" The "*meaningful existence for us*" of e.g. pain cannot be captured in any description whatsoever. 3."*no representation in our language, and thus no meaningful human existence*" Absurd. We use language to convey what we mean, so we need first to mean something. Things have to mean something to us before we can use language to convey what we mean about them. Wittgenstein go it badly wrong. – Speakpigeon Jan 15 '22 at 18:29
  • @Speakpigeon: W spends quite a few passages on things like 'pain' and 'color'. The fact that we can express that we are feeling pain is enough to make it an extant 'fact', despite our inability to convey exactly what pain *feels* like. In fact, that plays right into his point: the *feeling* of pain isn't a fact, because it cannot be expressed (that falls under the sense of the mystical); the *existence* of pain is perfectly expressible, and thus a fact. – Ted Wrigley Jan 15 '22 at 22:29
  • @TedWrigley 1. "*an extant 'fact'*" Oh, so it's not about *facts*, it's about "*extant 'facts'*"? 2. "*because it cannot be expressed*" You are repeating yourself. This is not what we think of as facts. When I am in pain, it is a fact that I am in pain, and this *only* because I know I am in pain. And I couldn't possibly ignore that I am in pain, because if I did, I wouldn't be in pain at all. 3. "*that falls under the sense of the mystical*" This gives the game away. Wittgenstein just analyse away the subjective ground of all facts. Just call it "mystical" and, poof, it disappears. – Speakpigeon Jan 16 '22 at 11:29
  • @Speakpigeon: Don't engage rhetoric (e.g. nitpick words and phrase); use logic and reason. And if I'm repeating myself it's because you're not understanding me. No one denies that when one feels pain one feels pain. But without the word 'pain' one cannot do anything except suffer through. Western doctors have this problem with some Asian patients who weren't raised with Western medical or psychological terms; they complain that their stomach or liver hurts; the doctor has to intuit stress or depression. And yes, early W waved away the subjective; later W engaged it. But that's not the point – Ted Wrigley Jan 16 '22 at 14:08
  • @Speakpigeon: The fact is I'm not trying to argue with you (even though you're trying hard to argue with me). I'm trying to find where we're miscommunicating so that the seeds of the argument disappear. A little help would be nice. – Ted Wrigley Jan 16 '22 at 14:10
  • @TedWrigley 1. Alright, so why do you write "*an extant 'fact'*", which nobody knows what it means except perhaps you and which is not in any dictionary, and this instead of writing just the normal word "fact", which everybody understands and if not can find in a dictionary? 2. As to pain, I provided to reply to your previous comment a detailed explanation which apparently you are not even interested in discussing except to misrepresent what I said, so I don't see what else there is to discuss. – Speakpigeon Jan 16 '22 at 18:28
  • @Speakpigeon: I expect I was just aiming for emphasis, not trying to establish a new philosophical category, but honestly it wasn't the product of deep clinical analysis. It was a turn of phrase, and if you dislike it I won't use it. In any case, you're argument would do better if you tried to dig into one-offs like that (as you did here) than run with your knee-jerk assumptions about them. That approach might be natural when dealing with undisciplined minds (as we all have to do), but it isn't really *effective* as a philosophical tactic. – Ted Wrigley Jan 16 '22 at 18:51
  • @Speakpigeon: With respect to your reply, I thought I covered that adequately, but I guess not. The issue I have with your reply is that it is self-inconsistent, as embodied in the phrase "This is not what we think of as facts." The nature of 'facts' is precisely what we are disagreeing about, so how can you possibly make such a statement with proper self-refection? I mean I'm sure that ducks (who lack language) feel pain, and I imagine that the pain a duck feels is similar to the pain that you and I feel. But is that pain a 'fact'? – Ted Wrigley Jan 16 '22 at 18:59
  • @Speakpigeon: Consider as a corollary the observation that if I throw a stone in the air it will fall every time. That is something you and I can talk about, and eventually we will (collectively) arrive at some Law of Gravity: such a Law of Gravity is a 'fact', in the sense that we can use it fruitfully to describe and control our observations of the world. But this Law of Gravity is separate and distinct from whatever-it-is that causes the stone to fall. Whatever-it-is is not a fact about the world; it's a condition of the world that we make 'facts' about. – Ted Wrigley Jan 16 '22 at 19:04
  • @TedWrigley You are just disregarding the fact that the word "fact" has already a definition given by English dictionaries. Oxford, for example, says that a fact is *A thing that is known or proved to be true.*" This falsifies your claims. I speak English, and I'm not interested having a conversation where the other side is using a private language I don't speak. – Speakpigeon Jan 17 '22 at 18:28
  • @TedWrigley Can you even quote any philosopher using the word "fact" the way you do? – Speakpigeon Jan 18 '22 at 18:27
  • @Speakpigeon: Can you quote a philosopher who uses 'fact' the way *you* do (in a non-tongue-in-cheek context)? Even Russell and Popper didn't make such a crude use of the term, and any philosopher more modern than them acknowledges that the term is contested. And you forget that we began with a quote from early Wittgenstein; shall we get into later Wittgenstein's entirely convention-driven understanding of language and knowledge? Please... – Ted Wrigley Jan 18 '22 at 18:33
  • @TedWrigley So you can't do it. Right, I was asking you only because I'm pretty sure you misconstrue what these people say. I would be very surprised if Popper or Russell didn't use the word "fact" in the ordinary sense. I'm pretty sure they did. But you don't want to support your claim. I'm surprised, though. If you have read a lot as you just let me know so delicately, how come you can't remember what you have read? Still, I guess there is nothing else to say about this particular fact, if you understand what I mean with that particularly misunderstood word. – Speakpigeon Jan 19 '22 at 17:58
  • @Speakpigeon: If you've seen any of my other posts, you might know that I pay no attention to random demands for 'proof' or such unless I think it's warranted. I don't think it's warranted in this case; my statements hold up perfectly well without it, and i have better things to do with my time than piddle with silly rhetorical ploys. I honestly don't care if you agree with the point (because I see no possibility that you ever will); the value to this conversation is that others can see and follow the logic that you refuse. And it seems I've reached the point of diminishing returns on that. – Ted Wrigley Jan 19 '22 at 18:09
  • @Speakpigeon: You've abandoned reason; this is merely *ad hominem* nonsense. I"m flagging it as such. – Ted Wrigley Jan 19 '22 at 20:50
  • @TedWrigley "*You've abandoned reason; this is merely ad hominem nonsense.*" Are you aware that the second part of your sentence appropriately qualifies the first part? And the ad hominem started with your comment "*You have a good 5 years of dense reading ahead of you if you want to get a handle on those concepts*". I ignored that but I see now that I should have reported it at the time. I just flagged your comment. Please support you position with an example of Popper or Russell using the word "fact" in the sense you use. – Speakpigeon Jan 20 '22 at 11:21
  • @Speakpigeon: You don't seem to 'get' the nature of an *ad hominem*. If I suggested that *you* were unreasonable, that is ad hominem: an attack on your character or person. But when I say you've abandoned reason, it's a comment about your argument subject to analysis and possible refutation. Admittedly, I could have phrased it better, for which I apologize, but let's keep perspective please. Likewise the '5 years of dense reading' comment was factual. People spend a lot of years mastering these topics; you can't just toss a dictionary at it ands expect to get anywhere. – Ted Wrigley Jan 20 '22 at 16:28
  • @Speakpigeon: And no: I didn't see a need for references earlier, and I'm not inclined to consider peremptory demands from someone who is refusing to do any analysis. DO your own legwork; prove your own point. I'm satisfied with what I've said until you give me an intellectual reason not to be. – Ted Wrigley Jan 20 '22 at 16:30
  • @TedWrigley 1. There is no substantial difference between "*You've abandoned reason*" and "*you are unreasonable*". Both aspersions on the character of the person, both are ad hominem. 2. "*You don't seem to 'get' the nature of an ad hominem.*" I'm sure you do but you still made ad hominem and pretend you didn't. 3. "*Likewise the '5 years of dense reading' comment was factual*" Here is what you wrote: "*"You have a good 5 years of dense reading ahead of you if you want to get a handle on those concepts".*" You implied here I didn't understand these concepts. How could you know that? – Speakpigeon Jan 20 '22 at 17:40
  • Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/133383/discussion-between-speakpigeon-and-ted-wrigley). – Speakpigeon Jan 20 '22 at 17:56
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There is a nonzero epistemic chance that change in general is inconsistent; that article describes inconsistent change theory as "surprisingly robust." If laws of physics are laws governing physical changes, then if change itself is inconsistent, in some sense the laws must be, too; one could even argue that the compatibility question regarding quantum physics and relativistic physics might be an example of necessary inconsistency in known physical laws.

I also would suggest looking up the essay "A Paraconsistent Approach to Quantum Computing" (I would link the essay directly but my browser is acting up, so just search that quoted title). This reflects on earlier talk of "dialethic machines" (see the IEP article on paraconsistent logic); intuitively, a dialethic machine tolerating inconsistent inputs and yielding manageable inconsistent outputs resembles a quantum computer superpositioning information over both the 0 and 1 values (untrue and true together).

Lastly, Schrodinger IIRC proposed a logic for quantum objects in which the law of identity has been abrogated. Depending on how tightly-knit one thinks the LOI and the LNC are, this will affect one's picture of an option in inconsistent physics. I myself think that DNE (~~A = A) is more like the merger of the LOI and the negation concept, though it is often said that the LNC is expressive of "what negation means."

Kristian Berry
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  • I'm interested in your answer and I will get back to it when I have read some of the sources you quote. Please could you unpack some of those acronyms? In particular LNC and DNE? – Clumsy cat Jan 10 '22 at 16:29
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    LNC = law of noncontradiction, DNE = double-negation elimination. There is an argument going back to Aristotle that the LNC "expresses what we mean by 'not'," or in other words is the law of identity applied to the concept of 'not.' However, it seems to me that it is more like the LNC is the law of identity applied to the conjunction and negation operators together, not the negation operator alone, which maps more to DNE/DNI (~~A = A or A = ~~A), or even to an inequality (A ~= ~A). – Kristian Berry Jan 10 '22 at 16:43
  • I would doubt change by itself is inconsistent. Rather it is studied by some approaches with inappropriate tools. That is tools that are fundamentally static. Like trying to capture motion through photography alone. It is certain to appear inconsistent. – Nikos M. Jan 10 '22 at 21:23
  • So I've only read the first essay so far. It's a lot to take in at once, but it's also a very satisfying comparison of many different takes. I certainly need to read it again. I'm lookign forward to reading the second one. Did you mention dialethic machines because you think that to some extent we are a dialethic machine? – Clumsy cat Jan 11 '22 at 09:01
  • @NikosM. I do see your objection to that "motion is inconsistent" argument. Though an objects whole momentum, phase and energy tie in with questions about self identity perhaps? There is a "motion paradox" that I like rather more, about rotation and centrifugal force in an empty universe; https://physics.stackexchange.com/questions/1372/is-rotational-motion-relative-to-space – Clumsy cat Jan 11 '22 at 11:07
  • @Clumsycat the whole poinr of inconsistency of change is related to wanting to identify the object, but identity is the wrong approach to that,rather a notion of "similarity" is more appropriate and does not result in paradoxes. But elaborating further cannot be done here – Nikos M. Jan 11 '22 at 14:11
  • @NikosM. if you have a link about it you like I'd be grateful to a read a counterargument to the essay in this answer? – Clumsy cat Jan 11 '22 at 14:15
  • @Clumsycat to be honest, my only personal application of the phrase "dialethic machines" is to think that it would be an awesome name for a science fiction story of some kind. I personally accept strong forms of the LNC and EFQ (the logical explosion principle), as both mental and physical restrictions, but for the sake of methodological pluralism I have been compelled to try to harmonize paraconsistent logic with the system of logic that I "accept" as true for humans (and rational agents in general). – Kristian Berry Jan 11 '22 at 17:08
  • @Clumsycat, I dont have a link handy, but it is not difficult to figure it out yourself. Once a more versatile notion of "similarity" is introduced, instead of strict identity, then a number of paradoxes, related to identity, between objects which cannot be strictly speaking identical (since sth changed), are resolved. On the other hand paradoxes related to arbitrary continuity are not so grave either and there is no need to assume arbitrary continuity (ie change may be discontinous but with sufficiently small "quanta"). So a number of issues raised are not that grave nor irrefutable – Nikos M. Jan 11 '22 at 17:17
  • This answer offered two things that got me further than any other; some language/notation for discussing inconsistency and considerable references to existing contemplations of fundamental consistency/inconsistency. It's been a pleasure to read all the answers and I thank you all for sharing your understanding. – Clumsy cat Jan 11 '22 at 17:51
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Reality cannot be inconsistent with itself because there is no two properties that are the negation of each other. Black is not non-white, rich is not non-poor. The only pair of truly contradictory predicates is the pair existence/non-existence, but of course, our own notion of reality limits it by definition to what is existent. Thus, the fact that the Eiffel Tower exists cannot be contradicted by the fact that the Eiffel Tower doesn't exist because any Eiffel Tower that wouldn't exist wouldn't be part of reality.

Logical consistency is a cognitive property of our mental representations, not any property of whatever it is that we are trying to represent, whether in the real world or outside of it. We can make inconsistent statements, but we cannot even imagine or conceive what such could possibly represent.

One example of an inconsistent notion is omnipotence when conceived maximally as the power to perform any action whatever. Anyone can say that some being is omnipotent, but no one can really make sense of such a statement precisely because omnipotence in this sense is illogical and therefore nonsensical.

There is nothing we know of in the real world that would make an omnipotent being impossible, but the idea itself is nonsensical to us. That an idea is nonsensical does not say anything about whether there is or not something in the real world satisfying this idea, but it does prevent us from making sense of the idea itself.

So for all we know the universe might be somehow incompatible with itself, but it is very unlikely that anyone will ever be able to find out.

Speakpigeon
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  • This is a very good understanding of what I was attempting (somewhat ineffectively) to ask. When you say "Reality" in the first paragraph do you refer to the world as we perceive it? When you say "the universe" in the last paragraph do you mean a possible external reality? I ask because you have different conclusions for them. – Clumsy cat Jan 11 '22 at 17:34
  • @Clumsycat Reality is the whole of what exist. The world, or misleadingly, "the real world", is what we tend to call now the physical or material world. It is what we believe exists outside our own mind. We normally take it to be a part of reality. The universe has now a scientific description. The universe is either a part or the totality of the world. We think of it therefore as obviously a part of reality. Nature is whatever we can perceive. We also experience the contents of our own mind and so we see that as a part of reality, and indeed the only part we really know. – Speakpigeon Jan 12 '22 at 18:14
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I would take kutschkem's answer one step further and assert that if our universe were internally inconsistent on large physical scales then we wouldn't be here to ponder that fact- because such a universe would not support the formation of galaxies, stars, planets, or the evolution of life.

niels nielsen
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  • Why not? Naively I would say that many fictional universes exist that lack internal consistency and support the existence of things like stars? My understanding of kutschkem's answer at present is that our universe may be either way and that cannot be proven. – Clumsy cat Jan 11 '22 at 08:49
  • How are you planning to prove that an "inconsistent universe" is incapable of formation of galaxies, stars, planet or life? This feels like just someone's opinion – Tvde1 Jan 11 '22 at 16:37
  • @Tvde1, this is the opinion of a physicist whose business it is to know what's required to create those formations. An inconsistent universe is one in which different portions of it possess different physical laws, and those laws change from time to time. In the simplest case, if gravity doesn't always work at all times with a 1/(distance)^2 dependency, then you don't get galaxies. – niels nielsen Jan 11 '22 at 22:52
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So, maybe a more pragmatic answer:

  • In is entirely possible that the universe is not gouverned by coherent rules. Most of it might not even exist it's all in your head; it may be a simulation; it may be governed by some whimsical demon that decides the results of any process ore experiment for teh lulz. All of these ideas have been seriously argued for by educated poeple.
  • On the other hand, the main answer to the question in the title is that it seems to be like that. That is, we have been able to find laws that describe the behvaiour of nature. In some fields, these laws are more explicit and/or more succesful than in others. In many cases, the laws are not quite what people initially thought, because our intuition doesn't cover more exotic circumstances. Furthermore, the laws or theories change every now and then in more or less radical ways.
  • Thus, I guess there won't be an experiment that refutes a law-based universe: Assume some experiment contradicts our best theories, or even seems to give totally unpredictable results. Essentially, you could now conclude that the universe is incoherent and lawless, or that the true laws are more complicated than you thought, and there are some more factors you have to take into account. The second choice has proved to be successfull in the past, so that's what most people (including most physicicists) would choose.
Toffomat
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I think of this problem as a computer scientist. The universe is a giant state machine. Time is what separates one state from another. The laws of physics are a compact description of the state transition table. When we talk about "consistency", we are really asking: "How small is the transition table?" Because the most general answer is: any state can transition to any other state, stochastically. Such a universe, on average, would be utterly incomprehensible and would just look like noise if we could observe it from without. On the other end, the smallest transition table is the identity function: every state transitions only to itself. Such a universe is static, frozen solid for all time, no matter which configuration it starts in.

Many scientists would say that the "frozen" universe is extremely consistent, but boring. And they would say that the "maximally free" universe is chaotic and incomprehensible. But would they say it is inconsistent? I suspect not. But that is simply because this level of freedom hardly exists anywhere in our universe. If the freedom were dialed down to our universe + a few notable and observable exceptions, then there would be strong talk of "consistency".

For instance, if we found that the mass of the electron varied depending on which research group and machine was measuring it, but all our large-scale observations depend on it having a static, universal value, then some folks might tend to declare an inconsistency in the laws of physics. However, it should be clear that other folks would simply say there is deeper physics afoot and we just need to discover it (c.f. muon mass).

"Consistency" is basically presumed by scientists, and science is fundamentally built upon this presumption as an unstated axiom. If we admitted that physical law need not be consistent, then there would be effectively no way to discriminate between one theory and another. Take the Hubble constant, for instance. We have multiple values estimated by multiple teams. Astronomers generally believe that the Hubble constant has one value, and that there are deep, underlying reasons that different teams get different values. But in a world where inconsistency is accepted as possible and legitimate, there would be no reason to try to resolve the contradiction. The Hubble constant may take on different values depending on how it is measured, even if each of those methods were arbitrarily precise. Obviously, this kind of relaxation would make a hash of science.

Going back to the state machine, science is predicated on the notion that the "state machine" for the universe is indeed small. Small enough to write on a single sheet of paper at a size that the average human could read it. That's a pretty bold and remarkable idea, if we think about it! Instead of believing that the Standard Model is a fairly accurate description of the universe, we could instead accept thousands of competing, mutually incompatible models which each explain a small set of observations extremely well, while failing miserably on others (e.g., MOND). We would explain away the failures as "natural inconsistencies". After all, how could you possibly tell the natural ones from the unnatural ones?

So in this sense, science must assume that the universe operates according to consistent rules, because you simply cannot have objective science without this assumption. If you allow inconsistency, then every scientist can have their own theory, and you have no strong basis on which to object to it. Even a theory which predicts no observations could be correct, because it might explain something which will happen in the future but which has eluded our notice up until now.

Non-science has no such compulsion to believe in consistency, and indeed, religion practically demands that certain "inconsistent" events occur (i.e. "miracles"). At the same time, human nature (and indeed, all intelligence) must presume some level of consistency, because we need it just to operate in a hostile environment (predict food sources, threats, mating opportunities, etc.).

Lawnmower Man
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Before asking about consistency you probably should agree upon the logic you are using. For example, quantum logic is far from being well understood. For another example, there are paraconsistent logics in which you might encounter assertions A such that you might be unable to establish that "A and not A" is false: the only thing you might hope for is to know that if A happens to hold then "A and not (A and not A)" holds as well.

PS Could the downvoter please explain what's wrong with this answer? I would probably benefit from knowing that.

მამუკა ჯიბლაძე
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  • Is quantum logic poorly understood? https://en.wikipedia.org/wiki/Quantum_logic I'd argue, it's just weird, & that isn't the same thing. The https://en.wikipedia.org/wiki/Quantum_Turing_machine shows there is not a fundamental discontinuity between the quantum & classical worlds. – CriglCragl Jan 11 '22 at 13:04
  • @CriglCragl I meant that a logic that would be adequate for arguing about quantum physics is poorly understood, as can be in particular seen from the [limitations](https://en.wikipedia.org/wiki/Quantum_logic#Limitations) and [criticism](https://en.wikipedia.org/wiki/Quantum_logic#Criticism) sections in the Wikipedia article about existing versions of it that you linked to. As for your second statement, could you explain better what do you mean by it? I never addressed any fundamental discontinuity, nor do I understand what that article about Quantum Turing machines says about its absence. – მამუკა ჯიბლაძე Jan 11 '22 at 15:56
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In fact, basic laws of physics can be derived purely via math from the assumption that these laws must be consistent with respect to certain aspects:

  • Consistency of movement regarding mirroring in space leads to conservation of momentum.
  • Consistency of movement regarding rotation leads to conversation of angular momentum.
  • Consistency over time leads to conversation of mass and energy.
  • Consistency of the vacuum speed of light being the maximum speed leads to ¿general? relativity theory.

For details (e.g. the math involved) on the first points, look up the Noether theorem.

So there's not only reason to believe that the rules of the universe are consistent. There's also reason to reject the opposite proposition: Inconsistent rules would be inconsistent with the empirical verification of models mathematically derived from the assumption that the rules are consistent.

Regarding

There are an abundance of ways that a reality can have rules that are not possible to obtain. Nor do I place any constraint on the structure of these rules. But does the reality itself have to behave in a way that does not require contradictions in those rules?

there's really not so much of "an abundance of ways that a reality can have rules that are not possible to obtain". The only way that "observing, formulating hypothesis and verification" (aka the scientific method) couldn't obtain some laws of physics is, if there would be an omniscient, omnipotent force that actively changes rules whenever those rules are being investigated:

  • A non-omniscient force could miss out on a scientist, who investigates in this field.
  • A non-omnipotent force could be unable to change a rule being investigated.
  • A non-active force wouldn't act to change the rules, exactly when they are investigated.

Even if the rules were changing based on time (instead of as a reaction to investigation), there could be scientists that investigate the current rules fast enough to formulate laws and then start investigating the time-based rules of change in rules.

Completely inconsistent rules would quickly lead to total chaos. For illustration, just watch a physics simulation that allows a gain of energy: Worlds simulated this way tend to explode violently rather quickly. Again an omniscient, omnipotent and active force could be an arbiter resolving conflicting rules on a case-by-case basis while keeping a potential energy gain "manageable". However such a force has long died by Occam's razor: There's simply no need to assume such a force exists considering repeatability of observations in our universe.

In reality, the closest you get to "inconsistent" rules is quantum mechanics, in which rules of Newtonian Physics and even Relativity Theory and the intuitions that follow break down. This is in part due to the effect that an observer has in quantum mechanics (Heisenberg's uncertainty and Schrödinger's cat comes to mind). However the effects can still be observed, replicated and put to use, e.g. in quantum computing. This is simply because the rules of quantum mechanics are although complex, confusing and dependent on the observation still consistent. It's just very hard to wrap your head around them.

NoAnswer
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  • So regarding your first part, we run into problems with things that would be consistent with all existing rules, but we don't find them. For example, a moderate supersymmetry model would carry all sorts of benefits, in terms of fitting together other parts of the standard model, but it has been excluded by experiment. So it's a pretty perfect theory, which doesn't actually exist. Noethers rules are amazing, and about as close as any physics gets to truth, but quantising them is fraught. They are the backbone of physics, but they cannot give you everything you need. – Clumsy cat Jan 11 '22 at 11:31
  • As for the second part, I offer you two (hypothetical) universes in which the rules of the universe cannot be enumerated; in universe 1 the universe does not last for sufficient time to complete the required observations, in universe 2 the complexity of the rules of the universe exceed the complexity of the universe, making some dynamic attribute appear either random or static. – Clumsy cat Jan 11 '22 at 11:34
  • Your comments seem to indicate that I didn't (fully) understand your question. Where in your question, did you ask about the rules being possible to determine (in full)? Also Universe 1 is clearly not ours while your question specifies "our universe". Plus, it is irrelevant, because it's already gone. Universe 2 is a paradox, how can the universe be simpler than itself? The rules are part of the universe, aren't they? – NoAnswer Jan 11 '22 at 11:40
  • ah, that comment was intended to illustrate ways there could be rules that we cannot obtain, but that are not due to any omnipresent being. As for universe 1, in our universe we cannot yet put an upper bound on the lifetime of a proton, having never seen one decay. Maybe one day we will quantify this upper limit, but we are not guaranteed that opportunity. It may be that protons last so long we never see a decay. – Clumsy cat Jan 11 '22 at 11:46
  • Well, I thought about leaving out the whole part of omniscient, omnipotent and active force, because it was very hypothetical. However I get the feeling that you want hypotheticals like that. If that's the case, you should ask a separate question, possibly linking back to this one and specifying that you're not asking about our universe. – NoAnswer Jan 11 '22 at 11:50
  • You mean to say "Yes, there is reason to believe; in fact, here is why...." – Marxos Jan 19 '22 at 05:32
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I think that very little can actually be proved about the universe.

For instance, it's possible that we're actually in a Matrix-like universe inside a computer, and nothing in our experience is actually "real". The programmers of this computer could change the rules any time they wish.

Another possibility is that there's no actual change in the universe. We're actually at a frozen moment in a static existence, and what we experience as memories is just the state of all our neurons in that frozen moment. This is similar to the argument that Creationists make regarding fossils -- the dinosaurs didn't actually live billions of years ago, God created these buried bones after creation thousands of years ago.

We only have our senses to go by, but since they're a part of the universe they're studying, they can be fooled by it.

If you believe any of these kinds of ideas, then you can conclude that nothing matters. But since it feels like things are actually happening, and that includes noticing that the universe seems to follow rules that we're able to discover, we've adopted this as an axiom.

Physicists and philosophers do wonder and debate why mathematics seems to be so good at describing physics. But it's hard to deny that empirically, it does. Assuming that the past is prologue tends to be useful.

Another way to look at this is that the question itself is vacuous. What does it mean for the universe's rules to be "consistent"? Consistent with what? As another answer says, the universe is what it is, and the rules are whatever actually happens. If something appears inconsistent to us, that's just our own ignorance of all the rules. This can be related to related to Goodman's riddle of induction.

Barmar
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This has been brought up in the comments, but deserves an answer of its own:

It makes no sense to ask whether a) the universe is consistent or b) obeys consistent rules; doing so is a category error.

Regarding the first part of that statement: Consistency is defined to be a property of a theory. A theory is a "set of sentences in a formal language." The universe clearly is not a set of sentences in a formal language. So asking whether the universe is consistent makes no sense whatsoever.

Regarding the second part: we have no indication whatsoever that the universe and its set of rules are two separate entities. This would be a worldview where the universe is some kind of (actual) computer which follows some algorithm (which we could approximate with our physical theories) in something vaguely like a von-Neumann architecture. Our theories can of course, being "sentences in a formal language", be consistent or not. They can also fit experiment or not.

But nowhere do we have any indication that there are real rules governing anything out there, for a definition of "real" which is comparable with the realness of the physical objects we see or describe. So it makes no sense to ask anything about the rules of the universe, beyond our formal systems, which obviously are just a description of the universe, not mandating its behaviour, because by all evidence we have so far (which is none, i.e. Occam's Razor), there are no rules.

Of course, as the plethora of other answers saying "yes" or "no" tell you, people have come up with interesting concepts surrounding this; but you'd have to define the concept of "consistency" (and possibly of "universe" and "rules" and "internally" and so on) very carefully to make any meaningful statement possible.

AnoE
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A single belief can also be said to be consistent (if it is possible for it to be true) or inconsistent (if it is not possible)... A single belief which could not be false is said to express a necessary truth.

http://logic.philosophy.ox.ac.uk/tutorial1/tut1-01.htm

So, an inconsistent belief is about something impossible, expresses something that is necessarily not true: necessity is being violated.

Inconsistent with which "rules"?

  1. Nomological necessity (most agree "God" can break these rules)
  2. Metaphysical necessity
  3. Logical necessity: even if you don't assume classical logic makes for laws of thought (the basis of all rationality), paraconsistent logic need not entail there are true contradictions, dialetheism, inconsistencies.

In general

if consistency turns out not to be an essential requirement for all theories, then the way is open for the rational exploration of areas in philosophy and the sciences that have traditionally been closed off.

However, I'd probably think that inconsistencies in the law of physics cannot be explained by science, as they are like miracles, and will never be subsumed by any scientific theory. Whether or not that argument is acceptable for those sufficiently hard nosed.

  • I'm a bit confused if you only mean logical contradiction. obviously, explanations of contingent events can include some form of contradiction broadly thought, because they allow that it could be otherwise (it could be raining in Paris) –  Jan 17 '22 at 21:25
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The universe simply is what it is. It does not answer to anything. Like God it is. Our understanding of it evolves but the universe is today exactly like it will be tomorrow regardless of what we learn about it.

The universe posits nothing. It makes no claim, it simply is. What does it mean for a non corporal entity to be consistent internally or externally? What sort of epistemology does the universe have that can be said it is inconsistent? I'm assaulted by an illogical universe every time I climb out of bed.

Why do good people suffer and bad people flourish? How could the shower scene from Schindlers list have actually happened? Maybe if you subscribe to many worlds interpretation of quantum mechanics you could find a universe that has logic to it, but it ain't this one.

Neil Meyer
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