How does "quantum darwinism" effectively select a state? Like how does that work in principle- what is the selection criteria.
The author does say the approach is a combination of Copenhagen and MWI, removing the outlandish parts of both. Seems to preserve the randomness of the former though.
To call something random doesn't mean it's impossible to model, in fact all sorts of natural facts seemed random one day before being covered by a model. One very relatable example example is the motion of stars in the the night sky, which seemed random for ages, until the Copernican revolution.
The fact we have access to random() function in programming seems to trip many people. random() is a particular model implementation of random, but stuff in nature isn't random().
My point is, using "just random" to do work in any scientific explanation is a clutch.
It does not have to mean something inherently non-deterministic or something that can't be modelled, although it certainly is the case that if something is inherently non-deterministic then it would necessarily have to be modelled randomly. Modelling things as a random process is very useful even in cases where the underlying phenomenon has a fully understood and deterministic model; a simple example of this would be chess. It's an entirely deterministic game with perfect information that is fully understood, but nevertheless all the best chess engines model positions probabilistically and use randomness as part of their search.
Output of of a pseudorandom generater is a good example.
The use of "random" as explanation or characterization in science has certainly spanned everything from "we don't know", to "there is inherent indivisible physical randomness".
And I would agree, in the latter case it is a crutch. A postulate that something gets decided by no mechanisms whatsoever (randomness obeying a distribution still leaves the unexplained "choice").
It is remarkable that people still suggest the latter, when the theory, both in theory and experiment, doesn't require a physical choice at all (even if we experience a choice, that experience is explained without the universe making a choice).
https://arxiv.org/abs/2503.15776
In this paper a plurality of physicists stated that they felt that the initial conditions of the universe are brute facts that warrant no further explanation. This is not "our model doesn't yet account for it", it's "there is no explanation to be given".
That doesn't make a model wrong. All models we have are partial explanations.
But that doesn't make it rational to claim that an incomplete model is complete. Or to treat unexplained specifics as inherently "just so", without cause or reason (i.e. magic), and we must just accept them as unexplainable instead of pursuing them with further inquiry.
I've just explained that this is not strictly true. I don't know what else to say. Brute contingencies, by definition, do not require explanation. I then gave you a paper where scientists largely believe in brute contingencies.
I think if you want to know more you can look into this. Just look for topics about brute facts and brute contingencies.
If you want to deny that brute contingencies are possible, by all means. That's a totally valid view. Just understand that it's probably not the majority view among scientists and that you aren't necessarily "right" (just as those who hold to brute contingencies aren't necessarily "right").
Things are what they are because of constraints. Which is more general, and assumes less, than appeals to causes.
Constraints need not be prior. They can can be simultaneous, i.e. co-constraints. And they can be internal to the whole, i.e. all of reality can be a co-constrained structure without external constraint.
An ultimate law of conservation is a strong candidate for a self-constrained reality. All versions of forms existing that neither locally create nor destroy. And since all possible forms within that exist, no choices made universally and there are no conserving forms it excludes. A coherent, infinite, unique, zero information structure. (Uniqueness is inherent to a zero information structure. Non-uniqueness necessitates choice.)
But claiming that some things just are, with no structural necessity, is an appeal to magic. A specific, with no actual constraint matching the specificity isn’t coherent.
You don’t get something for nothing. There is no outside of reality to provide that.
Any “outside” just means that total reality was not being included in the analysis.
I am not saying we can practically figure everything out. Or that there may not be questions, that given the limited resources/laws of our universe may not be answerable from our position, even theoretically. There may be questions we can’t answer. But nothing specific “appears” with some magical independence from the rest of reality.
That is the non-taulogy of it “just is”.
It would also make reality as a whole irrational. Not even a structure that obeys a conservation law. Because it would have specifics that had no reason.
None of your conclusions actually follow from this, which you would be welcome to explore on your own. You can learn why conservation can be held as true while also allowing for brute contingencies. As the leading cosmologists I've cited do.
No, it's not magic. You just don't know what you're talking about. Only you can fix that.
> It is not incomplete to say that something does not require explanation
> Values of physical constants of nature
> the most popular choice was that the constants are considered brute facts and thus require no exotic explanation
So yes, I deny the coherence of the concept of "brute facts".
If something is determined, something determined it. Some mechanism, constraint, context, structure, ... Perhaps we don't have the right word or connotations, but something.
A specific from a choice is a specific relation. That relation exists, as exemplified by our encountering the specific. Our experience of coming across the specific is not extricable from that specific's consistent connection to the rest of reality. That consistency has some basis, or there would be inconsistency.
A "maintaining" mechanism for an arbitrary consistency doesn't work, because that just pushes the choice of the specific that is maintained into the maintainer, which makes it more than a maintainer.
I can believe in things we will never be able to explain, as a result of observability limitations imposed on us by local physics. Eternal ignorance for any reason is always a practical possibility.
I can believe in undetermined things, which appear with each possibility, where we only experience one, because in the product of possibilities each plays out separately.
That would be the closest I could come to a "brute fact". Because it is in fact completely determined. The specific was not uniquely chosen, because the specific is not unique. Information is conserved, no explanation of each specific is needed. Even though each specific will behave as unique, across each possibility respectively, because differing specifics interact with a disjoint relation. The disjoint relation is the operating condition creating a localization of choice.
People invent ways to explain away persistence ignorance, instead accepting it, like a fractal attractor, over and over. The psychological need to resolve the dissonance, when encountering challenges to investigation that are potentially insurmountable. And then some "way" of sweeping away the lack of explanation gets translated into a proposed lack of reasons, and given a name and connotations. But never an explanation or reason for itself. It is always faith based. The existence or principle of brute facts, must remain meta-brute facts themselves. All untestable.
Scientists can "believe" that is a valid viewpoint. But inherently cannot every demonstrate any evidence for it.
The same reasoning, with different connotations and contexts, is rejected over and over by scientists. Mystical or religious connotations doom those different "versions". But stated in a sciency way, the same situation becomes palatable to some or many. But it doesn't become more coherent by virtue of being the "physics" version of "explanation" by acceptance of non-explanation.
Cool, that is fine. I deny lots of things as well. It's a position you can hold.
> If something is determined, something determined it.
That's fine but you'll likely find yourself in an infinite regress. That's a cost you'll have to take on under your theory.
> People invent ways to explain away our ignorance of the reasons behind things, instead of accepting the reality of ignorance, almost like an attractor fractal pattern, over and over.
That's not what's happening here. These concepts are pretty rigorously discussed and debated, it's certainly not a "cop out" - it's a metaphysical cost to your world view that you have to justify.
> Scientists can "believe" that is a valid viewpoint. But inherently cannot every demonstrate any evidence for it.
You've already said that you don't believe all things can be proven via evidence, so that's fine.
But it's incorrect to say that there is no evidence for the position. There are many arguments to support the view of brute facts or brute contingencies. One example is that it seems to not accept them would lead to infinite regress, which many people have reasons to reject as well. These are well evidenced positions, that is why so many scientists believe in them.
This has nothing to do with religion or mysticism. There is nothing about this that requires "magic". Many of our most advanced cosmological models support this view. You are just not aware of this, and so it sounds like magic, but it isn't. If you think it is then I would just suggest that you learn more about it, there are many scientists and philosophers writing on the topic and I'm sure quite a few youtube videos on the topic.
Edit: Sorry didn't see you had already replied.
Zero information constraints: Specifics only as fully determined, full coverage of undetermined specifics, conservation of information. These axioms, unlike most, impose a lack of external information not just as a desirable property, but harness them as a tautological universal constraint. Unlike most axioms, which are imposed information themselves.
You have to explain these constraints if you don't want them to be brute.
edit: > Edit: Sorry didn't see you had already replied.
It's cool. I don't understand the distinction you're trying to draw here about "zero information constraints".
edit: > but harness them as a tautological universal constraint.
This just sounds like a brute contingent fact. It's almost the definition of a brute contingency, as far as I can tell.
It has many forms. One is, nothing can be created (no external source), or destroyed (no external dump), so any local structures can be transformed, but must be conserved in some way. Transforms must be reversible. We now have the necessity for a law of conservation as a "for-free" requirement, as a result of no external information/interaction.
Local zero information constraints:
No specific exists, except those that are completely determined. Anything else would require external information. This is a law of fully determined intersection.
Anything not completely specified, must exist in all its disjoint alternatives. This is a law of fully exhausted union.
Think of the exhaustive superpositions (unions) over all possible conserving interactions (intersections) in quantum mechanics. A real "local physics" example of this principle.
Cancellation is caused by conservation. Duals that can be generated must be reducible. And it is cancellation of duals that create the non-trivial distributions that superposition and entanglement produce, out of otherwise a neutral exhaustion of possibilities. Instead of noise or uniformity, we get structure.
This all comes from "no external information or interaction".
It turns out, that tautology is far from a trivial constraint. I believe there will only be one structure that will meet that requirement. And its uniqueness will be another manifestation of no external information, no external choice. Uniqueness doesn't require choice.
In fact it is a very active constraint. Try to come up with a form in which everything is either determined, or exhaustively covered, and always locally conserved (i.e. all transforms are fully and exactly reversible). It will be a challenge! Exactly what we want. But you can fit a lot of our current physics in as consistent pieces. Like quantum mechanics. And historically, we have understood the universe better every time we have generalized or unified laws of conservation.
Superposition is simply conservation of information across disjoint conserving intersections. It doesn't collapse, because that would require external or created or "just is" information. Which besides being incoherent (in my opinion), would throw away the only "free axioms" we have as an explanation for why any structure exists at all. Conservation, closure, uniqueness.
edit: Okay, I think I am sort of getting what you're saying about tautologies but it's wrong. Either way, I don't think it matters much. You can just deny brute facts, I have no problem with that. I'm just saying you shouldn't assert that brute facts don't exist as if that's the standard position.
That is a tautology, no?
> One is, nothing can be created (no external source), or destroyed (no external dump), so any local structures can be transformed, but must be conserved in some way.
This is not a tautology, it is a metaphysical claim.
Nor can anything in reality, be exported outside of reality.
Reality is the one thing, the only thing, that cannot depend on anything undetermined or unchosen by itself.
The fact that reality must account for both itself, and any of its specifics, with no other domain to draw from, is a higher level of demand than for any other theory. That demand is a hard and unique constraint. A tautological constraint that is therefore usable as an axiom.
Even if I grant your "axiom", which is just that "reality exclusively contains reality", nothing interesting follows from that for this conversation.
We would just know there was a unique self-consistent all consistent form covering structure. And that any form within that structure, with a sophisticating self-sensing self-interpretive ability, would experience its own existence.
Existence would then mean, part of the unique self-consistent, zero-information, independent of any externality, structure.
A perceived existence as a result of a unique tautological structure, not a result of any external composition.
And the phrase "I think therefore I am", would be tautological in both senses. As evidence. But also, as the actual meaning of existence. Given a self-aware form within a tautology, its perception of existence is the nature of existence.
Reality was always going to be something that forms structures, that are somehow inevitable, the only possibility, not something selected or manufactured by something else.
> Reality was always going to be something that includes structure, that is somehow inevitable, the only possibility, not something selected or manufactured by something else.
This is a brute fact. I mean, literally it just is.
That is the definition of fully determined. X can uniquely be Y. And it can't be anything else than Y.
The extreme opposition to a brute fact.
Can we accept that any proposed model of reality potentially must, at a minimum, be self-determining without resort to any "other"?
The unique constraint of strict self-containment and determination is a tautological challenge, but therefore also a valid axiom.
> And that it can't be the full reality if it is not self-determining, draws from anything else, any other domain, depends on any non-internal choice, any wisp of external determination?
No, brute contingent facts do not require external determination, so I reject this obviously. Or, I accept it and it's irrelevant because, again, brute contingent facts do not require external determination.
So determined non-internally if you prefer. Non-internal to reality.
My point is that is a tautological impossibility. Reality by definition is all. That is what we want to explain (or at least, zoom in on a potential form of explanation).
Reality can't depend on anything making a choice that is not a part of itself.
There is no "choice", there is determination, there is no explanation. If you're still framing things there, then you're just denying brute facts, but you're not about to prove that brute facts aren't possible in a HN thread and you're getting the concepts of necessity, brute, and contingent mixed up along the way.
Here I distinguish between "explanation" and "determination". Hoping that helps.
My understanding of brute facts, is they are free values in theory, but measured values in practice. And somehow we just accept experimental measurements of some things as the end of explanation.
I am arguing against the validity of less than full determination, and pointing out that does not imply endless chains of determination.
But our explanations may forever be more limited than reality, for any. number of reasons, but not because reality doesn't fully determine everything. I can see a practical acceptance of values without full explanation, if we have reason to believe we cannot probe further.
Maybe that is a level of agreement?
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As for complete determination, without any need for infinite regress:
Unique self-consistencies are co-constraints that can fully determine things without infinite regress. There is a unique determination loop, not an endless spiral. Uniqueness avoids the inadequacies of non-unique circular reasoning. And reality itself must have this property. The only possible explanation (from our point of view) or determiner (as it actually exists), of its own properties, is itself. As a unique self-consistent form it can do that. Constrained by self-consistency and self-containment.
I am very much trying to understand the line we disagree on, interpret differently, or not.
What you accept as a brute fact is conditional on your world view. For most people it's going to be very little, like "the initial state of the universe" or "the constant values of the universe" etc, although the latter is not necessarily the case either.
You seem to be trying to argue that the infinite regress can be avoided, and it's where things seem to be falling apart. You're trying to leap from a simple tautology to specific metaphysical claims that do not necessarily follow, and you're just ending up with brute facts.
You're saying that all things must be explained by reality, but that's fine and consistent with the existence of brute facts. I suspect that this is at least one of the core things we are not on the same page about. Brute facts do not appeal to things outside of reality. So any argument that starts with a tautology "reality exclusively contains reality" is just not going to get you to "brute facts don't exist" because brute facts are perfectly consistent with that tautology.
Your appeal to uniqueness isn't justified either. Why must reality have that property? This is a heavy metaphysical claim that you are asserting here, it's your "brute fact" that you're trying to say isn't a brute fact.
Perhaps a simple question will help. Under your model, what determines the speed of light? I assume your only position here would be to say that it is logically necessary?
> Maybe that is a level of agreement?
We can agree that there are limits to knowledge but we definitely don't agree that all things are determined by some other thing. I don't really commit either way, personally.
Thanks again, for your patience on this.
Ok, is there is a subjective aspect? Driven by practicality of course? A pragmatic limit to explanation searches would make sense to me. It could even be for objective reasons, such as that our universes laws somehow prevent us from gathering enough information to pin down why something is determined the way it is.
(While not denying that something did determine the property, but is just inaccessible to us as far as we can tell.)
But as a hard principle, that there are specifics that had no complete determination, they just are this way instead of that way, "because because (period)" ... that concept seems both incoherent and slippery to even process for me.
But as a pragmatic concept about the search for explanations, it would make full sense to me.
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> brute facts are perfectly consistent with that tautology.
I really seem to be having trouble with some nuance.
I think everything is fully determined, even if we may not ever achieve a full explanation of that determination. Is that consistent with brute facts?
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> You seem to be trying to argue that the infinite regress can be avoided
> You're trying to leap from a simple tautology to specific metaphysical claims
Almost. I am not trying to make the full leap, but am pointing out that reality must be fully self-determining, and that is a strong and therefore useful constraint for searching for a theory of reality.
No other situation provides such a strong requirement. And a strong unique-to-theories-of-everything constraint provides us with an axiom to start reasoning toward a theory of reality/existence.
That is a significant foothold, and not commonly pointed out.
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> Your appeal to uniqueness isn't justified either. Why must reality have that property?
Two reasons, the first is trivial. By reality I am talking about "everything". So in that trivial sense reality must be unique.
But also in terms of guidance or verification of a theory of reality. Reality has to not only explain its own structure, but its own inevitability, i.e. its existence, and without recourse to anything else.
A provably unique theory, that meets the terms of a theory of reality, would do that.
A theory of reality is going to come down to mathematical verification, in a way that local physics never can. Local physics is not so strictly determined. Local structure can reflect structure from other parts of reality it is a part of, which we have no access to yet or even ever. So we always have to perform experiments, and even mathematically derived conjectures must verified with prediction and experiment.
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> Under your model, what determines the speed of light?
Good specific.
> I assume your only position here would be to say that it is logically necessary?
Yes. The speed of light is a result of conservation constraints and local (i.e. our universe's) structure. The topology of space-time, general relativity, quantum properties of photons must all contribute. And presumably other factors we have yet to understand.
Just like all the relations, ratios and other mysteries we have already solved, regardless if we ever thought we could.
Presumably, anyone who operates with the principle of brute facts, could have named those as brute facts, before they were solved?
Likewise, the ratio of matter and anti-matter is a product of some structure and history we haven't sorted out yet. And the puzzling distribution of masses of the leptons and hadrons are determined by some structure, perhaps involving the fine structure of space-time, that we haven't worked out yet.
> I think everything is fully determined, even if we may not ever achieve a full explanation of that determination. Is that consistent with brute facts?
That depends. Your statement is effectively the "Strong PSR" - every fact is preceded by another explanatory fact.
There are weaker forms of the PSR or you can reject the PSR. I believe Sean Carrol, for example, completely rejects the PSR. This is not out of laziness, it's because he considers the PSR to be an unnecessary and costly commitment with weak justification, and that our best models of physics don't require or benefit from it (my recollection).
> Yes. The speed of light is a result of conservation constraints and local (i.e. our universe's) structure. The topology of space-time, general relativity, quantum properties of photons must all contribute. And presumably other factors we have yet to understand.
This seems to be framing the speed of light as contingent on other properties of the universe, but that just pushes us back. We could just ask if the gravitational constant is a result of other facts, for example, since you have appealed to that as an explanatory factor for C.
I could ask what explains the structure of the universe. You can then say that it's logically necessary, which is basically just saying that it's brute but with a heavier burden (you'd have to show the logical primitives you use to assert that, but the outcome is the same) or brute or brute contingent, or you'd have to say there's an infinite regress.
You can keep saying "Ah but there's this property of a photon" but now you have to explain that property. Your approach seems to be to try to derive a logical necessitarian view here by appealing to a principle like "Reality exists, reality contains all things necessarily" and then to derive metaphysical constraints from that but I'm not sure that any of the metaphysical claims are well justified here.
> Presumably, anyone who operates with the principle of brute facts, could have named those as brute facts, before they were solved?
Of course. And they would have been wrong. In general, models attempt to minimize brute facts because of their cost, but all models have costs. If you want to express that the universe is unique, or non-contingent, that is a cost of your model. Strong PSR is itself a heavy metaphysical claim that will bring along its own commitments.
> Your statement is effectively the "Strong PSR"
I would agree with that.
But coming across the Münchhausen trilemma, the idea that all proofs need prior assumptions, or must be one of: (1) a circular argument, (2) an infinite regression, or (3) dogma, I disagree with that.
Some truths are the result of co-constraint. This is where each component of the solution is both an implication of all other components, and an antecedent for all other components. This avoids the trap of being a circular argument, when it can show that any alteration of choices leads to contradiction. Strong proofs of contradiction can be made without infinite regression.
If N co-constrained features can be shown to be consistent, and for N-1 features at least, alternatives to each can be shown to lead to contradiction, then we have a unique solution - it must be the solution. (N-1 comes from the fact, that given co-constraints that lead to one solution, any single feature can be determined by the other N-1.)
That demonstrates that constraint/determination can avoid infinite regression, with recurrent loops of implication, which don't just prove consistency (sufficient), but failure of alternatives (necessity).
Reality must have this form of being. (1) It cannot be determined by any priors or assumptions, because there are no priors. (2) It cannot be determined by infinite regress, because there is no where beyond reality to regress. And obviously, (3) dogma isn't an explanation.
Specific structure must be due to internal consistency (sufficiency), without external or unexplained facts (self-sufficiency), the demonstrated insufficiency or contradiction of any variation or alternative (necessity), and compatibility with our physics (experimental testing that can be made ever more stringent).
> This seems to be framing the speed of light as contingent on other properties of the universe, but that just pushes us back.
I agree. In terms of explaining local physics.
Local properties are most likely to be explainable with the typical regression of explanation, backed up by experimentally verified "axioms", which will then lead to deeper explanations. For local physics, we cannot just prove mathematically that a relationship can work, or even must work, but that the local conditions also require it.
Even a perfect Platonic tautological necessity for a sub-structure of reality, must be experimentally demonstrated to apply locally. We have to establish that we are "there", experimentally.
Even then, in a less pure sense, we may still beneficially use co-constraints, while also regressive knowledge. I.e. explanation = (regressive knowledge) + (co-constraint = circular consistency + inconsistency of alternatives), in order to validate both sufficiency and necessity.
Many proofs of inconsistency can rule out local solutions, without regression. Contradictions are contradictions regardless of priors.
> I could ask what explains the structure of the universe. You can then say that it's logically necessary, which is basically just saying that it's brute but with a heavier burden.
My view is, an explanation of reality will need to demonstrate sufficiency, in terms of being (1) self-consistent, (2) consistent with hosting a region with what we know of our local physics, and (3) to avoid simply being a circular argument, demonstrate that alternatives to the explanation necessarily are contradictory.
Those are three kinds of knowledge to triangulate from.
That would be an approach compatible with strong PSR.
And starting with that, I work from self-containment, self-consistency, and self-determination, as tautological constraints, leveraged as working tautological axioms.
I think it is fair to say, while some may believe a theory of everything with unexplained brut facts can be valid (some things being just what they are), few or none would be unsatisfied with a theory that demonstrated all facts were well determined, was consistent, could be shown to be compatible with our region of reality, and could not be altered without creating a contradiction.
So that is my target.
Glad to hear it. I'm not an expert on these topics, so it's probably best to be skeptical on this. You may find the paper and some of the names I've mentioned (ie: Carrol) worth reading/ listening to.
> Some truths are the result of co-constraint.
This is a fine claim to make and it's not totally insane or unheard of. The concept of simultaneous causality, for example, is definitely something people argue.
> Reality must have this form of being.
This is a claim, and a fine one to make. It's still a claim though. I think it's worth reminding you that I haven't actually said anything other than that it's not really reasonable to assert things like randomness not being scientific, or that all things have a cause, etc - that most physicists probably disagree with that is notable. It's your position that those claims are true, and that's fine, but it's just notable that you're plainly asserting rather controversial claims.
> (2) It cannot be determined by infinite regress, because there is no where beyond reality to regress. And obviously
FWIW you can actually just say that you accept infinite regress. That'd be fine. You would have some other metaphysical commitments there, but it's a move you can make.
> Contradictions are contradictions regardless of priors.
You can also just reject the law of non-contradiction. Or I could. Or you have to assert it.
> in terms of being (1) self-consistent, (2) consistent with hosting a region with what we know of our local physics, and (3) to avoid simply being a circular argument, demonstrate that alternatives to the explanation necessarily are contradictory.
It's probably notable that all of these are just assertions. Consistency is a property that you're claiming. (2) seems reasonable. (3) I'm not sure of. And again, law of non-contradiction would have to be shown as being necessary. Neither of us is right or wrong, which is sort of my point - these are valid metaphysical theories.
Your view is not unreasonable. A lot of people hold to the strong PSR, it's just notable that it's controversial.
> I think it is fair to say, while some may believe a theory of everything with unexplained brut facts can be valid (some things being just what they are), few or none would be unsatisfied with a theory that demonstrated all facts were well determined, was consistent, could be shown to be compatible with our region of reality, and could not be altered without creating a contradiction.
Sure. A theory with no axioms would be desirable. But also, like, we wanted that in mathematics and accepted that it was impossible too. Would we have preferred otherwise? Well yeah. But we know it's not the case.
Yes, I am confident. But not ambiguous that my confidence is backed up with some aesthetic factors, not just squeezing out the hand waving.
> FWIW you can actually just say that you accept infinite regress.
I think my claim that everything that has a specific value, has been constrained to it, is very strong. And the inverse, that where something isn't constrained, it will appear in all its forms.
In that sense, I admit brut facts. We don't need to explain a specific, if we know its alternatives play out disjointly. Exhaustion instead of determination.
(The possibilities in that survey didn't include exhaustion! A much simpler explanation than evolutionary universes, or inverting the arrow of the anthropic principle.)
Superposition and entanglement are an exact example of mutual determination/exhaustion. Along with cancellation as a direct expression of conservation.
But my view that finite regions are potentially always characterizable with an unbounded finite region it is embedded in, as apposed to characterized by an infinity of other independent specifics, is easily my weakest conjecture.
> You can also just reject the law of non-contradiction.
I think contradiction is a category error for primitives of reality. Conservation is the right view.
I make a clear distinction between descriptions, partial models, conjectured models, etc. Contradictions can occur in our descriptions. But I don't believe reality is constrained by logical primitives. Just conservation. And with primitives whose generative/reductive properties are not constrained by logic, because there are not even "virtual" contradictions to prune.
I expect logic to be necessary for us to reason about primitives. But that logic is the wrong way to think of basis elements. Those are very different things.
> A theory with no axioms would be desirable.
I think this is necessary. I am 100% confident in that, for what that is worth to anyone else. Realty is able to exist precisely because it requires no priors, and has structure because it creates nothing, destroys nothing (conservation). Tautological anti-axioms that become axioms.
> But also, like, we wanted that in mathematics and accepted that it was impossible too.
This is not nearly as well established as is assumed. Whether we look at Russell's Paradox, or Gödel/Turings incompleteness theorems, there is a repeated issue. The proofs are about machines (or sets) that return (or are defined by) true or false. But any logical system with open (cycle) expressions admits two more possibilities, undetermined and contradictory statements. Not for some deep reason, but because notation is not reality, and we can trivially say things with notation that are undetermined or contradictory. "x in {x}, is unknown". "x in { logical x = not(x) }" is a contradiction. A universal mathematical discriminator needs to be defined as first, determining whether a statement is unknown or a contradiction. Then decide true or false for remaining expressions.
Note that the problem is implicitly collapsing unknown into true (i.e. "satisfiable") and contradiction into false ("unsatisfiable"), but then still treating those values as if they were just primitive true and false, which they no longer are.
To be concrete: If M is the mathematic machine, and we defined it reduce expressions (any kind of reducable structure, including 4-valued logic, not just Boolean truth), and it is tasked with evaluating a copy of itself operating on a self-referencing contradiction "M will say this is false", it is trivial to show M(M("M will say this is false")) = M("M will say this is false") = <contradiction>. No inconsistency, and no window to rework the statement into a problematic alternate, because we have avoided a special dependency, inconsistent treatment (t/f vs. u/c), or premature limitation around logic.
M may still have limits, but Gödel's incompleteness is not one of them.
This is another indicator to me, that a fundamental description of math (as with reality), needs to be based on sub-logical primitives. Another big clue is that Boolean logic is not reversible. Logic will be easily created from the fundamental relationship, but it creates a premature deadend to start there.
There are a number of well accepted famous theorems with this limited scope problem. They are absolutely solid proofs. But they define something more restricted than it needs to be, then knock it down. Leaving trivial possibilities unrestricted.
Cantors diagonalization proof for cardinality of R being greater than for N, is also trivially defanged. But there are better reformulations of it, and I haven't had the time to work though them yet.
I find that mathematicians, like everyone else, have trouble truly seeing what they looking at. I could go on and on.
Well thanks for pushing me, I am sure I have taken up enough of your time. But, I am now aware of more philosophical viewpoints on the big questions!
I think that's fine. I'm actually sort of agnostic about it myself. I find nothing particularly striking about brute facts or contingencies, certainly it's not magical to me, but I wouldn't say that they're logically necessary. I find it a bit interesting to consider.
> I think contradiction is a category error for primitives of reality. Conservation is the right view.
It may be interesting as a thought exercise to wonder if non-contradiction could be an emergent property. It would certainly make for an interesting model for the beginning of the universe.
> I expect logic to be necessary for us to reason about primitives. But that logic is the wrong way to think of basis elements. Those are very different things.
I think this would probably be contentious, I think most people believe that logical values are basically "necessary". I don't really know though.
I will perhaps spend some time reflecting on the concepts you're referring to with regards to logic and primitives. I'm not really familiar enough with that sort of grounding or reduction.
> Well thanks for pushing me, I am sure I have taken up enough of your time. But, I am now aware of more philosophical viewpoints on the big questions!
I think that's a very good outcome, thank you for pursuing that, it's always interesting to reflect on such topics, to me at least.
Any theory of reality must have full closure. Meaning what happens when two constraints/structures collide depends on the two components, but that there is always a definite result, and it is the solution to conservation.
It isn't just that reality doesn't or can't ever "contradict" itself, but that contradiction dodging doesn't happen either. Bolted on contradiction avoidance, isn't needed when there is closure. Mixing up logic as tool, with logic as inherent reality is a category error. Things cancel, reduce, etc. All operations that happen locally where structure connects. They don't produce potential solutions, then winnow them down. We do that.
Thats what we do when we don't completely understand something, or we only have partial knowledge. Not scenarios that reality operates in. Entirely different.
> I think this would probably be contentious, I think most people believe that logical values are basically "necessary". I don't really know though.
Unknown is obviously a factor of notation, or our knowledge. Its dual is contradiction. Those concepts are foundational in terms of our ability to analyze things we only have partial knowledge of, or may be describing incompletely or inaccurately. Analysis needs that meta-level to handle all the provisionalism inherent in conjectural knowledge.
What is true, what is not?
What don't we know?
What have we incorrectly assumed?
We cannot operate on provisional/conjectural knowledge without all four of those concepts. (We rarely actually operate with just boolean true/false logic, even if unknown/contradiction are handled implicitly instead of explicitly, which only works in trivial systems. Which makes the major proofs of fundamental limitations' dependency on an excluded middle a bright red flag.)
Logic is how we analyze arbitrary structures. In that sense it is universal. Whether the artifacts we analyze have any resemblance to logic or not. We traverse them with logic as an external scaffolding that allows us to represent and operate directly on our understanding of the artifact.
Keeping those things separate sheds a lot more light on things like mathematical and computational limits. I.e. the weaknesses of starting with logic in Russell's Paradox and Gödel's theorems, instead of structure-agnostic reduction, are pretty stunning. Of course a system fundamentally restricted to true/false, without explicit "either/unknown/undetermined" or "both/contradiction/overdetermined", can't be consistent or complete.
Analysis without the four possible states of analysis inherently breaks. Whether that is a Russell set ("a set that includes all sets that don't include themselves", given sets are defined as boolean mappings), or a Gödel system (a Boolean mathematical system can't consistently handle something as simple as, "this system will say this statement is false"). Not how both of these examples pull the means of analysis into the contradictory statement loop. A set, in a set system. The mathematical system, into analysis of itself. So analysis as the subject. True, false, unknown and contradiction need to all be first class values in any study of analysis.
How would you feel if I sent you an email? I have a question but asking offline works better.
There are numerous academics in this area though who I suspect would be quite interested in discussion, and I'd point you towards the Stanford Encyclopedia of Philosophy as the defacto resource for these topics.
I'm actually quite sick with a fever currently so you'll have to excuse me for such a brief response, I'm barely awake as it is.
If you change your mind email me. I am collecting a few people for informal feedback on a series of essays and programming concepts. Noticed you have a Rust background which is relevant.
There is no possible finite way to describe if this were the case or not.
No one is deciding anything.
Well, duh. It's not like classic objects actually exist, or the classical/quantum divide: everything is quantum, including the "observers". The "classical observer" is a crude approximation that breaks down to a pointy enough question. Just like shorting the perfect battery (with zero internal resistance) with a perfect wire (with zero external resistance) — this scenario is not an approximation of any possible real scenario so it's paradoxicality (infinite current!) is irrelevant.