For example that some events within a simulated universe can be unintelligible. Or maybe that there are emergent phenomena within a universe that can't be explained from within the system itself.

I'll have to skim Tegmark's philosophy on the matter and get back to you with some actual arguments or theories of his. His multiverse philosophy get's complicated; yet, intelligible fast.

What does "unintelligible" mean? The laws of physics are all computable - that means that any finite physical system may be simulated to arbitrary accuracy by a universal computer. For something to be "unintelligible" that means it is contra the laws of physics, which is impossible.

The REASON for Godel's theorems is that the laws of physics do not support non-computable functions, which almost always involve infinite processes. Godel states that the overwhelming majority of mathematic truths cannot be proved by a physical process.

All this does is put mathematics on the same footing as physics - nothing in physics can be proved!

If no physical law can be proven, then doesn't that mean that physics will always be incomplete? In other words, you can have a supposed infinite amount of degrees of freedom and never accurately model a phenomena due to that.

I suppose the crux of my issues in asking these questions is how do you prove the Church-Turing-Deutsch Principle?

It means we can conjecture true laws, but just as in mathematics, they cannot be certified as true by any algorithmic process. Not sure why you think that significant.

Progress is never-ending, but guaranteed. All problems are soluble. How can we be expected to solve a problem if we don't know it exists.

My question to you, is do you respect that there is such a thing as categorical boundaries? — Metaphysician Undercover

What I say is that (metaphysical strength) categories are in fact boundaries. They are limit states. And they come in dialectical pairs. They are the opposing extremes of what could definitely be the case.

So if a metaphysical separation is possible - such as the discrete and the continuous - then the separation "exists" to the degree it is crisp ... or not-vague.

I'm not sure why you are struggling so much with the natural logic of this.

As an Aristotelean you should see how this is the same as Aristotle's own argument for substance as the ur-category - the argument from contrariety.

Categories 4a10

It seems most distinctive of substance that what is numerically one and the same is able to receive contraries. In no other case could one bring forward anything, numerically one, which is able to receive contraries.

For example, a colour which is numerically one and the same will not be black and white, nor will numerically one and the same action be bad and good; and similarly with everything else that is not substance.

A substance, however, numerically one and the same, is able to receive contraries. For example, an individual man—one and the same—becomes pale at one time and dark at another, and hot and cold, and bad and good.

So it is the same metaphysical logic. The difference is that Aristotle was still talking about what sounds like an actuality - substance has primal existence - and I'm talking about a "state" of potential in talking instead of primal vagueness. So my emphasis is on the possibility of developing contrariety as opposed to receiving it.

And remember the classical importance of making the distinction between contradiction and contariety, as represented in the square of opposition for example -https://en.wikipedia.org/wiki/Square_of_opposition

So I think you are fixed on thinking about categories in terms of contradiction where to get down to primal being, you have to apply contrariety as the deeper principle.

Progress is never-ending, but guaranteed. All problems are soluble.

Don't know how you can possibly believe that when there are so many conceptual gaps in theory of matter.

Incidentally, an article here about the fact that ''wave-particle duality' is simply the quantum 'uncertainty principle' in disguise, reducing two mysteries to one.

"The connection between uncertainty and wave-particle duality comes out very naturally when you consider them as questions about what information you can gain about a system. Our result highlights the power of thinking about physics from the perspective of information," says Wehner, who is now an Associate Professor at QuTech at the Delft University of Technology in the Netherlands.'


Read more at: http://phys.org/news/2014-12-quantum-physics-complicated.html#jCp

What I say is that (metaphysical strength) categories are in fact boundaries. They are limit states. And they come in dialectical pairs. They are the opposing extremes of what could definitely be the case. — apokrisis

I disagree with this, in a number of ways. First and foremost, you haven't distinguished between the category itself, and the defining features of the category, such that the defining features, the limits, are the category for you. I believe this is a mistake. So for example, if the category is temperature, you haven't distinguished this from the limit states, the opposing extremes, hot and cold. Therefore you no longer have the category of temperature, you have hot and cold. If you want to allow that temperature exists as a category, you must accept that it is something other than hot and cold.

So if a metaphysical separation is possible - such as the discrete and the continuous - then the separation "exists" to the degree it is crisp ... or not-vague. — apokrisis

But your claim was that there are degrees of in-between, between discrete and continuous. How is this possible, if discrete and continuous are different categories? What would it mean to assign to a thing as a property, that it is in between discrete and continuous?

As an Aristotelean you should see how this is the same as Aristotle's own argument for substance as the ur-category - the argument from contrariety. — apokrisis

I don't see your argument. The contrarieties which Aristotle refers to are each of the same category, black and white, hot and cold, good and bad. Each pair of contrary terms represents the extremities of the category. When we assign to a substance, a property according to a category, we cannot say that the substance has contrary properties of that category, though it can at different times. The same substance can be at one time hot and at another time cold, but it cannot be both hot and cold at the same time.

So I think you are fixed on thinking about categories in terms of contradiction where to get down to primal being, you have to apply contrariety as the deeper principle. — apokrisis

It seems quite clear to me that you have this backwards. Categorization is the deeper principle. Contrariety exists within each category, but there is no contrariety between the categories, only a type of difference.

What would it mean to assign to a thing as a property, that it is in between discrete and continuous? — Metaphysician Undercover

Look up fractal geometry - https://en.wikipedia.org/wiki/Hausdorff_dimension

The in-between spectra are now mathematically well defined.

When we assign to a substance, a property according to a category, we cannot say that the substance has contrary properties of that category, though it can at different times. The same substance can be at one time hot and at another time cold, but it cannot be both hot and cold at the same time. — Metaphysician Undercover

Huh? We say it is cold because it lacks heat, and hot because it lacks chill. So it is about "both things at once" - except it is about that as a broken symmetry or asymmetry. At any particular time or place, we have more of the one in terms of having less of the other.

Again the logic of this just seems really simple.

It seems quite clear to me that you have this backwards. — Metaphysician Undercover

Well, I've already said you can turn around and treat vagueness as the ur-category - the limit on contrariety. And that recreates Aristotle's argument for hylomorphic substance, but just recasts it in more suitably developmental or dynamic terms.

Now my point, Andrew M. Appeals to identity do not support the real existence of the apple. "Identity" claims, asserts, or presupposes existence, but what we need here is the principles by which such a claim of existence is justified. Then we can apply these principles in an attempt to justify the existence of the particle, as an identified existent. — Metaphysician Undercover

Asking for justification for the existence of the apple is misplaced here. The thing on the table that we can publicly point to is what we mean when we talk about apples. And part of what we mean is that they exist. (As opposed, say, to our talk about unicorns - we can only point to pictures of unicorns.)

This just is the Aristotelian approach that you mention. There really is an apple there and it has a particular form such that we can point to it and identify it. How the apple appears to us depends both on the apple and on the surrounding environment, including the body and brain of the observer and the interacting light particles.

So here's the problem. The logical system at work here is set up with the premise that the existence of the object is justified if, or, "the object exists if", it has contextual relations with other objects (relativity). So any mathematics used will produce conclusions from this premise. If we desire to assume a "Cosmos", "universe", or "world", to objectify such relationships, and validate the existence of any particular object, that very premise, will not allow that the assumed "world" has existence except in relation to other worlds. — Metaphysician Undercover

I agree that is the problem. A scientific theory such as QM is an explanation of the world, not a mere formalism. And it is testable on that basis. We can plug in particles (or, in principle, apples) and compare what the theory predicts with our subsequent observations.

Asking for justification for the existence of the apple is misplaced here. The thing on the table that we can publicly point to is what we mean when we talk about apples. And part of what we mean is that they exist. (As opposed, say, to our talk about unicorns - we can only point to pictures of unicorns.) — Andrew M

But don't you agree that if you eat the apple, at some point it will no longer exist? And, don't you think that the apple came into existence at some time? Unless you can describe what marks the difference between the existence and the non-existence of the apple, why do you feel so confident that the apple exists? I mean, to me, it appears like you just take it for granted that the apple exists, without even knowing what it means to exist. If you knew what it means to exist you could probably tell me what constituted the apple coming into existence, and what constitutes the apple going out of existence.

I agree that is the problem. A scientific theory such as QM is a description of the world, not a mere formalism. And it is testable on that basis. We can plug in particles (or, in principle, apples) and compare what the theory predicts with our subsequent observations. — Andrew M

OK, if we agree here, then let's go back and take a look at the Aristotelian principle, to see the difference. Instead of defining the existence of the object through its relations with other objects (relativity theory), or as I discussed with apokrisis, defining the object as being in a context, Aristotle defined a principle of existence (matter) which is inherent within the object.

Do you agree that these are two very distinct ways of defining existence? The way of modern physics is to define the object's existence through its relations to other objects. The way of Aristotelian physics is to assume that there is existence inherent within any object, regardless of its relationships with other objects, it has substance. Now let's consider the apple on the table. Which do you think is the truth concerning the existence of the apple? Do you think that the apple only has existence because it has relationships with other objects, the table etc., or do you think that there is something inherent within the apple itself, which constitutes its existence?

Not sure why you think that significant. — tom

This is an issue because given any sufficiently sophisticated universal computing device there will be "truths" or what can be called manifest physical laws (through mathematics, e.g in Hilbert Space) that can't be proven to be true.

This is essentially putting a thorn via Godel's Incompleteness Theorems into the validity of the Church-Turing-Deutsch Principle. I don't know if you see the link there yet or if I haven't made the causal link sufficiently clear.

If you want to take this line of reasoning as far as possible, then this conundrum extends all the way to ANY physical law, in that we can never be certain of it being true in all circumstances. Even in a deterministic universe via Everttian QM, we could have a computer that will never be able to tell us that every Entscheidungsproblem will be able to be resolved in a deterministic manner.

This is an issue because given any sufficiently sophisticated universal computing device there will be "truths" or what can be called manifest physical laws (through mathematics, e.g in Hilbert Space) that can't be proven to be true. — Question

Nothing in science can be proven true. This isn't news.

This is essentially putting a thorn via Godel's Incompleteness Theorems into the validity of the Church-Turing-Deutsch Principle. I don't know if you see the link there yet or if I haven't made the causal link sufficiently clear. — Question

Godel's theorem is irrelevant.

If you want to take this line of reasoning as far as possible, then this conundrum extends all the way to ANY physical law, in that we can never be certain of it being true in all circumstances. — Question

It is logically impossible to certify a physical law as true. This isn't news.

So, the Church-Turing-Deutsch Principle can never be known to be true. Thus, we don't know if we can simulate Everittian QM and know it is deterministic at the same time.

So, the Church-Turing-Deutsch Principle can never be known to be true. Thus, we don't know if we can simulate Everittian QM and know it is deterministic at the same time. — Question

No, you can't certify any scientific theory as true (for the nth time) and that has been known since at least 1936.

Now, what difference does that make?

But don't you agree that if you eat the apple, at some point it will no longer exist? And, don't you think that the apple came into existence at some time? Unless you can describe what marks the difference between the existence and the non-existence of the apple, why do you feel so confident that the apple exists? I mean, to me, it appears like you just take it for granted that the apple exists, without even knowing what it means to exist. If you knew what it means to exist you could probably tell me what constituted the apple coming into existence, and what constitutes the apple going out of existence. — Metaphysician Undercover

At some point the apple grew on a tree and before that the tree grew from a seed. And in the other direction, at some point the apple will be eaten or decompose and perhaps its seeds will grow into into new trees. This is just matter changing form such that we can identify substances like apples. So the boundaries at the coming-into-existence and going-out-of-existence of an apple can be vague or ill-defined. But the apple is clearly identifiable when it is fully formed. And so we can develop language to talk about it.

OK, if we agree here, then let's go back and take a look at the Aristotelian principle, to see the difference. Instead of defining the existence of the object through its relations with other objects (relativity theory), or as I discussed with apokrisis, defining the object as being in a context, Aristotle defined a principle of existence (matter) which is inherent within the object. — Metaphysician Undercover

Right. The logical form of the apple is not sufficient for existence. Matter is also required.

Do you agree that these are two very distinct ways of defining existence? The way of modern physics is to define the object's existence through its relations to other objects. The way of Aristotelian physics is to assume that there is existence inherent within any object, regardless of its relationships with other objects, it has substance. Now let's consider the apple on the table. Which do you think is the truth concerning the existence of the apple? Do you think that the apple only has existence because it has relationships with other objects, the table etc., or do you think that there is something inherent within the apple itself, which constitutes its existence? — Metaphysician Undercover

The latter. The way I would put this is to say that if the apple has form and matter then it is substantial. That is, it exists.

To relate this back to QM. The formalism is the Schrodinger equation. The primary dispute is whether the equation is substantial. That is, is the wave function real? If it is, then that explains why we see interference effects.

So, what I am getting at is what you can ask.

My main point is that how can we know for certain that the MWI is actual/real/valid/.../true if the only practical means of verifying it is via trying to simulate the laws of the universe via the Church-Turing-Deutsch Principle, which itself can't be known to be true?

What's even more damning is that Godel showed that even if the Church-Turing-Deutsch Principle is by some means true, then even if one were to create such a sophisticated logical Turing Machine, then even then we would not be able to know whether halting problems (physical phenomena taking place within such a machine) are deterministic (via computational means) or not.

It's kinda like standing on a rug and pulling at it at the same time.

I'm going to try and simplify my question to a more simple one pertaining as to whether Godel's Incompleteness Theorems negates the possibility of constructing a universal Turing machine that would be capable of computing all known physical laws. Or am I running in circles in trying to state that all physical laws can be proven to be true (computable or replicable?). I mean, the act of a computer able enough to simulate them, would be sufficient evidence despite not being able to verify them from within such a system.

If anyone want's to take a stab at it here, then by all means.

Or am I running in circles in trying to state that all physical laws can be proven to be true — Question

How can you possibly prove physical laws with a calculation? Being computable or otherwise neither proves nor disproves anything. Nor does this have anything to do with Incompleteness theorems, as far as I know.

I'm going to try and simplify my question to a more simple one pertaining as to whether Godel's Incompleteness Theorems negates the possibility of constructing a universal Turing machine that would be capable of computing all known physical laws. — Question

Those sorts of machines already exist, and a theorem regarding proofs in mathematics didn't stop that happening!

Quantum computers and classical computers share the same set of computable functions. Given eternity, infinite power, infinite memory, then a classical computer can perform the same calculations that would take a rudementary quantum computer a few cycles.

In the case of the classical computer, we are happy to point to where the calculation is taking place - here's the cpu, here's the memory etc. Where does all this happen in a quantum computer?

To put this in a bit of perspective, the visible universe is thought to contain ~2^149 bits of information (from memory). A rudimentary quantum computer with a few hundred qubits outstrips that by an astronomical figure. Actually, "astronomical" doesn't even begin to express the magnitude of the difference.

As David Deutsch has said, when the first quantum computer is constructed, its major impact will be psychological.

Or am I running in circles in trying to state that all physical laws can be proven to be true (computable or replicable?). — Question

I think I have already mentioned that no scientific law can be "proven to be true". They can however, be tested.

So, then how can we know for certain that the MWI is actual/real/valid/.../true if the only practical means of verifying it is via trying to simulate the universe via the Church-Turing-Deutsch Principle? — Question

Everett's is the only explanation of quantum mechanics known. It is also the only explanation that is testable and which agrees with quantum mechanics.

https://arxiv.org/abs/1508.02048

What about the seven eighths of the iceberg below the surface to speak by analogy?

I made a post about this issue over at physics forum.

See:
https://www.physicsforums.com/threads/proving-the-church-turing-deutsch-principle.894529/

No, if something is computable (doesn't encounter the Halting problem), then it is real in some sense. If something can't be computed then that is indicative of a gap in understanding or that there are some things that are unintelligible.

If all the laws of physics can be computed, then doesn't that presuppose that logic is at least synonymous or at least as important as physics is. Or rather that physics relies on the laws of logic?

I always had a problem with understanding the importance of physics, mathematics, and logic and which of them follows from the rest.

I made a post about this issue over at physics forum. — Question

Best of luck with that.

Could you ask them to prove the Principle of the Conservation of Energy while you're at it?

The CTD Principle is proved under quantum mechanics. Otherwise, it is a conjecture about future unknown laws. It is a guide to what they must be like. Just as we expect any future law to be Unitary.

No, if something is computable (doesn't encounter the Halting problem), then it is real in some sense. If something can't be computed then that is indicative of a gap in understanding or that there are some things that are unintelligible. — Question

No aspect of physical reality in non-computable.

If all the laws of physics can be computed, then doesn't that presuppose that logic is at least synonymous or at least as important as physics is. Or rather that physics relies on the laws of logic? — Question

No, it means that physics is a subset of reason. Science is constrained by the fact that it only deals with physical reality. Reason is not constrained in any way.

Yet, that statement requires much-needed justification!

Is it all platonism in modeling logical relations between objects in logical space?