David Deutsch has proposed such a conceptual principle that every physical law is computable. This is called the Church-Turing-Deutsch Principle. — Question

This is problematical, because there are very few people who claim to understand what this 'principle' means; and then, of course, if you don't understand it, then you can't argue with them, or about the question, because you don't 'get it'. As soon as you introduce Deutsch and Turing, you're in a very strange no-mans-land somewhere between schrodinger's cat and Alice in Wonderland. That's why you're running in circles.

The scientific method - or rather the range of scientific methods, sometimes idealised as 'the scientific method' - works brilliantly.

Metaphysics is another matter. For instance, even if it could be demonstrated according to some principle or other that every word Tolstoy wrote had a computable micro-physical cause, would you learn more about life by reading David Deutsch who invented the principle ? Or Tolstoy?

Natch, my reply is Tolstoy. There is a way of knowing which is scientific, but there are other ways, at present and for the foreseeable future irreducible to computation, which are just as if not more important: ethical, artistic, political, spiritual. Personal; emotional.

I am here channelling the absent spirit of Landru, a former forumite.

You will doubtless find Deutsch and his followers rather adamant in their advocacy of the Principle. To be frank that makes me suspicious: their rhetoric seems too sure of itself and unable to imagine disagreement.

Yeah, you need to explain what it means for something to be computable. Generally, this has a very specific meaning, to do with being able to model processes through the iteration of a finite set of algorithms which allows for the transformation of states in time across a system. Even this definition leaves alot to be unpacked, and frankly unless you can really engage with the detail here, there's little discussion to had.

So, my question is...

In order to answer such fascinating questions as 'Is the universe deterministic?', then one need compute said physical laws as per the Church-Turing-Deutsch Principle and via such a method of replicating the laws of nature inside a computer, then it can be asserted the truth or falsehood of such statements.

If not, then how else to determine the validity of such statements?

There is a way of knowing which is scientific, but there are other ways, at present and for the foreseeable future irreducible to computation, which are just as if not more important: ethical, artistic, political, spiritual. Personal; emotional. — mcdoodle

I think mentioning 'emergent phenomena' is apt here. Take Escher's paintings for example... These are properties of a system that are at the same time dependent and independent of the system itself. I guess you can call them 'language games' without logical hinges or bedrock beliefs...

Again, computability doesn't mean just 'can be replicated inside a computer', which is a vague and imprecise statement. Computers do their computations in specific ways, and to claim computability is to claim that those specific ways and not others can model natural systems in their entirety. If you can't flesh out what those specific ways are, and why they matter - if you don't understand the mechanisms by which computability functions - then you can't even begin to mount a discussion of truth and validity. You keep wanting to skip meat of it and arrive at the end - but that's cheating.

You need to speak about the how of computability before you ask questions about the scope of it.

Let's take quantum theory - for example - irrespective of what interpretation of quantum theory is right or wrong (true or false), we know that quantum mechanics is apparently true. The laws of nature are absolute, intelligible, and unchanging. Now, I don't think many will doubt the validity of the preceding statement. — Question

Here's where your problem lies. There is a distinct difference between the "truth" concerning the mathematics of prediction, and the "truth" concerning the description of the predicted event, true interpretation. So the mathematics of prediction may give us a true "law" which is accurate for prediction, but it doesn't give us the whole truth about the event. It doesn't give us why the law holds, and therefore it doesn't give us the complete truth about the event. This can only be provided by the appropriate interpretation.

For example, human beings could map for years, the exact position and time, when and where, the sun rises on the horizon, every morning. From this, they could project, and make predictions, far into the future, the exact place and time that the sun would rise, day after day. This would constitute the mathematical law of prediction. It would be a very true law, because it would predict with great accuracy the position and time of sunrise each day. The problem is, that this predictive law tells us nothing about the real relationship between the earth and the sun, why this event of sunrise occurs as it does, with the changes that it incurs, and why those changes are so predictable. The whole truth is not revealed until this "why" is uncovered, and this is a matter of interpretation. As you can see from the example, the mathematical truth of prediction, constitutes a rather small portion of the overall "whole truth", and it is really just a starting point in uncovering the whole truth.

So, my question is...

In order to answer such fascinating questions as 'Is the universe deterministic?', then one need compute said physical laws as per the Church-Turing-Deutsch Principle and via such a method of replicating the laws of nature inside a computer, then it can be asserted the truth or falsehood of such statements.

If not, then how else to determine the validity of such statements? — Question

You can tell if certain physical laws are deterministic just by looking at them. In particular, if they are time-symmetric, then they are deterministic.

General relativity is time-reversible, and therefore deterministic. As I'm sure you are aware, it is a little more than that - it predicts a stationary block-universe in which all instants coexist.

Realist non-collapse quantum mechanics is also time-reversible therefore deterministic. More than that, it predicts a stationary block-multiverse in which all instants and universes coexist.

Have you noticed no CTD-Principle yet? The determinism questioned is answered already!

Here's another question, "How is knowledge possible?" Or if you prefer, "If reality is comprehensible, then what makes it so?"

The CDT-Principle answers that question.

And, by the way, the CDT_Principle is proved.

You can tell if certain physical laws are deterministic just by looking at them. In particular, if they are time-symmetric, then they are deterministic. — tom

Yep. Our physical laws are constructed by excluding change or spontaneity. That aspect of existence is instead the job of measurement. We are left to measure variables like initial conditions and plug them into the "computable" models.

So time symmetry in equations is the way we construct the no-change that a measurement can then meaningfully break.

Scientific modelling is based on this epistemic dichotomy. We work to separate the symmetries and the symmetry-breakings. The laws are the frozen view. The measurements are how the laws are animated.

Importantly, the measurement part of the deal is incomputable. One simply has to ... enter the picture as an "observer".

Realist non-collapse quantum mechanics is also time-reversible therefore deterministic. More than that, it predicts a stationary block-multiverse in which all instants and universes coexist. — tom

Fortunately the fact that the measurement part of the deal is informal and thus incomputable means we can dismiss such metaphysical flights of fancy. We already know the epistemology of the scientific method doesn't support it.

So the measurement issue in physics plays the same role as the axiom-forming issue in Godel's critique of mathematical formalism. In the end, the whole point about eternal symmetries is that as some stage they did get broken and there was something to actually talk about.

You need to speak about the how of computability before you ask questions about the scope of it. — StreetlightX

I am no computer science expert or know all that much about computer architecture; but, what I do know about computational entities is that they are real in logical space. They exist as true or false entities in the logical space that computers recreate. See, this forum is a kind of logical space. The internet is a logical space. A calculator is also a logical space that comes handy. We don't need to know how a TV works to be able to enjoy television, which you might be doing here? Map territory distinction?

Logical space is a concept I've been mulling over for a while now, which I believe was first proposed by Wittgenstein in his Tractatus. I find it an apt description of how the universe might work in a Hilbert space with N dimensions with the wavefunction describing and evolving (deterministically or randomly).

I hope I didn't muddle the waters too much.

I am no computer science expert or know all that much about computer architecture; but, what I do know about computational entities is that they are real in logical space. They exist as true or false entities in the logical space that computers recreate. See, this forum is a kind of logical space. We don't need to know how a TV works to be able to enjoy television. — Question

I don't understand what you mean by a 'computational entity'. And while 'logical space' has a close analog in the notion of state-space, which can be employed in talking about computability, the two are not the same, and the way you employ the term - especially with respect to 'true and false entities', seems to have nothing to do with the latter. I think you seem to be stuck on this idea of 'computability' without really knowing what it actually is.

The whole truth is not revealed until this "why" is uncovered, and this is a matter of interpretation. As you can see from the example, the mathematical truth of prediction, constitutes a rather small portion of the overall "whole truth", and it is really just a starting point in uncovering the whole truth. — Metaphysician Undercover

I'm confused. You seem to be making an issue about degrees of truth or different categories of truth. In logical space all truths are equal, depending on the relations between different objects.

Yes; but, you're asking me how does this forum exist. I'm just saying that it exists in logical space or if you prefer 'state-space'. It could be that I require further education on the matter; but, it seems to me as if you're asking something akin to 'How does the logical symbol ~(not) exist'?

I can't prove its existence; but, merely show it to you in action.

Here's another question, "How is knowledge possible?" Or if you prefer, "If reality is comprehensible, then what makes it so?"

The CDT-Principle answers that question. — tom

Truth. Truth makes it possible. This is where I contest with the JTB theory of knowledge. Truth comes before beliefs and justification.

I don't quite see how the CTD principle answers that question, care to enlighten me?

Yes; but, you're asking me how does this forum exist. I'm just saying that it exists in logical space or if you prefer 'state-space'. It could be that I require further education on the matter; but, it seems to me as if you're asking something akin to 'How does the logical symbol ~(not) exist'?

I can't prove its existence; but, merely show it to you in action. — Question

No, I'm not asking that (I have no idea where you even pulled that from?), and no, I don't simply 'prefer' the term state-space, insofar as state space is not 'logical space'. I'm asking you to demonstrate that you know what you're talking about with respect to computability before you start to talk about truth, which you do not seem to be able to do.

Well, I am quite ignorant and uneducated so forgive my lack of knowledge. May I ask if a universal Turing machine is an object that can simulate an artificial 'state-space'?

Why or why not?

Thank you.

I'm confused. You seem to be making an issue about degrees of truth or different categories of truth. In logical space all truths are equal, depending on the relations between different objects. — Question

This appears to be a problem. Do you recognize the fundamental distinction between a correspondence theory of truth, and a coherence theory of truth. In practise, this manifests as two distinct types of truth, true because it corresponds to reality, and true because it is logically valid. It seems like you believe in only one type of truth, coherence. That's fine if all space were logical space, but from this, how do you gain any real knowledge about real objects in real space?

Well, there is just one concrete thing, the world. There is no reason to assume a gap in intelligibility/understanding between the brain and all its functions and objects in the real world. If there were then we wouldn't even be able to know of it due to its inherent nature, otherwise called an unknown unknown...

So, this makes truth uniform with respect to any potential configuration of objects and things in the world.

I should say that I am a firm believer in the PoS (Principle of Sufficient Reason) namely that every cause or effect is intelligible in nature (which kind of automatically makes me a subscriber to Everettian Quantum Mechanics).

Fortunately the fact that the measurement part of the deal is informal and thus incomputable means we can dismiss such metaphysical flights of fancy. We already know the epistemology of the scientific method doesn't support it. — apokrisis

Under realist no-collapse quantum mechanics, measurements are no different from any other type of interaction - they are reversible.

In fact, it is this reversibility that will eventually settle the case, as it leads to different predictions. So much for metaphysics.

A universal Turing machine just is a system that evolves through state space. Or better, it simulates (computes) by means of its sequential progression through such a space, which is itself generally programmed beforehand through transformation rules provided by a set of algorithms. The question - and I'm channelling the biologist Robert Rosen here - is whether or not this type of system has a rich enough 'entailment structure' to model the world in it's entirety. That is, can such a system interact with both itself and the environment in all the ways that systems in nature itself can?

Answering this question requires a pretty close analysis of how causality is encoded or modeled in state systems, but there are pretty great arguments against answering in the affirmative. Hence Rosen's conclusion regarding such enterprises: "[Computable systems] are indeed infinitely feeble in terms of entailment. As such, they are excessively nongeneric, infinitely atypical of mathematical (inferential) systems at large, let alone “informal” things like natural languages. Any attempt to objectify all of mathematics by imposing some kind of axiom of constructibility, or by invoking Church’s Thesis only serves to estrange one from mathematics itself." (Rosen, Essays on Life Itself). There's alot of ground to be covered before arriving at this conclusion, but one needs to be at least familiar with the exact manner in which computable systems work before arguing either way. And this before one can even begin to discuss questions of truth and so on.

I should say that I am a firm believer in the PoS (Principle of Sufficient Reason) namely that every cause or effect is intelligible in nature (which kind of automatically makes me a subscriber to Everettian Quantum Mechanics). — Question

The Principle of Sufficient Reason is shown to be false* by the Free Will Theorem of Kochen and Conway. This is discussed in the 1st hour of the 6hr series of lectures given by Conway at Princeton:



*Conway's arguments seem to imply that super-determinism would rescue the PSR, but I'm not sure the PSR has any meaning in that context.

I've been pondering for a while about how to verify the truth or falseness (computability) — Question

You think that is the definition of computability?

So what you are saying is that Chaitin's number is false or what?

There are non-computable numbers, you know. With computation, we can verify some "truths", I would say.

Proceeding further, in my mind, the only way for a scientific theory (in this case physics) to be logically sound is for it to be replicable or rather computable. David Deutsch has proposed such a conceptual principle that every physical law is computable. This is called the Church-Turing-Deutsch Principle. If it is computable, then it is true or false (depending on the circumstances) and nothing else. — Question

Turing Machine is a way to show the limitations of computability, an answer to the Entscheidungsproblem. That's something that people seem to forget.

Well, there is just one concrete thing, the world. — Question

OK, let's start with this premise, there is just one concrete thing, the world. Now, in your last repy to me, you said "all truths are equal, depending on the relations between different objects". The premise that there are different objects contradicts that other premise, that there is just one concrete thing. So according to these two premises, which are contradictory, the idea of truth appears to be a fiction.

So, this makes truth uniform with respect to any potential configuration of objects and things in the world. — Question

No, it makes a "configuration of objects and things in the world" impossible. There is just one thing, the world.

There are non-computable numbers, you know. — ssu

Most number, overwhelmingly most, are non-computable. Most mathematical functions are similarly non-computable. No physics involves these numbers or functions, so that mathematical truth is irrelevant to computing or simulating reality. In reality, only computable numbers and functions matter.

Under realist no-collapse quantum mechanics, measurements are no different from any other type of interaction - they are reversible. — tom

Well, at least they are reversible all the way back to the first instant of the Big Bang and any other such event horizon. :)

So you are appealing to an infinite regress and I guess some God eventually provides you with the measurement basis you need to define your universal wavefunction.

The OP displays a basic epistemic confusion which is indeed fairly widespread in physics since it has jumped sides and gone from a materialist ontology over to an informational ontology. This bedevils all "interpretations".

This passage from Howard Pattee is a typically lucid analysis of the epistemic issues - and an introduction into how a pan-semiotic metaphysics (one that sees physical existence in terms of matter AND symbol, nor matter OR symbol) is the path out of the maze.

This matter-symbol separation has been called the epistemic cut (e.g., Pauli, 1994). This is simply another statement of Newton’s categorical separation of laws and initial conditions.

Why is this fundamental in physics? As I stated earlier, the laws are universal and do not depend on the state of the observer (symmetry principles) while the initial conditions apply to the state of a particular system and the state of the observer that measures them.

What does calling the matter-symbol problem “epistemological” do for us? Epistemology by its very meaning presupposes a separation of the world into the knower and the known or the controller and the controlled. That is, if we can speak of knowledge about something, then the knowledge representation, the knowledge vehicle, cannot be in the same category of what it is about.

The dynamics of physical laws do not allow alternatives paths between states and therefore the concept of information, which is defined by the number of alternative states, does not apply to the laws themselves.

A measurement, in contrast, is an act of acquiring information about the state of a specific system. Two other explicit distinctions are that the microscopic laws are universal and reversible (time-symmetric) while measurement is local and irreversible.

There is still no question that the measuring device must obey the laws. Nevertheless, the results of measurement, the timeless semantic information, cannot be usefully described by these time-dependent reversible laws (e.g., von Neumann, 1955).

http://www.academia.edu/3144895/The_Necessity_of_Biosemiotics_Matter-Symbol_Complementarity

So the gist is that the "space" in which maths or computation takes place is physically real - in the sense that material spacetime is a generalised state of constraint in which all action is regulated to a Planckian degree of certainty ... except the kind of action which is informational, symbolic, syntactic, computational, etc.

Physics can describe every material characteristic of a symbol ... and none of its informational ones.

And in being thus an orthogonal kind of space to physical space, information is a proper further dimension of existence. It is part of the fundamental picture in the way quantum mechanics eventually stumbled upon with the irreducible issue of the Heisenberg cut or wavefunction collapse.

So the mistake is to try to resolve the irreducibility of information to physics by insisting "everything is computation", or alternatively, "everything is matter". Instead, the ontic solution is going to have to see both as being formally complementary aspects of existence.

Aristotle already got that by the way with his hylomorphic view of substance.

So nature keeps trying to tell us something. Duality is fundamentally necessary because there is nothing without a symmetry breaking. But then we keep looking dumbly at the fact of a world formed by symmetry breaking and trying to read off "the big symmetry" that therefore must lurk as the "the prime mover" at the edge of existence.

The logic of the principle of sufficient reason fools us into believing that only concrete beginnings can have concrete outcomes. Therefore if we see a broken symmetry, then this must point back to an equally physical (or informational) symmetry that got broke.

But that simple habit of thought - so useful in the everyday non-metaphysical sphere of causal reasoning - is what blinds almost all efforts at "interpretation".

The duality of existence will never make sense until your metaphysics includes a third developmental dimension by which beginnings are vague or fundamentally indeterministic.

Clinging onto a belief in the definiteness of beginnings, the concreteness of initial states, is just going to result in the usual infinite regress stories of creating gods or universal wavefunctions. Folk are very good at pushing the question they can't answer as far out of sight as possible.

Most number, overwhelmingly most, are non-computable. Most mathematical functions are similarly non-computable. . — tom

That's not the point here. Question started the thread by assuming that verifying truth or falsehood is done by computation. I don't think it is so. You can do also it otherwise too, even if the vast majority of proofs are either computations or something equivalent to a computation. Still, you can prove the existence with indirect proofs. And indirect proofs matter. Computation is a direct proof equation. The point I am making is that giving a proof by computation isn't universal and adaptable to all models.

No physics involves these numbers or functions, so that mathematical truth is irrelevant to computing or simulating reality. In reality, only computable numbers and functions matter. — tom

No models that we use involve these numbers of functions, so that mathematical truth is irrelevant to our present models that we use. Just like non-Euclidean geometry or Computer science was irrelevant to people during Antiquity.

I think it would really matter when you would understand that the best model of something is noncomputable. And in that case you just use a second best model ...and understand that there are limitations just what you get. Because otherwise we fall into falsehoods like Laplacian Determinism, the asumption that if we had all data and knowledge, laws, SuperTuring Computers or whatever, everything would be computable.

The question - and I'm channelling the biologist Robert Rosen here - is whether or not this type of system has a rich enough 'entailment structure' to model the world in it's entirety. — StreetlightX

Yep. Rosen did a great job on highlighting the logical impossibility of "computing nature". And the holographic principle now shows that it is materially impractical as well. The speed of light creates absolute event horizon limits so the world itself doesn't even have the physical resources to nail down every event in super-deterministic fashion.

And then there is the flipside to the issue of modelling the world. It is not just that computation can't nail every event down - Rosen's issue of incommensurability. But instead, modelling is based on the principle of nailing down the very least amount of information possible. The aim of modelling is not to simulate the world - re-present it in some veridical sense - but to reduce an "understanding of the world" to its simplest possible collection of habits.

So less is more when it comes to modelling. And that is what the practice of creating physical laws follows. That is why the mechanics of Newton, and all the other varieties of mechanics that came after, feel so pragmatically right. The messy dynamical world can be reduced to the simplicity of timeless universals and particular acts of measurement. You measure how things begin, and then the equations predict how they will unwind forever.

So the current computational bandwagon - the digital physics - is wrong both in believing the entirety of the material world (including its fundamental indeterminism due to holographic limits on decoherence) is actually computable, and wrong also even in presuming this kind of veridical simulation would be "a good thing".

Instead, for modelling minds, it is clear that efficiency arises from the opposite of being "completely consciously aware of every detail of the world." Minds actually arise as a "orthogonal subjective dimension" because of an an ability to pretty much detach from such detail. And that detachment is based on the materiality of the world being reduced to a well-worn system of sign or habit.

Then this biosemiotic insight - this efficiency principle - can now be extended to the physical world in general. That is pan-semiotics. Quantum decoherence is an expression of the same thing. The world is seeking its simplest informational states. Classicality is what emerges as its simplest self-model, the one that minimises the messiness of the causal tale it is telling in terms of its own evolving temporal history.

So there is a duality that pervades all these levels of discussion - the matter~symbol distinction - for a reason. There is a single causal mechanism at work that links it all from quantum to mind.

But that mechanism is also irreducibly complex or triadic in involving the third thing of an axis of development - the vague~crisp distinction.

The matter~symbol distinction is pretty easy to understand. But the vague~crisp distinction is far subtler in being "beyond standard logic" as well as "beyond standard physics". :)

The question - and I'm channelling the biologist Robert Rosen here - is whether or not this type of system has a rich enough 'entailment structure' to model the world in it's entirety. — StreetlightX

To be frank, I don't think any formal system can entail (or simulate) the world in its entirety. There will be inconsistencies within such a model system.

A conceptual example that comes to my mind is that there are mathematical truths that are unanswerable within the universe itself. However, it is not impossible to recreate a simpler version of the apparent world within the system itself (the universe).

However, I have yet to see a logical proof that a formal system can't replicate itself within the system itself. This might just be my feeble understanding of Godel's Incompleteness Theorem's.

The Principle of Sufficient Reason is shown to be false* by the Free Will Theorem of Kochen and Conway. This is discussed in the 1st hour of the 6hr series of lectures given by Conway at Princeton: — tom

This is interesting and I don't dare to contest those findings by such brilliant minds. However, how does one explain that man can do what he wills but he cannot will what he wills?

Or in other words, why is this reality apparent as opposed to being in any other state of affairs?