I think a limiting aspect of this debate is the automatic, almost innate assumption that the laws of physics are always invariant under time-reversal. But if you model dissipation and friction in Newtonian mechanics with a velocity-dependent component, the way it's usually done, then invariance under time-reversal goes away. Like so (in a 1-d system):

F = m ( dx^2 / dt^2 ) - k dx/dt

Clearly F is not the same if I take t to -t. This matters at a macroscopic level because we do have friction, collisions, vibrations, and other dissipative phenomena, which are collectively responsible for the irreversibility of macroscopic events and interactions. Dissipation can be related to entropy since all irreversible phenomena generate some useless heat and increase the combined entropy of the system and the surroundings.

Point taken, and thanks for clarifying. Personally I don't think anything is riding on whether invariance under time reversal is true for all laws, the claim is that even where it is the case,you don't get time-reversal symmetry without it being a symmetry between two distinct and well defined states of a system.
However, now you've raised the point (although it's a little off topic) is there not a way to model the friction/dissipation (in Hamiltonian mechanics perhaps) such that invariance under reversal of sign of the time parameters is preserved? It's a genuine question - I don't know the answer, but I assume there is one, and perhaps you do.

I just joined this conversation on the fly so I apologize if I don't understand everything right away. Eventually what I want to do here is explain why symmetries are important and place them in a proper mathematical and ontological context (explain why physicists use them and what they mean and don't mean).

Before I get to that, let me address this issue of initial conditions. One thing that confuses me about this debate is the idea that you need any kind of "condition" on a differential equation for the solution to exhibit time-reversal symmetry. Suppose I have a simple differential equation:

dy/dt = t

The solution is y(t) = (t^2 / 2) + C, where C is a constant of integration. If a physical system is described by this equation, then it exhibits time-reversal symmetry even without me specifying anything about initial conditions. The main reason why you would specify an initial condition is to get a unique solution. So if I told you that y(0) = 1, then we would conclude right away that C = 1 (just plug t = 0 in the equation for y). So maybe I'm just slow today but I don't really get what this debate is about: whether an equation is invariant under time-reversal depends on the terms of the equation, not on the initial or boundary conditions associated with the equation.

The fundamental reason why we care about time-reversal symmetry in physics is because it's associated with equilibrium conditions and the conservation of energy. There is a beautiful result in classical physics by Emmy Noether, called Noether's theorem, which states that any continuous symmetry is associated with a corresponding conserved quantity. So if an equation for a physical system exhibits time-reversal symmetry, then the energy of the system is conserved. If it exhibits translational symmetry, linear momentum is conserved. Rotational symmetry means angular momentum is conserved. Gauge symmetry in electrodynamics implies that charge is conserved. This fundamental idea has also been extended to quantum systems in different ways, so the basic idea is not just a classical result. Whether these relationships represent something bizarre and fundamental about nature or whether they are just amazing mathematical connections is still up for debate.

What do physicists do with these results? One thing they do is use experiments to find systems where these quantities are conserved or not, and then they write down an equation that preserves or violates the underlying symmetries. If a system violates a symmetry, that's associated with cool things happening: perhaps the system starts interacting with other systems and loses or gains energy through those interactions. The boring equilibrium conditions give way to something more dynamic. In these kinds of symmetry-breaking Hamiltonians, there is usually a term in the Hamiltonian which acts to break the symmetry under some reversal. So if a system's Hamiltonian changes under time-reversal, then the Hamiltonian is not conserved, which is physically interpreted as the system interacting and forming correlations with other systems. The integer quantum Hall effect is a famous example of a system that breaks time-reversal symmetry. By contrast, the invariance of the Hamiltonian under some transformation is often seen as a sign that a system can be capable of preserving some really interesting feature.

These methods are so powerful in condensed matter physics that entirely new states of matter have been predicted just from writing down an ingenious equation that either preserves or violates a symmetry. Then the experimentalists go and look to find the corresponding system, under the energetic or dynamical constraints implied by the equation.

I think we should take this onto a different thread as it is getting way off the point. As I follow things the debate starts off being about the role of causation in physics and really kicks off with the following claim from tom

Deterministic physical theories, being time-invariant, render causality meaningless.

MetaphysicsNow asked tom to explain what conception he had of determinism that was free of the notion of causality (most usual notions of determinism being very closely tied to causality). Tom still hasn't answered that question. Then the dispute becomes about time-reversal and differential equations and it loses me a little, but what does seem clear is that tom believes that given merely the initial description of a physical system, the laws of physics allow you to calculate backwards as well as forwards in time, i.e allow you to calculate how the system actually arrived in that state in the first place. As far as I can see, that is just false, and MetaphysicsNow gave a pretty convincing reason why - there are indefinitely many physical possibilities regarding how that physical state came to be, and since they are physical possibilities, the laws of physics and the initial conditions will not provide you with the means to select just one of those possibilities. I think perhaps this links to your idea that the course of the universe has always involved symmetry breaking and not boring equilibrium, and given merely the initial conditions, we cannot say exactly how the symettry was broken to arrive at them.
Anyway, that's my take on it.

Oh yeah Tom is wrong. I just gave an example above of a purely deterministic differential equation that is not invariant under time-reversal, and this equation describes actual physical systems experiencing friction or drag. Easy.

These methods are so powerful in condensed matter physics that entirely new states of matter have been predicted just from writing down an ingenious equation that either preserves or violates a symmetry. — Uber

However, such accomplishments appear to me to be examples of what Kant categorised as 'synthetic a priori reasoning' - in logic, a proposition the predicate of which is not logically or analytically contained in the subject—i.e., synthetic—and the truth of which is verifiable independently of experience—i.e., a priori. In general the truth or falsity of synthetic statements is proved only by whether or not they conform to the way the world is, and not by virtue of the meaning of the words they contain. So such statements are validated, or falsified, against the physical evidence - but I can't see how they themselves can be understood to be physical. And if they're not physical, then they provide an example of something that is not physical.

Yawn. You and I rehashing this debate on another thread is pointless.

Mathematical ideas are mental constructs in the brain. They are physical mental states. How do I know? The last 100 years of neuroscience and all that jazz. Where did the mathematical ideas come from? From the interaction of the brain with the external world. Why do they have predictive power? Sometimes they have predictive power because they do a good job of approximating the real interactions of the physical world. Other times certain math systems may do a poor job of approximating reality. Then human brains interacting with the external world and other brains come up with new math ideas (ie. develop new mental states that can better process the information they're getting from the world). Outside a series of organized mental states, math statements can also exist in symbolic expressions on a particular medium (like an equation written on a t-shirt). Bla bla bla we already played this game and you lost.

It's all physical.

They are physical mental states. — Uber

A ‘physical mental state’ is a contradiction in terms.

You’ve simply adopted a belief as a consequence of the culture in which you’re situated. This belief is that science replaces religion, in part, although if you go back and study the exact sequence of developments that have occurred, which resulted in the particular mythos that you subscribe to, it is quite complex and would take a long post to unpack. And I know it’s pointless to try and persuade you, as what you actually subscribe to is a religious ideology masquerading as a scientific theory, but it’s worth calling it out from time to time, if only for the benefit of other readers.

So I will just rehearse the basic 'argument from reason' approach to the question of materialism once more.

I contend that number, logical laws, and scientific principles are real, but not physical. They comprise the relations of ideas, and their practical usefulness arises from being able to compare them with observations, predictions and measurements (hence the computer on which this is being written, among other things).

But such faculties are not simply subjective or internal to the act of thought, however, because they are predictive with respect to natural phenomena - hence the unreasonable effectiveness of mathematics in the natural sciences.

Scientific reason depends on these faculties, but, contrary to widespread popular myth, it still doesn't actually comprehend, much less explain, them. This is shown by the fact that philosophy of maths and philosophy of science are still controversial subjects (among other things).

It is currently accepted by many people that neuroscience and/or evolutionary biology can in principle account for rational ability, but this is a consequence of the role that science has now occupied in secular culture in replacing the traditional 'creation mythology' of yore with what is thought to be a more scientific attitude (for which, see Michael Ruse, Is Evolution a Secular Religion?). But if you actually drill down into the subject-matter, it is still highly contentious and contested, as evolutionary biology itself was never intended as an account of the nature of reason as such, but simply as an account of the origin of species; so to extrapolate it to such questions (aside from whatever legitimate basis it has in actual biological science) amounts to pop philosophy, which has now thoroughly taken root in the imagination of the secular intelligentsia.

Thanks for the confirmation.

So tom, seems you are wrong about this:

Nope, you only need initial conditions, which can be given at any time. Differential equations are by their very nature time-symmetric, deterministic.

And for at least two connected reasons:
1) There are differential equations used in physics which are not invariant under time reversal, and so symmetry gets broken
2) Because of this there is no way to tell just given intitial conditions what exact symmetry breaking occured in order for the initial conditions to obtain.
I expect MetaphysicsNow will be along to gloat at some point.

Having descended from the cloud of cluelessness to which I'd retreated after the withering critique of my scientific credentials by tom, I feel too serene to gloat. From previous experience on other threads, tom seems to believe that the first and last word in metaphysics is owed to science, and it seems to rankle with him when people point out to him that scientists take for granted many of the assumptions that are challenged when one is engaged in doing metaphysics. Having said that, I think it is extremely useful if you do do metaphysics that you have actually done some science, since it can help you identify the hidden assumptions (and dare I say errors) behind some of the more gradiose metaphysical claims that some scientists are sometimes inclined to make.

Oh, and thanks again to @Uber for the technical clarifications.

Wayfarer:

I contend that the predictive capacities of logic and math are entirely explainable by seeing them as emergent properties of human cognition. Some fundamental work has already been done along these lines by neuroscientists like Anil Seth, Karl Friston, and Giulio Tononi, among many others. Anil Seth's predictive theory of consciousness addresses the major points that you raised. He literally sees the brain as a biochemical prediction machine. Now I don't claim that these theories are finished or that the puzzle of conscious experience has been solved, but there has been enough fundamental progress to at least begin to understand these issues and to see how they concretely relate to each other.

You mentioned the limits of evolutionary biology. That's funny, because hundreds of years ago people thought that the explanation of life required a soul or an 'animating' force beyond the body that was in control of our motion. Then biology, chemistry, and physics had their say and no one (who should be taken seriously) believes that anymore. The useless effort to stall the progress of neuroscience now is very much reminiscent of that: there is this deeply held belief that people just cannot possibly be physical systems subject to energetic constraints! The thought alone to some is horrifying. And yet, that's exactly what we are. To me that's worth celebrating: it shows that we too are a part of this big beautiful family called nature.

You are obviously a fan of the history of philosophy, in a morbid kind of way that holds a tragic nostalgia for what has been lost. But cheer up, not everyone back then was totally clueless. Here is good old Lucretius in the Nature of Things:

Since the Nature of the mind and spirit, as we learn, is basically a part of a human being - then return
The name of harmony to the musicians.

Now pay attention here:
I tell you mind and spirit are bound up with one another,
And that together they combine to form a single nature.

Impressive realizations for someone writing so long ago. Now he got many things wrong too in the poem, but the things he got basically right are just astounding. And just for kicks since I have the book open:

All in the void beneath our feet lies open to our sight,
Such revelations and I'm seized by a divine delight,
I shiver, for due to your power, Nature everywhere
In every part lies open; all her secrets are laid bare.

Is a physical mental state a contradiction? To truly argue that, you would need to provide your understanding of the word "physical." Have you automatically defined "physical" as everything that exists outside the mind or the brain? If so, then it's a contradiction just by definition, which doesn't bother me in the slightest, because that definition is nonsense and no one with a few brain cells should use it.

Here's an actual contradiction:

How do you address the epistemological problem of Benacerraf? How does the transcendent Platonic realm communicate with the human mind? How does the mind gain access to the rational treasures of the "world beyond" if not through physical causation?

As for science and metaphysics:

I do think it's necessary and important for science to use some level of metaphysics in its analysis of the world. Otherwise the world just doesn't make sense. To me metaphysical ideas are useful mental constructs that help organize and process information about reality, which would otherwise be too complicated to barely grasp. Scientists who think they can do without metaphysics are misguided. They do metaphysics without even realizing it. After all, no car driving down the road has a shiny yellow vector pointing out the front! Vectors are useful mathematical abstractions, a way for the mind to organize concepts like speed and direction.

On the other hand, metaphysics has often flirted with becoming totally detached from empirical reality, depending on who was using it. And that's when you start getting things like angels, Platonic realms, and Jedis. So I think philosophers also need to be careful in how they use metaphysics. But I get that the main problem now is the stereotypical ignoramus, like a Lawrence Krauss, who does not seem to understand the fundamental value of philosophy.

Have you read Norman Malcolm's "The Conceivability of Mechanism"? If not, and you have the time/inclination, I'd be interested to hear your thoughts on it - although it is a little dated it still bears on the idea that the kind of proposals that those like Seth are making are conceptually confused. Here's a link https://www.pdf-archive.com/2017/02/02/malcolm-cm/ to a free copy.

It's all physical. — Uber

If so, mental would be a type of physical (just as inorganic and organic). I don't have a problem with that in principle. But can science demonstrate that nothing except physical things exist, or that nothing is real?

I do have a problem with reducing mental to corporeal (e.g., the brain) in the absence of empirical evidence establishing causation ("we already played this game and you lost").

Brains don't do anything but send and receive neural signals. And minds don't do anything but experience the conditions (e.g., consciousness, affect, personality, mood, and emotion) and exercise the functions (e.g., processing semantics, syntactics, and pragmatics) which produce human (not brain, not mind) behaviour.

A ‘physical mental state’ is a contradiction in terms. — Wayfarer

Perhaps, but I don't think that a physical-mental (i.e., physical and mental) state is a contradiction in terms. The above list of conditions are in fact mind-body states.

Some fundamental work has already been done along these lines by neuroscientists like Anil Seth, Karl Friston, and Giulio Tononi, among many others. — Uber

Sure. And I'm very much interested in examining the Free-Energy Principle mentioned by Wellwisher and yourself in the New Dualism thread. But disappointed to read that it is "based upon Helmholtz's observations on unconscious inference". Because, according to Bennett & Hacker, that is a "misconception of perceptions as conclusions of inferences".

I have not read it entirely, but I am familiar with the gist of the argument. If everything is just physical causes, then humans cannot have intentions and desires. But the statements about mechanisms are themselves expressions of intent, hence contradiction.

I also don't know if you are aware that this argument has been mercilessly refuted by now, to the point that later on Malcolm himself had to drop it in favor of other fantasies about why the mind cannot be physical. Charles Taylor had a brilliant takedown in 1985. He argued that it is not the goal of neuroscience to provide an a priori explanation for wants and desires separate from the organisms to which these conditions apply, which is the kind of linguistic game Malcolm was engaged in. The goal of neuroscience, in the context of our debate, is to explain the physical relations between brain states, bodily states, and the external world. As Taylor writes:

We could indeed never show why wanting peanuts is followed by trying to get peanuts, but we could show why this behavior follows [some state] Px; and this contingent nomological regularity would be what underlies our present use of the concept "wanting peanuts."

Once you have those relations, then you can apply conceptual metaphysics like, "Johny wants to eat an apple." And you can take that to mean: the world has produced physical configurations where Johny is thinking very hard about an apple. Maybe even a configuration where Johny is hungry, the apple is the only thing around, etc. Maybe one where Johny saw something, recalled a childhood memory stored in the brain, then started thinking of an apple. You get the idea.

I contend that the predictive capacities of logic and math are entirely explainable by seeing them as emergent properties of human cognition.

By "them" do you mean logic and mathematics themselves of their predictive capacties?
If the latter, then it seems pretty clear that the predictive uses to which human beings put logic and mathematics is a result of human cognitive activity - but that almost sounds trivial. It would also leave unaddressed the question of what the subject matter of logical and mathematical statements actually is. Wayfarer, as far as I understand him, is claiming that their subject matter is non-physical (numbers/sets/relations between them etc).
On the other hand, if by "them" you actually mean logic and mathematics themselves, so that they aren their subject matter are emergent properties of human cognition, that's a bold claim - not a particularly recent one though, it goes by the name of psychologism. I think J.S.Mill is the usual point of reference for that kind of view, although perhaps it is to be found in certain kinds of pragmatist as well. It faces a number of serious difficulties (I'm not saying that they are insurmountable) - Frege and Husserl had a range of arguments against the position. One key difficulty is that psychologism might lead to relativism about truth.

I also don't know if you are aware that this argument has been mercilessly refuted by now,

It lives on under other guises - most attempts to refute philosophical arguments end up being refuted themselves.

I think your opening question is the most important one: can science demonstrate in principle that only physical things exist?

No I don't think it can and I don't think it should try to, nor should that be the standard by which someone can reasonably believe that naturalism is, broadly speaking, the most accurate description of reality. I think a combination of sound theoretical arguments and the "weight of the empirical evidence" is good enough for believing that naturalistic explanations are sufficient to describe what we see, notice, and measure.

I don't think it's inaccurate to say that the canonical versions of the argument from reason, as proposed by Lewis, have been completely refuted. Sure bad arguments resurface in all kinds of different ways. They will never go away entirely. The ontological argument is still going strong in certain theological circles.

I don't think it's inaccurate to say that the canonical versions of the argument from reason, as proposed by Lewis, have been completely refuted

Who refuted it? I know Anscombe went to town on the first version of the argument Lewis presented, but Lewis revised the argument in light of her criticisms. Peter van Inwagen had a crack at the second formulation a few years ago, and as far as I remember claims that Lewis didn't do enough to establish the idea that mechanistic explanations for beliefs exclude rational explanations for them, but I'd be astonished if his was the last word on the subject.

David Johnson had a great takedown:

Naturalism Undefeated: A Refutation of the Argument from Reason

As you implied yourself, there is never a "last word" on any philosophical subject. By "refuted" I mean both that the argument has been shown to be faulty and that its implications are rejected or not accepted by a substantial majority of professional philosophers. This widely cited survey from Chalmers showed that 57% were physicalists about the mind. That number will probably go up as neuroscience makes additional breakthroughs. Granted the survey had methodological problems, but the years spent studying this issue do not give me the impression that the argument holds much currency among professional philosophers.

I've met quite a few professional philosophers, I wouldn't trust their opinions about anything :wink: I'll take a look at that article, thanks for the link.

David Johnson had a great takedown:

Naturalism Undefeated: A Refutation of the Argument from Reason — Uber

That is a good paper - but here is why I wouldn't agree that it amounts to a refutation. At issue is the fact that all of the arguments in such a paper rely on the very faculty which they're trying to rationalise, or to declare as being within the scope of naturalism. Whenever a judgement is made about what is objectively the case, what a neural phenomenon means, and so on, the very faculty which is the subject of the analysis is being utilised to make the case. To provide a completely objective and indeed physical account of the operations of reason, you would have to treat reason from a point that is outside of it; put it aside, so to speak, and then demonstrate that it is inherent in the object of analysis, or located in the objective domain, without appealing to it - otherwise, you're essentially appealing to the thing which needs to be explained, or begging the question. But that, you cannot do.

So I am saying you can't 'get outside' of reason, or treat it as an entirely objective process (which is the subject of a chapter in Nagel's book The Last Word). Indeed I claim that reason is required to determine what is objective, so reason is ontologically prior to objectivity. That is why, as Maritain says, in humans, the sensory faculties are 'permeated with reason'. Even to define naturalism or make such arguments as those in the paper, relies on the very 'ground-consequent relations' which the paper is trying to argue can be explained or understood in naturalistic terms. Every time a conclusion is argued, that Y must be the case because of X and Z, then you're engaging in ground-consequent arguments or syllogisms, which by definition comprise the relationship of ideas.

So, the very fact that we're able to arrive at the generalisations required to frame such arguments, relies on the capacity of abstraction, which in turn relies on the grasp of meaning. And that is epistemologically prior to even defining what 'physicalism' or 'naturalism' comprises.

Aristotle, in De Anima, argued that thinking in general (which includes knowledge as one kind of thinking) cannot be a property of a body; it cannot, as he put it, 'be blended with a body'. This is because in thinking, the intelligible object or form is present in the intellect, and thinking itself is the identification of the intellect with this intelligible. Among other things, this means that you could not think if materialism is true… . Thinking is not something that is, in principle, like sensing or perceiving; this is because thinking is a universalising activity. This is what this means: when you think, you see - mentally see - a form which could not, in principle, be identical with a particular - including a particular neurological element, a circuit, or a state of a circuit, or a synapse, and so on. This is so because the object of thinking is universal, or the mind is operating universally.

….the fact that in thinking, your mind is identical with the form that it thinks, means (for Aristotle and for all Platonists) that since the form 'thought' is detached from matter, 'mind' is immaterial too.

Lloyd Gerson, Platonism vs Naturalism. (Emphasis added.)

Is a physical mental state a contradiction? To truly argue that, you would need to provide your understanding of the word "physical." Have you automatically defined "physical" as everything that exists outside the mind or the brain? — Uber

The definition of the word 'physical' is the domain of the discipline of physics. And as you're no doubt well aware, there are enormous philosophical issues surrounding this very question, many of which arise from the 'nature of the probability wave'.

But, leaving that aside, I have a much more quotidian argument for the distinction of matter and meaning (as this is what is basically at stake). This is based on a form of the multiple realisability argument, although one original to me, as far as I can tell. It is the fact that the same information/proposition/idea can be represented in any number of languages or physical media. I can write out the recipe for chocolate cake, or the specifications for building a box-girder bridge, in any number of languages or codes. I could even invent a completely novel system for representing numbers, provided I made the key available to others. But in both cases, the thing being described, and the outcome of the operation, is identical; you end up with a chocolate cake, or a bridge.

So, the material representation is completely different, but the information is the same. So how can the information be the same as the material representation?

This is where I tend towards dualism. But the crucial caveat is, that mind is *not* a 'substance' in the sense that it is now universally misunderstood. It never appears as an object, but is always that to which everything appears. The profound error of modern philosophy is to reify or objectify mind and then ask what kind of thing it could be. It is simply 'that which grasps meaning', and in that sense the ground of meaning itself. I think from my sketchy knowledge of philosophy generally, the philosopher that I'm nearest to in this regard is Husserl.

I think a combination of sound theoretical arguments and the "weight of the empirical evidence" is good enough for believing that naturalistic explanations are sufficient to describe what we see, notice, and measure. — Uber

The problem with this is that it looses sight of the fundamental concerns of philosophy, as distinct from science. Philosophy is concerned with the human condition and questions of meaning and value; science is a method of analysis of objects and forces. (Incidentally, this does not at all deprecate science, I am an absolute believer in the application of science in its proper domain.) The problem is that philosophical materialists mistake the axiom of methodological naturalism, for a conclusion or an hypothesis - which it is not. This shows up in the 'is/ought problem' which is a constant undercurrent of debates on ethics here.

On the other hand, metaphysics has often flirted with becoming totally detached from empirical reality, depending on who was using it. And that's when you start getting things like angels, Platonic realms, and Jedis. — Uber

No - it is detached from 'the empirical domain', but if you look at the Platonists, they always attempt to ground such arguments in reason (although it's true that some neoplatonism got pretty far out). But that rationalist element is what distinguished Greek philosophy from mysticism pure and simple (although it does have its mystical side.)

Again, the 'realm of natural numbers' is real but it is emphatically *not* an aspect of the empirical domain. But to equate it then with Star Wars does indeed betoken the deep cultural confusion that arises as one of the cultural consequences of empiricism.

People often insist that science is 'rational' - which it is. But it's more than that - it is 'empirico-rational', in that it insists that whatever it is to investigate is knowable in the third person, quantifiable, and demonstrable in public. Empiricist rationalism is to declare that only what is tangible and measurable is real: not what might be rationally compelling, but what can be detected by senses or by instrument. This is the sense in which scientific empiricism is essentially anthropocentric: because it declares the human sensory faculties the yardstick of what is real. As far as the scientist is concerned, he or she is the only detectable intelligence or intentional agent in the Universe (although if you were to believe Dennett even that is questionable.)

Here is good old Lucretius in the Nature of Things: — Uber

I got a high distinction for my essay on Lucretius, back in the day (Philosophy of Matter, under Keith Campbell.)

To provide a completely objective and indeed physical account of the operations of reason, you would have to treat reason from a point that is outside of it.

I'm probably more sympathetic to your position than I am to Uber's - the psychologism that seems to be implied by it gives me pause for one thing - but this remark of yours bothers me a little. Why do you have to operate outside of reason in order to show that reason is amenable to a naturalistic treatment? There seems to be no obvious contradiction in supposing that we can use the tools of reason to investigate what reason is and how it surfaced. I've not seen an argument to say that the only approach to understanding reason is the Kantian one of attempting to delimit its bounds. You might be inclined to think that naturalists are trying to go (surreptitiously) transcendental with reason, but that would take some serious argument.
I suppose there is an issue about burden of proof here. The anti-naturalist seems to think that it is for the naturalist to show that his/her position is not self-refuting in some way, whilst the naturalist seems to think that it is for the anti-naturalist to show that it is self-refuting. I've not seen an argument to show who really has the burden of proof here.

Let me put it this way: exactly what question is being begged if we use the tools of reason to investigate the possibility that reason is a natural phenomenon?
That reasonis a tool that we can use to investigate that reason is a natural phenomenon, presumably.
Well, of course naturalists are assuming this to be the case, but what is wrong with making that assumption as a working hypothesis? It is not as if the opposite claim: reasonis not a tool we can use to investigate that reason is a natural phenomenon, is obviously true.
You might want to argue that if you do make that hypothesis then if you are right and reason is a natural process, it cannot be used to investigate that it is a natural process. But that seems contentious to say the least - the entailment from one to the other would require an argument wouldn't it?

1) Reason is a natural phenomenon.
2) Reason is a tool that can be used to investigate all natural phenomena.
These two propositions are supposed, by the antinaturalist (of a certain kind) to be contradictory in some way I presume, but certainly their surface logical form shows no such contradiction.
Sorry, babbling on a bit here, but I'm trying to get clear exactly what's at stake with this kind of argument against naturalism.

It is the fact that the same information/proposition/idea can be represented in any number of languages or physical media. I can write out the recipe for chocolate cake, or the specifications for building a box-girder bridge, in any number of languages or codes.

So, the material representation is completely different, but the information is the same. So how can the information be the same as the material representation?...This is where I tend towards dualism. — Wayfarer

I very much like Gerson's notion of the incommensurability of form and matter, but I find your use of the term "representation" to be equivocal, and your use of the term "information" to be confused.

Because I associate "mental representation" with semantics, and "material representation" with physical signs, I would re-phrase your conclusion as follows:

The signs (in this case, recipes and specifications encoded in different languages, i.e., physical information) are completely different, but their associated semantic information is the same.

Some of my current relevant working definitions:
1) Signs are empirical (i.e., physical and/or mental) objects (actualities) associated with semantic information.
2) Data (Form): asymmetries.
3) Pure Data (General, Platonic, Form): idea asymmetries.
a) Transcendental Data (General Form): transcendental asymmetries.
b) Universal Data (General Form): universal asymmetries.
4) Empirical Data (Particular, Aristotelian, Form): object asymmetries.
a) Physical Data (Particular Form): physical asymmetries.
b) Mental Data (Particular Form): mental asymmetries.
5) Information (Process Asymmetries): communicated data (form).

And so on, down to semantic, syntactic, and pragmatic data/information as types of mental data/information.

So, your question ("So how can the information be the same as the material representation?") doesn't make sense to me.

I think Gerson is talking about the incommensurability of pure data/information (i.e., universals) which is intelligible, and empirical data/information (i.e., "particular elements") which is matter.

To further confuse things (or not) my current working definition of communication is: pure data (general form) discovery and reaction(s), or empirical data (particular form) production, encoding, transmission, conveyance, reception, decoding, and reaction(s).

So, dualism in terms of separating physical and mental? I don't think so. But dualism in terms of separating reality and existence? Definitely. Maybe it's better to call the latter Platonism?

This is where I tend towards dualism. But the crucial caveat is, that mind is *not* a 'substance' in the sense that it is now universally misunderstood. It never appears as an object, but is always that to which everything appears. The profound error of modern philosophy is to reify or objectify mind and then ask what kind of thing it could be. It is simply 'that which grasps meaning', and in that sense the ground of meaning itself. — Wayfarer

If I define "object" as "actuality", can noumena be called mental objects? I agree that "mind" per se, does not exist, however; as a mass noun, it is the label we attach to the set of conditions experienced, and functions exercised, by an organism which produce its behaviour. So, calling it simply 'that which grasps meaning' is a gross oversimplification (which we can explore in greater detail if you like).