This is an interesting post but, I have to say, kind of frustrating. I have tried to follow the discussions between Esar and RobbBB and your substantial elucidation as well as many other great comments, but I remain kind-of in the dark. Below are some questions which I had, as I read.

This question doesn't feel like it should be very hard.

What question? What exactly is the problem you are purporting to solve, here? If it is, "What is the truth condition of 'If we took the number of apples in each pile, and multiplied those numbers together, we'd get six.'", then doesn't Tarski's disquotation schema give us the answer?

Navigating to the six requires a mixture of physical and logical reference

Not sure why you obscure matters with idiosyncratic metaphors like 'navigating to the six', but never mind. Can we infer from the distinction between logical and physical reference that there is a distinction between logical and physical truth? It appears you countenance the Analytic/Synthetic distinction - precisely the distinction which is usually considered to have undone logical positivism. Do you have a preferred response to Quine's famous argument in 'Two Dogmas of Empiricism', or do you have a reason for thinking you are immune to it? I think you think you aren't doing philosophy, so it doesn't apply, but then I really don't know how to understand what you're saying. If your problems are just computational, then surely you're making matters much harder for yourself than they should be (not that computational problems aren't sometimes very hard).

Next we have to call the stuff on the table 'apples'. But how, oh how can we do this...?

How about by saying "Those are apples"? What exactly is the problem, here?

...when grinding the universe and running it through a sieve will reveal not a single particle of appleness?

Here's my best guess at what is exercising you. You reason that only those properties needed to account for the constitution and behaviour of the smallest parts of matter are real, that being an apple is not among them, and hence that being an apple is not a real property. Assuming this guess is right, what exactly is your reason for accepting the first premise? It is not immediately obvious, though I know there are traditionally different reasons. The reason will inform the adequacy of your answer.

Standard physics uses the same fundamental theory to describe the flight of a Boeing 747 airplane, and collisions in the Relativistic Heavy Ion Collider. Nuclei and airplanes alike, according to our understanding, are obeying special relativity, quantum mechanics, and chromodynamics.

So far so good...

We also use entirely different models to understand the aerodynamics of a 747 and a collision between gold nuclei in the RHIC. A computer modeling the aerodynamics of a 747 may not contain a single token, a single bit of RAM, that represents a quark. (Or a quantum field, really; but you get the idea.)

Nothing controversial here, but it of course has nothing to do with our understanding of the problem. If the understanding is correct, the problem exists regardless of whether anyone or thing ever imagines or represents or refers to apples or anything else. To introduce representations and models into the discussion is only to confuse matters, no?

So is the 747 made of something other than quarks?

Where does this question come from? If my guess about the problem is correct, it is irrelevant. It may be that the property of being a 747 (apple) is not identical to the property of being in any very complicated way composed of quarks, bosons and leptons, even though a given 747 (apple) is made only of these particles. The (philosophical) thesis about properties is different than the scientific thesis about the constitution of physical objects.

No, we're just modeling the 747 with representational elements that do not have a one-to-one correspondence with individual quarks. Similarly with apples.

Please clarify - what precisely does the relation between a computer model of a 747 and a 747 have to do with the metaphysics of properties?

To compare a mental image of high-level apple-objects to physical reality,

Can you say what you mean by this? For myself, this is someting I only ever do very rarely -conjure a mental image, then see how it agrees or differs from what I'm looking at. To be sure, sets of neurons in my brain are being activated all the time by patterns of light hitting my retinas, but there's a lot of explanatory distance to cover to show these (the story about neural events and the story about images) are the same thing. In any case, this seems entirely irrelevant to the present concerns.

for it to be true

Are mental images the sorts of thngs which can be true (in the sense in which a sentence or proposition can be, as opp. merely accurate)? Suppose I have a mental picture of a certain cat on a certain table and that the cat is indeed on the table. Is my mental image true? Even if the cat in my image is the wrong colour? Or is sitting when the cat is standing? As far as I can see this isn't just nit-picking. You have some kind of AI model which involves mental images and which you seem to think needs a semantic theory, and it's just not clear how it all fits together.

...doesn't require that apples be fundamental in physical law.

If my guess is correct, your answer to the problem as far as I can see is something like "The problem is not a problem".

A single discrete element of fundamental physics is not the only thing that a statement can ever be compared-to. We just need truth conditions that categorize the low-level states of the universe, so that different low-level physical states are inside or outside the mental image of "some apples on the table" or alternatively "a kitten on the table".

Can you give an example of a low-level state being 'inside a mental image' of "some apples on the table"? I really don't know what this means.

Having gone through this once, here's a second pass at a gloss. You accept, reasonably, that "That is an apple" is true in English iff that (pointing to a certain apple) is an apple. The referent of the "that" we can take to be a certain object. The question arises, however, as to what the referent or other semantic value is of "is an apple". Plausibly, it is the property of being an apple. But, we may reasonably ask, what sort of thing is being and apple? I understand your answer is as follows:

Just as an individual apple is nothing more than a quite large number of quarks and leptons and bosons interestingly assembled, being an apple is nothing more than being a quite large number of quarks and leptons and bosons assembled in a certain interesting way.

Is this roughly a fair understanding? If so, please consider:

1) You will need to augment your story to include so-called etiology. The property of being a 10-dollar bill is not equivalent to the property of being in a certain way composed of matter - causal origin/history matters, too (perfect counterfeits).

2) The problem of vagueness often seems like a paradigm of philosophical futility but it is a real problem. Suppose you could cross-breed apples and pears, and have a spectrum of individuals ranging from unproblematic apple to unproblematic pear (= non-apple). What will the truth-condition be of the statement 'That is an apple', pointing to the piece of fruit in the middle? Do you give up on bivalence, or do you say that the statement is determinately true or false, but there are deep epistemological problems? Neither answer seems satisfactory, and where you come down may affect your theory.

3) If this story is correct, it will presumably apply to the whole very large hierarchy of properties, ranging from being a quark through being a proton and being a carbon atom up to being an apple and beyond. And the high-level properties will have at a minimum to be disjunctions of lower properties, even to accomodate such mundane facts as the existence of both green and red apples. And you may find ultimately that what is in question is more like a family-resemblance relation among the cases which constitute being an apple (if not apples, then tables and 747s, very likely). And then aren't you in danger simply of laboriously re-capitulating the history of 20th c. philosophical thought on the subject?

This is all philosophy, which you've repeatedly said you aren't interested in doing. But that's what you're doing! If you're just doing AI, you really shouldn't be wasting your time on these questions, surely. Research into neural nets is already making great progress on the question of how we make the discriminations we do. Why isn't that enough for your purposes?

A last thought: there's something of a debate on this site about the value of traditional philosophy. I think it has value, a big part of which is that it encourages people to think carefully and to express themselves precisely. I don't claim always to be as careful or precise as I should be, but these are values. Doing analytic philosophy is some of the best rationality training you can get.

Following the sequence link at the top, I found this similar post, which has an impressive list of references. You include there this paper by Timothy Williamson. It seems to me an oversight you don't mention the paper's argument at all, as it's a sustained critique of the position you're representing.

The basic idea is that the kind of doubts about intuitions you raise are relevantly similar to more familiar forms of philosophical scepticism (scepticism about the external world, etc). I understand Williamson sees a dilemma: either they are mistaken for the same reasons familiar scepticism is mistaken (Williamson's position, to which most of the paper is dedicated), or the doubts undermine way more than its proponents think they do.

It'd be great to hear your summary of the argument there, and what you consider to be its flaw(s).

If you like Williamson, check out also this excellent bit on naturalism.

I think philosophers include some smart people, and they produced some excellent work (some of which might still help us today). I also think philosophy is not a natural class. You would never lump the members of this category together without specific social factors pushing them together. Studying "philosophy" seems unlikely to produce any good results unless you know what to look for.

I have little confidence in your recommendations, because your sole concrete example to date of a philosophical question seems ludicrous. What would change if a neurally embodied belief rather than a sentence (or vice versa) were the "bearer of meaning"? And as a separate question, why should we care?

Your comment carries the assumption that studying the work of experts makes you better at understanding epistemology, and I'm not sure why you think that. Much of philosophy has a poor understanding of epistemology, in my mind. Can you explain why you think reading the work of experts is important for having worthwhile thoughts on epistemology?

I'm saying, "Show me something in particular that I should've looked at, and explain why it matters; I do not respond to non-specific claims that I should've paid more homage to whatever."

Give me an example of a specific thing relevant to constructing an AI which I should have referenced, plus the role it plays in a (self-modifying) AI. Keep in mind that I only care about constructing self-modifying AIs and not about "what is the bearer of truth".

I've read works-not-referenced on "meaning", they just don't seem relevant to anything I care about. Though obviously there's quite a lot of standard work on mathematical proof that I care about (some small amount of which I've referenced).

A criticism - somewhat harsh but hopefully constructive.

As you know, lots of people have written on the subjects of truth and meaning (aside from Tarski). It seems, however, that you don't accord them much importance (no references, failure to consider alternate points of view, apparent lack of awareness of the significance of the matter of what the bearer of truth (sentence, proposition, 'neurally embodied belief') properly is, etc.). I put it to you this is a manifestation of irrationality: you have a known means at your disposal to learn reliably about a subject which is plainly important to you, but you apparently reject it in favour of the more personally satisfying but much less reliable alternative of blogging your own ideas -you willingly choose an inferior path to belief formation. If you want to get a good understanding of such things as truth, reference and mathematical proof, I submit that the rational starting point is to read at least a survey of what experts in the fields have written, and to develop your own thoughts, at least initially, in the context they provide.

I don't understand what single thing, if any, disqualifies them. Tell me if I'm wrong, but I think you would agree they have unique issues, just as "being an empty label" is something that won't be wrong with, say, denying subjective experience.

You made a good point about the inexhaustibility of wrong explanations, which I suppose is true for everything. So I certainly don't ask for anything like a complete list of bad explanations and their problems! But of the other three you mentioned, do they share a problem, or what are their unique problems, or is it too complicated to explain in a comment? Can you explain why the other three are hopeless as well as you did for the first?

I feel a bit like I'm Eliezer expaining the instant failure modes of most AGI research (but not as smart), and that there could be a whole sequence of postings on the instant failure modes of explanations of consciousness.

Well, I don't think I can write those postings, or at least, devote the many days it would take me. Just some brief notes here amplifying the fallacies with examples.

What evidence is there about whether people are working on something correctly, aside from a complete and finished explanation?

A partial and unfinished explanation. But it must go some distance: it must suggest practical experiments and predict their results. (Thought experiments do not count.) Consider the four different fallacies I described by this standard:

1. Empty labels: saying consciousness is "the soul", "a spark of the divine within us", "self-awareness", etc. fails to constrain expectations.

2. Denying the existence of subjective experience: well, we do have it. At least, I do, and I've no reason to suppose I'm exceptional in this. (Those who seriously deny it might be exceptions in the other direction.) So this one has the virtue of constraining expectations but is instantly refuted by observation. It amounts to sticking one's fingers in one's ears and going "la la la can't hear you!" Arguments against the existence of subjective experience (consciousness, qualia, etc.) generally take the form of arguing against other people's arguments in favour. Since no-one has a good account of what it is, it is not difficult to demolish their bad accounts. This is like refuting the phlogiston theory to prove that fire does not exist.

3. In the p-zombie category is Minsky's "society of mind", which gives a hypothetical account of how a system might come to talk to itself about itself in the ways that we do. But how we talk about ourselves and how we feel about ourselves are two different things, and the latter is left unaddressed. Besides, there are plenty of computer systems that talk to themselves about themselves, and we see no reason to attribute consciousness to them. In the form in which Greg Egan expressed the theory in his story "Mr. Volition", consciousness is the piece of brain that does consciousness, just as the cerebellum is the piece of brain that does motor control. This is no better than any other homunculus theory: it is either passing the buck or asserting that we are all philosophical zombies, beings that talk about consciousness without having it.

4. Physical correlates: Neuroscience is always finding more and more physical correlates of mental phenomena, from the fact that gross lesions to various brain locations produce predictable patterns of cognitive impairment, to the results of live brain imaging during task performance. This is compelling evidence that the brain must be either the physical substrate of consciousness or an interface with something else. Neither alternative goes very far. We still don't know how the brain or anything else made of atoms could be a physical substrate for consciousness, however compelling the evidence that it is. Contrast this with the fact that we do know how ever-so-slightly impure silicon can be a substrate for computation. And the brain as an interface to something else fares even worse, as we have no idea what that something else could be. The soul? See (1).

So those are four basic ways in which attempts to explain consciousness can go wrong. I have yet to see an attempt that doesn't fail one or more.

Timothy Bays has a reply to Putnam's alleged proof sufficient to render the latter indecisive, as far as I can see. The set theory is a challenge for me, though.

As for Quine, on the one hand I think he underestimates the kinds of evidence that can bear, and he understates the force of simplicity considerations ("undetached rabbit-parts" could only be loved by a philosopher). But on the other hand, and perhaps more important, he seems right to downplay any remaining "difference" of alternative translations. It's not clear that the choice between workable alternatives is a problem.

Can you say more about how you got that second bullet item?

It's not clear to me that being committed to the idea that mental states can be reduced to smaller components (which is one of the options the OP presented) commits one to stop talking about mental states, or to stop using them in explanations.

I mean, any economist would agree that dollars are not ontologically fundamental, but no economist would conclude thereby that we can't talk about dollars.