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Esar comments on Mixed Reference: The Great Reductionist Project - Less Wrong
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No, I didn't say that constraining possible worlds is a necessary condition on meaning. I said this:
This leaves open the possibility of meaningful, non-world-constraining propositions (e.g. tautologies, such as the claims of logic), only they are not physics+logic expressible, but only logic expressible.
That's not relevant to my point. I'd be happy to replace it with any proposition we can agree (for the sake of argument) to be meaningful. In fact, my argument will run with an unmeaningful proposition (if such a thing can be said to exist) as well.
No, this isn't what I mean. By 'proposition' I mean a sentence, considered independently of its particular manifestation in a language. For example, 'Schnee ist weiss' and 'Snow is white' express the same proposition. Saying and writing 'shnee ist weiss' express the same proposition.
I didn't understand this. Propositions (as opposed to things which express propositions) are not "in" worlds, and nothing of my argument involved identifying anything across multiple worlds. EY's OP stated that in order for an [empirical] claim to be meaningful, it has to constrain possible worlds, e.g. distinguish those worlds in which it is true from those in which it is false. Since a statement about the meaningfulness of propositions doesn't do this (i.e. it's a priori true or false of all possible worlds), it cannot be an empirical claim.
So I haven't said anything about essence, nor does any part of my argument require reference to essence.
Agreed, it is not a merely logical claim. Given that it is also not an empirical (i.e. a physics+logic claim), and given my premise (1), which I take EY to hold, then we can conclude that the GRT is meaningless.
My mistake. When you said "physics+logic," I thought you were talking about expressing propositions in general with physics and/or logic (as opposed to reducing everything to logic), rather than talking about mixed-reference assertions in particular (as opposed to 'pure' logic). I think you'll need to explain what you mean by "logic"; Eliezer's notion of mixed reference allows that some statements are just physics, without any logical constructs added.
What 'Schnee ist weiss' and 'Snow is white' have in common is their meaning, their sense. A proposition is the specific meaning of a declarative sentence, i.e., what it declares.
Then they don't exist. By 'the world' I simply mean 'everything that is,' and by 'possible world' I just mean 'how everything-that-is could have been.' The representational content of assertions (i.e., their propositions), even if they somehow exist outside the physical world, still have to be related in particular ways to our utterances, and those relations can vary across physical worlds even if propositions (construed non-physically) cannot. The utterance 'the cat is on the mat' in our world expresses the proposition <the cat is on the mat>. But in other worlds, 'the cat is on the mat' could have expressed a different proposition, or no proposition at all. Now let's revisit your (4):
A clearer way to put this is: If the proposition p, <the cat is on the mat>, varies in truth-value across possible worlds, then the distinct proposition q, <p is meaningful>, does not vary in truth-value across possible worlds. But what does it mean to say that a proposition is meaningful? Propositions just are the meaning of assertions. There is no such thing as a 'meaningless proposition.' So we can rephrase q as really saying: <p exists>. In other words, you are claiming that all propositions exist necessarily, that they exist at (or relative to) every possible world, though their truth-value may or may not vary from world to world. Once we analyze away the claim that propositions are 'meaningful' as really just the claim that certain propositions/meanings exist, do you still have any objections or concerns?
(Also, it should be obvious to anyone who thinks that 'possible worlds' are mere constructs that do not ultimately exist, that 'propositions' are also mere constructs in the same way. We can choose to interrelate these two constructs in various ways, but if we endorse physicalism we can also reason using one while holding constant the fact that the other doesn't exist.)
No, GRT is an empirical claim. You defined GRT as the proposition <everything meaningful can be expressed by [physics+logic] eventually>. But the actual Great Reductive Thesis says: <everything true can be expressed by [physics+logic] eventually>. Everything true is meaningful, so your formulation is part of GRT; but it isn't the whole thing. An equivalent way to formulate GRT is as the conjunction of the following two theses:
Both 1 and 2 are empirical claims; we could imagine worlds where either one is false, or where both are. But we may have good reason to suspect that we do not inhabit such a world, because there are no inexpressible truths and no irreducibly neither-physical-nor-logical truths. For example, we could have lived in a world in which qualia were real and inexpressible (which would violate Expressibility), and/or one in which they were real and irreducible (which would violate Logico-Physicalism). But the physicalistically inclined doubt that there are such qualia in our universe.
We have a couple of easy issues to get out of the way. The first is the use of the term 'proposition'. That term is famously ambiguous, and so I'm not attached to using it in one way or another, if I can make myself understood. I'm just trying to use this term (and all my terms) as EY is using them. In this case, I took my cue from this: http://lesswrong.com/lw/eqn/the_useful_idea_of_truth/
EY does not seem to intend 'proposition' here to be identical to 'meaning'. At any rate, I'm happy to use whatever term you like, though I wish to discuss the bearers of truth value, and not meanings.
I don't want to define the GRT at all. I'm using EY's definition, from the OP:
You might want to disagree with EY about this, but for the purposes of my argument I just want to talk about EY's conception of the GRT. Nevertheless, I think EY's conception, and therefore mine, follows from yours, so it may not matter much as long as you accept that everything false should also be expressible by physics+logic (as EY, I believe, wants to maintain).
I'd like to get these two issues out of the way before responding to the rest of your interesting post. Let me know what you think.
Eliezer is not very attentive to the distinction between propositions, sentences (or sentence-types), and utterances (or sentence-tokens). We need not import that ambiguity; it's already caused problems twice, above. An utterance is a specific, spatiotemporally located communication. Two different utterances may be the same sentence if they are expressed in the same way, and they intend the same proposition if they express the same meaning. So:
A) 'Schnee ist weiss.' B) 'Snow is white.' C) 'Snow is white.'
There are three utterances above, two distinct sentences (or sentence-types), and only one distinct proposition/meaning. Clearer?
EY misspoke. As with the proposition/utterance confusion, my interest is in evaluating the substantive merits or dismerits of an Eliezer steel man, not in fixating on his overly lax word choice. Reductionism is falsified if they are true sentences that cannot be reduced, not just if there are meaningful but false ones that cannot be so reduced. It's obvious that EY isn't concerned with the reducibility of false sentences because he doesn't consider it a grave threat, for example, that the sentence "Some properties are not reducible to physics or logic." is meaningful.
Which one is the proper object of truth-evaluation, and which one is subject to the question 'is it meaningful'? EY's position throughout this sequence, I think, has been that whichever is the proper object of truth-evaluation is also the one about which we can ask 'is it meaningful?' If you don't think these can be the same, then your view differs from EY's substantially, and not just in terminology. How about this? I'll use the term 'gax' for the thing that is a) properly truth-evaluable, and b) subject to the question 'is this meaningful'.
Maybe, but the entire sequence is about the question of a criterion for the meaningfulness of gaxes. His motivation may well be to avert the disaster of considering a true gax to be meaningless, but his stated goal throughout the sequence is establishing a criterion for meaningfulness. So I guess I have to ask at this point: other than the fact that you think his argument stands stronger with your version of the GRT, do you have any evidence (stronger than his explicit statement otherwise) that this is EY's actual view?
The proposition/meaning is what we evaluate for truth. Thus utterances sharing the same proposition cannot differ in truth-value.
Utterances or utterance-types can be evaluated for meaningfulness. To ask 'Is that utterance meaningful?' is equivalent to asking, for apparent declarative sentences, 'Does that utterance correspond to a proposition/meaning?'
You could ask whether sentence-types or -tokens intend propositions (i.e., 'are they meaningful?'), and, if they do intend propositions, whether they are true (i.e., whether the propositions correspond to an obtaining fact). But, judging by how Eliezer uses the word 'proposition,' he doesn't have a specific stance on what we should be evaluating for truth or meaningfulness. He's speaking loosely.
I think the sequence is about truth, not meaning. He takes meaning largely for granted, in order to discuss truth-conditions for different classes of sentence. He gave a couple of hints at ways to determine that some utterance is meaningless, but he hasn't at all gone into the meta-semantic project of establishing how utterances acquire their content or how content in the brain gets 'glued' (reference magnetism) to propositions with well-defined truth-conditions. He hasn't said anything about what sorts of objects can and can't be meaningful, or about the meaning of non-assertive utterances, or about how we could design an A.I. with intentionality (cf. the Chinese room), or about what in the world non-empirical statements denote. So I take it that he's mostly interested in truth here, and meaning is just one of the stepping stones in that direction. Hence I don't take his talk of 'propositions' too seriously.
It would be a waste of effort to dig other evidence up. Ascribing your version of GRT to Eliezer requires us to theorize that he didn't spend 30 seconds thinking about GRT, since 30 seconds is all it would take to determine its falsehood. If that version of GRT is his view, then his view can be dismissed immediately and we can move on to more interesting topics. If my version of GRT is closer to his view, then we can continue to discuss whether the balance of evidence supports it. So regardless of EY's actual views, it's pointless to dwell on the Most Absurd Possible Interpretation thereof, especially since not a single one of his claims elsewhere in the sequence depends on or supports the claim that all irreducibly non-physical and non-logical claims are meaningless.
Okay, it doesn't look like we can make any progress here, since we cannot agree on what EY's stance is supposed to be. I think you're wrong that EY hasn't said much about the problem of meaning in this sequence. That's been its explicit and continuous subject. The question throughout has been
...and this seems to have been discussed throughout, e.g.:
But if you've been reading the same sequence I have, and we still don't agree on that, then we should probably move on. That said...
I'd be interested to know what you have in mind here. Why would the 'meaningfulness' version of the GRT be so easy to dismiss?
I want, first, to be clear that I've found this conversation very helpful and interesting (as all my conversations with you have been). Second, the above is unfair: understanding EY in terms of what he explicitly and literally says is not 'the most absurd possible interpretation'. It may be the wrong interpretation, but to take him at face value cannot be called absurd.
The colloquial meaning of "proposition" is "an assertion or proposal". The simplest explanation for EY's use of the term is that he was oscillating somewhat between this colloquial sense and its stricter philosophical meaning, "the truth-functional aspect of an assertion". A statement's philosophical proposition is (or is isomorphic to) its meaning, especially inasmuch as its meaning bears on its truth-conditions.
Confusion arose because EY spoke of 'meaningless' propositions in the colloquial sense, i.e., meaningless linguistic utterances of a seemingly assertive form. If we misinterpret this as asserting the existence of meaningless propositions in the philosophical sense, then we suddenly lose track of what a 'proposition' even is.
The intuitive idea of a proposition is that it's what different sentences that share a meaning have in common; treating propositions as the locus of truth-evaluation allows us to rule out any doubt as to whether "Schnee ist weiss." and "Snow is white." could have different truth-values while having identical meanings. But if we assert that there are also propositions corresponding to meaningless locutions, or that some propositions are non-truth-functional, then it ceases to be clear what is or isn't a 'proposition,' and the term entirely loses its theoretical value. Since Eliezer has made no unequivocal assertion about there being meaningless propositions in the philosophical sense, the simpler and more charitable interpretation is that he was just speaking loosely and informally.
My sense is that he's spent a little too much time immersed in positivistic culture, and has borrowed their way of speaking to an extent, even though he rejects and complicates most of their doctrines (e.g., allowing that empirically untestable doctrines can be meaningful). This makes it a little harder to grasp his meaning and purpose at times, but it doesn't weaken his doctrines, charitably construed.
I just have higher standards than you do for what it takes to be giving a complete account of meaning, as opposed to a complete account of 'truth'. My claim is not that Eliezer has said nothing about meaning; it's that he's only touched on meaning to get a better grasp on truth (or on warranted assertion in general), which is why he hasn't been as careful about distinguishing and unpacking metasemantic distinctions such as utterance-vs.-proposition as he has been about distinguishing and unpacking semantic and metaphysical distinctions such as physical-vs.-logical.
As I said above, "Some properties are not reducible to physics or logic." is a meaningful statement that is incompatible with the GRT world-view. It is meaningful, though it may be false; if the denial of GRT were meaningless, then GRT would be a tautology, and Eliezer would assign it Pr approaching 1, whereas in fact he assigns it Pr .5.
Eliezer's claim has not been, for example, that epiphenomenalism, being anti-physicalistic, is gibberish; his claim has been that it is false, and that no evidence can be given in support of it. If he thought it were gibberish, then his rejection of it would count as gibberish too.
It's not the most absurd interpretation in that it has the least evidence as an interpretation. It's the most absurd inasmuch as it ascribes a maximally absurd (because internally inconsistent) world-view to EY, i.e., the world-view that the negation of reductionism is both meaningless and (with probability .5) true. Again, the simplest explanation is simply that he was speaking loosely, and when he said "everything meaningful can be expressed this way eventually" he meant "everything expressible that is the case can be expressed this way [i.e., physically-and-logically] eventually". He was, in other words, tacitly restricting his domain to truths, and hoping his readership would recognize that falsehoods are being bracketed. Otherwise this post would be about arguing for the meaninglessness of doctrines like epiphenomenalism and theism, rather than arguing for the reducibility of unorthodox truths (e.g., counterfactuals and applied/'worldly' mathematics).
Rob, you are better at being EY than EY is.
So we're assuming for the purposes of your argument here that the GRT is about meaningfulness, and we should distinguish this from your (and perhaps EY's) considered view of the GRT. So lets call the 'meaningfulness' version I attributed to EY GRTm, and the one you attribute to him GRTt.
We can gloss the difference thusly: the GRTt states that anything true must be expressible in physical+logical, or merely logical terms (tautologies, etc.).
The GRTm states that anything true or false must be expressible physical+logical, or merely logical terms.
Your argument appears to be that on the GRTm view, the sentence "some properties are not reducible to physics or logic" would be meaningless rather than false. You take this to be a reductio, because that sentence is clearly meaningful and false. Why do you think that, on the GRTm, this sentence would be meaningless? The GRTm view, along with the GRTt view, allows that false statements can be meaningful. And I see no reason to think that the above sentence couldn't be expressed in physics+logic, or merely logical terms.
So I'm not seeing the force of the reductio. You don't argue for the claim that "some properties are not reducible to physics or logic" would be meaningless on the GRTm view, so could you go into some more detail there?
One way to get at what I was saying above is that GRTt asserts that all true statements are analyzable into truth-conditions that are purely physical/logical, while GRTm asserts that all meaningful statements are analyzable into truth-conditions that are purely physical/logical. If we analyze "Some properties are not reducible to physics or logic." into physical/logical truth-conditions, we find that there is no state we can describe on which it is true; so it becomes a logical falsehood, a statement that is false given the empty set of assumptions. Equally, GRTm, if meaningful, is a tautology if we analyze its meaning in terms of its logico-physically expressible truth-conditions; there is no particular state of affairs we can describe in logico-physical terms in which GRTm is false.
But perhaps focusing on analysis into truth-conditions isn't the right approach. Shifting to your conception of GRTm and GRTt, can you find any points where Eliezer argues for GRTm? An argument for GRTm might have the following structure:
On the other hand, if Eliezer is really trying to endorse GRTt, his arguments will instead look like this:
Notice that the latter argumentative approach is the one he takes in this very article, where he introduces 'The Great Reductionist Project.' This gives us strong reason to favor GRTt as an interpretation over GRTm, even though viewed in isolation some of his language does suggest GRTm. Is there any dialectical evidence in favor of the alternative interpretation GRTm? (I.e., evidence derived from the structure of his arguments.)