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RobbBB comments on Mixed Reference: The Great Reductionist Project - Less Wrong
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I don't see anything wrong with this kind of self-reference. We can only explain what generalizations are by asserting generalizations about generalization; but that doesn't undermine generalization itself. GRT would only be an immediate problem for itself if GRT didn't encompass itself.
Okay, so lets assume that the generalization side of things is not a problem, though I hope you'll grant me that if a generalization about x's is meaningful, propositions expressing x's individually are meaningful. That is, if 'every meaningful proposition can be expressed by physics+logic (eventually)', then 'the proposition "the cat is on the mat" is meaningful' is meaningful. It's this that I'm worried about, and the generalization only indirectly. So:
1) A proposition is meaningful if and only if it is expressible by physics+logic, or merely by logic.
2) If a proposition is expressible by physics+logic, it constrains the possible worlds.
3) If the proposition "the cat is on the mat" is meaningful, and it is expressible by physics+logic, then it constrains the possible worlds.
4) If the proposition "the cat is on the mat" constrains the possible worlds, then the proposition "the proposition 'the cat is on the mat' is meaningful" does not constrain the possible worlds. Namely, no proposition of the form '"XYZ" constrains the possible worlds' itself constrains the possible worlds.
So if 'XYZ' constrains the possible worlds, then for every possible world, XYZ is either true of that world or false of that world. But if the proposition '"XYZ" constrains the possible worlds' expresses simply that, namely that for every possible world XYZ is either true or false of that world, then there is no world of which '"XYZ" constrains the possible worlds' is false.
5) The proposition 'the proposition "the cat is on the mat" is meaningful' is not both meaningful and expressible by physics+logic. But it is meaningful, and therefore (as per premise 1) it is expressible by mere logic.
6) Every generalization about a purely logical claim is itself a purely logical claim (I'm not sure about this premise)
7) The GRT is a purely logical claim.
I'm thinking EY wants to get off the GRT boat here: I don't think he intends the GRT to be a logical axiom or derivable from logical axioms. Nevertheless, if he does want the GRT to be an axiom of logic, and in order for it to be a meaningful axiom of logic, it still has to pick out one logical model as opposed to another.
But here, the problem simply recurs. If 'The proposition 'GRT' is meaningful' is meaningful then it doesn't, in the relevant respect, pick out one logical model as opposed to another.
Does that make sense?
I don't think we need this rule. It would make logical truths / tautologies meaningless, inexpressible, or magical. (We shouldn't dive into Wittgensteinian mysticism that readily.)
That depends on what you mean by "proposition." The written sentence "the cat is on the mat" could have been ungrammatical or semantically null, like "colorless green ideas sleep furiously." After all, a different linguistic community could have existed in the role of the English language. So our semantic assertion could be ruling out worlds where "the cat is on the mat" is ill-formed.
On the other hand, if by "proposition" you mean "the specific meaning of a sentence," then your sentence is really saying "the meaning of 'the cat is on the mat' is a meaning," which is just a special case of the tautology "meanings are meanings." So if we aren't committed to deeming tautologies meaningless in the first place, we won't be committed to deeming this particular tautology meaningless.
This looks like a problem of self-reference, but it's really a problem of essence-selection. When we identify something as 'the same thing' across multiple models or possible worlds, we're stipulating an 'essence,' a set of properties providing identity-conditions for an object. Without such a stipulation, we couldn't (per Leibniz's law) identify objects as being 'the same' while they vary in temporal, spatial, or other properties. If we don't include the specific meaning of a sentence in its essence, then we can allow that the 'same' sentence could have had a different meaning, i.e., that there are models in which sentence P does not express the semantic content 'Q.' But if we instead treat the meaning of P as part of what makes a sentence in a given model P, then it is contradictory to allow the possibility that P would lack the meaning 'Q,' just as it would be contradictory to allow the possibility that P could have existed without P existing.
What's important to keep in mind is that which of these cases arises is a matter of our decision. It's not a deep metaphysical truth that some essences are 'right' and some are 'wrong;' our interests and computational constraints are all that force us to think in terms of essential and inessential properties at all.
Only because you've stipulated that meaningfulness is essential to GRT (and to propositions in general). This isn't a spooky problem; you could have generated the same problem by claiming that 'all cats are mammals' fails to constrain the possible worlds, on the grounds that cats are essentially mammals, i.e., in all worlds if x is a non-mammal then we immediately know it's a non-cat (among other things). Someone with a different definition of 'cat,' or of 'GRT,' would have arrived at a different conclusion. But we can't just say willy-nilly that all truths are essentially true; otherwise the only possible world will be the actual world, perhaps a plausible claim metaphysically but not at all a plausible claim epistemically. (And real possibility is epistemic, not metaphysical.)
Also, 'GRT' is not in any case logically true; certainly it is not an axiom, and there is no reason to treat it as one.
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.