Either the Great Reductionist Thesis (“everything meaningful can be expressed by [physics+logic] eventually”) is itself expressible with physics+logic (eventually) or it isn’t. If it is, then it might be true.
If it isn’t, then the great reductionist thesis is not true, because the proposition it expresses is not meaningful. I’m worried about this possibility because the phrase ‘everything meaningful’ strikes me as dangerously self-referential.
Let me first say that I am grateful to Esar and RobbBB for having this discussion, and double-grateful to RobbBB for steelmanning my arguments in a very proper and reasonable fashion, especially considering that I was in fact careless in talking about “meaningful propositions” when I should’ve remembered that a proposition, as a term of art in philosophy, is held to be a meaning-bearer by definition.
I’m also sorry about that “is meaningless is false” phrase, which I’m certain was a typo (and a very UNFORTUNATE typo) - I’m not quite sure what I meant by it originally, but I’m guessing it was supposed to be “is meaningless or false”, though in the context of the larger debate now that I’ve read it, I would just say “colorless green ideas sleep furiously” is “meaningless” rather than false. In a strict sense, meaningless utterances aren’t propositions so they can’t be false. In a looser sense, an utterance like “Maybe we’re living in an inconsistent set of axioms!” might be impossible to render coherent under strict standards of meaning, while also being colloquially called ‘false’ meaning ‘not actually true’ or ‘mistaken’.
I’m coming at this from a rather different angle than a lot of existing philosophy, so let me do my best to clarify. First, I would like to distinguish the questions:
R1) What sort of things can be real?
R2) What thoughts do we want an AI to be able to represent, given that we’re not certain about R1?
A (subjectively uncertain probabilistic) answer to R1 may be something like, “I’m guessing that only causal universes can be real, but they can be continuous rather than discrete, and in that sense aren’t limited to mathematical models containing a finite number of elements, like finite Life boards.”
The answer to R2 may be something like, “However, since I’m not sure about R1, I would also like my AI to be able to represent the possibility of a universe with Time-Turners, even though, in this case, the AI would have to use some generalization of causal reference to refer to the things around it, since it wouldn’t live in a universe that runs on Pearl-style causal links.”
In the standard sense of philosophy, question R2 is probably the one about ‘meaning’ or which assertions can be ‘meaningful’, although actually the amount of philosophy done around this is so voluminous I’m not sure there is a standard sense of ‘meaning’. Philosophers sometimes try to get mileage out of claiming things are ‘conceivable’, e.g., the philosophical catastrophe of the supposed conceivability of P-zombies, and I would emphasize even at this level that we’re not trying to get R1-mileage out of things being in R2. For example, there’s no rule following from anything we’ve said so far that an R2-meaningful statement must be R1-possible, and to be particular and specific, wanting to conservatively build an AI that can represent Conway’s Game of Life + Time-Turners, still allows us to say things like, “But really, a universe like that might be impossible in some basic sense, wihch is why we don’t live there—to speak of our possibly living there may even have some deeply buried incoherence relative to the real rules for how things really have to work—but since I don’t know this to be true, as a matter of my own mere mental state, I want my AI to be able to represent the possibility of time-travel.” We might also imagine that a non-logically-omniscient AI needs to have an R2 which can contain inconsistent axiom sets the AI doesn’t know to be inconsistent.
For things to be in R2, we want to show how a self-modifying AI could carry out its functions while having such a representation, which includes, in particular, being able to build an offspring with similar representations, while being able to keep track of the correspondence between those offspring’s quoted representations and reality. For example, in the traditional version of P-zombies, there’s a problem with ‘if that was true, how could you possibly know it?’ or ‘How can you believe your offspring’s representation is conjugate to that part of reality, when there’s no way for it to maintain a correspondence using causal references?’ This is the problem of a SNEEZE_VAR in the Matrix where we can’t talk about whether its value is 0 or 1 because we have no way to make “0” or “1″ refer to one binary state rather than the other.
Since the problems of R2 are the AI-conjugates of problems of reference, designation, maintainance of a coherent correspondence, etcetera, they fall within the realm of problems that I think traditional philosophy considers to be problems of meaning.
I would say that in human philosophy there should be a third issue R3 which arises from our dual desire to:
Not do that awful thing wherein somebody claims that only causal universes can be real and therefore your hypotheses about Time-Turners are meaningless noises.
Not do that awful thing wherein somebody claims that since P-zombies are “conceivable” we can know a priori that consciousness is a non-physical property.
In other words, we want to avoid the twin errors of (1) preemptively shooting down somebody who is making an honest effort to talk to us by claiming that all their words are meaningless noises, and (2) trying to extract info about reality just by virtue of having an utterance admitted into a debate, turning a given inch into a taken mile.
This leads me to think that human philosophers should also have a third category R3:
R3) What sort of utterances can we argue about in English?
which would roughly represent what sort of things ‘feel meaningful’ to a flawed human brain, including things like P-zombies or “I say that God can make a rock so heavy He can’t lift it, and then He can lift it!”—admitting something into R3 doesn’t mean it’s logically possible, coherent, or ‘conceivable’ in some rigorous sense that you could then extract mileage from, it just means that we can go on having a conversation about it for a while longer.
When somebody comes to us with the P-zombie story, and claims that it’s “conceivable” and they know this on account of their brain feeling able to conceive it, we want to reply, “That’s what I would call ‘arguable’ (R3) and if you try to treat your intuitions about arguability as data, they’re only directly data about which English sentences human brains can affirm. If you want to establish any stronger sense of coherence that you could get mileage from, such as coherence or logical possibility or reference-ability, you’ll have to argue that separately from your brain’s direct access to the mere affirmability of a mere English utterance.”
At the same time, you’re not shoving them away from the table like you would “colorless green ideas sleep up without clam any”; you’re actually going to have a conversation about P-zombies, even though you think that in stricter senses of meaning like R2, the conversation is not just false but meaningless. After all, you could’ve been wrong about that nonmembership-in-R2 part, and they might be about to explain that to you.
The Great Reductionist Thesis is about R1 - the question of what is actually real—but it’s difficult to have something that lies in a reductionist’s concept of a strict R2, turn out to be real, such that the Great Reductionist Thesis is falsified. For example, if we think R1 is about causal universes, and then it turns out we’re in Timetravel Life, the Great Reductionist Thesis has been confirmed, because Timetravel Life still has a formal logical description. Just about anything I can imagine making a Turing-computable AI refer to will, if real, confirm the Great Reductionist Thesis.
So is GRT philosophically vacuous from being philosophically unfalsifiable? No: to take an extreme case, suppose we have an uncomputable and non-logically-axiomatizable sensus divinatus enabling us to directly know God’s existence, and by baptizing an AI we could give it this sensus divinatus in some way integrated into the rest of its mind, meaning that R2, R1, and our own universe all include things referrable-to only by a sensus divinatus. Then arguable utterances along the lines of, “Some things are inherently mysterious”, would have turned out, not just to be in R2, but to actually be true; and the Great Reductionist Thesis would be false—contrary to my current belief that such utterances are not only colloquially false, but even meaningless for strict senses of meaning. But one is not licensed to conclude anything from my having allowed a sensus divinatus to be a brief topic of conversation, for by that I am not committing to admitting that it was strictly meaningful under strong criteria such as might be proposed for R2, but only that it stayed in R3 long enough for a human brain to say some informal English sentences about it.
Does this mean that GRT itself is merely arguable—that it talks about an argument which is only in R3? But tautologies can be meaningful in GRT, since logic is within “physics + logic”. It looks to me like a completed theory of R2 should be something like a logical description of a class of universes and a class of representations corresponding to them, which would itself be in R2 as pure math; and the theory-of-R1 “Reality falls within this class of universes” could then be physically true. However, many informal ‘negations’ of R2 like “What about a sensus divinatus?” will only be ‘arguable’ in a human R3, rather than themselves being in R2 (as one would expect!).
R3) “What sort of utterances can we argue about in English?” is (perhaps deliberately) vague. We can argue about colorless green ideas, if nothing else at the linguistic level. Perhaps R3 is not about meaning, but about debate etiquette: What are the minimum standards for an assertion to be taken seriously as an assertion (i.e., not as a question, interjection, imperative, glossolalia, etc.). In that case, we may want to break R3 down into a number of sub-questions, since in different contexts there will be different standards for the admissibility of an argument.
I’m not sure what exactly a sensus divinatus is, or why it wouldn’t be axiomatizable. Perhaps it would help flesh out the Great Reductionist Thesis if we evaluated which of these phenomena, if any, would violate it:
Objective fuzziness. I.e., there are entities that, at the ultimate level, possess properties vaguely; perhaps even some that exist vaguely, that fall in different points on a continuum from being to non-being.
Ineffable properties, i.e., ones that simply cannot be expressed in any language. The specific way redness feels to me, for instance, might be a candidate for logico-physical inexpressibility; I can perhaps ostend the state, but any description of that state will underdetermine the precise feeling.
Objective inconsistencies, i.e., dialetheism. Certain forms of perspectivism, which relativize all truths to an observer, might also yield inconsistencies of this sort. Note that it is a stronger claim to assert dialetheism (an R1-type claim) than to merely allow that reasoning non-explosively with apparent contradictions can be very useful (an R2-type claim, affirming paraconsistent logics).
Nihilism. There isn’t anything.
Eliminativism about logic, intentionality, or computation. Our universe lacks logical structure; basic operators like ‘and’ and ‘all’ and ‘not’ do not carve at the joints. Alternatively, the possibility of reference is somehow denied; AIs cannot represent, period. This is perhaps a stronger version of 2, on which everything, in spite of its seeming orderliness, is in some fashion ineffable.
Are these compatible with GRT? What else that we can clearly articulate would be incompatible? What about a model that is completely expressible in classical logic, but that isn’t ontologically ‘made of logic,’ or of physics? I intuit that a classically modelable universe that metaphysically consists entirely of mind-stuff (no physics-stuff) would be a rather severe break from the spirit of reductive physicalism. But perhaps you intended GRT to be a much more modest and accommodating claim than everyday scientific materialism.
I have no objection to your description of R3 - basically it’s there so that (a) we don’t think that something not immediately obviously being in R2 means we have to kick it off the table, and (b) so that when somebody claims their imagination is giving them veridical access to something, we can describe the thing accessed as membership in R3, which in turn is (and should be) too vague for anything else to be concluded thereby; you shouldn’t be able to get info about reality merely by observing that you can affirm English utterances.
Insofar as your GRT violations all seem to me to be in R3 and not R2 (i.e., I cannot yet coherently imagine a state of affairs that would make them true), I’m mostly willing to agree that reality actually being that way would falsify GRT and my proposed R2. Unless you pick one of them and describe what you mean by it more exactly—what exactly it would be like for a universe to be like that, how we could tell if it were true—in which case it’s entirely possible that this new version will end up in the logic-and-physics R2, and for similar reasons, wouldn’t falsify GRT if true. E.g., a version of “nihilism” that is cashed out as “there is no ontologically fundamental reality-fluid”, denial of “reference” in which there is no ontologically basic descriptiveness, eliminativism about “logic” which still corresponds to a computable causal process, “relativized” descriptions along the lines of Special Relativity, and so on.
This isn’t meant to sneak reductionism in sideways into universes with genuinely ineffable magic composed of irreducible fundamental mental entities with no formal effective description in logic as we know it. Rather, it reflects the idea that even in an intuitive sense, sufficiently effable magic tends toward science, and since our own brains are in fact computable, attempts to cash out the ineffable in greater detail tend to turn it effable. The traditional First-Cause ontologically-basic R3 “God” falsifies reductionism; but if you redefine God as a Lord of the Matrix, let alone as ‘natural selection’, or ‘the way things are’, it doesn’t. An irreducible soul falsifies GRT, until I interrogate you on exactly how that soul works and what it’s made of and why there’s still such a thing as brain damage, in which case my interrogation may cause you to adjust your claim and adjust it some more and finally end up in R2 (or even end up with a pattern theory of identity). It should also be noted that while the adjective “effable” is in R2, the adjective “ineffable” may quite possibly be in R3 only (can you exhibit an ineffable thing?)
I intuit that a classically modelable universe that metaphysically consists entirely of mind-stuff (no physics-stuff)
What does it mean to consist entirely of mind-stuff when all the actual structure of your universe is logical? What is the way things could be that would make that true, and how could we tell? This utterance is not yet clearly in my R2, which doesn’t have anything in it to describe “metaphysically consists of’”. (Would you consider “The substance of the cracker becomes the flesh of Christ while its accidents remain the same” to be in your equivalent of R2, or only in your equivalent of R3?)
Expressibility. Everything (or anything) that is the case can in principle be fully expressed or otherwise represented. In other words, an AI is constructible-in-principle that could model every fact, everything that is so. Computational power and access-to-the-data could limit such an AI’s knowledge of reality, but basic effability could not.
Classical Expressibility. Everything (or anything) that is the case can in principle be fully expressed in classical logic. In addition to objective ineffability, we also rule out objective fuzziness, inconsistency, or ‘gaps’ in the World. (Perhaps we rule them out empirically; we may not be able to imagine a world where there is objective indeterminacy, but we at least intuit that our world doesn’t look like whatever such a world would look like.)
Logical Physicalism. The representational content of every true sentence can in principle be exhaustively expressed in terms very similar to contemporary physics and classical logic.
Originally I thought that your Great Reductionist Thesis was a conjunction of 1 and 3, or of 2 and 3. But your recent answers suggest to me that for you GRT may simply be Expressibility (1). Irreducibly unclassical truths are ruled out, not by GRT, but by the fact that we don’t seem to need to give up principles like Non-Contradiction and Tertium Non Datur in order to Speak Every Truth. And mentalistic or supernatural truths are excluded only insofar as they violate Expressibility or just appear empirically unnecessary.
If so, then we should be very careful to distinguish your confidence in Expressibility from your confidence in physicalism. Neither, as I formulated them above, implies the other. And there may be good reason to endorse both views, provided we can give more precise content to ‘terms very similar to contemporary physics and classical logic.’ Perhaps the easiest way to give some meat to physicalism would be to do so negatively: List all the clusters that do seem to violate the spirit of physicalism. For instance:
mental (perspectival, ‘subjective,’ qualia-laden...) facts that cannot be fully expressed in non-mental terms.
otherwise anthropocentric (social, cultural, linguistic...) facts that cannot be fully expressed in non-anthropocentric terms.
spatiotemporal events without spatiotemporal causes
spatiotemporal events without spatiotemporal effects
abstract (non-spatiotemporal) objects that have causes
abstract objects that have effects
(perhaps) ineffable properties or circumstances
A list like this would give us some warning signs that a view, even if logically specifiable, may be deviating sharply from the scientific project. If you precisely stipulated in logical terms how Magic works, for instance, but its mechanism was extremely anthropocentric (e.g., requiring that Latin-language phonemes ‘carve at the joints’ of fundamental reality), that would seem to violate something very important about reductive physicalism, even if it doesn’t violate Expressibility (i.e., we could program an AI to model magical laws of this sort).
What does it mean to consist entirely of mind-stuff when all the actual structure of your universe is
logical?
I’m not sure what you mean by ‘actual structure.’ I would distinguish the Tegmark-style thesis ‘the universe is metaphysically made of logic-stuff’ from the more modest thesis ‘the universe is exhaustively describable using purely logical terms.’ If we learned that all the properties of billiard balls and natural numbers are equally specifiable in set-theoretic terms, I think we would still have at least a little more reason to think that numbers are sets than to think that billiard balls are sets.
So suppose we found a way to axiomatize ‘x being from the perspective of y,’ i.e., a thought and its thinker. If we (somehow) learned that all facts are ultimately and irreducibly perspectival (i.e., they all need an observer-term to be saturated), that might not contradict the expressibility thesis, but I think it would violate the spirit of physicalism.
(Would you consider “The substance of the cracker becomes the flesh of Christ while its accidents remain the same” to be in your equivalent of R2, or only in your equivalent of R3?)
I’m not sure. I doubt our universe has ‘substance-accident’ structure, but there might be some negative way to R2ify transubstantiation, even if (like epiphenomenalism or events-outside-the-observable-universe) it falls short of verifiability. Could we coherently model our universe as a byproduct of a cellular automaton, while lacking a way to test this model? If so, then perhaps we could model ‘substance-properties’ as unobservables that are similarly Behind The Scenes, but are otherwise structurally the same as accidents (i.e., observables).
So… in my world, transubstantiation isn’t in R2, because I can’t coherently conceive of what a substance is, apart from accidents. For a similar reason, I don’t yet have R2-language for talking about a universe being metaphysically made of anything. I mean, I can say in R3 that perhaps physics is made of cheese, just like I can say that the natural numbers are made of cheese, but I can’t R2-imagine a coherent state of affairs like that. A similar objection applies to a logical universe which is allegedly made out of mental stuff. I don’t know how to imagine a logically structured universe being made ofanything.
Having Latin-language phonemes carve at the joints of fundamental reality seems very hard, because in my world Latin-language phonemes are already reduced—there’s already sequential sound-patterns making them up, and the obvious way to have a logic describing the physics of such a world is to have complex specifications of the phonemes which are ‘carving at the joints’. It’s not totally clear to me how to make this complex thing a fundamental instead, though perhaps it could be managed via a logic containing enough special symbols—but to actually figure out how to write out that logic, you would have to use your own neuron-composed brain in which phonemes are not fundamental.
I do agree that—if it were possibly to rule out the Matrix, I mean, if spells not only work but the incantation is “Stupefy” then I know perfectly well someone’s playing an S-day prank on me—that finding magic work would be a strong hint that the whole framework is wrong. If we actually find that prayers work, then pragmatically speaking, we’ve received a hint that maybe we should shut up and listen to what the most empirically powerful priests have to say about this whole “reductionism” business. (I mean, that’s basically why we’re listening to Science.) But that kind of meta-level “no, you were just wrong, shut up and listen to the spiritualist” is something you’d only execute in response to actually seeing magic, not in response to somebody hypothesizing magic. Our ability to hypothesize certain situations that would pragmatically speaking imply we were probably wrong about what was meaningful, doesn’t mean we’re probably wrong about what’s meaningful. More along the lines of, “Somebody said something you thought was in R3(only), but they generated predictions from it and those predictions came true so better rethink your reasons for thinking it couldn’t go in R2.”
With all that said, it seems to me that R3-possibilities falsifying 1, 2, or (a generalization of 3 to other effectively or formally specified physics (e.g. Time-Turners)), and with the proviso that we’re dealing in second-order logic rather than classical first-order logic, all seem to me to pretty much falsify the Great Reductionist Thesis. Some of your potential examples look to me like they’re not in my R2 (e.g. mental facts that can’t be expressed in non-mental terms) though I’m perfectly willing to discuss them colloquially in R3, and others seem relatively harmless (effects which aren’t further causes of anything? I could write a computer program like that). I am hard-pressed to R2-meaningfully describe a state of affairs that falsifies R1, though I can talk about it in R3.
I have an overall agenda of trying to think like reality which says that I want my R1 to look as much like the universe as possible, and it’s okay to contemplate restrictions which might narrow my R2 a lot relative to someone’s R3, e.g. to say, “I can’t seem to really conceive of a universe with fundamentally mental things anymore, and that’s a triumph”. So a lot of what looked to me years ago like meaningful non-reductionism, now seems more like meaningless non-reductionism relative to my new stricter conceptions of meaning—and that’s okay because I’m trying to think less like a human and more like reality.
So… in my world, transubstantiation isn’t in R2, because I can’t coherently conceive of what a substance is, apart from accidents.
Many mathematicians, scientists, and philosophers believe in things they call ‘sets.’ They believe in sets partly because of the ‘unreasonable effectiveness’ of set theory, partly because they help simplify some of our theories, and partly because of set theory’s sheer intuitiveness. But I have yet to hear anyone explain to me what it means for one non-spatiotemporal object to ‘be an element of’ another. Inasmuch as set theory is not gibberish, we understand it not through causal contact or experiential acquaintance with sets, but by exploring the theoretical role these undefined ‘set’ thingies overall play (assisted, perhaps, by some analogical reasoning).
‘Substance’ and ‘accident’ are antiquated names for a very commonly accepted distinction: Between objects and properties. (Warning: This is an oversimplification. See The Warp and Woof of Metaphysics for the historical account.) Just as the efficacy of mathematics tempts people into reifying the set-member distinction, the efficacy of propositional calculus (or, more generally, of human language!) tempts people into reifying the subject-predicate distinction. The objects (or ‘substances’) are whatever we’re quantifying over, whatever individual(s) are in our domain of discourse, whatever it is that predicates are predicated of; the properties are whatever it is that’s being predicated.
And we don’t need to grant that it’s possible for there to be an object with no properties (∃x(∀P(¬P(x)))), or a completely uninstantiated property (∃P(∀x(¬P(x)))). But once we introduce the distinction, Christians are free to try to exploit it to make sense of their doctrines. If set theory had existed in the Middle Ages, you can be sure that there would have been attempts to explicate the Trinity in set-theoretic terms; but the silliness of such efforts would not necessarily have bled over into delegitimizing set theory itself.
That said, I sympathize with your bafflement. I’m not committed to taking set-membership or property-bearing completely seriously. I just don’t think ‘I can’t imagine what a substance would be like!’ is an adequate argument all on its own. I’m not sure I have a clear grasp on what it means for a set to have an element, or what it means for a number line to be dense and uncountable, or what it means for my left foot to be a complexly-valued amplitude; but in all these cases we can gain at least a little understanding, even from initially undefined terms, based on the theoretical work they do. Since we rely so heavily on such theories, I’m much more hesitant to weigh in on their meaninglessness than on their evidential justification.
I don’t yet have R2-language for talking about a universe being metaphysically made of anything.
You sound like a structural realist. On this view, as I understand it, we don’t have reason to think that our conceptions straightforwardly map reality, but we do have reason to think that a relatively simple and uniform transformation on our map would yield a pattern in the territory.
it seems to me that R3-possibilities falsifying 1, 2, or (a generalization of 3 to other effectively or formally specified physics (e.g. Time-Turners)), and with the proviso that we’re dealing in second-order logic rather than classical first-order logic, all seem to me to pretty much falsify the Great Reductionist Thesis.
So is this a fair characterization of the Great Reductionist Thesis?: “Anything that is the case can in principle be exhaustively expressed in classical second-order predicate logic, relying only on predicates of conventional mathematics (identity, set membership) and of a modestly enriched version of contemporary physics.”
We could then elaborate on what we mean by ‘modest enrichment’ if someone found a good way to add Thoroughly Spooky Doctrines (dualism, idealism, traditional theism, nihilism, trivialism, ineffable whatsits, etc.) into our language. Ideally, we would do this as un-ad-hocily as possible.
I think we both agree that ‘meaning’ won’t ultimately carve at the joints. So it’s OK if R2 and R3 look a bit ugly; we may be eliding some important distinctions when we speak simply of a ‘meaningful vs. meaningless’ binary. It’s certainly my own experience that I can incompletely grasp a term’s meaning, and that this is benign provided that the aspects I haven’t grasped are irrelevant to what I’m reasoning about.
Can I run something by you? An argument occurred to me today that seems suspect, but I don’t know what I’m getting wrong. The conclusion of the argument is that GRTt entails GRTm. For the purposes of this argument, GRTt is the statement that all true statements have a physico-logical expression (meaning physical, logical, or physical+logical expression). GRTm is the statement that all true and all false statements have a physico-logical expression.
P1) All true statements have a physico-logical expression. (GRTt)
P2) The negation of any false statement is true.
P3) If a statement has a physico-logical expression, its negation has a physico-logical expression.
P4) All false statements have a physico-logical expression.
C) All true and all false statements have a physical-logical expression. (GRTm)
So for example, suppose XYZ is false, and has no physico-logical expression. If XYZ is false, then ~XYZ is true. By GRTt, ~XYZ has a physico-logical expression. But if ~XYZ has a physico-logical expression, then ~(~XYZ), or XYZ, does. Throwing a negation in front of a statement can’t change the nature of the statement qua reducible.
I think your argument works. But I can’t accept GRTm; so I’ll have to ditch GRTt. In its place, I’ll give analyzing GRT another go; call this new formulation GRTd:
‘Every true statement can be deductively derived from the set of purely physical and logical truths combined with statements of the semantics of the non-physical and non-logical terms.’
This is quite unlike (and no longer implies) GRTm, ‘Every meaningful statement is expressible in purely physical and logical terms.’
The problem for GRTt was that statements like ‘there are no gods’ and ‘there are no ghosts’ seem to be true, but cast in non-physical terms; so either they are reducible to physical terms (in which case both GRTt and GRTm are true), or irreducible (in which case both GRTt and GRTm are false). For GRTd, it’s OK if ‘there are no ghosts’ can’t be analyzed into strictly physical terms, provided that ‘there are no ghosts’ is entailed by a statement of what ‘ghost’ means plus all the purely physical and logical truths.
For example, if part of what ‘ghost’ means is ‘something non-physical,’ then ‘there are no ghosts’ will be derivable from a complete physical description of the world provided that such a description includes a physical/logical totality fact. You list everything that exists, then add the totality fact ‘nothing except the above entities exists;’ since the semantic of ‘ghost’ ensures that ‘ghost’ is not identical to anything on the physicalism list, we can then derive that there are no ghosts.
Note that the semantic ‘bridge laws’ are themselves entailed by (and, in all likelihood, analyzable into) purely physical facts about the brains of English language speakers.
Well done, I like GRTd especially in that it pulls free of reference to expressibility and meaningfulness. My only worry at the moment is the totality fact, partly because of what I take EY to want from the GRT in reference to R1. I take it we will agree right off that the totality fact can’t follow from having listed all the physico-logical facts. Otherwise we could derive ‘there are no ghosts’ right now, just given the meaning of ‘ghost’. But we need the answer to the question posed by R1 to be (in every case which doesn’t involve a purely logical contradiction) an empirical answer. What we want to say about ghosts is not that they’re impossible, but that their existence is extremely unlikely given the set of physico-logical facts we do have. We won’t ever have opportunity to deploy a totality fact (since this requires omniscience, it seems), but it seems like an important part of the expression of the GRTd.
But if we can’t get the totality fact just from having listed all the physico-logical facts, and if the totality fact must itself be a physico-logical fact then I have a hard time seeing how we can deduce from physico-logical omniscience that there are no ghosts. In order to deduce the non-existence of ghosts, we’d need first to deduce the totality fact (since this is a premise in the former deduction), but if the totality fact is not deducible from all the physico-logical facts, then in order to deduce it, it looks like we need ‘there are no ghosts’ as a premise. But then our deduction of ‘there are no ghosts’ begs the question.
Unless I’m missing something, it seems to me that the totality fact has to end up being deducible from all the physico-logical facts if deductions which employ it are to be valid. But this again makes the GRTd (specifically that part of it which describes the totality fact) an a priori claim, which we’re trying to avoid especially because it means that GRTd is not an answer to R1 (which is what EY, at least, is looking for).
The totality fact could take a number of different forms. For instance, ‘Everything is a set, a spacetime region, a boson, or a fermion’ would suffice, if our semantics for ‘ghost’ made it clear that ghosts are none of those things. This is why we don’t need omniscient access to every object to formulate the fact; all we need is a plausibly finished set of general physical categories. If ‘physical’ and ‘logical’ are themselves well-defined term in our physics, we could even formulate the totality fact simply as: ‘Everything is physical or logical.’
Another, more modest totality-style fact would be: ‘The physical is causally closed.’ This weaker version won’t let us derive ‘there are no ghosts,’ but it will let us derive ‘ghosts, if real, have no causal effect on the physical,’ which is presumably what we’re most interested in anyway.
GRTd itself doesn’t force you to accept totality facts (also known as Porky Pig facts). But if you reject these strange facts, then you’ll end up needing either to affirm GRTm too, or needing to find some way to express negative existential facts about Spooky Things in your pristine physical/logical language. All three of these approaches have their costs, but I think GRTd is the most modest option, since it doesn’t commit us to any serious speculation about the limits of semantics or translatability.
I take it we will agree right off that the totality fact can’t follow from having listed all the physico-logical facts.
I think the totality fact is a physical (or ‘mixed’) fact. Intuitively, it’s a fact about our world that it doesn’t ‘keep going’ past a certain point.
it seems to me that the totality fact has to end up being deducible from all the physico-logical facts if deductions which employ it are to be valid
The totality fact can’t be strictly deduced from any other fact. In all cases these totality facts are empirical inferences from the apparent ability of our physical predicates to account for everything. Inasmuch as we are confident that (category-wise) ‘That’s all, folks,’ we are confident in there being no more categories, and hence (if only implicitly) in there being no Spooky addenda.
Notice this doesn’t commit us to saying that we can meaningfully talk about Spooky nonphysical entities. All it commits us to is the claim that if we can meaningfully posit such entities, then we should reject them with at least as much confidence as we affirm the totality fact.
So, I like GRTd, insofar as it captures both what is so plausible about physicalism, and insofar as the ‘totality fact’ expresses an important kind of empirical inference: from even a small subset of all the physico-logical facts, we can get a good general picture of how the universe works, and what kinds of things are real.
I still have questions about the GRTd as a principle however. I don’t see how the following three statements are consistant with one another:
S1) GRTd: ‘Every true statement can be deductively derived from the set of purely physical and logical truths combined with statements of the semantics of the non-physical and non-logical terms.’
S2) The totality fact is true.
S3) ‘The totality fact can’t be strictly deduced from any other fact.’
One of these three has to go, and I strongly suspect I’ve misunderstood S3. So my question is this: Given all the physical and logical facts, combined with statements of the semantics of any non-physical and non-logical terms one might care to make use of, do you think we could deduce the totality fact?
The totality fact is one of the physical/logical facts, and can be expressed in purely physical/logical terms. For instance, in a toy universe where the only properties were P (‘being a particle’) and C (‘being a spacetime point’), the totality fact would have the form ∀x(P(x) ∨ C(x)) to exclude other categories of entity. A more complete totality fact would exclude bonus particles and spacetime points too, by asserting ∀x(x=a ∨ x=b ∨ x=c...), where {a,b,c...} is the (perhaps transfinitely large) set of particles and points. You can also express the same idea using existential quantification.
S1, S2, and S3 are all correct, provided that the totality fact is purely physical and logical. (Obviously, any physical/logical fact follows trivially from the set of all physical/logical facts.) GRTd says nothing about which, if any, physical/logical facts are derivable from a proper subset of the physical/logical. (It also says nothing about whether there are non-physicological truths; it only denies that, if there are some, their truth or falsehood can fail to rest entirely on the physical/logical facts.)
A single giant totality fact would do the job, but you could also replace it (or introduce redundancy) by positing a large number of smaller totality facts. Suppose you want to define a simple classical universe in which a 2x2x2-inch cube exists. You can quantify over a specific 2x2x2-inch region of space, and assert that each of the points within the interval is occupied. But that only posits an object that’s at least that large; we also need to define the empty space around it, to give it a definite border. A totality fact (or a small army of them) could give you the requisite border, establishing ‘there’s no more cube’ in the same way that the Giant Totality Fact establishes ‘there’s no more reality.’ But if you get a kick out of parsimony or concision, you don’t need to do this again and again for each new bounded object you posit. Instead, you can stick to positive assertions until the very end, and then clean up after yourself with the Giant Totality Fact. That there’s no more reality than what you’ve described, after all, implies (among other things) that there’s no more cube.
(Obviously, any physical/logical fact follows trivially from the set of all physical/logical facts.)
Ah, I took GRTd to mean that ‘every true statement (including all physical and logical truths) can be deductively derived from the set of purely physical and logical truths (excluding the one to be derived)...’.Thus, if the totality fact is true, then it should be derivable from the set of all physico-logical facts (excluding the totality fact). Is that right, or have I misunderstood GRTd?
I may, I think, just be overestimating what it takes to plausibly posit the totality fact: i.e. you may just mean that we can have a lot of confidence in the totality fact just by having as broad and coherent a view of the universe as we actually do right now. The totality fact may be false, but its supported in general by the predictive power of our theories and an apparent lack of spooky phenomena. If we had all the physico-logical facts, we could be super duper confident in the totality fact, as confident as we are about anything. It would by no means follow deductively from the set of all physico-logical facts, but it’s not that sort of claim anyway. Is that right?
The edit is fine. Let me add that ‘the’ totality fact may be a misleading locution. Nearly every model that can be analyzed factwise contains its own totality fact, and which model we’re in will change what the ‘totality’ is, hence what the shape of the totality fact is.
We can be confident that there is at least one fact of this sort in reality, simply because trivialism is false. But GRTd does constrain what that fact will have to look like: It will have to be purely logical and physical, and/or derivable from the purely logical and physical truths. (And the only thing we could derive a Big Totality Fact from would be other, smaller totality facts like ‘there’s no more square,’ plus a second-order totality fact.)
I didn’t intend for you to read ‘(excluding the one to be derived)’ into the statement. The GRTd I had in mind is a lot more modest, and allows for totality facts and a richer variety of causal relations.
GRTd isn’t a tautology (unless GRTm is true), because if there are logically underivable nonphysical and nonlogical truths, then GRTd is false. ‘X can be derived from the conjunction of GRTd with X’ is a tautology, but an innocuous one, since it leaves open the possibility that ‘X’ on its lonesome is a garden-variety contingent fact.
What could it mean for a ghost to exist but be nonphysical?
I think that what you think are counterexamples to GRTm are a large number of things which, examined carefully, would end up in R3-only, and not in R2.
I furthermore note that you just rejected GRTt, which sounds scarily like concluding that actual non-reductionist things exist, because you didn’t want to accept the conclusion that talk of non-physical ghosts might fail strict qualifications of meaning. How could you possibly get there from here? How could your thoughts about what’s meaningful, entail that the laws of physics must be other than what we’d previously observed them to be? Shouldn’t reaching that conclusion require like a particle accelerator or something?
Alternatively, perhaps your rejection of GRTt isn’t intended to entail that non-reductionist things exist. If so, can you construe a narrower version of GRTt which just says that, y’know, non-reductionist thingies don’t exist? And then would Esar’s argument not go through for this version?
I think Esar’s argument mainly runs into trouble when you want to call R3-statements ‘false’, in which case their negations are colloquially true but in R3-only because there’s no strictly coherent and meaningful (R2) way to describe what doesn’t exist (i.e. non-physical ghosts). If your desire to apply this language demands that you consider these R3-statements meaningful, then you should reject GRTm, I suppose—though not because you disagree with me about what stricter standards entail, but because you want the word “meaningful” to apply to looser standards. However, getting from there to rejecting R1 is a severe problem—though from the description, it’s possible you don’t mean by GRTt what I mean by R1. I am a bit worried that you might want ‘non-physical ghosts don’t exist’ to be true, hence meaningful, hence its negation to also be meaningful, hence a proposition, hence there to be some state of affairs that could correspond to non-physical ghosts existing, hence for the universe to not be shaped like my R1. Which would be a very strange conclusion to reach starting from the premise that it’s ‘true’ that ‘ghosts do not exist’.
you just rejected GRTt, which sounds scarily like concluding that actual non-reductionist things exist
To reject GRTt is to affirm: “Some truths are not expressible in physical-and/or-logical terms.” Does that imply that irreducibly nonphysical things exist? I don’t quite see why. My initial thought is this: I am much more confident that physicalism is true than that nonphysicalism is inexpressible or meaningless. But if this physicalism I have such faith in entails that nonphysicalism is inexpressible, then either I should be vastly more confident that nonphysicalism is meaningless, or vastly less confident that physicalism is true, or else GRTt does not capture the intuitively very plausible heart of physicalism. Maybe GRTt and GRTm are correct; but that would take a lot of careful argumentation to demonstrate, and I don’t want to hold physicalism itself hostage to GRTm. I don’t want a disproof of GRTm to overturn the entire project of reductive physicalism; the project does not hang on so thin a thread. So GRTd is just my new attempt to articulate why our broadly naturalistic, broadly scientific world-view isn’t wholly predicated on our confidence in the meaninglessness of the assertions of the Other Side.
This dispute is over whether, in a physical universe, we can make sense of anyone even being able to talk about anything non-physical. Four issues complicate any quick attempts to affirm GRTm:
1) Meaning itself is presumably nonfundamental. Without a clear understanding of exactly what is neurologically involved when a brain makes what we call ‘representations,’ attempts to weigh in on what can and can’t be meaningful will be somewhat speculative. And since meaning is nonfundamental, truth is also nonfundamental, is really an anthropological and linguistic category more than a metaphysical one; so sacrificing GRTt may not be as devastating as it initially seems.
2) ‘Logical pinpointing’ complicates our theory of reference. Numbers are abstracted from observed regularities, but we never come into causal contact with numbers themselves; yet we seem to be able to talk about them. So if there is some way to abstract away from physicality itself, perhaps ‘ghost’ could be an example of such abstraction (albeit of a less benign form than ‘number’). The possibility doesn’t seem totally crazy to me.
3) It remains very unclear exactly what work is being done by ‘physical’ (and, for that matter, ‘logical’) in our formulations of GRT. This is especially problematic because it doesn’t matter. We can define ‘physical’ however we please, and then it will be much easier to work out whether we can talk about anything nonphysical.
One worry is that if we can’t speak of anything nonphysical, then the term ‘physical’ itself risks falling into meaninglessness. GRTd doesn’t face this problem, and allows us to take the intuitive route of simply asserting the falsehood of anti-physicalisms; it lets us do what we originally wanted with ‘physicalism,’ which was to sift out the excessively Spooky doctrines at the outset. In contrast, it’s not clear what useful work ‘physicalism’ is doing if we follow the GRTm approach. If GRTm’s physicalism is a doctrine at all, it’s a very strange (and perhaps tautologous) one.
4) Traditionally, there’s been a split between positivists who wanted to reduce everything to logical constructs plus first-person experience, and positivists who wanted to reduce everything to logical constructs plus third-person physical science. I personally find the latter approach more plausible, though I understand the post-Cartesian appeal of Russell’s phenomenalist project. But it troubles me to see the two sides insisting, with equal vehemance, that the other side is not only mistaken but speaking gibberish. Even as an eliminative physicalist and an Enemy of Qualia, I find it plausible that we have some (perhaps fundamentally mistaken) concept of a difference between experiences (which are ‘from a vantage point’) and objective events (which lack any ‘point-of-view’ structure). If there’s anything genuinely under dispute between the first-person camp and the third-person camp, then this provides a simple example of why GRTt is false: Simply for grammatical reasons, there are falsehoods (indexicals, perhaps) that cannot be perfectly expressed in physical terms. That doesn’t mean that we can’t physicalistically describe why and how someone came to assert P; it just means we can’t assert P ourselves in our stripped-down fundamental language.
Perhaps this is a more palatable way to put it: We can explain in purely physical and logical terms why every false sentence is false. But there is no one-to-one correspondence between false non-fundamental assertions and false fundamental assertions. Rather, in cases like ‘there are no gods’ and ‘there are no ghosts,’ there is a many-to-one relationship, since all statements of those sorts are made true by the conjunction of all the physical and logical truths (including the totality fact). But it’s implausible to treat this Gigantic Fact as the physical meaning or final analysis of falsehoods like ‘I have experienced redness-qualia.’
there’s no strictly coherent and meaningful (R2) way to describe what doesn’t exist (i.e. non-physical ghosts)
That seems like too strong of a statement. Surely we can express falsehoods (including false existential generalizations) in our finished physical/logical language. We can describe situations and objects that don’t exist. The question is just whether the descriptive elements our sparse language utilizes will be up to the task of constructing every meaningful predicate (and in a way that allows our language to assert the predication, not just to describe the act of someone else asserting it). So far, that seems to me to be more open to doubt than does garden-variety physicalism.
The need for a totality fact is reminiscent of the beginning of Wittgenstein’s Tractatus,
1 The world is everything that is the case.
1.1 The world is the totality of facts, not of things.
1.11 The world is determined by the facts, and by these being all the facts.
1.12 For the totality of facts determines both what is the case, and also all that is not the case.
It is interesting how the same (or at least analogous) problems, arguments and concerns reappear in successive iterations of the Great Reductionist Project.
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.
2) If a proposition is expressible by physics+logic, it constrains the possible worlds.
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.)
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.
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.
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.
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.
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.
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.
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.)
No, I didn’t say that constraining possible worlds is a necessary condition on meaning. I said this:
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.
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 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.”
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.
On the other hand, if by “proposition” you mean “the specific meaning of a sentence,”
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.
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...
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.
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.
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.
On the other hand, if by “proposition” you mean “the specific meaning of a sentence,”
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.
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.
I didn’t understand this. Propositions (as opposed to things which express propositions) are not “in” worlds
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 . 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):
“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.”
A clearer way to put this is: If the proposition p, , varies in truth-value across possible worlds, then the distinct proposition q,
, 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:
. 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.)
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.
No, GRT is an empirical claim. You defined GRT as the proposition . But the actual Great Reductive Thesis says: . 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:
Expressibility: All propositions that are true in our world can be expressed by utterances in our world.
Logico-Physicalism: Every proposition that is true in our world is either purely physical-and/or-logical, or can be completely analyzed into a true proposition that is purely physical-and/or-logical.
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/
Meditation: What rule could restrict our beliefs to just propositions that can be meaningful, without excluding a priori anything that could in principle be true?
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.
You defined GRT as the proposition . But the actual Great Reductive Thesis says: .
I don’t want to define the GRT at all. I’m using EY’s definition, from the OP:
And the Great Reductionist Thesis can be seen as the proposition that everything meaningful can be expressed this way eventually.
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?
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.
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.
There are three utterances above, two distinct sentences (or sentence-types), and only one distinct proposition/meaning. Clearer?
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’.
EY misspoke.
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?
Which one is the proper object of truth-evaluation
The proposition/meaning is what we evaluate for truth. Thus utterances sharing the same proposition cannot differ in truth-value.
and which one is subject to the question ‘is it meaningful’?
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?’
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?’
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.
the entire sequence is about the question of a criterion for the meaningfulness of gaxes (in his words).
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.
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?
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.
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.
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
What rule would restrict our beliefs to just statements that can be meaningful, without excluding a priori anything that could in principle be true?
...and this seems to have been discussed throughout, e.g.:
Being able to imagine that your thoughts are meaningful and that a correspondence between map and territory is being maintained, is no guarantee that your thoughts are true. On the other hand, if you can’t even imagine within your own model how a piece of your map could have a traceable correspondence to the territory, that is a very bad sign for the belief being meaningful, let alone true. Checking to see whether you can imagine a belief being meaningful is a test which will occasionally throw out bad beliefs, though it is no guarantee of a belief being good.
Okay, but what about the idea that it should be meaningful to talk about whether or not a spaceship continues to exist after it travels over the cosmological horizon? Doesn’t this theory of meaningfulness seem to claim that you can only sensibly imagine something that makes a difference to your sensory experiences?
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...
If that version of GRT is his view, then his view can be dismissed immediately and we can move on to more interesting topics.
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?
it’s pointless to dwell on the Most Absurd Possible Interpretation thereof
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.
But if you’ve been reading the same sequence I have, and we still don’t agree on that
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.
Why would the ‘meaningfulness’ version of the GRT be so easy to dismiss?
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.
understanding EY in terms of what he explicitly and literally says is not ‘the most absurd possible interpretation’.
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).
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.
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:
Some sentences seem to assert non-physical, non-logical things.
But the non-physicologicality of those things makes those sentences meaningless.
So non-physicologicality in general probably makes statements meaningless.
On the other hand, if Eliezer is really trying to endorse GRTt, his arguments will instead look like this:
Some sentences seem to be true but non-physicological.
But those sentences are either false or analyzable/reducible to purely physicological truths.
So non-physicological truths in general are probably expressible purely physicologically.
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.)
In your latest sequence article, you described the great reductionist thesis as “the proposition that everything meaningful can be expressed this way [i.e. physics and/or logic] eventually.”
Another LWer and I are in a debate over your intention here. One of us thinks that you must mean “everything true (and not necessarily everything false) can be expressed this way”
The other thinks you mean “everything true and everything false (i.e. everything meaningful) can be expressed this way”.
Can you clear this up for us?
EY replied:
Everything true and most meaningful false statements can be expressed this way. Sufficiently confused verbal statements may have no translation, even as a set of logical axioms possessing no model, yet still be operable as slogans. I.e. “Like all members of my tribe, I firmly believe that clams up without no finger inside plus plus claims in the clams without no finger!”
So I replied:
So, just to be super clear (since I’m now losing this argument) you mean that there are statements that are both meaningful and false, but are not expressible in the terms you describe in Logical Pinpointing, Causal Reference, and Mixed Reference?
And he said:
Nope. That statement is meaningless is false.
So I’m actually not much less confused. His first reply seems to support GRTt. His second reply (the first word of it anyway) seems to support GRTm. Thoughts?
Thanks for taking the time to hunt down the facts!
I think “Everything true and most meaningful false statements can be expressed this way.” is almost completely clear. Unless a person is being deliberately ambiguous, saying “most P are Q” in ordinary English conversation has the implicature “some P aren’t Q.”
I’m not even clear on what the grammar of “That statement is meaningless is false.” is, much less the meaning, so I can’t comment on that statement. I’m also not clear on how broad “the terms you describe in Logical Pinpointing, Causal Reference, and Mixed Reference” are; he may think that he’s sketched meaningfulness criteria somewhere in those articles that are more inclusive than “The Great Reductionist Project” itself allows.
I’m also not clear on how broad “the terms you describe in Logical Pinpointing, Causal Reference, and Mixed Reference” are; he may think that he’s sketched meaningfulness criteria somewhere in those articles that are more inclusive than “The Great Reductionist Project” itself allows.
I think that was fairly clear. Each of those articles is explicitly about a form of reference sentences can have: logical, physical, or logicophysical, and his statement of the GRT was just that all meaningful (or in your reading, true) things can be expressed in these ways.
But it occurs to me that we can file something away, and tomorrow I’m going to read over your last three or four replies and think about the GRTt whether or not it’s EY’s view. That is, we can agree that the GRTm view is not a tenable thesis as we understand it.
One possible source of confusion: What is the meaning of the qualifier “physical”? “Physical,” “causal,” “verifiable,” and “taboo-able/analyzable” all have different senses, and it’s possible that for some of them Eliezer is more willing to allow meaningful falsehoods than for others.
Yeah. I’ll re-read his posts, too. In all likelihood I didn’t even think about the ambiguity of some of his statements, because I was interpreting everything in light of my pet theory that he subscribes to GRTt. I think he does subscribe to GRTt, but I may have missed some important positivistic views of his if I was only focusing on the project of his he likes. Some of the statements you cited where he discusses ‘meaning’ do create a tension with GRTt.
You’d just about convinced me, until I reread the OP and found it consistently and unequivocally discussing the question of meaningfulness. So before we go on, I’m just going to PM Eliezer and ask him what he meant. I’ll let you know what he says if he replies.
Either the Great Reductionist Thesis (“everything meaningful can be expressed by [physics+logic] eventually”) is itself expressible with physics+logic (eventually) or it isn’t. If it is, then it might be true.
If it isn’t, then the great reductionist thesis is not true, because the proposition it expresses is not meaningful. I’m worried about this possibility because the phrase ‘everything meaningful’ strikes me as dangerously self-referential.
This is a reply to the long conversation below between Esar and RobbBB.
Let me first say that I am grateful to Esar and RobbBB for having this discussion, and double-grateful to RobbBB for steelmanning my arguments in a very proper and reasonable fashion, especially considering that I was in fact careless in talking about “meaningful propositions” when I should’ve remembered that a proposition, as a term of art in philosophy, is held to be a meaning-bearer by definition.
I’m also sorry about that “is meaningless is false” phrase, which I’m certain was a typo (and a very UNFORTUNATE typo) - I’m not quite sure what I meant by it originally, but I’m guessing it was supposed to be “is meaningless or false”, though in the context of the larger debate now that I’ve read it, I would just say “colorless green ideas sleep furiously” is “meaningless” rather than false. In a strict sense, meaningless utterances aren’t propositions so they can’t be false. In a looser sense, an utterance like “Maybe we’re living in an inconsistent set of axioms!” might be impossible to render coherent under strict standards of meaning, while also being colloquially called ‘false’ meaning ‘not actually true’ or ‘mistaken’.
I’m coming at this from a rather different angle than a lot of existing philosophy, so let me do my best to clarify. First, I would like to distinguish the questions:
R1) What sort of things can be real?
R2) What thoughts do we want an AI to be able to represent, given that we’re not certain about R1?
A (subjectively uncertain probabilistic) answer to R1 may be something like, “I’m guessing that only causal universes can be real, but they can be continuous rather than discrete, and in that sense aren’t limited to mathematical models containing a finite number of elements, like finite Life boards.”
The answer to R2 may be something like, “However, since I’m not sure about R1, I would also like my AI to be able to represent the possibility of a universe with Time-Turners, even though, in this case, the AI would have to use some generalization of causal reference to refer to the things around it, since it wouldn’t live in a universe that runs on Pearl-style causal links.”
In the standard sense of philosophy, question R2 is probably the one about ‘meaning’ or which assertions can be ‘meaningful’, although actually the amount of philosophy done around this is so voluminous I’m not sure there is a standard sense of ‘meaning’. Philosophers sometimes try to get mileage out of claiming things are ‘conceivable’, e.g., the philosophical catastrophe of the supposed conceivability of P-zombies, and I would emphasize even at this level that we’re not trying to get R1-mileage out of things being in R2. For example, there’s no rule following from anything we’ve said so far that an R2-meaningful statement must be R1-possible, and to be particular and specific, wanting to conservatively build an AI that can represent Conway’s Game of Life + Time-Turners, still allows us to say things like, “But really, a universe like that might be impossible in some basic sense, wihch is why we don’t live there—to speak of our possibly living there may even have some deeply buried incoherence relative to the real rules for how things really have to work—but since I don’t know this to be true, as a matter of my own mere mental state, I want my AI to be able to represent the possibility of time-travel.” We might also imagine that a non-logically-omniscient AI needs to have an R2 which can contain inconsistent axiom sets the AI doesn’t know to be inconsistent.
For things to be in R2, we want to show how a self-modifying AI could carry out its functions while having such a representation, which includes, in particular, being able to build an offspring with similar representations, while being able to keep track of the correspondence between those offspring’s quoted representations and reality. For example, in the traditional version of P-zombies, there’s a problem with ‘if that was true, how could you possibly know it?’ or ‘How can you believe your offspring’s representation is conjugate to that part of reality, when there’s no way for it to maintain a correspondence using causal references?’ This is the problem of a SNEEZE_VAR in the Matrix where we can’t talk about whether its value is 0 or 1 because we have no way to make “0” or “1″ refer to one binary state rather than the other.
Since the problems of R2 are the AI-conjugates of problems of reference, designation, maintainance of a coherent correspondence, etcetera, they fall within the realm of problems that I think traditional philosophy considers to be problems of meaning.
I would say that in human philosophy there should be a third issue R3 which arises from our dual desire to:
Not do that awful thing wherein somebody claims that only causal universes can be real and therefore your hypotheses about Time-Turners are meaningless noises.
Not do that awful thing wherein somebody claims that since P-zombies are “conceivable” we can know a priori that consciousness is a non-physical property.
In other words, we want to avoid the twin errors of (1) preemptively shooting down somebody who is making an honest effort to talk to us by claiming that all their words are meaningless noises, and (2) trying to extract info about reality just by virtue of having an utterance admitted into a debate, turning a given inch into a taken mile.
This leads me to think that human philosophers should also have a third category R3:
R3) What sort of utterances can we argue about in English?
which would roughly represent what sort of things ‘feel meaningful’ to a flawed human brain, including things like P-zombies or “I say that God can make a rock so heavy He can’t lift it, and then He can lift it!”—admitting something into R3 doesn’t mean it’s logically possible, coherent, or ‘conceivable’ in some rigorous sense that you could then extract mileage from, it just means that we can go on having a conversation about it for a while longer.
When somebody comes to us with the P-zombie story, and claims that it’s “conceivable” and they know this on account of their brain feeling able to conceive it, we want to reply, “That’s what I would call ‘arguable’ (R3) and if you try to treat your intuitions about arguability as data, they’re only directly data about which English sentences human brains can affirm. If you want to establish any stronger sense of coherence that you could get mileage from, such as coherence or logical possibility or reference-ability, you’ll have to argue that separately from your brain’s direct access to the mere affirmability of a mere English utterance.”
At the same time, you’re not shoving them away from the table like you would “colorless green ideas sleep up without clam any”; you’re actually going to have a conversation about P-zombies, even though you think that in stricter senses of meaning like R2, the conversation is not just false but meaningless. After all, you could’ve been wrong about that nonmembership-in-R2 part, and they might be about to explain that to you.
The Great Reductionist Thesis is about R1 - the question of what is actually real—but it’s difficult to have something that lies in a reductionist’s concept of a strict R2, turn out to be real, such that the Great Reductionist Thesis is falsified. For example, if we think R1 is about causal universes, and then it turns out we’re in Timetravel Life, the Great Reductionist Thesis has been confirmed, because Timetravel Life still has a formal logical description. Just about anything I can imagine making a Turing-computable AI refer to will, if real, confirm the Great Reductionist Thesis.
So is GRT philosophically vacuous from being philosophically unfalsifiable? No: to take an extreme case, suppose we have an uncomputable and non-logically-axiomatizable sensus divinatus enabling us to directly know God’s existence, and by baptizing an AI we could give it this sensus divinatus in some way integrated into the rest of its mind, meaning that R2, R1, and our own universe all include things referrable-to only by a sensus divinatus. Then arguable utterances along the lines of, “Some things are inherently mysterious”, would have turned out, not just to be in R2, but to actually be true; and the Great Reductionist Thesis would be false—contrary to my current belief that such utterances are not only colloquially false, but even meaningless for strict senses of meaning. But one is not licensed to conclude anything from my having allowed a sensus divinatus to be a brief topic of conversation, for by that I am not committing to admitting that it was strictly meaningful under strong criteria such as might be proposed for R2, but only that it stayed in R3 long enough for a human brain to say some informal English sentences about it.
Does this mean that GRT itself is merely arguable—that it talks about an argument which is only in R3? But tautologies can be meaningful in GRT, since logic is within “physics + logic”. It looks to me like a completed theory of R2 should be something like a logical description of a class of universes and a class of representations corresponding to them, which would itself be in R2 as pure math; and the theory-of-R1 “Reality falls within this class of universes” could then be physically true. However, many informal ‘negations’ of R2 like “What about a sensus divinatus?” will only be ‘arguable’ in a human R3, rather than themselves being in R2 (as one would expect!).
R3) “What sort of utterances can we argue about in English?” is (perhaps deliberately) vague. We can argue about colorless green ideas, if nothing else at the linguistic level. Perhaps R3 is not about meaning, but about debate etiquette: What are the minimum standards for an assertion to be taken seriously as an assertion (i.e., not as a question, interjection, imperative, glossolalia, etc.). In that case, we may want to break R3 down into a number of sub-questions, since in different contexts there will be different standards for the admissibility of an argument.
I’m not sure what exactly a sensus divinatus is, or why it wouldn’t be axiomatizable. Perhaps it would help flesh out the Great Reductionist Thesis if we evaluated which of these phenomena, if any, would violate it:
Objective fuzziness. I.e., there are entities that, at the ultimate level, possess properties vaguely; perhaps even some that exist vaguely, that fall in different points on a continuum from being to non-being.
Ineffable properties, i.e., ones that simply cannot be expressed in any language. The specific way redness feels to me, for instance, might be a candidate for logico-physical inexpressibility; I can perhaps ostend the state, but any description of that state will underdetermine the precise feeling.
Objective inconsistencies, i.e., dialetheism. Certain forms of perspectivism, which relativize all truths to an observer, might also yield inconsistencies of this sort. Note that it is a stronger claim to assert dialetheism (an R1-type claim) than to merely allow that reasoning non-explosively with apparent contradictions can be very useful (an R2-type claim, affirming paraconsistent logics).
Nihilism. There isn’t anything.
Eliminativism about logic, intentionality, or computation. Our universe lacks logical structure; basic operators like ‘and’ and ‘all’ and ‘not’ do not carve at the joints. Alternatively, the possibility of reference is somehow denied; AIs cannot represent, period. This is perhaps a stronger version of 2, on which everything, in spite of its seeming orderliness, is in some fashion ineffable.
Are these compatible with GRT? What else that we can clearly articulate would be incompatible? What about a model that is completely expressible in classical logic, but that isn’t ontologically ‘made of logic,’ or of physics? I intuit that a classically modelable universe that metaphysically consists entirely of mind-stuff (no physics-stuff) would be a rather severe break from the spirit of reductive physicalism. But perhaps you intended GRT to be a much more modest and accommodating claim than everyday scientific materialism.
I have no objection to your description of R3 - basically it’s there so that (a) we don’t think that something not immediately obviously being in R2 means we have to kick it off the table, and (b) so that when somebody claims their imagination is giving them veridical access to something, we can describe the thing accessed as membership in R3, which in turn is (and should be) too vague for anything else to be concluded thereby; you shouldn’t be able to get info about reality merely by observing that you can affirm English utterances.
Insofar as your GRT violations all seem to me to be in R3 and not R2 (i.e., I cannot yet coherently imagine a state of affairs that would make them true), I’m mostly willing to agree that reality actually being that way would falsify GRT and my proposed R2. Unless you pick one of them and describe what you mean by it more exactly—what exactly it would be like for a universe to be like that, how we could tell if it were true—in which case it’s entirely possible that this new version will end up in the logic-and-physics R2, and for similar reasons, wouldn’t falsify GRT if true. E.g., a version of “nihilism” that is cashed out as “there is no ontologically fundamental reality-fluid”, denial of “reference” in which there is no ontologically basic descriptiveness, eliminativism about “logic” which still corresponds to a computable causal process, “relativized” descriptions along the lines of Special Relativity, and so on.
This isn’t meant to sneak reductionism in sideways into universes with genuinely ineffable magic composed of irreducible fundamental mental entities with no formal effective description in logic as we know it. Rather, it reflects the idea that even in an intuitive sense, sufficiently effable magic tends toward science, and since our own brains are in fact computable, attempts to cash out the ineffable in greater detail tend to turn it effable. The traditional First-Cause ontologically-basic R3 “God” falsifies reductionism; but if you redefine God as a Lord of the Matrix, let alone as ‘natural selection’, or ‘the way things are’, it doesn’t. An irreducible soul falsifies GRT, until I interrogate you on exactly how that soul works and what it’s made of and why there’s still such a thing as brain damage, in which case my interrogation may cause you to adjust your claim and adjust it some more and finally end up in R2 (or even end up with a pattern theory of identity). It should also be noted that while the adjective “effable” is in R2, the adjective “ineffable” may quite possibly be in R3 only (can you exhibit an ineffable thing?)
What does it mean to consist entirely of mind-stuff when all the actual structure of your universe is logical? What is the way things could be that would make that true, and how could we tell? This utterance is not yet clearly in my R2, which doesn’t have anything in it to describe “metaphysically consists of’”. (Would you consider “The substance of the cracker becomes the flesh of Christ while its accidents remain the same” to be in your equivalent of R2, or only in your equivalent of R3?)
PS: I misspelled it, it’s http://en.wikipedia.org/wiki/Sensus_divinitatis
Here are three different doctrines:
Expressibility. Everything (or anything) that is the case can in principle be fully expressed or otherwise represented. In other words, an AI is constructible-in-principle that could model every fact, everything that is so. Computational power and access-to-the-data could limit such an AI’s knowledge of reality, but basic effability could not.
Classical Expressibility. Everything (or anything) that is the case can in principle be fully expressed in classical logic. In addition to objective ineffability, we also rule out objective fuzziness, inconsistency, or ‘gaps’ in the World. (Perhaps we rule them out empirically; we may not be able to imagine a world where there is objective indeterminacy, but we at least intuit that our world doesn’t look like whatever such a world would look like.)
Logical Physicalism. The representational content of every true sentence can in principle be exhaustively expressed in terms very similar to contemporary physics and classical logic.
Originally I thought that your Great Reductionist Thesis was a conjunction of 1 and 3, or of 2 and 3. But your recent answers suggest to me that for you GRT may simply be Expressibility (1). Irreducibly unclassical truths are ruled out, not by GRT, but by the fact that we don’t seem to need to give up principles like Non-Contradiction and Tertium Non Datur in order to Speak Every Truth. And mentalistic or supernatural truths are excluded only insofar as they violate Expressibility or just appear empirically unnecessary.
If so, then we should be very careful to distinguish your confidence in Expressibility from your confidence in physicalism. Neither, as I formulated them above, implies the other. And there may be good reason to endorse both views, provided we can give more precise content to ‘terms very similar to contemporary physics and classical logic.’ Perhaps the easiest way to give some meat to physicalism would be to do so negatively: List all the clusters that do seem to violate the spirit of physicalism. For instance:
mental (perspectival, ‘subjective,’ qualia-laden...) facts that cannot be fully expressed in non-mental terms.
otherwise anthropocentric (social, cultural, linguistic...) facts that cannot be fully expressed in non-anthropocentric terms.
spatiotemporal events without spatiotemporal causes
spatiotemporal events without spatiotemporal effects
abstract (non-spatiotemporal) objects that have causes
abstract objects that have effects
(perhaps) ineffable properties or circumstances
A list like this would give us some warning signs that a view, even if logically specifiable, may be deviating sharply from the scientific project. If you precisely stipulated in logical terms how Magic works, for instance, but its mechanism was extremely anthropocentric (e.g., requiring that Latin-language phonemes ‘carve at the joints’ of fundamental reality), that would seem to violate something very important about reductive physicalism, even if it doesn’t violate Expressibility (i.e., we could program an AI to model magical laws of this sort).
I’m not sure what you mean by ‘actual structure.’ I would distinguish the Tegmark-style thesis ‘the universe is metaphysically made of logic-stuff’ from the more modest thesis ‘the universe is exhaustively describable using purely logical terms.’ If we learned that all the properties of billiard balls and natural numbers are equally specifiable in set-theoretic terms, I think we would still have at least a little more reason to think that numbers are sets than to think that billiard balls are sets.
So suppose we found a way to axiomatize ‘x being from the perspective of y,’ i.e., a thought and its thinker. If we (somehow) learned that all facts are ultimately and irreducibly perspectival (i.e., they all need an observer-term to be saturated), that might not contradict the expressibility thesis, but I think it would violate the spirit of physicalism.
I’m not sure. I doubt our universe has ‘substance-accident’ structure, but there might be some negative way to R2ify transubstantiation, even if (like epiphenomenalism or events-outside-the-observable-universe) it falls short of verifiability. Could we coherently model our universe as a byproduct of a cellular automaton, while lacking a way to test this model? If so, then perhaps we could model ‘substance-properties’ as unobservables that are similarly Behind The Scenes, but are otherwise structurally the same as accidents (i.e., observables).
So… in my world, transubstantiation isn’t in R2, because I can’t coherently conceive of what a substance is, apart from accidents. For a similar reason, I don’t yet have R2-language for talking about a universe being metaphysically made of anything. I mean, I can say in R3 that perhaps physics is made of cheese, just like I can say that the natural numbers are made of cheese, but I can’t R2-imagine a coherent state of affairs like that. A similar objection applies to a logical universe which is allegedly made out of mental stuff. I don’t know how to imagine a logically structured universe being made of anything.
Having Latin-language phonemes carve at the joints of fundamental reality seems very hard, because in my world Latin-language phonemes are already reduced—there’s already sequential sound-patterns making them up, and the obvious way to have a logic describing the physics of such a world is to have complex specifications of the phonemes which are ‘carving at the joints’. It’s not totally clear to me how to make this complex thing a fundamental instead, though perhaps it could be managed via a logic containing enough special symbols—but to actually figure out how to write out that logic, you would have to use your own neuron-composed brain in which phonemes are not fundamental.
I do agree that—if it were possibly to rule out the Matrix, I mean, if spells not only work but the incantation is “Stupefy” then I know perfectly well someone’s playing an S-day prank on me—that finding magic work would be a strong hint that the whole framework is wrong. If we actually find that prayers work, then pragmatically speaking, we’ve received a hint that maybe we should shut up and listen to what the most empirically powerful priests have to say about this whole “reductionism” business. (I mean, that’s basically why we’re listening to Science.) But that kind of meta-level “no, you were just wrong, shut up and listen to the spiritualist” is something you’d only execute in response to actually seeing magic, not in response to somebody hypothesizing magic. Our ability to hypothesize certain situations that would pragmatically speaking imply we were probably wrong about what was meaningful, doesn’t mean we’re probably wrong about what’s meaningful. More along the lines of, “Somebody said something you thought was in R3(only), but they generated predictions from it and those predictions came true so better rethink your reasons for thinking it couldn’t go in R2.”
With all that said, it seems to me that R3-possibilities falsifying 1, 2, or (a generalization of 3 to other effectively or formally specified physics (e.g. Time-Turners)), and with the proviso that we’re dealing in second-order logic rather than classical first-order logic, all seem to me to pretty much falsify the Great Reductionist Thesis. Some of your potential examples look to me like they’re not in my R2 (e.g. mental facts that can’t be expressed in non-mental terms) though I’m perfectly willing to discuss them colloquially in R3, and others seem relatively harmless (effects which aren’t further causes of anything? I could write a computer program like that). I am hard-pressed to R2-meaningfully describe a state of affairs that falsifies R1, though I can talk about it in R3.
I have an overall agenda of trying to think like reality which says that I want my R1 to look as much like the universe as possible, and it’s okay to contemplate restrictions which might narrow my R2 a lot relative to someone’s R3, e.g. to say, “I can’t seem to really conceive of a universe with fundamentally mental things anymore, and that’s a triumph”. So a lot of what looked to me years ago like meaningful non-reductionism, now seems more like meaningless non-reductionism relative to my new stricter conceptions of meaning—and that’s okay because I’m trying to think less like a human and more like reality.
Many mathematicians, scientists, and philosophers believe in things they call ‘sets.’ They believe in sets partly because of the ‘unreasonable effectiveness’ of set theory, partly because they help simplify some of our theories, and partly because of set theory’s sheer intuitiveness. But I have yet to hear anyone explain to me what it means for one non-spatiotemporal object to ‘be an element of’ another. Inasmuch as set theory is not gibberish, we understand it not through causal contact or experiential acquaintance with sets, but by exploring the theoretical role these undefined ‘set’ thingies overall play (assisted, perhaps, by some analogical reasoning).
‘Substance’ and ‘accident’ are antiquated names for a very commonly accepted distinction: Between objects and properties. (Warning: This is an oversimplification. See The Warp and Woof of Metaphysics for the historical account.) Just as the efficacy of mathematics tempts people into reifying the set-member distinction, the efficacy of propositional calculus (or, more generally, of human language!) tempts people into reifying the subject-predicate distinction. The objects (or ‘substances’) are whatever we’re quantifying over, whatever individual(s) are in our domain of discourse, whatever it is that predicates are predicated of; the properties are whatever it is that’s being predicated.
And we don’t need to grant that it’s possible for there to be an object with no properties (∃x(∀P(¬P(x)))), or a completely uninstantiated property (∃P(∀x(¬P(x)))). But once we introduce the distinction, Christians are free to try to exploit it to make sense of their doctrines. If set theory had existed in the Middle Ages, you can be sure that there would have been attempts to explicate the Trinity in set-theoretic terms; but the silliness of such efforts would not necessarily have bled over into delegitimizing set theory itself.
That said, I sympathize with your bafflement. I’m not committed to taking set-membership or property-bearing completely seriously. I just don’t think ‘I can’t imagine what a substance would be like!’ is an adequate argument all on its own. I’m not sure I have a clear grasp on what it means for a set to have an element, or what it means for a number line to be dense and uncountable, or what it means for my left foot to be a complexly-valued amplitude; but in all these cases we can gain at least a little understanding, even from initially undefined terms, based on the theoretical work they do. Since we rely so heavily on such theories, I’m much more hesitant to weigh in on their meaninglessness than on their evidential justification.
You sound like a structural realist. On this view, as I understand it, we don’t have reason to think that our conceptions straightforwardly map reality, but we do have reason to think that a relatively simple and uniform transformation on our map would yield a pattern in the territory.
So is this a fair characterization of the Great Reductionist Thesis?: “Anything that is the case can in principle be exhaustively expressed in classical second-order predicate logic, relying only on predicates of conventional mathematics (identity, set membership) and of a modestly enriched version of contemporary physics.”
We could then elaborate on what we mean by ‘modest enrichment’ if someone found a good way to add Thoroughly Spooky Doctrines (dualism, idealism, traditional theism, nihilism, trivialism, ineffable whatsits, etc.) into our language. Ideally, we would do this as un-ad-hocily as possible.
I think we both agree that ‘meaning’ won’t ultimately carve at the joints. So it’s OK if R2 and R3 look a bit ugly; we may be eliding some important distinctions when we speak simply of a ‘meaningful vs. meaningless’ binary. It’s certainly my own experience that I can incompletely grasp a term’s meaning, and that this is benign provided that the aspects I haven’t grasped are irrelevant to what I’m reasoning about.
Can I run something by you? An argument occurred to me today that seems suspect, but I don’t know what I’m getting wrong. The conclusion of the argument is that GRTt entails GRTm. For the purposes of this argument, GRTt is the statement that all true statements have a physico-logical expression (meaning physical, logical, or physical+logical expression). GRTm is the statement that all true and all false statements have a physico-logical expression.
P1) All true statements have a physico-logical expression. (GRTt)
P2) The negation of any false statement is true.
P3) If a statement has a physico-logical expression, its negation has a physico-logical expression.
P4) All false statements have a physico-logical expression.
C) All true and all false statements have a physical-logical expression. (GRTm)
So for example, suppose XYZ is false, and has no physico-logical expression. If XYZ is false, then ~XYZ is true. By GRTt, ~XYZ has a physico-logical expression. But if ~XYZ has a physico-logical expression, then ~(~XYZ), or XYZ, does. Throwing a negation in front of a statement can’t change the nature of the statement qua reducible.
Therefore, GRTt entails GRTm. What do you think?
I think your argument works. But I can’t accept GRTm; so I’ll have to ditch GRTt. In its place, I’ll give analyzing GRT another go; call this new formulation GRTd:
‘Every true statement can be deductively derived from the set of purely physical and logical truths combined with statements of the semantics of the non-physical and non-logical terms.’
This is quite unlike (and no longer implies) GRTm, ‘Every meaningful statement is expressible in purely physical and logical terms.’
The problem for GRTt was that statements like ‘there are no gods’ and ‘there are no ghosts’ seem to be true, but cast in non-physical terms; so either they are reducible to physical terms (in which case both GRTt and GRTm are true), or irreducible (in which case both GRTt and GRTm are false). For GRTd, it’s OK if ‘there are no ghosts’ can’t be analyzed into strictly physical terms, provided that ‘there are no ghosts’ is entailed by a statement of what ‘ghost’ means plus all the purely physical and logical truths.
For example, if part of what ‘ghost’ means is ‘something non-physical,’ then ‘there are no ghosts’ will be derivable from a complete physical description of the world provided that such a description includes a physical/logical totality fact. You list everything that exists, then add the totality fact ‘nothing except the above entities exists;’ since the semantic of ‘ghost’ ensures that ‘ghost’ is not identical to anything on the physicalism list, we can then derive that there are no ghosts.
Note that the semantic ‘bridge laws’ are themselves entailed by (and, in all likelihood, analyzable into) purely physical facts about the brains of English language speakers.
Well done, I like GRTd especially in that it pulls free of reference to expressibility and meaningfulness. My only worry at the moment is the totality fact, partly because of what I take EY to want from the GRT in reference to R1. I take it we will agree right off that the totality fact can’t follow from having listed all the physico-logical facts. Otherwise we could derive ‘there are no ghosts’ right now, just given the meaning of ‘ghost’. But we need the answer to the question posed by R1 to be (in every case which doesn’t involve a purely logical contradiction) an empirical answer. What we want to say about ghosts is not that they’re impossible, but that their existence is extremely unlikely given the set of physico-logical facts we do have. We won’t ever have opportunity to deploy a totality fact (since this requires omniscience, it seems), but it seems like an important part of the expression of the GRTd.
But if we can’t get the totality fact just from having listed all the physico-logical facts, and if the totality fact must itself be a physico-logical fact then I have a hard time seeing how we can deduce from physico-logical omniscience that there are no ghosts. In order to deduce the non-existence of ghosts, we’d need first to deduce the totality fact (since this is a premise in the former deduction), but if the totality fact is not deducible from all the physico-logical facts, then in order to deduce it, it looks like we need ‘there are no ghosts’ as a premise. But then our deduction of ‘there are no ghosts’ begs the question.
Unless I’m missing something, it seems to me that the totality fact has to end up being deducible from all the physico-logical facts if deductions which employ it are to be valid. But this again makes the GRTd (specifically that part of it which describes the totality fact) an a priori claim, which we’re trying to avoid especially because it means that GRTd is not an answer to R1 (which is what EY, at least, is looking for).
The totality fact could take a number of different forms. For instance, ‘Everything is a set, a spacetime region, a boson, or a fermion’ would suffice, if our semantics for ‘ghost’ made it clear that ghosts are none of those things. This is why we don’t need omniscient access to every object to formulate the fact; all we need is a plausibly finished set of general physical categories. If ‘physical’ and ‘logical’ are themselves well-defined term in our physics, we could even formulate the totality fact simply as: ‘Everything is physical or logical.’
Another, more modest totality-style fact would be: ‘The physical is causally closed.’ This weaker version won’t let us derive ‘there are no ghosts,’ but it will let us derive ‘ghosts, if real, have no causal effect on the physical,’ which is presumably what we’re most interested in anyway.
GRTd itself doesn’t force you to accept totality facts (also known as Porky Pig facts). But if you reject these strange facts, then you’ll end up needing either to affirm GRTm too, or needing to find some way to express negative existential facts about Spooky Things in your pristine physical/logical language. All three of these approaches have their costs, but I think GRTd is the most modest option, since it doesn’t commit us to any serious speculation about the limits of semantics or translatability.
I think the totality fact is a physical (or ‘mixed’) fact. Intuitively, it’s a fact about our world that it doesn’t ‘keep going’ past a certain point.
The totality fact can’t be strictly deduced from any other fact. In all cases these totality facts are empirical inferences from the apparent ability of our physical predicates to account for everything. Inasmuch as we are confident that (category-wise) ‘That’s all, folks,’ we are confident in there being no more categories, and hence (if only implicitly) in there being no Spooky addenda.
Notice this doesn’t commit us to saying that we can meaningfully talk about Spooky nonphysical entities. All it commits us to is the claim that if we can meaningfully posit such entities, then we should reject them with at least as much confidence as we affirm the totality fact.
So, I like GRTd, insofar as it captures both what is so plausible about physicalism, and insofar as the ‘totality fact’ expresses an important kind of empirical inference: from even a small subset of all the physico-logical facts, we can get a good general picture of how the universe works, and what kinds of things are real.
I still have questions about the GRTd as a principle however. I don’t see how the following three statements are consistant with one another:
S1) GRTd: ‘Every true statement can be deductively derived from the set of purely physical and logical truths combined with statements of the semantics of the non-physical and non-logical terms.’
S2) The totality fact is true.
S3) ‘The totality fact can’t be strictly deduced from any other fact.’
One of these three has to go, and I strongly suspect I’ve misunderstood S3. So my question is this: Given all the physical and logical facts, combined with statements of the semantics of any non-physical and non-logical terms one might care to make use of, do you think we could deduce the totality fact?
The totality fact is one of the physical/logical facts, and can be expressed in purely physical/logical terms. For instance, in a toy universe where the only properties were P (‘being a particle’) and C (‘being a spacetime point’), the totality fact would have the form ∀x(P(x) ∨ C(x)) to exclude other categories of entity. A more complete totality fact would exclude bonus particles and spacetime points too, by asserting ∀x(x=a ∨ x=b ∨ x=c...), where {a,b,c...} is the (perhaps transfinitely large) set of particles and points. You can also express the same idea using existential quantification.
S1, S2, and S3 are all correct, provided that the totality fact is purely physical and logical. (Obviously, any physical/logical fact follows trivially from the set of all physical/logical facts.) GRTd says nothing about which, if any, physical/logical facts are derivable from a proper subset of the physical/logical. (It also says nothing about whether there are non-physicological truths; it only denies that, if there are some, their truth or falsehood can fail to rest entirely on the physical/logical facts.)
A single giant totality fact would do the job, but you could also replace it (or introduce redundancy) by positing a large number of smaller totality facts. Suppose you want to define a simple classical universe in which a 2x2x2-inch cube exists. You can quantify over a specific 2x2x2-inch region of space, and assert that each of the points within the interval is occupied. But that only posits an object that’s at least that large; we also need to define the empty space around it, to give it a definite border. A totality fact (or a small army of them) could give you the requisite border, establishing ‘there’s no more cube’ in the same way that the Giant Totality Fact establishes ‘there’s no more reality.’ But if you get a kick out of parsimony or concision, you don’t need to do this again and again for each new bounded object you posit. Instead, you can stick to positive assertions until the very end, and then clean up after yourself with the Giant Totality Fact. That there’s no more reality than what you’ve described, after all, implies (among other things) that there’s no more cube.
Ah, I took GRTd to mean that ‘every true statement (including all physical and logical truths) can be deductively derived from the set of purely physical and logical truths (excluding the one to be derived)...’.Thus, if the totality fact is true, then it should be derivable from the set of all physico-logical facts (excluding the totality fact). Is that right, or have I misunderstood GRTd?
I may, I think, just be overestimating what it takes to plausibly posit the totality fact: i.e. you may just mean that we can have a lot of confidence in the totality fact just by having as broad and coherent a view of the universe as we actually do right now. The totality fact may be false, but its supported in general by the predictive power of our theories and an apparent lack of spooky phenomena. If we had all the physico-logical facts, we could be super duper confident in the totality fact, as confident as we are about anything. It would by no means follow deductively from the set of all physico-logical facts, but it’s not that sort of claim anyway. Is that right?
The edit is fine. Let me add that ‘the’ totality fact may be a misleading locution. Nearly every model that can be analyzed factwise contains its own totality fact, and which model we’re in will change what the ‘totality’ is, hence what the shape of the totality fact is.
We can be confident that there is at least one fact of this sort in reality, simply because trivialism is false. But GRTd does constrain what that fact will have to look like: It will have to be purely logical and physical, and/or derivable from the purely logical and physical truths. (And the only thing we could derive a Big Totality Fact from would be other, smaller totality facts like ‘there’s no more square,’ plus a second-order totality fact.)
Excellent, I think I understand. GRTd sounds good to me, and I think you should convince EY to adopt it as opposed to GRTt/m.
I didn’t intend for you to read ‘(excluding the one to be derived)’ into the statement. The GRTd I had in mind is a lot more modest, and allows for totality facts and a richer variety of causal relations.
GRTd isn’t a tautology (unless GRTm is true), because if there are logically underivable nonphysical and nonlogical truths, then GRTd is false. ‘X can be derived from the conjunction of GRTd with X’ is a tautology, but an innocuous one, since it leaves open the possibility that ‘X’ on its lonesome is a garden-variety contingent fact.
Sorry, I didn’t expect you to read my post so quickly, and I edited it heavily without marking my edits (a failure of etiquette, I admit).
EY, please hand the SIAI keys to Rob!
What could it mean for a ghost to exist but be nonphysical?
I think that what you think are counterexamples to GRTm are a large number of things which, examined carefully, would end up in R3-only, and not in R2.
I furthermore note that you just rejected GRTt, which sounds scarily like concluding that actual non-reductionist things exist, because you didn’t want to accept the conclusion that talk of non-physical ghosts might fail strict qualifications of meaning. How could you possibly get there from here? How could your thoughts about what’s meaningful, entail that the laws of physics must be other than what we’d previously observed them to be? Shouldn’t reaching that conclusion require like a particle accelerator or something?
Alternatively, perhaps your rejection of GRTt isn’t intended to entail that non-reductionist things exist. If so, can you construe a narrower version of GRTt which just says that, y’know, non-reductionist thingies don’t exist? And then would Esar’s argument not go through for this version?
I think Esar’s argument mainly runs into trouble when you want to call R3-statements ‘false’, in which case their negations are colloquially true but in R3-only because there’s no strictly coherent and meaningful (R2) way to describe what doesn’t exist (i.e. non-physical ghosts). If your desire to apply this language demands that you consider these R3-statements meaningful, then you should reject GRTm, I suppose—though not because you disagree with me about what stricter standards entail, but because you want the word “meaningful” to apply to looser standards. However, getting from there to rejecting R1 is a severe problem—though from the description, it’s possible you don’t mean by GRTt what I mean by R1. I am a bit worried that you might want ‘non-physical ghosts don’t exist’ to be true, hence meaningful, hence its negation to also be meaningful, hence a proposition, hence there to be some state of affairs that could correspond to non-physical ghosts existing, hence for the universe to not be shaped like my R1. Which would be a very strange conclusion to reach starting from the premise that it’s ‘true’ that ‘ghosts do not exist’.
To reject GRTt is to affirm: “Some truths are not expressible in physical-and/or-logical terms.” Does that imply that irreducibly nonphysical things exist? I don’t quite see why. My initial thought is this: I am much more confident that physicalism is true than that nonphysicalism is inexpressible or meaningless. But if this physicalism I have such faith in entails that nonphysicalism is inexpressible, then either I should be vastly more confident that nonphysicalism is meaningless, or vastly less confident that physicalism is true, or else GRTt does not capture the intuitively very plausible heart of physicalism. Maybe GRTt and GRTm are correct; but that would take a lot of careful argumentation to demonstrate, and I don’t want to hold physicalism itself hostage to GRTm. I don’t want a disproof of GRTm to overturn the entire project of reductive physicalism; the project does not hang on so thin a thread. So GRTd is just my new attempt to articulate why our broadly naturalistic, broadly scientific world-view isn’t wholly predicated on our confidence in the meaninglessness of the assertions of the Other Side.
This dispute is over whether, in a physical universe, we can make sense of anyone even being able to talk about anything non-physical. Four issues complicate any quick attempts to affirm GRTm:
1) Meaning itself is presumably nonfundamental. Without a clear understanding of exactly what is neurologically involved when a brain makes what we call ‘representations,’ attempts to weigh in on what can and can’t be meaningful will be somewhat speculative. And since meaning is nonfundamental, truth is also nonfundamental, is really an anthropological and linguistic category more than a metaphysical one; so sacrificing GRTt may not be as devastating as it initially seems.
2) ‘Logical pinpointing’ complicates our theory of reference. Numbers are abstracted from observed regularities, but we never come into causal contact with numbers themselves; yet we seem to be able to talk about them. So if there is some way to abstract away from physicality itself, perhaps ‘ghost’ could be an example of such abstraction (albeit of a less benign form than ‘number’). The possibility doesn’t seem totally crazy to me.
3) It remains very unclear exactly what work is being done by ‘physical’ (and, for that matter, ‘logical’) in our formulations of GRT. This is especially problematic because it doesn’t matter. We can define ‘physical’ however we please, and then it will be much easier to work out whether we can talk about anything nonphysical.
One worry is that if we can’t speak of anything nonphysical, then the term ‘physical’ itself risks falling into meaninglessness. GRTd doesn’t face this problem, and allows us to take the intuitive route of simply asserting the falsehood of anti-physicalisms; it lets us do what we originally wanted with ‘physicalism,’ which was to sift out the excessively Spooky doctrines at the outset. In contrast, it’s not clear what useful work ‘physicalism’ is doing if we follow the GRTm approach. If GRTm’s physicalism is a doctrine at all, it’s a very strange (and perhaps tautologous) one.
4) Traditionally, there’s been a split between positivists who wanted to reduce everything to logical constructs plus first-person experience, and positivists who wanted to reduce everything to logical constructs plus third-person physical science. I personally find the latter approach more plausible, though I understand the post-Cartesian appeal of Russell’s phenomenalist project. But it troubles me to see the two sides insisting, with equal vehemance, that the other side is not only mistaken but speaking gibberish. Even as an eliminative physicalist and an Enemy of Qualia, I find it plausible that we have some (perhaps fundamentally mistaken) concept of a difference between experiences (which are ‘from a vantage point’) and objective events (which lack any ‘point-of-view’ structure). If there’s anything genuinely under dispute between the first-person camp and the third-person camp, then this provides a simple example of why GRTt is false: Simply for grammatical reasons, there are falsehoods (indexicals, perhaps) that cannot be perfectly expressed in physical terms. That doesn’t mean that we can’t physicalistically describe why and how someone came to assert P; it just means we can’t assert P ourselves in our stripped-down fundamental language.
Perhaps this is a more palatable way to put it: We can explain in purely physical and logical terms why every false sentence is false. But there is no one-to-one correspondence between false non-fundamental assertions and false fundamental assertions. Rather, in cases like ‘there are no gods’ and ‘there are no ghosts,’ there is a many-to-one relationship, since all statements of those sorts are made true by the conjunction of all the physical and logical truths (including the totality fact). But it’s implausible to treat this Gigantic Fact as the physical meaning or final analysis of falsehoods like ‘I have experienced redness-qualia.’
That seems like too strong of a statement. Surely we can express falsehoods (including false existential generalizations) in our finished physical/logical language. We can describe situations and objects that don’t exist. The question is just whether the descriptive elements our sparse language utilizes will be up to the task of constructing every meaningful predicate (and in a way that allows our language to assert the predication, not just to describe the act of someone else asserting it). So far, that seems to me to be more open to doubt than does garden-variety physicalism.
The need for a totality fact is reminiscent of the beginning of Wittgenstein’s Tractatus,
It is interesting how the same (or at least analogous) problems, arguments and concerns reappear in successive iterations of the Great Reductionist Project.
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 . 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, , varies in truth-value across possible worlds, then the distinct proposition q,
, 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:
. 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 . But the actual Great Reductive Thesis says: . 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:
Expressibility: All propositions that are true in our world can be expressed by utterances in our world.
Logico-Physicalism: Every proposition that is true in our world is either purely physical-and/or-logical, or can be completely analyzed into a true proposition that is purely physical-and/or-logical.
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:
Some sentences seem to assert non-physical, non-logical things.
But the non-physicologicality of those things makes those sentences meaningless.
So non-physicologicality in general probably makes statements meaningless.
On the other hand, if Eliezer is really trying to endorse GRTt, his arguments will instead look like this:
Some sentences seem to be true but non-physicological.
But those sentences are either false or analyzable/reducible to purely physicological truths.
So non-physicological truths in general are probably expressible purely physicologically.
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.)
Here’s my exchange with EY:
EY replied:
So I replied:
And he said:
So I’m actually not much less confused. His first reply seems to support GRTt. His second reply (the first word of it anyway) seems to support GRTm. Thoughts?
Thanks for taking the time to hunt down the facts!
I think “Everything true and most meaningful false statements can be expressed this way.” is almost completely clear. Unless a person is being deliberately ambiguous, saying “most P are Q” in ordinary English conversation has the implicature “some P aren’t Q.”
I’m not even clear on what the grammar of “That statement is meaningless is false.” is, much less the meaning, so I can’t comment on that statement. I’m also not clear on how broad “the terms you describe in Logical Pinpointing, Causal Reference, and Mixed Reference” are; he may think that he’s sketched meaningfulness criteria somewhere in those articles that are more inclusive than “The Great Reductionist Project” itself allows.
I think that was fairly clear. Each of those articles is explicitly about a form of reference sentences can have: logical, physical, or logicophysical, and his statement of the GRT was just that all meaningful (or in your reading, true) things can be expressed in these ways.
But it occurs to me that we can file something away, and tomorrow I’m going to read over your last three or four replies and think about the GRTt whether or not it’s EY’s view. That is, we can agree that the GRTm view is not a tenable thesis as we understand it.
One possible source of confusion: What is the meaning of the qualifier “physical”? “Physical,” “causal,” “verifiable,” and “taboo-able/analyzable” all have different senses, and it’s possible that for some of them Eliezer is more willing to allow meaningful falsehoods than for others.
Yeah. I’ll re-read his posts, too. In all likelihood I didn’t even think about the ambiguity of some of his statements, because I was interpreting everything in light of my pet theory that he subscribes to GRTt. I think he does subscribe to GRTt, but I may have missed some important positivistic views of his if I was only focusing on the project of his he likes. Some of the statements you cited where he discusses ‘meaning’ do create a tension with GRTt.
My reply to this conversation so far is at:
http://lesswrong.com/lw/frz/mixed_reference_the_great_reductionist_project/8067
You’d just about convinced me, until I reread the OP and found it consistently and unequivocally discussing the question of meaningfulness. So before we go on, I’m just going to PM Eliezer and ask him what he meant. I’ll let you know what he says if he replies.