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Eliezer_Yudkowsky comments on Mixed Reference: The Great Reductionist Project - Less Wrong
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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:
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.