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.
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.