Helen interviewed on Idealism

In a rare online appearance, Helen is interviewed on Mind Chat by Philip Goff and Keith Frankish about her book-in-progress, The View From Everywhere: Realist Idealism Without God.

For highlights, see especially:

36:00 - Helen explains the basics of her novel form of idealism (and how it differs from Berkeley's).

53:45 - Why idealism is more plausible than you might have thought.

58:20 - How idealism enables a direct realist account of perception like no other.

1:56:42 - Why philosophy monographs should be followed up with a "for kids" version.

There's also a bunch of interesting meta-philosophical discussion throughout, reacting to Helen's explanation that she only has about 30% credence in idealism, and correspondingly aims not to convince others that it's true, but just that they should take it more seriously than they had previously.

Check out the full interview on YouTube.

Idealism Without God: a must-read paper!

... by the brilliant Helen Yetter-Chappell [forthcoming in T. Goldschmidt & K. Pearce (eds.) Idealism: New Essays in Metaphysics, Oxford University Press].

PDF pre-print available here.

I may be a tad biased, but I can't think of a more creative, ambitious, and interesting paper than Helen's 'Idealism Without God', which manages to improve upon Berkeley's original view in significant respects (especially regarding the nature of perception) whilst depending upon less controversial theoretical resources (as indicated by the title).  It's cool stuff.  A prominent philosopher of mind even declared it, "the coolest metaphysical view ever!"  It should especially delight those who worry that philosophers these days too often lose sight of the "big issues".

The paper's upshot:

Contemporary philosophers are overwhelmingly materialists (at least about the domain of physical objects). I think it’s unfortunate that this view is taken for granted, as idealism both has much to offer and need not be as radical in its commitments as it might first appear. In making the case for taking idealism seriously, I’ve outlined a non-theistic, quasi-Berkeleyan view. On this view, reality is a vast unity of consciousness that binds together the sensory impressions of every point-from-a-perspective. This does not do away with the physical world, but gives a unique account of its nature – one on which the world is fundamentally intelligible. Just as on materialist views, reality is governed by physical laws (the sorts of laws that physicists tell us about, and which it’s clearly not the business of philosophers to dispute). Because reality is phenomenal, we open up the possibility that we can have a very robust sort of direct contact with reality. I’ve offered a view of perception on which (in perception) our minds are literally constituted by threads of reality. If this is right, I can stand in the same relation to the blueness of the sky as I do to the pain in my thigh. 

While the idealist account that I’ve developed faces challenges – particularly worries about quantitative profligacy – it also offers some unique and intriguing benefits: (i) Due to the robust account it gives of our direct connection to reality, it yields an especially strong vindication of Johnston’s neglected epistemic virtue. (ii) It renders reality fundamentally intelligible in a way that materialism does not. (iii) It captures our common-sense intuition that the world is as it appears. While the theory doubtless faces challenges not addressed in this short paper, these advantages are such that the view surely merits consideration. 

In conclusion, idealism is awesome and everyone should take it more seriously.

Read the whole thing!

E.J. Lowe on the Inescapability of Metaphysics

"How is it possible for creatures like us to chart the realm of possibilities? Of course, this is a curious question, to the extent that it is, itself, a question -- addressed to ourselves -- about the very realm of possibilities, access to which, by us, is being put in question.  Suppose, however, that we were to come up with an argument whose conclusion was that it is not possible for us to chart the realm of possibilities. That conclusion would seem to undermine itself, because the conclusion itself concerns the realm of possibilities, maintaining that that realm does not include the possibility of our charting it.  We could thus only have reason to believe the conclusion if the conclusion were false: so we can have no reason to believe it.  Is this just a trick? I don't think so; rather, it is yet another example of the unavoidability of metaphysics. As rational beings, we cannot but consider ourselves capable of knowing at least something about the realm of possibilities. This should not be surprising. Reasoning itself depends upon a grasp of possibilities, because a valid argument is one in which it is not possible for the conclusion to be false if the premises are true -- and a rational being is a creature which can discern the validity of at least some arguments." -- p.137 of 'Metaphysical Knowledge', in Matthew Haug (ed.) Philosophical Methodology: The Armchair or the Laboratory?

Unexperienced Virtual Realities

I've long thought that a shared virtual world could, in principle, be just as "real" (in any sense that matters) as the material world.  But Helen recently got me thinking about what we metaphysical anti-chauvinists should say about "virtual worlds" that, though capable of supporting interactions between conscious minds, never actually do support any such experiences or interactions.  (Many of the following thoughts I owe to her.)

Two Metaphysical Pictures

While there are any number of logically consistent combinations of metaphysical views that one could hold, it seems to me that there are two particularly coherent and ideologically unified competing "pictures" on offer.  We might call them the objects in flux view vs. the timeless qualities view.  Let me sketch each view in turn.

The "Necessary Being" Argument Tailor

Here's a fun "interactive survey" (ht: Joshua Rasmussen) that asks you about a bunch of general metaphysical principles, and constructs an argument for a necessary being out of your answers.

Though this probably isn't the intended purpose of the site, I find it nicely illustrates the methodological lesson that general principles that sound plausible at first (when we think of only paradigmatic instances, say) may no longer seem so plausible once certain (less "normal") instances of their use are brought to our attention.

Epiphenomenal Explanations

Explanations come in various different forms. Sometimes we are interested in strictly causal "actual sequence" explanations, which tell us which particular causal forces happened to bring about the outcome in question. Other times we want a higher-level, "robust process" explanation, identifying the broader patterns that secure similar outcomes across nearby possible worlds (though the particular "sequence" details may vary, compatibly with maintaining the same high-level pattern). These explanatory patterns might be considered 'causes' in a weaker sense -- they're certainly eligible to feature in true "because" claims, though there's an obvious sense in which such abstracta lack the direct causal "oomph" of their particular physical constituents. Further, I think we sometimes appeal -- esp. regarding ethics and phenomenal consciousness -- to what might be called "correlative" explanations, when we speak of some familiar epiphenomenal byproduct as being explanatory, even when strictly speaking it is a correlated physical state that provides the causal "oomph".

Why We Needn't Hold Politics Hostage to Metaphysics

Oh dear -- Reason Online has just (re)published a morass of philosophical confusion:

The brain is a physical organ. As such, it follows the laws of biology, chemistry, physics, quantum physics, and of any other hard science we have yet to discover. The brain cannot make choices. It is not free. So when someone says that mind is nothing but brain, he is saying that the things we associate with mind—choosing, preferring, thinking—aren’t real.

In philosophy this is called epiphenomenalism.

Non-Metaphysical Cognitivism

In Chapter 31 of On What Matters, Parfit defends a view he calls 'non-metaphysical cognitivism':

There are some claims that are irreducibly normative in the reason-involving sense, and are in the strongest sense true. But these truths have no ontological implications. For such claims to be true, the reason-involving properties need not exist either as natural properties in the spatio-temporal world, or in some nonspatio-temporal part of reality.

It's an appealing view, and one that I defended in an old post on 'non-spooky moral realism'. But it also raises some puzzling questions.

Holism and Metaphysical Grounds

[Some thoughts inspired by Shamik's recent talk 'On the Plurality of Grounds'...]

Suppose comparativism about mass is true, i.e. "the fundamental facts about mass are facts about the mass-relations between things". Absolute mass claims, such as that my laptop is 2 kgs, must ultimately be grounded in mass-relational facts, such as that my laptop is twice as massive as the standard kilogram weight in Paris. Of course, no single such relation suffices: the standard kilogram might have been twice as heavy as it actually is (in comparative terms: mass-related to the vast majority of other objects at double its actual ratios), in which case the aforementioned relation would imply that my laptop was 4 kgs rather than just 2. So the full ground of my laptop's being 2 kgs must instead be massively plural, perhaps depending on the entire universe of comparative mass facts.

At this point, Shamik worries that the universe of comparative facts can't ground the single absolute fact about my laptop's mass, because it includes facts that are (intuitively) explanatorily irrelevant. For example, the mass relation between my laptop and some particle on Alpha Centauri seems irrelevant to my laptop's being 2 kgs. Shamik's solution is to introduce plural grounding: no single absolute mass fact has a ground, but the set of all such facts is plurally grounded in the set of all relational mass facts. Neat enough, but I wonder whether we should really accept the intuition of explanatory irrelevance that prevents us from simply grounding each individual absolute mass fact in the set of all relational mass facts.

Hallucination, Virtual Reality, and Reality

Some consider virtual reality to be akin to mere hallucination, whereas others see it as potentially on a par with physical reality. Both seem possible to me (depending on the precise nature of the VR we're imagining), so let's try to clarify matters by drawing some distinctions. First, we can consider the epistemic dimension of whether you remain aware (on some level) that you're in a virtual world, or if the VR is all-consuming. More importantly, I think we can identify variation along a metaphysical dimension of sorts, as per the following three alternatives:

Accommodating Common Sense

Kenny Pearce has an interesting post contrasting Locke's and Berkeley's diverging approaches to common sense:

Locke's goal, it seems, is to turn our ordinary beliefs into a system of metaphysics... Berkeley's project is, as he famously put it, to "think with the learned, and speak with the vulgar." His metaphysical system, he is well aware, bears no resemblance whatsoever to common sense. Nevertheless, he claims, his system preserves the correctness of common sense within its own domain.

It's a nice distinction, and I'm with Berkeley at least in thinking that we shouldn't read too much into the platitudes of common sense. "Folk ontology", for example, strikes me as an oxymoron: the folk don't have anything to say about the questions that interest contemporary ontologists. Ordinary talk of 'existence' invokes the 'superficial', non-ontological sense of the word. I'm skeptical whether there is any sense to ontology at all, but even if there is (say we can make conceptual sense of the objective structure of reality), that sure isn't a domain the folk are concerned with in their everyday talk of how many chairs are in the room. (It would miss the point to answer, "None; there are only atoms arranged chair-wise." This is not a difference of any concern to the folk.)

I think we also need to be careful about how we seek to integrate "common sense" moral intuitions into our moral theory. The folk concepts of 'right' and 'wrong' again strike me as fairly superficial, and so not of great philosophical interest. Moral philosophers (of my stripe) are instead concerned with the most fundamental normative questions, e.g. about what we have most reason to do. To say it's intuitively "wrong" to push the fat guy in front of the trolley is neither here nor there. The vague intuitive idea being expressed here may correspond to any number of more precise claims (e.g. that it's a bad rule/decision procedure to allow killing innocents, or that we should censure someone for acting so) that are quite compatible with consequentialism. So, properly understood, I don't think consequentialism is really counter to common sense at all. It's orthogonal -- addressing a different, deeper, question.

So, accommodating the claims of commonsense is often less philosophically demanding than one might expect. Still, we shouldn't be too complacent. In particular, it is not enough to simply give an account on which the folk platitudes come out true, if this involves revising their meaning beyond recognition. One might think David Lewis guilty of this, for example, when he analyzes modality in terms of concrete spatio-temporal regions. Such regions just don't seem to be the right kind of thing to be that in virtue of which our ordinary modal claims are true. At least, this surely violates the folk understanding of what their modal talk is about. That's not an automatic disqualification -- I'm often sympathetic to philosophical revisionism -- but it is worth noting as a genuinely "counterintuitive" result. (Similar remarks may apply to Berkeley's phenomenalism.)

Proving Grue's Temporality

Background: we define 'grue' such that it applies to any object satisfying the disjunctive condition: either the object is first observed prior to 2020 and it is green, or the object is not observed prior to 2020 and it is blue. For example, every emerald so far observed has been grue, and so (presumably) is a sapphire that's first dug up in 2021. Define 'bleen' conversely. Goodman's new riddle of induction is to distinguish which of the following two inductive inferences is a good one, and why:

(MORE GREEN) All emeralds so far observed have been green, so an emerald discovered in 2021 will also be green.

(MORE GRUE) All emeralds so far observed have been grue, so an emerald discovered in 2021 will also be grue.

The obvious answer is that 'grue' is a gerrymandered predicate which makes reference to a particular time, whereas 'green' applies consistently to the same colour throughout. The standard objection to this proposed answer is that in fact the temporal reference is merely an artifact of our language, since we happen to be 'green'-speakers. We can imagine a 'grue'-speaker, whose natural language takes 'grue' and 'bleen' as the fundamental notions and defines 'green' and 'blue' as time-relative disjunctive predicates. (E.g. they define 'green' = grue if first observed before 2020, bleen otherwise.)

Now, I want to show that this linguistic defense is inadequate, and in fact even the natural grue-speaker must admit that it is their colour terms, not ours, which are really time-relative. Importantly, this is not a linguistic claim, but a metaphysical one. I'm willing to grant that they may take 'grue' rather than 'green' as their linguistic primitive, not to be defined in terms of any other words (relative to times). But words don't matter. What matters is that their word 'grue' denotes a temporally gerrymandered property or thing in the world.

Here's my demonstration. Let us fast-forward to the year 2025. Suppose it turns out that all emeralds are still green, in which case all those discovered from 2020 onwards are called 'bleen' rather than 'grue'. Suppose I take an emerald to a grue-speaker, and let him look at it as closely as he likes, in the clearest possible viewing conditions (good lighting, etc.). Surely he should then be able to tell what colour it is. He has adequate epistemic access to how the object is in itself. He can see it just fine. Yet when I ask him, "What colour is this emerald?" he cannot say. He must ask for more information: "When was it first observed?" The grue-speaker thereby reveals the implicit time-relativity of his colour concepts. It is not enough to look at the object in itself; whether it is grue or bleen depends on the further, extrinsic question of whether it was observed prior to 2020 or not.

The green speaker needs no such further information. We can tell the emerald is green just by looking at it, without needing to also know any temporal information. This shows that 'green' denotes a temporally neutral property, whereas 'grue' denotes something that is time-relative or temporally gerrymandered.

(This seems like an obvious point, so I imagine some other philosopher must have beat me to it. Can anyone recall seeing this argument before in the literature? Any pointers would be greatly appreciated.)

Natural and Projectible Predicates

Rachael remarks on the 'structure and similarity' discussion:

Should we distinguish between predicates that are projectable and predicates that are natural? "Green", "ultraviolety-looking to bees", "owned by Rachael", and "tasty to alpacas" are fairly projectable, but I doubt they're natural. I don't expect a bee to care which objects are green, a mouse to care which objects are owned by Rachael, or a human (who doesn't have a special interest in bees or alpacas) to care which objects are ultraviolety-looking to bees or tasty to alpacas. There's a sense in which all the above concepts are parochial, and are only worth adopting because they're convenient. Furthermore, there's a sense in which there's no conflict between these different ways of carving up the world: I don't think the alpacas are wrong, and I might find it very important to adopt their concepts when interacting with them.

Also, maybe "Having mass m before time t or mass m* after" is an example of a natural predicate that isn't projectable.

That last example sounds gerrymandered (i.e. not a natural way to carve things up) to me. I'd need to hear more about why we'd consider it 'natural'. (Note that complex predicates may invoke natural terms like 'mass' in a gerrymandered or non-natural manner.) On the other hand, I'm also unsure why green and ultraviolet are thought not to be very natural. There is a natural respect -- namely, surface reflectance properties -- in which all green things (or all ultraviolet things) exhibit a genuine similarity.

The other examples are plausibly less natural, but also (and, I imagine, to the same degree) unprojectible. Here I should clarify something that may not have been clear in my first post. 'Projectibility' does not just mean stability across time, i.e. that if something satisfies the predicate now, it will also do so in future. Any tenseless predicate, however gerrymandered -- e.g. 'exists in 1907 or 2008' -- will be temporally stable in this sense. Genuine projectibility is more general, since we can inductively project along dimensions other than time. If a bunch of Fs are green, that may be evidence that other Fs (and not just these same ones in future) are also green. On the other hand, if a bunch of Fs are owned by Rachael, that's probably not enough to justifably project ownership-by-Rachael onto any other arbitrary F.*

Overall, then, I remain of the opinion that 'natural' predicates, i.e. those that carve nature at the joints, or highlight objective similarities, are also those that will tend to support inductive projection.

[* = I'm not sure if that's the best way to explain projectibility. Any suggestions?]

Sider on Semantic and Metaphysical Intuitions

It is important to separate the two kinds of intuitions. Suppose you are initially inclined to intuit thus: "the property of being a dog is intrinsic". This might well be because you are simply presupposing the worm view [of 4-d objects], and thus presupposing that 'being a dog' refers to the property of being a dog-worm, and metaphysically intuiting that this property is intrinsic. It might well be that, once the question is raised of whether the worm-view or the stage-view is correct, your initial conviction disappears, and is replaced with agnosticism about whether "being a dog is intrinsic", despite your certainty that being a dog-worm is intrinsic and being a dog-stage is extrinsic.

[From his paper on counterpart theory: 'Beyond the Humphrey Objection'.]

Natural Baselines

After my uncharacteristic espousal of some form of metaphysical realism, I feel a more deflationary argument is in order. In particular, I want to explore the idea that there is no objective basis for talk of the 'natural progression of things', or a default outcome which an agent's actions may interfere with. In other words: is there a natural distinction to be made between 'doing' and 'allowing'?

I've been reading Dan Dennett's 'A route to intelligence: oversimplify and self-monitor', in which he discusses the queer idea of "changing the course of history":

How could you change the course of history? From what to what? If history is simply the sequence of events that actually occur, then of course you can't change history. People say you can't change the past, and that's true enough, but then you can't change the future either...

[O]ne has to be thinking of an anticipated history, the way history is going to go ceteris paribus, the way history is going to go unless someone does something, or until someone does something, or in spite of what someone does. These verbs of agency can have no foothold outside the framework of a projected, aniticpated history, even when they are used to characterize the effects brought about by entirely inanimate objects.

He goes on to describe a scenario whereby a meteor is heading towards the earth, and we're all frantic until an unnoticed second meteor deflects the first one, "narrowly averting the catastrophe, preventing calamity." However, given full information, we could have seen that "there was never going to be a catastrophe. It was merely an anticipated catastrophe -- a mis-anticipated catastrophe." Dennett thus suggests that the sense in which the meteor was 'set' to hit earth is merely epistemic, rather than reflecting any natural disposition or 'default outcome' in the world, from which we were narrowly saved.

I'm not sure that's the full answer, though. There seems a sense in which the meteor really was, quite literally, 'on course' to hit the earth. It was 'deflected', which is precisely to say that its course was changed. This may be reflected in the modal fact (if it is one) that in most close possible worlds, the catastrophe indeed occurs. It's an open question whether this modal fact actually holds of the scenario, however. It might if small changes to the course of the second meteor would cause it to miss the first, while equivalent changes to the first meteor would not have caused it to miss earth. Otherwise - if the course of catastrophe was not modally robust in the first place - my modal account implies that the meteor was not really 'set' to hit the earth in any objective sense at all.

Let's see how this modal account applies to the puzzle discussed in my old post on framing thought experiments:

Weatherson notes that "where we set the 'zero-point' or status quo makes a big difference for how we act." But is there really any fact of the matter about what the 'default' outcome is? Kahneman and Tversky's classic example seems to suggest that this is merely a difference in our descriptions, not in reality. Whether you say that 400/600 will die, or that 200/600 will be saved, you describe one and the same fact. But the descriptions differ in their implied baseline, or what they convey as being "the natural progression of things". Could there be a metaphysical fact of the matter regarding where the true baseline lies? What sort of fact could this be, that would tell us whether a survivor was saved from the jaws of death, or whether it was simply a matter of death failing to cut his life tragically short? When faced with branching possibilities, how can we say that one is the "default" path of fate, and the other some kind of unnatural "diversion"? (But if we can't do this, then what is our basis for caring more about "losses" than "forfeited gains"? Doesn't this distinction require a baseline?)

My new suggestion is that the modal facts can provide such a baseline. The baseline is whichever event (dying or being saved) occurs in most close possible worlds. If you are overwhelmingly likely to obtain some benefit, then failure to obtain it in the actual world is properly classified as a loss, and not merely a forfeited gain.

Eh, so much for deflationism. It turns out I'm a "realist" about baselines too! A somewhat revisionary one, though. This certainly doesn't match our common understanding of the doing/allowing distinction, and nor would I expect it to have such (or, perhaps, any) normative significance. What do you think?

Structure and Similarity

I once thought that all possible ways of categorizing the world were metaphysically on a par. We may find it more useful to talk of tables and chairs, but objectively speaking this way of dividing up the world is not metaphysically privileged over alternatives that seem "gerrymandered" to us, e.g. combining chairs and cockroaches into a single category.

I now realize that my past self was very silly. Though it may at first seem puzzling that there could be privileged categories, or 'structure' to the world, it seems perfectly obvious that some pairings are objectively more similar than others. Two chairs are more alike -- have more natural properties in common -- than a chair and a cockroach, and this is nothing to do with our words and everything to do with how the world is. (A tribe might have a but a single word X that means 'chair or cockroach', but in that case their language would be objectively inferior to ours in this respect, for it fails to carve nature at the joints.)

One way to bring this out is to think about projectability, or what properties you can reason inductively from. All the emeralds I've seen so far have been green, so I expect the first emerald I see after 2020 will also be green. That seems a perfectly reasonable induction. On the other hand: "All emeralds I've seen so far have been grue, so I expect the first emerald I see after 2020 will also be grue" is clearly not good reasoning. This is because green is a more natural property than grue. It is an objectively better way to categorize reality.

Ontological Reduction

Is consciousness ontologically irreducible? Richard Brown thinks that the question is incoherent:

What [the identity theorist] says is that there is only ONE thing there, the brain and its various states, and you cannot reduce something to itself!

He goes on to contrast this with linguistic, theoretical reductions, and explains how those are irrelevant to the debate between physicalists and dualists. I agree with that part. But I think he's wrong to think that linguistic reductions are the only coherent form of reduction.

We can see this because, as I've been saying all along, the question is whether qualia are reducible in the same sense that tables and chairs are, whatever that may be. Now, it's an open question whether our talk of tables and chairs could be replaced by (perhaps complicated and long-winded) talk purely in the language of microphysical theory. But we don't care about talk. What matters is that the facts about tables are obviously settled by the microphysical facts. If you have a coarse-grained conception of 'facts', maybe they are even one and the same fact. Even so, we can get to a metaphysical notion of reduction by appeal to the truthmakers for our sentences. Regardless of whether table talk is linguistically replaceable by particle talk, there's no question that the microphysical facts are what make our table statements true (if they are true).

Once you've included the microphysical facts in your base facts, you do not need to add any further 'table facts' in addition. Those are already covered. It is in this sense that table facts are reducible to physical facts. And it is in this sense that the question of physicalism comes down to the question whether qualia are reducible. It is simply the question whether we need to add phenomenal facts to our fundamental base facts, or whether they "come along for free" (like tables do) given the physical facts P.

(I find it convenient to use the term 'reducible' to invoke this idea, but you're of course free to pick another word if you prefer. What's not helpful is to simply insist, "the debate between the dualist and the materialist is in no way a debate about reduction", and so ignore my underlying idea concerning what the debate is about. RB wanted to focus on what counts as 'physical' or 'non-physical', but that soon degrades into semantics. The substantive issue, as I see things, is whether we must include qualia as an additional primitive among the base facts. This understanding makes it clear why RB's "non-physical zombie" parody argument falls flat (to put it mildly). See my 'Zombie Review' for more detail.)

Subtracting Presuppositions

Follow-up to: Logical Subtraction and Partial Truth

Yablo proposes that (1) the real content of a statement S is what it says as opposed to presupposes; (2) what it says is what S adds to the presupposition π. That is, the real content R = S - π.

How can we tell what's presupposed? Linguists have developed various tests for this, including the negation test: Denying The # of planets is 8 is not thereby to assert There is no such entity or it is not 8. No, whether we assert or deny the claim, this way of talking presupposes numbers either way. So the real content is merely about how things stand concretely so far as the planets are concerned.

Plugging into the formula:
R = S - π
    = 'The # of planets is 8' - 'There are numbers'.

This remainder, the real content of what's said, is true even if the literal statement S isn't (due to the false presupposition). S is merely partly true, but it's true in the part that we care about.

Here's a vital question for metaphysicians concerned with ontological commitment: Are we committed to the truth of our presuppositions, or merely to what we say (i.e. what our assertions add to what's presupposed)? Ordinary talk presupposes all sorts of ontological extravagance: composite objects, numbers, propositions, properties, tensed reality (past/future), mere possibilia, etc. Such talk helps us to convey important truths, some of which may not even be possible to express in less ontologically loaded terms. So it would be nice if we could maintain this talk in good conscience, without thereby committing ourselves to the ontological presuppositions. Can we?

Sometimes, at least, we can knowingly adopt a false presupposition. Yablo mentions talk of 'the King' to denote Harold the usurper. Harold is not really the King, we all know -- the King is locked away in the dungeon. But nonetheless we may use 'The King is coming!' to warn of Harold's approach. This does not commit one to thinking that Harold truly is the King rather than a mere usurper. The false presupposition is adopted merely for sake of communication, and can be safely subtracted to get at the real content of our assertions. Similarly, we may think, for ontological presuppositions. We presuppose that there are numbers in order to more easily describe how things stand in concrete reality. But we may do this while remaining neutral on the question whether the presupposition is really true.

Yablo also briefly mentioned the popular meta-ontological view that various ontological disputes (e.g. whether numbers really exist) are 'empty' or meaningless. He suggests that we have this intuition in cases where the presupposition that X really exists is perfectly extricable from the ordinary claims which rest upon it. We have no trouble simply subtracting away the disputed metaphysical claims, and assessing the concrete remainder. So it seems like the metaphysics isn't really doing anything. That seems to describe my intuitions pretty well, I must admit. But what are the implications for meta-ontology? Can the subtraction method vindicate our deflationary intuitions? Or does it debunk them, suggesting that there is a further question there -- just not one we're typically concerned with in everyday life? Or must we look elsewhere to adjudicate this issue?

Fascinating questions, I reckon. Now if only I could find some answers...

Logical Subtraction and Partial Truth

Stephen Yablo gave a very impressive series of lectures here last week. His core insight was that often we can communicate important truths by way of assertions that are literally false. The rough explanation for this is that the assertion, though false, may be "partly true", or "true insofar as it concerns a certain subject matter." For example, 'the number of dragons is zero' may be literally false if numbers do not exist. But it is partly true, i.e. true in what it says about dragons (namely, that there aren't any). If you take the literal meaning, and subtract the claim that there are numbers, the remaining content is wholly true.

Sometimes logical subtraction seems unproblematic, as the subtracted element is "perfectly extricable" from what's being said. Other cases, however, are more problematic. When you subtract the redness from scarlet, what's left? 'Tom [the tomato] is scarlet - Tom is red' does not leave any remainder that we can make sense of. It seems perfectly inextricable. Then there may be inbetween cases, such as Wittgenstein's famous question: "what is left over if I subtract the fact that my arm goes up from the fact that I raise my arm?" We have some grasp of this, but as Jaeger has pointed out, "it is not the case that there is exactly one statement R such that 'R & my arm goes up' is logically equivalent to 'I raise my arm'."

Yablo's solution is to say that "P-Q always exists, but it doesn't always project very far out of the Q-region [of logical space]. Inextricability simply means that it is hard [or impossible] to evaluate P-Q in worlds where Q fails."

Intuitively, we can say that:
(i) P-Q is false iff P adds falsity to Q.
(ii) P-Q is true iff not-P adds falsity to Q.
(iii) If neither P nor its negation adds falsity to Q, then P-Q is undefined (lacks a truth value).

Yablo systematizes our intuitive judgments here by appeal to truthmakers, or the reasons why a proposition is true/false. P "adds falsity" to Q if it is false for a Q-compatible reason, i.e. there is a Q-compatible falsity-maker for P.

Example: Let P = 'The King of France is bald' and Q = 'France has a King'. Then P-Q is false, because of the following Q-compatible falsity-maker for P: the list of all the bald people, none of whom is a King of France. This falsity-maker could exist, and so make P false, even if Q were true and France did have a King. This shows that P is false for reasons over and above the falsity of its presupposition Q.

Here is a bit more technical detail. Let R be a potential candidate for P-Q. Yablo suggests that R is a successful candidate, i.e. R extrapolates P beyond Q, iff the following three conditions are satisfied:
- "Equivalence: within Q, R is true (false) in a world iff P is true (false)." That is, if R = P-Q, then it had better be the case that R&Q = P.
- "Reasons: within Q, a world is R (~R) for the same reasons it is P&Q rather than ~P&Q (...)" This is equivalence as applied to subject matter, rather than just truth conditions.
- "Orthogonality: outside Q, R is true (false) for the same reasons as within." This is the key principle, which really gets at the intuitive notion that we are genuinely extrapolating P rather than simply gerrymandering a proposition that happens to overlap with P in the Q-region (and then becomes wildly different beyond that point).

Example: The material conditional 'if Q then P' fails the orthogonality condition. Outside the Q region, it is true for the simple reason that Q is false, regardless of P. Compare the visual aid below: 'if Q then P' has truth conditions 'P or ~Q', so would include all the white region in R. The gerrymandering is visible in the fact that the R region would then turn a sharp 'corner' once it left the P & Q region. It should instead extrapolate cleanly as shown.