Yablo's "Is Conceivability a Guide to Possibility?": Classic Papers in Modal Epistemology Series

The publication of Yablo's 1993 PPR paper, "Is Conceivability a Guide to Possibility?" is widely considered a watershed in the history of the epistemology of modality. It's perhaps the most widely cited paper in the subfield to date. And while the subfield has progressed considerably since its publication, it still repays revisiting. And given the blog's aims, I've typed up a fairly careful outline of Yablo's paper. There are still some gaps, so I'll come back in due course to fill them in.

1. Introduction

1.1. Some statements express true propositions about what is metaphysically possible; others do not.

1.2. How can we tell the difference between the two?

1.3. The standard philosophical answer is captured by Hume’s maxim regarding conceivability-possibility inferences: 

1.4. Hume’s (modal epistemology) Maxim: “‘Tis an establish'd maxim in metaphysics, that whatever the mind clearly conceives, includes the idea of possible existence, or in other words, that nothing we imagine is absolutely impossible.”

1.5. Many philosophers have conflicting opinions about conceivability as evidence for possibility

1.5.1. On the one hand, they argue that conceivability is an unreliable guide to possibility

1.5.1.1. Arnauld: The inability to discern an essential connection between mind and body doesn’t entail that body does not belong to the essence of mind.  

1.5.1.2. Kripke and Putnam: there are necessities that are only knowable a posteriori. For example, prior to the discovery that water = H2O, it was conceivable that water could exist apart from H20. But given the necessity of identity, this is impossible. Therefore, conceivability-possibility inferences are unreliable.

1.5.1.3. Mill: Our ability or inability to conceive of something is a matter of accident, history, and our habits of mind; it has little to do with an ability to track real modal properties.

1.5.1.4. Reid and Kneale: If you find a proposition to be true for all you know (i.e., epistemically possible), then you will be inclined to think its truth is possible whether or not it really is so.

1.5.2. On the other hand, they rely heavily upon conceivability as evidence for possibility. Indeed, reliance on conceivability inferences seems not only entrenched, but indispensable to philosophical methodology.

1.5.2.1. Hume: 

1.5.2.1.1. We can conceive of nature diverging from its past patterns; therefore, it’s possible for it to do so.

1.5.2.1.2. We can conceive of any candidate cause to be followed by a different supposed effect, or no effect at all. Therefore, it’s possible for any candidate cause to be followed by different putative effects, and to produce no effect at all.  

1.5.2.1.3. Most philosophers take Hume’s arguments to have considerable epistemic force.

1.5.2.2. Kripke: We can conceive of a counterfactual scenario in which Aristotle (say) dies of dysentery before ever becoming the teacher of Alexander the Great. Therefore, such a state of affairs is possible. Therefore, “the teacher of Alexander the Great” is not a rigid designator.

1.6. There is thus pressure for philosophers who accept conceivability-possibility inferences, and who take them to be indispensable to philosophical practice, to make a serious inquiry and determine whether such inferences are legitimate.

1.7. Our focus: certain criticisms of conceivability-possibility inferences

1.7.1. The criticism that they illicitly trade on a slide between two senses of ‘could’.

1.7.2. The criticism that they are implicitly circular

1.7.3. The criticism that they misclassify most or all a posteriori impossibilities as possible

1.8. Two sweeping criticisms of conceivability-possibility inferences to dispose of before we begin in earnest:

1.8.1. 1st sweeping criticism: No evidence exists of the reliability of conceivability-possibility inferences that doesn’t already rely on such inferences. Therefore, such inferences are illegitimate, or at least dubious.

1.8.2. Reply: The same goes for perceptual experience, but few are persuaded by such a criticism to stop trusting perception as a guide to actuality.

1.8.3. 2nd sweeping criticism:  Although we don’t have a philosophically satisfying reason to think perception is a reliable guide to actuality, at least we can see how we could. For we know where our sensory mechanisms are located, and something about how they work. By contrast, we have no idea of where our supposed systems for detecting modal properties might be located or how they work. Therefore, we should treat them as suspect.

1.8.4. Reply: The same thing goes for our faculties of mathematical and logical intuition. But few are persuaded by such worries to stop relying on such intuitions when drawing mathematical and logical conclusions.

2. Conceivability and the Modal Appearance Test: Clarifying the basic notion of conceivability 

2.1. Conceiving is in a certain way analogous to perceiving: Just as perceiving that P involves the appearance that P is true, so conceiving involves the appearance that P is possible.

2.1.1. In slogan form: Conceivability is the appearance of possibility. 

2.2. On the truth-conditions of conceivability 

2.2.1. The intentional states involved in conceiving cannot be read off their contents alone.  

2.2.2. The “DeGaulle liked cheese” example: The agent’s propositional attitude and the proposition’s modal status are constitutive of the truth-conditions as well

2.3. Representative appearance vs. epistemic appearance

2.3.1. Representative appearance: the intentional content captured by the proposition corresponding to the conceived state plus its modal status and the agent’s propositional attitude. These correspond to the satisfaction conditions of the act or episode of conceiving that P.

2.3.2. Epistemic appearance: P epistemically appears to S iff the representative appearance prima facie motivates/moves S to believe that P by virtue of making the belief that P seem to S to be prima facie justified. 

2.3.3. Someone might well argue that representative appearance entails epistemic appearance.

2.3.3.1. Example: Perhaps a perceptual experience with the truth conditions that P cannot help but motivate/move/incline the perceiver to believe that P (although the perceiver might resist it. Cf. the Muller-Lyer illusion).

2.3.4. However, the converse doesn’t hold:

2.3.4.1. Example 1: For non-experts, it only epistemically appears that the bull is about to charge.

2.3.4.2. Example 2: For non-experts, it only epistemically appears that the car won’t make it through winter (because of the sounds it’s making). If your car should make it through winter, your experience tempted you to accept a false belief. But it’s not as though you had a perceptual illusion.

2.3.4.3. Fn. 18: “Admittedly it is hard to draw a definite line between representative and (merely) epistemic appearances. Experts (matadors and mechanics) can enjoy representative appearances which to most of us are available only epistemically. But expertise is acquired gradually, and on the road to it there will be appearances not happily classified either way. For our purposes the indeterminacy doesn't matter, what will matter is the contrast between cases where p appears in both senses and those where it appears in neither.”

2.3.4.4. ‘Conceive’ is here used in the non-factive sense. It’s possible to conceive that P is possible even though P is impossible. In this way, it differs from (say) Descartes’ notion of a clear and distinct perception of the intellect.

2.3.4.5. Another similarity between perceiving and conceiving: Just as perceptual experience that P prima facie justifies the putative perceiver in believing that P is true, and thereby moves/motivates/inclines one to believe that P, so conceiving that P is possible prima facie justifies the conceiver in believing that P is possible, and thereby moves/motivates/inclines the conceiver to believe that P is possible.

2.3.4.6. However, the notion of justification in play here is subjective justification. The perceiver and the conceiver may both feel justified in virtue of their perceptual or conceiving states, and yet fail to be justified in fact.

2.4. Conceivability: A first pass

2.4.1. S finds P conceivable iff: S is in a state that (i) is veridical only if P and (ii) the state thereby inclines/motivates/moves S to believe that P is possible.  

2.4.2. Proper conceiving requires both the representative and the epistemic senses of appearance 

2.4.3. Proper conceiving requires that the representative appearance is the basis of the epistemic appearance.

2.5. Paper thesis and plan

2.5.1. Thesis: Since the relevant kind of conceivability is that captured by Hume’s Maxim, since that kind essentially involves the appearance of possibility, and since the standard objections listed earlier attack kinds of conceivability that do not essentially involve the appearance of possibility, the standard objections fail.

2.5.2. Plan of the paper: Sections 3-9 address objections to conceivability as a guide to possibility. Section 10 fleshes out Yablo’s positive account of conceivability. Sections 11-14 discuss the problem of modal error, and how Yablo’s account can handle it. Section 15 discusses tentative morals for the issue of realism vs. antirealism about modality.

3. The Confusion Objection:  

3.1. To find P conceivable is not to find P true for all you know/unable to rule it out that P is true (i.e., believable).

3.2. While this is a common colloquial use of the term, it is not what is meant, or should be meant, by the philosophical use of the term

3.2.1. In philosophical cases, construing it in this way leads to absurdities

3.2.1.1. It implies that that the less you know about the relevant subject matter, the more likely it is that the proposition entertained it true!  So absolute ignorance with respect to that subject matter entails certainty that P is true!

3.2.1.2. In any case, arguments from believability are unreliable as guides to possibility.

3.2.1.3. Reid: Many propositions about the nature of things  that were in the past believable were later proven to be mathematically impossible. 

3.2.1.4. More recently: the axioms of naïve set theory are believable to the uninitiated and yet impossible

3.2.1.5. There are straight counterexamples to the believability account whenever the proposition is necessary but unknown (e.g., Goldbach’s conjecture): 

3.2.1.5.1. P is believable and not-P is believable.  

3.2.1.5.2. But it can’t be that both P is possible and not-P is possible, since P’s status is necessary or impossible -- it’s not a contingent or merely possible truth.

4. Believability (i.e., Conceivabilityb)

4.1. Conceivability is not believability

4.2. Many modal errors are due to an illicit slide from believability to possibility

4.3. This is the account that is most commonly attributed to Descartes. Even Arnauld attributed it to him in his famous objection.  

4.4. However, this is a very uncharitable attribution to Descartes

4.4.1. It’s such an awfully implausible view; charity speaks against attributing it to him unless there are strong reasons to do so

4.4.2. As a matter of fact, there are strong reasons against doing so

4.4.2.1. In Meditation One, Descartes finds his being essentially a body believable, but he doesn’t think it’s thereby metaphysically possible

4.4.2.2. In Meditation One Descartes finds God’s non-existence believable, but he doesn’t think it’s thereby metaphysically possible

4.5. In any case, it’s granted that this account of conceivability is inadequate. 

4.5.1. The Goldbach’s Conjecture (GC) case: 

4.5.1.1. It’s believable both that GC is true and that it’s false

4.5.1.2. Despite this, given its necessity, it’s not both metaphysically possible that it’s true and metaphysically possible that it’s false – i.e., it’s not a contingent truth.

4.5.1.3. Neither case is conceivable in the relevant sense – viz., as appearing to one as possible.

4.5.2. Conceivability doesn’t entail believability 

4.5.2.1. It’s conceivable that I should have never been born, but it’s not believable that I have never been born.

4.5.2.2. If conceivability entailed believability, then whenever one was certain that something was false, one would be unable to conceive of it as even a possibility. But this is absurd.

4.6. Believability doesn’t entail conceivability: 

4.6.1.  Hard to find a pure case, i.e., one where something is believable yet inconceivable

4.6.1.1. If you find something believable, then you think it could turn out to be true in the actual world

4.6.1.2. But if so, then how can it also appear to you that it can’t be true in any possible world? 

4.6.2. However, there do seem to be impure cases, i.e., cases where something is believable, but neither appears to you as possible nor as impossible – i.e., undecidable cases.

4.6.2.1. Case 1: Goldbach’s Conjecture: 

4.6.2.1.1. It’s believable that GC is true, and it’s believable that GC is false

4.6.2.1.2. However, it’s neither conceivable nor inconceivable that GC is possibly true or possibly false – no modal appearance either way

4.6.2.1.3. “No thought experiment that I, at any rate, can perform gives me the representational appearance of the conjecture as possible or as impossible, or the slightest temptation to believe anything about its modal character.” (p. 11)

4.6.2.1.4. Rather, it’s undecidable

4.6.2.2. Case 2: The wax flower/real flower case: 

4.6.2.2.1. Suppose you have before you two things that look like flowers. Call one ‘Jacob’ and the other ‘Esau’. 

4.6.2.2.2. Suppose further that one is a real flower and the other is a perceptually indistinguishable wax flower. 

4.6.2.2.3. Finally, suppose that you don’t know which is which. 

4.6.2.2.4. Then it’s believable of each one that it is the real flower and the other is the wax facsimile

4.6.2.2.5. And if one assumes that Jacob is the real flower, then one can conceive of Jacob (and not Esau) as being capable of sprouting real petals

4.6.2.2.6. And if one assumes that Esau is the real flower, then one can conceive of Esau (and not Jacob) as being capable of sprouting real petals

4.6.2.2.7. As it is, though, one can’t conceive of either one as being capable of sprouting real petals when no such assumptions are made.  

4.6.2.2.8. For conceivability involves the appearance of possibility, and such an appearance isn’t involved in such cases

4.6.2.2.9. That would require accessing information regarding which one is the real flower.  

4.6.2.2.10. But such information cannot be read off the representational content

4.6.2.2.11. Because of this, it’s undecidable.

4.6.2.3. Case 3:  Mary and Martha

4.6.2.4. It was believable to Solomon that Mary is the mother of the baby, and it was believable to Solomon that Martha is the mother of the baby

4.6.2.5. Despite this, it didn’t thereby appear to Solomon that the baby’s biological ancestry is metaphysically contingent.

5. Some Circularity Objections: i.e., bad, easily handled, circularity objections 

5.1. Bad objection 1

5.1.1. Since your argument is by admission fallible, you yourself recognize that it might fail in any given case. 

5.1.2. Therefore, you should refuse to draw the conclusion, until you get prior assurances that it won't fail in this case. 

5.1.3. And that means: prior assurances that p is possible. 

5.1.4. So, the argument becomes circular. 

5.2. Reply: 

5.2.1. Fallibility doesn’t mean unreliability. 

5.2.2. In fact, it’s generally reliable. 

5.2.3. There is thus a presumption in favor of trusting conceivability unless one has grounds for doubt in the particular case at stake.

5.3. Bad obection 2 

5.3.1. For all you know, you would not have found p conceivable if you had been better informed, specifically, if you had known that p was impossible. 

5.3.2. But evidence that might, for all you know, be dependent on ignorance is inherently untrustworthy. 

5.3.3. To be sure that your evidence is not thus dependent, you need to know that p is possible. 

5.3.4. But then your argument becomes circular: you must already know that p is possible, before you can know that it is from your ability to conceive it.

5.4. Reply 1: 

5.4.1. I take it that my conceiving that p is possible is evidence that makes it probable that p really is possible. 

5.4.2. But if so, then the other cases (if such there be) that were impossible despite being conceivable don’t have a bearing on the probability of the conceiving at hand.

5.4.3. In general, a method that generates a high ratio of true to false beliefs is compatible with that method generating some false beliefs.

5.5. Reply 2 (fn. 36): 

5.5.1. Perception generates prima facie justified beliefs, despite generating misleading perceptions that are perceptually indistinguishable from accurate perceptions (Cf. the plastic Chinese food case). 

5.5.2. But we don’t take this to be adequate grounds to reject perception as a source of prima facie justification

5.5.3. But if not, then by the same token, we shouldn’t take misleading conceivings as adequate grounds to reject conceivability as a source of prima facie justification

5.6. Bad objection 3 

5.6.1. You can’t infer p's possibility before you’ve ruled out alternative explanations of its conceivability. 

5.6.2. Since for p to be unbeknownst to you impossible would sufficiently account for your ability to conceive it, this is one of the alternative explanations you need to rule out. 

5.6.3. To rule it out, though, you need to know that p is possible, thus rendering the argument circular. 

5.7. Reply: 

5.7.1. The kernel of truth in the objection is that if you know, or have good evidence, that an alternative is epistemically possible, you have to rule it out to prevent your belief from being undercut.

5.7.2. However, the objection goes beyond that by saying that you have to rule out alternatives that you have no reason to believe obtain.

5.7.3. That would lead to an unacceptable radical skepticism in the case of perception.

5.7.4. Similarly, it would lead to an unacceptable radical skepticism in the case of conceivability

6. The Circularity Objection: The Decent One

6.1. The objection: 

6.1.1. On the basis of many confirmed instances, we are justified in believing that almost all unappreciated impossibilities are conceivable.  

6.1.2. But if so, then for any given putative veridical conceiving, you need a reason to think that it is not an unappreciated impossibility case.  

6.1.3. But this requires knowing that it is possible on grounds prior to and independent of the putative veridical conceiving.

6.2. Reply: 

6.2.1. Haven’t been given a sufficient sample size of conceivable impossibilities – few if any. 

6.2.2. The examples often offered aren’t conceptions that appear possible (e.g., Goldbach’s Conjecture), but rather cases in which the modal propositions are undecidable (e.g., it isn’t as if one feels moved to believe that either the truth or the falsity of GC is possible.)

7. Believability of Possibility (i.e., Conceivabilitybp)

7.1. Conceivabilitybp: It is (not un)believable that P is possible, i.e., for all I know, P is possible, i.e., my evidence doesn’t rule it out that P is possible

7.1.1. First criticism:

7.1.1.1. Recall the “more ignorant = more certain” objection to the believability account.  

7.1.1.2. Same basic problem here, but with respect to overtly modal claims: the less knowledge that you have with respect to evaluating “possibly P”, the more certain you are that it is possible. 

7.1.2. Second criticism:

7.1.2.1.  It fails both conditions of the modal appearance test: 

7.1.2.1.1. if P is merely possible-for-all-you-know, then it doesn’t appear true to one (it doesn’t move one to believe it)

7.1.2.1.2. nor is it a misrepresentation (since it doesn’t represent something as possible). 

8. The A Posteriority Objection

8.1. The Kripke/Putnam cases:

8.1.1. it is only discoverable a posteriori that “two” things are identical seem to present a problem for conceivability as a guide to possibility.  

8.1.2. For it seems that in such cases, if one is not aware of the identity, then one can imagine the “two” things as distinct. 

8.2. The objection:

8.2.1. Whenever p is a posteriori false, I find p conceivable whether it is possible or not. 

8.2.2. Often, a posteriori falsehoods are impossible.

8.2.3. Therefore, a posteriori falsehoods are often found conceivable despite their impossibility.

9. Epistemic Possibility:  The reply to the A Posteriority objection:  Since the a posteriori objection relies on the notion of “imagining that impossible things are true” (e.g., that a is not identical to b, even though, a = b, in which case the former statement is necessarily false), a number of construals of this notion are presented and evaluated.  This ultimately leads to clarifying the nature of Kripkean epistemic possibility.  Two misconstruals of Kripke’s notion are presented and rejected, and (after getting clear on the prerequisite idea of expressing a true proposition with a thought) an adequate account of Kripkean epistemic possibility is presented.  Once this is done, Yablo applies the distinctions to show that premise (1) of the objection is unjustified.

9.1. Distinction 1: Conceivableijb vs. Conceivableitb

9.1.1. Conceivableijb: I can imagine a scenario according to which I acquire evidence that justifies me in believing that p.

9.1.2. There are three ways in which such thought experiments might go: (a) the evidence imagined is disclosive of how things in the imagined situation really are, (b) the evidence, while persuasive, is misleading, and (c) it is left unspecified whether the evidence is misleading.

9.1.3. But conceivability requires that the imagined scenario makes it such that the relevant proposition appears true.  

9.1.4. But if so, then (b) and (c) aren’t cases of conceivability at all, in which case (a) – the one in which I believe justifiably and truly that p - is the only relevant type of conceivability case.

9.1.5. But if this is so, then it is irrelevant whether you are imagined as having justification for your belief that p is true.  For the imaginability of knowing that p in a scenario can’t be better evidence for the possibility that p than the imaginability of believing, truly, that p.  

9.1.6. But if so, then Conceivableijb isn’t a helpful notion of conceivability; thus, it isn’t relevant to determining the cogency of the a posteriority objection (or, if the objector does have this notion of conceivability in mind, then he is attacking a straw man).  This leads to the next candidate for being a relevant notion of conceivability:

9.2. Conceivableitb: I can imagine a scenario according to which I believe, truly, that p.

9.2.1. The worry is that the a posteriority objection arises all over again for this notion of conceivability. Can’t one imagine believing truly that cats are robots, that water is not H20, etc.?

9.2.2. This application of the objection to this version of conceivability is based on Kripke’s notion of epistemic possibility.  Kripke pointed out the distinction between “could have been” statements and “could have turned out” statements.

9.2.3. Most people misconstrue Kripke’s distinction, thus fallaciously applying it to the a posteriori identification cases as follows: 

9.2.3.1. we see that it could not have been that Hesperus is distinct from Phosphorus; for they are identical, and the identity relation holds necessarily.  

9.2.3.2. However, in some sense of the expression, it could have turned out that Hesperus and Phosphorus were not identical.

9.3. We can see that this must be a misconstrual of Kripke’s notion of epistemic possibility:

9.3.1. There are two ways to take the explanation of ‘it could have turned out that p’: 

9.3.1.1. (a) it is possible that I come to believe, truly, that p

9.3.1.2. (b) it is conceivable that I come to believe, truly, that p.

9.4. Reading (a) is absurd, for, obviously, if H and P are identical, it could not have turned out that H and P were distinct; in which case it is not possible that I come to believe, truly, that p.

9.5. But reading (b) is absurd as well; for this would require imagining a scenario according to which one believes truly that H and P are distinct.  But since H is P, there is no true scenario according H and P are distinct.

9.6. But if so, then if conceivableitb were the notion relevant to the a posteriority objection, as well as to Kripke’s notion of epistemic possibility, then since some – perhaps most – impossibilities that are known only a posteriori are not Conceivableitb, the objection would fail, and Kripke’s notion of epistemic possibility would be vacuous. 

9.7. So, conceivableitb is not the relevant notion of conceivability (nor is it an adequate account of Kripkean epistemic possibility).  But since there seems to be a stubborn intuition that there must be something to the notion of epistemic possibility – that we can imagine, in some sense, that water is not H20, etc. - we are led to examine the notion more carefully. In particular, it leads us to examine the notion of imagining oneself believing something truly.

9.8. There are two ways to construe the notion: (a) imagining that the proposition believed by your hypothetical self is true, and (b) imagining that the proposition believed by you in the actual world is true.  To get clear on this, we have to have in hand an account of propositional content and thought content, and their relations with one another.  

9.8.1. The nature of the contents of thought and propositions:

9.8.1.1.1. Let’s say that the content of a thought is what is often called “narrow content”

9.8.1.1.2. On this account, a thought plus the context – the world or scenario – in which it is entertained, gives us the content of the proposition believed.

9.8.1.1.3. So, thought T that Hesperus is distinct from Phosphorus, entertained in W, gives us the proposition p that we all know. But thought T, entertained in W*, gives us the proposition that has the truth conditions that Venus is distinct from Mars.

9.8.2. Applying the distinctions to the issue: in imagining, or seeming to imagine, myself truly believing an a posteriori impossibility p, do I (a) imagine believing truly the proposition that my thought expresses in the actual world, or do I (b) imagine believing truly some other proposition – i.e., the one that my thought would have expressed had the imagined scenario obtained?

9.8.2.1.1. Assume it’s (a).  Since the proposition imagined is just p in this case, this is just conceivabilityitb.  So, not-(a).

9.8.2.1.2. Assume it’s (b).  In this case, one can imagine believing truly some proposition – some proposition distinct from p -- say p’. For on our account of the contents of thoughts and of propositions, our thought T, that expressed proposition p in the context of the actual world, expresses a different proposition p’ in the world of our imagined scenario.  Thus, we finally have an adequate account of Kripkean epistemic possibility:

9.8.2.1.3. Conceivabilityep:  I can imagine believing truly with my thought T – which expresses p in the actual world - some other proposition p’, which is true in the imagined scenario. 

9.8.3. Applying all of the preceding discussion to the a posteriority objection:

9.8.3.1.Against premise 1: that all a posteriori falsehoods are conceivable:

9.8.3.1.1.1. The relevant notion of conceivability is either (a) conceivableijb, (b) conceivabilityep, or (c) conceivabilityitb.

9.8.3.1.2. If the relevant notion is conceivableijb, then it doesn’t show that conceivability is an unreliable guide to possibility in such cases.  For any genuine type of conceivability includes, essentially, the appearance that p is possible, and this sort of conceivability lacks this appearance. Rather, it conveys the idea that you could’ve been justified in believing that p.

9.8.3.1.3. If the relevant notion is conceivabilityep, then it doesn’t show that conceivability is an unreliable guide to possibility in such cases.  For conceivability essentially includes the appearance that p is possible, and this sort of conceivability lacks this appearance. Rather, it conveys the idea that you could’ve believed some other true proposition via the thought you use to believe that p in the actual world.

9.8.3.1.4. If the relevant notion is conceivabilityitb, then if it is true that all a posteriori falsehoods are conceivableitb, then this would show that conceivabilityitb (which is one genuine type of conceivability, since it involves the appearance of possibility) is unreliable as a guide to possibility in such cases.  However, this hasn’t been argued for – indeed, it’s doubtful that anyone would be willing to defend it (would someone argue that one can conceive, truly, that Hesperus is distinct from Phosphorus?)

10. What Conceivability Is: Yablo's finalized account of conceivability

10.1. All the other five putative versions of conceivability are impostors of the adequate account.

10.2. Conceivabilityitb comes the closest, but it’s inadequate; for one can’t conceiveitb of truly possible situations that conflict with the hypothesis of my knowing it (e.g., that I don’t exist, that no one has any beliefs, etc.)

10.3. So, to get around this problem, we say that p is conceivable if I can imagine a situation of which (not in which, as this formulation suffers the previously mentioned problem) one truly believes that p.

10.4. Developing the account: what is imaginability?

10.4.1. Preliminary stuff: varieties of imaginability and their respective types of content

10.4.1.1. Propositional imagining: includes alethic content

10.4.1.2. Objectual imagining: includes referential content – i.e., purports to depict the object

10.4.1.3. Propositional imagining may be accompanied by objectual imagining

10.4.1.4. But most importantly for the issue of conceivability as a guide to possibility, propositional imagining may be accompanied by, and proceed by way of, objectual imagining

10.4.2. The nature of objectual imagining

10.4.2.1. As a first approximation, objectual imagining is the imagining of a more or less determinate situation

10.4.2.2. How determinate is (must?) the objectually imagined object be?

10.4.2.2.1. not all the details need be determinate (e.g., imagining a tiger need not require imagining one determinate striping pattern – “the content of my imagining is satisfiable by variously striped tigers, but not of tigers of no determinate striping.”)

10.4.2.2.2. similarly for imagining whole situation

10.4.2.2.3. imagining a determinate object =df. Imagining for the relevant objects, its possessing for each determinable property, an underlying determinate.

10.4.2.2.4. imagining an object as determinate vs. determinately imagining it

10.4.2.2.4.1. determinately imagining an object: specifying, for each determinable of the object, what the underlying determinate is 

10.4.2.2.4.2. imagining an object as determinate: imagining the object as possessing a determinate property for each of its determinables.

10.4.2.2.4.3. Given the preceding clarifications, we may state what we mean by “imagining a more or less determinate object”: imagining the object as determinate.

10.4.2.2.4.4. However, when one imagines a situation, one imagines it as fully determinate – although the determinates for many objects in the situation are left unspecified.

10.4.2.2.4.5 Imagining a situation need not involve sensory imagery -- cf. Descartes' "chilliagon" case. Cf. fn. 55 for this crucial point. (Chalmers will later take this point on board as well).

10.4.2.3 Imagining a situation is not the same thing as imagining a possible world, but just a portion of one.  

10.4.2.4 However, you do imagine a whole possible world, in the sense that you imagine the situation as embedded in a complete (although largely unspecified) situation (i.e., a world).  The imagined situation is the part of the possible world that grounds the truth value of the relevant statement we are concerned with.

10.4.3. The formal statement of the account in light of the previous clarifications: 

10.4.3.1. CON: P is conceivable for S =def. S can imagine a world that S takes to verify P. 

10.4.3.1.1. Further elaboration: 

10.4.3.1.1.1. “…when I imagine a world of such and such a type, it appears to me that a world of that type could really have existed.  

10.4.3.1.1.2. But when I take it to verify p, I take it that if a world like that had existed, then p would have been the case.  

10.4.3.1.1.3. So, when I imagine a world which I take to verify p – and this is what it is to conceive that p on the proposed account – I have it appear to me that p is possible.” P. 30.

10.4.3.2. INC: P is inconceivable for S =def.  S cannot imagine a world that S doesn’t take to falsify P.

10.4.3.3. CONu: P is not decidably conceivable for S =def.  S cannot imagine a world that S takes to verify P

10.4.3.4. INCu: P is not decidably inconceivable for S =def.  S can imagine worlds that S doesn’t take to falsify P. 

10.4.4. Some brief remarks in favor of the account: 

10.4.4.1. “leads in interesting directions”(?)

10.4.4.2. fares better than any other account with respect to the modal appearance test.

10.4.4.3. doesn’t seem to fall prey to the unreliability objections

10.4.4.4. an argument that it really does seem that our modal intuitions are the result of these kinds of imaginings: the intuitions didn’t exist prior to the imaginings

10.4.4.5. witness the many philosophical propositions that we have changed in virtue of such imaginings: K isn’t JTB, etc.

11. Undecidability: undecidable modal propositions are those in which the conjunction of CONu and INCu apply to their corresponding imaginings: the worlds I imagine neither verify nor falsify the modal proposition under question.

11.1.1. Case 1: the wax flower/real flower case (see section 4 for review of the case)

11.1.1.1. Can’t know via conceiving whether it is Jacob or Easau is the real flower.

11.1.1.2. Furthermore, wax flowers are essentially such that they can’t sprout petals, while real flowers can.

11.1.1.3. These two facts render it impossible to imagine a possible world that verifies that Jacob can sprout petals.

11.1.1.4. However, it’s also true that one can imagine possible worlds where one is unready to describe as ones in which Jacob can’t sprout petals.

11.1.1.5. Therefore, “Possibly, Jacob sprouts petals” is undecidable.

11.1.2. Case 2: the Goldbach’s Conjecture case (see section 4 for review of the case)

11.1.2.1. Consider the proposition, “Possibly, GC is false”.

11.1.2.2. One can imagine a computer printing out some unspecified even number n, and mathematicians hailing it as a counterexample to GC. However, that’s compatible with GC having no counterexamples, and the computer made an error with respect to even number n as a genuine counterexample, unbeknownst to the mathematicians. As such, the scenario fails to verify not-GC.

11.1.2.3. You might think you can get around the problem by imagining a computer printing out a proof that n is a counterexample to GC. But such an imagining won’t generate an appearance in you of not-GC as possible unless you can imagine that the proof is correct. But since arithmetical truths are necessary truths, they don’t vary from world to world, and so your confidence that n is a counterexample to GC in some other possible world is limited by your confidence that it is a counterexample to GCs at the actual world. But you don’t know that and neither does anyone else. It therefore seems that, short of imagining the details of the proof of a counterexample to GC, one can’t verify its truth in another possible world. But of course, you can’t verify its falsehood, either. Therefore, not-GC is undecidable. 

12. Modal Error:  

12.1. Modal appearances are compared to perceptual appearances: Just as perceptual appearances provide prima facie, defeasible justification for perceptual beliefs, so appearances of possibility provide prima facie, defeasible justification for beliefs about possibilities.  

12.2. However, there is a disanalogy: we have a decent grip on the origin of perceptual error/misperception, how to guard against it, and how to correct such mistakes; but this isn’t so for modal error.  

12.3. So, even though conceivability is perhaps generally reliable, people do make modal errors (Hesperus/Phosphorus case, Oedipus/Jocasta case, etc.) we have no way of telling, in any particular case, whether it is a modal error case. 

12.4. The next section is an attempt to handle to this worry, to some extent.

13. Models of Modal Error:  Two models of modal error are presented and evaluated:

13.1. The Denial Model: to defeat a modal claim that p, based on a proper use of CON, one must come up with a known/justified proposition q, such that:

13.1.1. q,

13.1.2. if q, then ~p

13.1.3. that I find p conceivable is explained by my denial of (1) and/or (2)

13.2. The Unawareness Model: to defeat a modal claim that p, based on a proper use of CON, one must come up with a known/justified proposition q, such that:

13.2.1. q

13.2.2. if q, then ~p

13.2.3. That I find p conceivable is explained by my unawareness of (1) and/or (2).

13.2.2. one can’t just substitute the proposition that ~p for q.  For this is question-begging.  We need to substitute for q some proposition that we have good, independent reason to accept.

14. Modal Dialogue

14.1. In this section, Yablo puts the model(s) of modal error spelled out in XIII into practice (using dualistic intuitions as an example) to illustrate how they work, and thus how modal errors can be detected and corrected. 

14.2. Modal dialogue typically proceeds as follows: 

14.2.1. X finds p conceivable and calls it possible

14.2.2. if Y chooses to challenge X's intuition, she proposes a defeater q to explain how X was capable of it despite its falsity

14.2.3. if X is unable to accept this explanation, she takes issue either with q itself, or with Y's claim that it casts doubt on her intuition's accuracy. 

15. Factualism about Modality

15.1. In this section, Yablo discusses what should be done if modal dialogue breaks down (stalemates?).  

15.2. The main worry is that the correct response to breakdown – when it is (i) frequent and (ii) due to disagreement on fundamental matters -- is to deny factualism about modality (i.e., to deny that there are facts over which the disputants are disagreeing, and of which one of them is getting wrong).  

15.3. Yablo agrees with non-factualists that entitlement to modal factualism “turns on the effectiveness of our strategies against conflicts, or seeming conflicts, of conceivability intuitions.”     

15.4. However, he is optimistic (or at least not pessimistic) that we have such strategies, and that we will continue to make progress in constructing and utilizing them, if the last 30 years of philosophy is any indication. 

15.5. He presents three such strategies, all of which have been used earlier within the article

15.5.1. First strategy: Try to show that there is no conflict of conceivability intuitions because what looked like p’s conceivability was really only its believability, or epistemic possibility, or…; or what looked like its inconceivability was really only its unbelievability, or epistemic possibility, or …

15.5.1.1. the Goldbach’s Conjecture case

15.5.1.2. the Hesperus/Phosphorus case

15.5.2. Second strategy: Admit that there are conceivability intuitions on either side but try to show that they are not in conflict because what seemed to be the conceivability (inconceivability) of one proposition was really that of some closely related other:

15.5.2.1. the Hesperus/Phosphorus case

15.5.2.2. cases due to differences in idiolects in which the disputants talk past each other. (Personal identity disputes, etc.)

15.6. Third strategy: Admit that there is a conflict of conceivability intuitions but try to show that at least one of them has a defeater and is therefore open to doubt. 

15.7. What if, after utilizing the three strategies above, fundamental disagreement remains?  

15.7.1. We should keep developing dispute resolution strategies.  

15.7.2. In the last 30 years, this is exactly what has happened in modal metaphysics.  

15.7.3. So, we have reason to be hopeful that if we keep up with this, we will be able to resolve such conflicts increasingly as time goes by.