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The Conceivability-to-Possibility Entailment:How It Does (Not) Work*

© Dmytro Sepetyi, 2015(The paper is copyrighted in the State Service of Intellectual Property of

Ukraine)

0. IntroductionConceivability arguments for metaphysical

possibility play a considerable role in philosophicaldiscussions, especially in the philosophy of mind. Themost famous classical example is Rene Descartes’conceivability argument for the possibility of theunembodied mind; the most outstanding recent example isDavid Chalmers’ conceivability argument for the logicalpossibility of phenomenal zombies (as part of thezombie argument against materialism). Also, generaldiscussions about the conceivability-entails-possibility thesis (in the rest of the paper, I referto it as CP), including highly sophisticated accountsand defenses by Chalmers, are not lacking.Nevertheless, the way the entailment works—and whetherit really does work—remains obscure.

1. The kind of possibility at issueThe kind of possibility at issue is usually called

“metaphysical possibility.” This should be clearlydistinguished from what Chalmers calls “naturalpossibility.” Natural possibility is a matter of whatis possible in the actual world, given the laws ofnature. Metaphysical possibility is not a matter of theactual world but a matter of possible worlds, which maydiffer from the actual world in a lot of ways,including fundamentally (having different laws of* This is an original manuscript (preprint) of an articleforthcoming in the journal The Philosophical Forum, Fall 2017.

nature, for example). Such worlds are usually referredto as metaphysically possible. Thus, when philosopherstalk of something as metaphysically possible, they meanthat it could exist (or happen) in some metaphysicallypossible worlds. However, this does not get us far inunderstanding what it takes for something (be it aworld, a situation, or an event) to be metaphysicallypossible.

David Chalmers, in his magnum opus, The Conscious Mind(1996), and in several later papers, argues thatmetaphysical possibility should be identified withlogical possibility. Metaphysically possible worlds (orsituations or events) are just logically possibleworlds (or situations or events):

“… the space of logically possible worlds …suffices to account for all of the modal phenomenathat we have reason to believe in and that we mightinvoke possible worlds to explain. …there is nogood reason to postulate a separate space ofmetaphysically possible worlds. There is no clearexplanatory work left for such a space to do. Thespace of logically possible worlds, which we haveindependent reason to postulate, explains all theuntendentious modal data.” (Chalmers 2010, 187)(See also: Chalmers 2002)In what follows, I will proceed from the

supposition (which seems to me very plausible in thelight of Chalmers’ arguments, which I cannot recounthere in appropriate detail) that metaphysicalpossibility—the kind of possibility relevant to thearguments having to do with the CP entailment—islogical possibility. (Of course, arguments to thecontrary are invited.)

2. The circularity problem and ideal conceivabilityChalmers is probably the most prominent modern

defender of the conceivability arguments. He has

elaborated a sophisticated “supporting structure” thatis apparently based on the concept of “idealconceivability.” I think that there are good reasons tobe skeptical about it.

My principal objection to this major line is thatit makes the move from conceivability to logical(≡metaphysical) possibility a hidden tautology. Thetautology is that what is logically possible (not a priorifalse, as a matter of incoherence) is logicallypossible (not a priori false, as a matter of incoherence).

One can start worrying on reading one of Chalmers’earlier papers, “Materialism and the Metaphysics ofModality” (1999). In it, Chalmers explains theconnection between “conceivability” and “logicalpossibility” as follows: “On my usage, ‘logicallypossible’ … is tied by stipulation to conceivability.”After this statement, Chalmers quotes the passage fromThe Conscious Mind where he wrote that he “will henceforthtake this for granted as a claim about logicalpossibility; any variety of possibility for whichconceivability does not imply possibility will then bea narrower class,” and explains again that “‘taking forgranted’ here is stipulative” (pp. 477-8). Now, if itis just a matter of stipulation that logicalpossibility is tied to conceivability, we cannot expectanything non-trivial here, and no argument thatconceivability entails logical possibility is needed.It is just a matter of using two terms interchangeablyin nearly the same meaning (so that if there is anydifference, it does not matter for the argument).1 Inthis case, it is obviously useless to make theconceivability-to-possibility entailment into a sort offoundation for the zombie argument and to spend muchtime and effort inventing sophisticated arguments forthe entailment. However, does not Chalmers do exactlythis in some of his later papers? Or has he changed his1 Indeed, I think that Chalmers’ exposition of the zombieargument in The Conscious Mind fits well with such a construal.

construal of the relationship between conceivabilityand possibility, so that it lost its stipulative(tautological) character and became substantial?

Let us consider first the explanation Chalmersgives in the paper “Imagination, indexicality, andintensions” (2004). According to it, the zombieargument is based on two premises: “the first premiseis that zombies are conceivable, roughly in the sensethat there is no a priori contradiction in the idea ofa zombie,” and “the second premise is that if zombiesare conceivable in this sense, then they are possible.”Chalmers specifies that “possible” of the secondpremise means “‘primarily possible,’ in that there is apossible world satisfying the relevant primaryintension” (Chalmers 2004, 182-183). Given thisexplanation and supposing that nothing essential forthe argument hangs on the qualifier “roughly,”2 what isthe difference in the meanings of the first premise,that zombies are conceivable, and the conclusion, thatthey are possible? I fail to see any. Let us look intothis matter more closely.

Suppose that “conceivability” is used as a purelylogical category to mean nothing but “no a prioricontradiction.” (Remarkably, there is nothingpsychological about it, such as someone’s capability toconceive of something.) On the other hand, there is“primary logical possibility,” which means “that thereis a possible world satisfying the relevant primaryintension.” However, what does the latter mean?

Of course, the phrase “there is a logicallypossible world” does not mean that such a world issomewhere over there; we are not talking about reallyexisting parallel worlds; the phrase is just a looseway of saying “a world is logically possible.” All thatChalmers ever says about what he means by the logical2 Otherwise, the explanation would be glaringly inadequate, in omittingwhat is crucial for the argument.

possibility of a world involves nothing besides thecoherence of the description that specifies theproperties of the world. The requirement that the worldshould satisfy the relevant primary intension (as opposedto secondary intension) means that the terms in thedescription are construed (their referents in thepossible world at issue are picked out) according tothe way we understand these terms before (prior to) orindependently of empirical discoveries of their non-apparent identities.3 This requirement sets aside, atthis stage of the zombie argument, appeals to so called“a posteriori necessities,” because they are irrelevantfor primary possibility.4 In other words, the primarylogical possibility of a world means that its

3 For example “water” under primary intension picks out, in apossible world, the transparent drinkable thirst-quenching (ifnot salty) liquid in rivers, lakes, and seas, be it H20 orwhatever (XYZ), whereas “water” under secondary intension picksout H20, whether it is transparent and liquid and drinkable ornot.4 Chalmers deals with such appeals separately. First, he arguesthat Kripkean a posteriori necessities do not engender a spaceof metaphysically possible worlds distinct from the space oflogically possible worlds; they only prescribe that we shoulddescribe logically possible worlds taken as counterfactual in away that involves “a posteriori semantic twist,” so that theterms in which a world is described refer according to theirsecondary intensions. (Accordingly, there is no real differencebetween what is primarily possible and what is secondarilypossible; the possibilities are the same, but the samepossibilities go under different descriptions, and verbally thesame description may designate different possibilities, ifconstrued first under primary and then under secondaryintensions. Second, he argues against ad hoc postulating ofunexplainable “brute” necessities (that do not fit the Kripkeanpattern and defy two-dimensional analysis). Third, he allowsthat there may be sort of hidden identities on the physical side—namely, the intrinsic nature of the basic microphysicalentities—that is relevant for the zombie argument, leaving openthe possibility that Russellian monism (panpsychism orpanprotopsychism) can be true.

specifying description, construed aprioristically(without a posteriori, empirical considerations andsemantic twist involved), is coherent—there is no apriori contradiction in it. However, if we takeChalmers’ explanation at face value, “conceivability”means (“roughly”) the same.

Now, after making replacements (of “conceivable”and “possible”) with equivalent meanings (“no a prioricontradiction” or “logically possible”), we may rewriteChalmers’ argument as follows:Premise 1. There is no a priori contradiction in the

idea of (a world with) a zombie.Premise 2. If there is no a priori contradiction in

the idea of (a world with) a zombie, then thereis no a priori contradiction in the idea of (aworld with) a zombie.

Conclusion. Hence, there is no a priori contradictionin the idea of (a world with) a zombie.

Or equivalently:Premise 1. A (world with a) zombie is logically

possible.Premise 2. If a (world with a) zombie is logically

possible, then a (world with a) zombie islogically possible.

Conclusion. Hence, a (world with a) zombie is logicallypossible.

So it seems that we have no substantial argumentinvolving the conceivability-to-possibility entailment.At best, there is just a translation of “no a prioricontradiction” into a more technical language of two-dimensional semantics.

Can it be that there is, nevertheless, some subtledifference in what Chalmers means by “there is no apriori contradiction” and “there is a possible worldsatisfying the relevant primary intension” that evadesthe above analysis and that makes the conceivability-

to-possibility entailment non-trivial? Of course, sucha possibility cannot be excluded. However, if it werethe case, Chalmers should have explained what thedifference is and made an argument that despite thesemantic difference, the two descriptions arenecessarily coextensive. As I do not find such anexplanation and argument, I tentatively conclude thatthere is no relevant difference.

In the paper “Does Conceivability EntailPossibility?” (2002) Chalmers develops a moresophisticated explanation and defense of the move fromconceivability to logical (metaphysical) possibility.

He makes three kinds of distinctions aboutconceivability:

1) Primary and secondary conceivability. Primaryconceivability of S means that S is conceivable a prioriunder “primary intensions.” Secondary conceivability ofS means that S is conceivable under “secondaryintensions” that correspond to Kripkean “a posteriorinecessities”.

2) Negative and positive conceivability. “S is negativelyconceivable when S is not ruled out a priori, or whenthere is no (apparent) contradiction in S.” S ispositively conceivable if “one can form some sort ofpositive conception of a situation in which S is thecase,” “in some sense imagine a specific configurationof objects and properties,” “imagine situations inconsiderable detail.” (Chalmers 2002, 149-150)

3) Prima facie, secunda facie and ideal conceivability.S is prima facie conceivable for a subject when Sis conceivable for that subject on firstappearances. … S is ideally conceivable when S isconceivable on ideal rational reflection. (Chalmers2002, 147)As for secunda facie conceivability, Chalmers gives no

explicit definition, but he uses the term to signify

conceivability “on second appearances,” on “a littlereflection,” though the examples he adduces areexamples of considerably more than “a little”reflection. Roughly, we can say that secunda facieconceivability is conceivability on good reflection.The difference between prima facie and secunda facieconceivability is due to the possibility that S isincoherent (self-contradictory), but this incoherenceis not obvious, so that S may seem coherent prima facie,but its incoherence is revealed on better thought. So,some situations may be prima facie conceivable, but secundafacie (and ideally) inconceivable.

The difference between secunda facie and idealconceivability is of the same character: it is inprinciple possible that incoherence in S is so deepthat it is not revealed even on better thought, butwould be revealed on ideal rational reflection.Chalmers claims that such cases “seem to be extremelythin on the ground”; perhaps, there are some such casesin mathematics (for example, Frege’s set of all sets)(Chalmers 2002, 155).

I think that there is a grave problem with thisChalmers’ claim. The problem is that we are not idealreasoners; hence, we do not know what is ideallyconceivable (except by begging the question, i.e. onthe assumption that what seems conceivable in the lightof real current-state reflection is very probable to beideally conceivable); hence, we cannot judge whetherthe claim is true. We do not know what would berevealed on ideal rational reflection. All we know areresults of real current-state reflection, but we do notknow whether a result of real current-state reflectioncoincides with the would-be result of ideal reflection.

Chalmers summarizes his discussion with fourconceivability/possibility theses:(1) Ideal primary positive conceivability entails primary possibility…(2) Ideal primary negative conceivability entails primary possibility…

(3) Secunda facie primary positive conceivability is an extremely goodguide to primary possibility.(4) Ideal secondary (positive/negative) conceivability entails secondarypossibility. (Chalmers 2002, 171)

As far as I can judge, Chalmers has failed toescape trivialization (or tautologization) of the linkbetween conceivability and possibility in the case ofideal conceivability. The reason is that ideal conceivabilitypresupposes “ideal rational reflection”; while theideality of rational reflection seems to mean nothingbut that the reflection in question is a perfect-infallible guide from what prima facie seems possible towhat is possible. At least, I don’t see from Chalmers’discussion how the ideality of rational reflection canbe interpreted independently of its being such aperfect-infallible guide. But if so, theconceivability/possibility theses (1), (2), and (4)collapse into the statement that logical (metaphysical)possibility entails logical (metaphysical) possibility.On the other hand, if “ideal reasoning” isn’t taken tobe a perfect-infallible guide, then (1), (2), and (4)may well be false.

From Chalmers’ explanation about the meaning of“ideal rational reflection,” I gather that his answermay be that by “ideal rational reflection,” he meansnot a perfect-infallible guide but reflection thatcan’t be defeated by further reflection. But if so,there are two obvious objections. The first is that for(1), (2), and (4) to be true, we must assume that ifreflection is undefeatable, it is a perfect-infallibleguide. It doesn’t follow logically. And without thisassumption, (1), (2), and (4) may well be false. Thesecond objection is that we can never know that somereasoning is undefeatable; the most we can know is thatit was not defeated so far. Hence, Chalmers’ attemptsto support the theses (1), (2), and (4) by the absence

of counterexamples fail, because no possible example isrelevant.

Generally, I don’t see what does this ideal-reflection stuff matter at all, since our realreflection is inescapably nonideal (fallible) or, atleast, is never known to be ideal, and we cannot knowwhat would ideal reflection lead to.

Andrew Bailey (2007) made a similar objection,summarized by Chalmers as follows: “arguments fromideal conceivability are toothless, as non-idealcreatures such as ourselves cannot know whether or nota given statement is ideally conceivable.” Chalmersdisagrees:

I think that there is little reason to accept thisclaim. Although we are non-ideal, we can know thatit is not ideallyconceivable that 0=1, and that itis ideally conceivable that someone exists. We knowthat certain things about the world (say, that allphilosophers are philosophers) are knowable apriori, and that certain things about the world(say, that there is a table in this room) are notso knowable even by an ideal reasoner. Likewise,reasoning of this sort above gives us very goodreason to think that there is no a priorientailment from physical to phenomenal truths andthat zombie hypotheses are conceivable, even for anideal reasoner. (Chalmers 2010, 155)But now I wonder: how do (can) we know “that it is

not ideally conceivable that 0=1, and that it isideally conceivable that someone exists”? Can suchknowledge be prior to the knowledge that it isimpossible for 0 to equal 1, and that it is possiblefor someone to exist? Do we, in these cases, makeinferences from would-be results of “ideal rationalreflection” about conceivability to the conclusionsthat 0 cannot equal 1, and that it is possible for

someone to exist? Or vice versa, as we (nonidealreasoners) know (a priori) that 0 cannot equal 1, and thatit is possible for someone to exist, so we can concludethat on “ideal rational reflection” (by an idealreasoner), it is inconceivable that 0=1, and it isconceivable that someone exists? I think that thesecond is the case. But if so, then the concepts of“ideal rational reflection” and “ideal reasoner” do nojob whatever.

If you think that (CM) it is not ideallyconceivable that 0=1, it is only because you think that(M) 0 cannot equal 1. You cannot make a plausibleargument for CM that would not rely on the truth of M.And this holds for all cases about “idealconceivability.” In cases where an analogue of M—let itbe designated as N—is not so obvious and needsarguments, CN needs them no less, and can hardly beplausibly argued for without incorporating argumentsfor N.

Chalmers could object that an argument for theideal conceivability of Х can rely not on thepossibility of Х, but on the secunda facie conceivabilityof Х. But this makes ideal conceivability an entirelysuperfluous mediator between secunda facie conceivabilityand possibility. Instead of Chalmers’ thesis (3) thatsecunda facie conceivability is an extremely good guide topossibility, we would have two theses:(3.1) Secunda facie conceivability is an extremely goodguide to ideal conceivability.(3.2) Ideal conceivability entails primary possibility.It logically follows from (3.1) and (3.2) that (3).

But to consider (3) as an inference from (3.1) and(3.2) would be turning things upside down. (3.1) may beplausible only insofar as (3) is plausible. If you donot think that secunda facie conceivability is a goodguide to possibility, then you have no reason to think

that secunda facie conceivability is a good guide to idealconceivability.

I have sent these critical remarks to DavidChalmers by e-mail, and he has replied:

no circularity as there’s no need to mentionpossibility in the analysis of idealconceivability. E.g. for ideal negativeconceivability, p is conceivable iff it’s not apriori that ~p. No need to mention possibilitythere.I wonder about this reply: does not “not a priori

that ~p” ≡ “logically possible that p”? Is it not thevery meaning of the term “logical possibility”?

Thus, it seems that Chalmers’ “idealconceivability” cuts no ice. Is there anything in hisaccount of the conceivability-to-possibility entailmentto do a better job? The only plausible candidate seemsto be the thesis “(3) Secunda facie primary positive conceivabilityis an extremely good guide to primary possibility.” However, it stillremains for us to find out how—and whether—it works. Iwill return to this question after a digression on amore specific problem.

3. The problem of unknown (and, possibly,unknowable) logical necessities

Here, we are to confront the problem of unknownnecessities as purported counterexamples to the movefrom conceivability to possibility. The examplesadduced are always from mathematics. Most usually, itis Goldbach’s conjecture that every even integergreater than 2 is the sum of two primes.5 Mathematiciansdo not know whether it is true; they have not found outa proof of the truth or of the falsity of Goldbach’sconjecture. Possibly, there is a proof, but it is not

5 See, for example, Lowe 2010, 443.

found as yet; possibly, there is no proof at all. It ispossible that some mathematical truths are not provableand, hence, are not knowable (for in mathematics, theonly way to know a truth is to prove it); it seems thatGödel’s theorem proves that there are such unprovableand unknowable truths for any formal system. Howunknown, or even unknowable mathematical truths can betreated in terms of conceivability and logicalpossibility, and does not their existence undermineconceivability arguments? Let us examine the questioncarefully.

To begin with, let us note that whatever be thosemathematical truths, they are a priori, i.e. logicallynecessary. They do not depend on empirical facts; theyare constituted by the foundational principles,concepts, axioms of the formal system to which theybelong. If Goldbach’s conjecture is true, it is a prioritrue; it is logically impossible for it to be false;there are no logically possible worlds in which it isfalse. Otherwise, if Goldbach’s conjecture is false, itis a priori false; it is logically impossible for it to betrue; there are no logically possible worlds in whichit is true.

Nevertheless, it seems that it is in some sensepossible that Goldbach’s conjecture is true, andpossible that it is false. This possibility is neithernatural nor logical. We may call it epistemic possibility.Epistemic possibility can be defined as follows: X isepistemically possible if we do not know that X is notthe case. As far as logical and mathematical relationsare concerned, epistemic possibility is wider thanlogical possibility. For example, both the truth andthe falsity of Goldbach’s conjecture are epistemicallypossible, but only one of these possibilities (we don’tknow which one) is logically possible. Epistemicpossibility is not projectable into the space oflogically possible worlds: no logically possible worldcorresponds to some epistemic possibilities. For

example, if Goldbach’s conjecture is true, it is truein all logically possible worlds—there are no logicallypossible worlds in which it is false; otherwise, it isfalse in all logically possible worlds—there are nologically possible worlds in which it is true.

Whether a situation—or a world—in which Goldbach’sconjecture is true is conceivable? And whether asituation—or a world—in which it is false isconceivable? It is not clear whether—and how—thenotions of negative and positive conceivability areapplicable here at all.

Let us begin with negative conceivability.Is Goldbach’s conjecture, or its negation,

negatively conceivable on Chalmers’ definition? (Toremind, the definition is: “S is negatively conceivablewhen S is not ruled out a priori, or when there is no(apparent) contradiction in S.”) It depends on how weread the definition.

On one reading (“S is negatively conceivable whenthere is no apparent contradiction in S”), both arenegatively conceivable, even secunda facie. (The bestmathematicians reflected on the problem for a longtime, and they failed to discover a contradictioneither in the conjecture or in its negation.) However,only one of the two is logically possible. So on thisreading, (secunda facie) negative conceivability is not aguide to possibility for such cases.

On another reading (“S is negatively conceivablewhen S is not ruled out a priori, or when there is nocontradiction in S”), either Goldbach’s conjecture orits negation is not negatively conceivable, but wecannot know which one until we discover a proof of thetruth (falsity) of either the conjecture or itsnegation. If we discover such a proof, we would knowwhich one of the two is conceivable and which one isnot. But then the conceivability would be of no use, aswe already know which is true (and so logically

possible) and which is false (and so, as all falsemathematical statements, logically impossible).

Now, if we try to apply the notion of positiveconceivability to the cases of Goldbach’s conjecture andits negation, it is not clear what would count asforming “some sort of positive conception of asituation in which S is the case,” how “to positivelyconceive of a situation,” “imagine a specificconfiguration of objects and properties … inconsiderable detail” (Chalmers 2002, 150). How can onepositively conceive a situation in which Goldbach’sconjecture is true, as distinct from a situation inwhich it is false? I, for one, have no idea. So, Isuppose that the notion of positive conceivability isinapplicable to such cases (perhaps, to mathematics andother formal systems generally).

Let us compare this with Chalmers’ approach to theproblem.

Chalmers remarks that in philosophy, “theconceivability judgments that are usually taken asevidence of possibility are almost always positiveconceivability judgments,” and that “for just thisreason, the Goldbach case was never a very compellingcounterexample to this practice” (Chalmers 2002, 161).This fits well with my suggestion that the notion ofpositive conceivability is inapplicable to such cases,but Chalmers’ explanation is different.

Chalmers proposes that “a mathematical claim willbe positively conceivable insofar as there is rationalreason to accept that claim” (Chalmers 2002, 155). I amnot sure that this fits well with the definition ofpositive conceivability. More importantly, on thisapproach the positive conceivability of a mathematicalclaim is not a guide to the possibility of its truth but aloafer. If “there is rational reason to accept thatclaim,” then this reason is a guide to truth (and,hence, to possibility), and there is no furtherepistemic job to do for “positive conceivability.”

The conclusion is that on the one hand, cases likeGoldbach’s conjecture are not counterexamples to thethesis that conceivability entails possibility; on theother hand, in such cases, conceivability cannot serveas a guide to possibility, because in order to judgewhether a situation is conceivable, one need first tofind out whether it is possible. This result may besuggestive about other cases as well.

4. Is conceivability a guide to possibility?Now we return to Chalmers’ thesis “(3) Secunda facie

primary positive conceivability is an extremely good guide to primarypossibility.”

It should be noted that the entailment asserted inthis thesis is not from conceivability to possibilitybut from secunda facie conceivability to something likethere being extremely good reason to believe in the possibility. Itshould also be remarked that secunda facie conceivabilitymeans “seems conceivable on good reflection.” And, ofcourse, “seeming” is a personal psychologistic matter.Taking all this into account, CP arguments take thefollowing form:Premise 1. If X seems to P to be primarily positively

conceivable on good reflection, P has extremelygood reason to believe that X is logicallypossible.

Premise 2. X seems to P to be primarily positivelyconceivable on good reflection.

Conclusion. P has extremely good reason to believe thatX is logically possible.

However, there are a lot of problems with sucharguments. For one, it is not obvious that premise 1 istrue. What is the status of the asserted connectionbetween seeming conceivability and the reasonablenessof the belief in logical possibility? Is it a factualcorrelation or a logical entailment? If the first, howcan it be tested? If the second, how does it work? What

counts as good reflection? Is it enough that it seemsto a person that his/her reflection is good? How cansuch seeming be challenged? (Should I argue that whatyou think seems to you does not really seem to you?)Further, to begin with, what does “conceivability”mean? What seems to a person when it seems to him/herthat X is conceivable?

5. An analytical case for the CP entailment and itsuselessness

What is the relevant meaning of “conceivability”(to be distinguished from just seeming to beconceivable)? It certainly will not do to defineconceivability as “no a priori contradiction in the idea”(as Chalmers did), because this would make the CPentailment a straightforward tautology. “No a prioricontradiction in the idea” is a purely logicalrelation, and I take it to be exactly what “logicalpossibility” means. Conceivability should not be apurely logical relation; it should have something to dowith psychology, with our (mental) ability forsomething, that is, for conceiving.

On the other hand, analyzing our use of the termshows that conceivability is not a matter of merepsychology, too. It is not a term to designate some(feature of a) mental state of a person. This should beobvious from the following facts on the usage of theterm:

1) We distinguish “conceivable” from “seemsconceivable” and may argue that Х is not reallyconceivable even if it seems so prima facie.

2) In such an argument, we do not invoke mental(phenomenal) properties of the conceiver’s mind; weinvoke logical relations within the content of thestatement that describes the situation one tries toconceive of.

Let us try the following thought experiment. Thereis a statement S that describes a purportedly logically

possible situation. You hear (or read) the statement,seem to understand it clearly, and notice noincoherence in it. The situation seems conceivable toyou. You think that it is conceivable. Then someoneexplains to you that there is a hidden incoherence (apriori contradiction) in the statement. Once you see thatthere is such incoherence, you no longer think that thesituation is conceivable. You think that it is not.Moreover, you will not say that the situation wasconceivable but ceased to be so. Rather, you will saythat the situation did seem conceivable to you, but itturned out that it is not.

If this account is right, then “conceivability”works not as a psychological but as a logical term, inroughly the same way as “no a priori contradiction in theidea.” Are not we got caught in a magic circle?

I think that there is a simple way out of thecircle: “conceivability” is a success term that hasboth “internalist” (subjective) and “externalist”(objective) aspects.

Internalist (subjective) aspect. To judge whether asituation is conceivable, a person attempts to conceiveof the situation. If he/she judges that he/she succeedsin conceiving of the situation, then he/she judges thatthe situation is conceivable. (Of course, if asituation was conceived, then it is conceivable!) Otherwise,the person either judges that the situation isinconceivable or defers judgment. Now, the crucialquestions are: “How (based on what considerations) doesa person judge whether he/she succeeds in conceiving ofa situation?” and, for the negative judgment, “How doesa person choose between judging that the situation isinconceivable and deferring judgment?” Here, theexternalist (objective) aspect comes in.

Externalist (objective) aspect. “Conceivability” is asuccess term such that the success at issue crucially depends on thelogical coherence of the description of the situation (just as“seeing” is a success term such that the success

crucially depends on there being a thing that onethinks he/she sees).

If this interpretation is right, then although“conceivability” (“being within our ability to conceive—or to form a clear idea—of”) means not the same as“logical possibility” (“no a priori contradiction in theidea”), the judgment of conceivability is the same as—or wholly dependent on—the judgment of coherence. Wecannot judge the coherence of a description (thelogical possibility of a situation) in any other wayexcept by trying to conceive—to form a clear idea—ofthe situation as described. We judge a situation asconceivable if and only if we understand itsdescription and it seems coherent to us. If we see adescription as incoherent, we judge the situation asdescribed as inconceivable. If we do not understand adescription clearly enough, or if it seems to us thatthe description leaves space for a hidden incoherence(as in cases like Goldbach’s conjecture, for example),we would say that it is unclear whether the descriptionis coherent, that is, whether the situation asdescribed is logically possible.

The point of “positive” (as distinct from“negative”) conceivability is that to make a consideredjudgment of whether a description is coherent andwhether there is space for a hidden incoherence in it,one should think of details that may be relevant to theissue and see whether filling the description with suchdetails can make it incoherent. Let us take, forexample, the issue of the logical possibility of aphenomenal zombie. Given the definition of a phenomenalzombie as a creature that 1) is the exact physical copyof a human being and 2) has no consciousness(phenomenal mind), one would need to think of what itmay take to be the exact physical copy of a humanbeing, that is, what details of the human bodyconstitution and functioning may be relevant to theissue and whether some such (perhaps unknown at

present) details can make the description of aphenomenal zombie incoherent.

If this account of how “conceivability” works isright, then “conceivability arguments” gravelymisrepresent the conceivability-possibilityrelationship. Although conceivability does entaillogical possibility, this entailment is trivial andjust as useless as the entailment from logicalpossibility to itself. This does not mean that all sucharguments fail; rather, this means that, for them notto fail, they need to be reinterpreted so as not to bedependent on the substantially empty CP entailment.

The possibility of such reinterpretation remainsinsofar as the thesis that the relevant kind ofpossibility is logical possibility is not affected bythe failure of the CP enterprise.

The CP part of the purported CP arguments should bediscarded; the logical possibility premise shouldeither be proposed directly in virtue of its intuitiveplausibility (on the presumption that one can “see”that the description of the situation is coherent andthat there is no space for a hidden contradiction) orbe grounded in some further considerations. Forexample, in the case of the zombie argument, therelevant consideration seems to be that, as Chalmersremarks, the logical impossibility of brain-duplicatesthat are not mind-duplicates (phenomenal zombies orinverts) would “require an a priori entailment fromphysical to phenomenal, which will require an analysisof phenomenal concepts that can support thatentailment,” and this “requires a structural orfunctional analysis of phenomenal concepts,” whereas“there is good reason to believe that any such analysisof phenomenal concepts is a misanalysis” (Chalmers2002, 196-197). Other relevant considerations can befound in the earlier exposition of the zombie argumentby Chalmers, in The Conscious Mind, which has little to dowith the conceivability-to-possibility entailment but

proposes that “an assertion of this logical possibilitycomes down to a brute intuition,” “obvious coherence”just as in the case of the statement “that a mile-highunicycle is logically possible” (Chalmers 1996, 96).Besides, in that exposition, Chalmers invokes someindirect arguments to bolster the case for the logicalpossibility of phenomenal zombies.

The invitation to try to conceive of a hypotheticalsituation remains a legitimate and useful device.However, it should be construed as a way to make ajudgment about the logical possibility of the situation(the coherence of the description) that does not involvelogical inference from a conceivability premise to apossibility conclusion.

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