NOÛS 46:1 (2012) 127–158 Rational Imagination and Modal Knowledge JONATHAN ICHIKAWA The University of St Andrews BENJAMIN JARVIS Queen’s University Belfast Abstract How do we know what’s (metaphysically) possible and impossible? Arguments from Kripke and Putnam suggest that possibility is not merely a matter of (coherent) conceivability/imaginability. For example, we can coherently imagine that Hesperus and Phosphorus are distinct objects even though they are not possibly distinct. Despite this apparent problem, we suggest, nevertheless, that imagination plays an important role in an adequate modal epistemology. When we discover what is possible or what is impossible, we generally exploit important connections between what is possible and what we can coherently imagine. We can often come to knowledge of metaphysical modality a priori. The Red Sox won last night, but they could have lost. Knowledge of the first conjunct is secured via perception; what of the second? We cannot see that the Red Sox could have lost in the same way we saw that they won. Of course, we could learn the modal fact by testimony; one can learn pretty much anything by testimony. Still, not everybody could have learned it by testimony; someone has to have learned it in some other way. But how? If not through testimony, how can we know actually-false propositions to be possible? This is a central question of modal epistemology. We also know facts about impossibility: although it’s possible that the Sox lost, it is impossible that they both won and lost—and we know this, too. An attractive explanation for this knowledge is that we can perform a reductio on the alleged possibility. But not everything we know to be impossible conceptually entails an obvious absurdity in this fashion. (More on conceptual entailment in §4 below. For now, think of conceptual entailments as C 2011 Wiley Periodicals, Inc. 127 128 NOÛS entailments that are transparent.) It is impossible, for instance, for Hesperus to be closer to the Earth than Phosphorus, or for some water sample to contain no hydrogen. Call these latter kinds of propositions—ones that do not conceptually entail absurdities—conceptually possible propositions. We know many conceptually possible propositions to be impossible; another central question of modal epistemology is to explain how we can have this knowledge. In tackling these central questions throughout the history of modal epistemology, two ideas have emerged. The first is that our capacity for modal knowledge is closely tied to our faculty of imagination. The second is that our capacity for modal knowledge is partly explained by our rational capacities broadly construed.1 Our project in this paper is to develop these ideas with (relatively) minimal commitments to show how a priori modal knowledge is possible. We call the resulting position “moderate modal rationalism.” Our moderate modal rationalism departs from other versions of modal rationalism developed recently. David Chalmers (2002) and Frank Jackson (1998), for instance, have developed forms of modal rationalism on the basis of a two-dimensionalist semantic framework. This framework is controversial; we mean to do without it. George Bealer (2002) and (2004) has developed another approach on the basis of his theory of intuitions. While our position may well be compatible with his account, we are wary of many of his commitments concerning intuitions. (The word ‘intuition’ does not appear further in our paper.)2 One of the primary goals of this paper is to show that a version of modal rationalism can be developed without the substantive commitments of either of these two frameworks.3 Throughout our paper, we will rely on the notion of a proposition. For the purposes of this paper, we understand propositions as truth evaluable entities that are differentiated by the way that concepts are put together to grasp them—and hence more finely than the objects and properties the propositions are about. It should be possible, for those whose commitments require it, to reinterpret our comments in light of opposing (neo-Russellian and nominalist) views; we leave such exercise to the reader. In the next section, we will tackle some preliminaries, at which point will we give an overview of the paper. §1. Preliminaries We contend that our imaginative capacities underlie our capacity for modal knowledge. But what sort of imaginative capacities do we have in mind? In discovering what is possible or necessary, surely we deploy imagination in a variety of ways. Rational Imagination and Modal Knowledge 129 For our purposes, we will begin by focusing on the sort of propositional attitudes we principally come to have when engaging with fictions. Even on first glance it is clear that these imaginings are relatively unfettered when it comes to content. While there are notable instances of imaginative resistance—we typically resist imagining, for instance, that killing someone for our own pleasure is morally right, even if the story we’re reading says it is—these instances are the exception, rather than the rule, even in cases of fictions with impossible contents. People regularly engage imaginatively with fictions in which there are incidents of time travel that, upon some reflection, prove to be impossible. Moreover, philosophers have no difficulty engaging imaginatively with a thought experiment story in which per impossibile it is discovered that Hesperus is not Phosphorus after all.4 We contend that the propositional attitude we principally come to have when engaging with fictions is supposing. In our view, to say that someone imagines that p in response to fiction is roughly to commit oneself to the person’s supposing that p, and, furthermore, drawing what are, from the person’s point of view, immediately good inferences from this supposition without landing in an apparent absurdity. (For our purposes, “landing in an apparent absurdity” need not be inferring to outright contradictions. For certain propositions—to borrow an example from Stephen Yablo (2002), the proposition that someone found a five-fingered maple leaf that is also (simultaneously) shaped like a regular egg—one might infer that one should be able to visualize events sufficient for the truth of them, and, for the purposes of our rough account, this might ipso facto land one in an apparent absurdity if one finds oneself unable to carry out the corresponding offline visualization.) Imaginative resistance might occur when inferences that land the would-be imaginer in absurdities are altogether too immediate. It might also occur when, for one reason or another, the would-be imaginer disapproves (morally, aesthetically, etc.) of an author’s invitation (via fictionalizing) to imagine the proposition in question. For our purposes, then, when we talk about imaginative capacities underlying our capacity for modal knowledge, we are effectively proposing that engaging in supposition can be a guide to possibility and necessity. Henceforth, we will use ‘imagine’ and ‘suppose’ interchangeably, unless we state otherwise explicitly.5 No doubt, there will be some who do not share our view about the connection between propositional imaginings in response to fiction and supposing; indeed, some may reject that supposition is a kind of imagination of any sort. We invite such individuals to treat our language use here as stipulative. Supposing is, of course, wholly unfettered when it comes to content. So long as a supposition is merely for the sake of argument, we generally find ourselves capable of supposing any proposition that we can entertain.6 Indeed, for the purposes of a reductio, we frequently suppose propositions that we believe to be absurd. 130 NOÛS In light of these considerations, the Naı̈ve Modal-Imagination Hypothesis (NMIH) is obviously problematic: NMIH: For any proposition
,
is possible if you can imagine/conceive
, and impossible if you cannot.7 Some philosophers have advocated something that sounds like NMIH, but if we understand ‘imagining’/‘conceiving’ as supposing, NMIH is clearly false. (No doubt, these philosophers understand ‘imagining’ or ‘conceiving’ in some other way.) Thinkers can suppose any proposition that can entertain, but it is clearly not the case that every proposition they can entertain is possible. Matters do not improve much when we alter NMIH to restrict it to “imagining” not in the sense of merely supposing, but in the previously discussed sense of “imaginative engagement with some fictional story”— supposition along with the drawing of obvious inferences. Consider NMIH∗ : NMIH∗ : For any proposition
,
is possible if you can (propositionally) imagine
in engagement with some fictional story in which
is true, and impossible if you cannot. On our suggested view, (propositional) imagining in engagement with some fictional story requires not only supposing, but also drawing what are, from the thinker’s point of view, immediately good inferences from this supposition without landing in an apparent absurdity. Unlike NMIH, NMIH∗ does not have the implication that every entertainable proposition is possible; for some suppositions, e.g. the supposition that the Red Sox both won and lost, drawing immediate inferences does quite quickly land us in apparent absurdities. According to NMIH∗ , these supposed propositions are impossible. Nonetheless, NMIH∗ is also obviously inadequate. Someone could read a fictional story whose plot depends on spacetime’s being curved and resist imagining that spacetime is curved. Indeed, he may find he cannot so imagine. Perhaps he does not have the relevant concepts to do so, or perhaps he thinks that supposing that spacetime is curved leads to absurd consequences. Obviously, this is not an indication that the proposition that spacetime is curved is impossible—for him or anyone else. A philosophical egoist might imaginatively engage with a fictional story in which the protagonist rightly kills someone merely for a large sum of money without resistance. He finds drawing those inferences he takes to be immediately good from the supposition that someone rightly kills someone merely for a large sum of money does not land him in an absurdity apparent to him. Obviously, this is not sufficient to show that it is possible to rightly kill someone merely for a large sum of money. Rational Imagination and Modal Knowledge 131 It is almost certain that thinkers vary in what they can imagine in engagement with fictional stories, precisely because they vary in what they take to be immediately good inferences or when they take themselves to have landed in an absurdity. Possibility and necessity, however, do not vary according to the thinker. These obstacles for NMIH and NMIH∗ suggest another proposal. Perhaps when it comes to possibility and necessity, what matters is not whether the proposition might be supposed, but rather whether it might coherently be supposed. Of course, a proposition might be coherently supposable whether or not any particular thinker is capable of supposing it. Some thinkers might not have the relevant concepts necessary for entertaining the proposition in question. More importantly, coherent supposition is an objective matter that is not relative to a thinker. We coherently suppose
when we suppose
and supposing
and drawing good inferences from this supposition could never in fact lead one to conclude a genuine absurdity, e.g. a blatant contradiction. It makes no difference whether any particular thinker would find these (good) inferences good or whether upon drawing these (good) inferences he would take himself to have concluded a genuine absurdity or not. We will call the proposal under consideration the Strong ModalImagination Hypothesis (SMIH): SMIH: For any proposition
,
is possible if one might coherently imagine/conceive
and impossible if she could not.
(Again, ‘imagining’/‘conceiving’ stands for supposing.) While SMIH has an
air of plausibility, we contend it is also false. There is nothing incoherent
about imagining that
h: Hesperus is closer to the earth than is Phosphorus.
An agent who, in imagining this proposition, carried out all of the inferences
to which he was thereby rationally committed could imagine , if it is possible for someone coherently to
believe , it is possible for someone coherently to imagine .
(Most people make a distinction between beliefs that are merely false and/or
unwarranted, and beliefs that not only are false and/or unwarranted, but
fundamentally just don’t make any sense at all, e.g. the belief that you’re being
intentionally persecuted by the number two. A coherent belief is one that even
if false and unwarranted, can be made sense of.) A second highly plausible
thesis maintains that it is possible to believe metaphysical impossibilities:
HPT2: It is possible for someone coherently to believe metaphysical impossibilities like , someone may coherently believe the necessary falsehood
is to have in one’s belief box a sentence
expressing that p; to imagine it is to have such a sentence in the imagination
box. The denial of HPT1 on this model would amount to the claim that the
imagination box admits different sentences than does the belief box. But this
does not seem to be true; the mechanisms that regulate the contents of our
belief boxes seem to be just the same mechanisms that regulate the contents
of our imagination boxes. Certain incoherent sentences are automatically
removed from both boxes by a particular cognitive mechanism (the ‘Updater’,
in Nichols and Stich’s terminology)—and this mechanism operates without
regard to which box houses the relevant sentences. Indeed, the parallels
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between belief and imagination vis-à-vis patterns of inference prompt Nichols
(2004) to suggest that belief and imagination are “in the same code”—by
which he means that a wide variety of cognitive mechanisms process beliefs
and imaginings in the same ways.15 A belief is treated in a very similar
way to an imagining with the same content. It is implausible, then, that a
metaphysically impossible proposition could be represented in the belief box,
but not in the imagination box; no appropriate mechanism is sensitive to the
difference.
So there are compelling reasons to accept both HPT1 and HPT2. So far
as we can see, the only way to retain SMIH in light of our discussion is
to adopt a two-dimensionalist semantics so that in (coherently) supposing,
for instance, that water does not contain hydrogen, one is not supposing
the secondary intension of the sentence ‘Water does not contain hydrogen’,
which is necessarily false, but rather the primary intension, which is true at
some possibilities, even thought it is not true of the actual world.16
While we are not prepared to enter a full critique of two-dimensionalist
semantics here, we are inclined to reject it. Given our own commitments, we
see no way to accept SMIH. It is possible coherently to imagine metaphysical
impossibilities.
§3. Conceptual Possibility
We must admit, then, that coherently imagining some proposition does not
ensure that the proposition is metaphysically possible. But it does seem as
though there is some interesting status in the neighborhood of possibility
being picked out by coherent imagining. An alternative to SMIH involves
considering conceptual possibility, to be contrasted with metaphysical possibility, as a status important to modal epistemology. Conceptual possibility,
on this line, could be established by recognizing one’s imagining as coherent;
the counterexamples to SMIH, though metaphysically impossible, can be
counted as conceptually possible.
(Some philosophers object to the term ‘conceptual possibility’ on the
grounds that propositions like Hesperus is not Phosphorus ought not to be
judged possible in any sense.17 As far as we can see, this is a mere terminological disagreement; those with insuperable aversion to the idea of something
weaker than metaphysical possibility traveling under the name ‘conceptual
possibility’ are invited to substitute their own preferred term.)
To employ this strategy, we face two challenges: first, to explain the notion
of conceptual possibility at work, i.e. the notion of coherently imagining,
and second, to defend against the charge of having changed the subject.
Modal epistemology is, at least traditionally, ultimately thought to be about
metaphysical possibility. We begin now with the first challenge.
What is conceptual possibility? A conceptual possibility can be coherently
imagined to obtain; it is a situation that the constraints of rationality make
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room for. Metaphorically, it is a point in the conceptual space of an agent.
More precisely, a proposition is conceptually possible just in case it does
not conceptually entail an absurdity. was not explicitly or tacitly
used to specify the scenario.21 In general, when we question of a scenario
imagined to obtain whether it is a scenario in which p, we have not two but
three choices:
(1) We answer that it is a scenario in which p because we are rationally
committed, in imagining that the scenario obtains, to imagining that p.
(2) We answer that it is not a scenario in which p because we are rationally
committed, in imagining that the scenario obtains, to not imagining that
p.
(3) We reply that it is indeterminate, or we need more information, because
imagining that the scenario obtains does not rationally commit us to
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imagining one way or the other whether or not p is true. (Suppose that it
is raining in Vegas. Is this a scenario in which it is cold?)
Notice that these choices parallel the three choices we face when, in doxastic
deliberation, we ask whether the actual world is such that p by consulting
what our current beliefs dictate:
(1) We answer that the actual world is such that p because we are rationally
committed by our current beliefs to believing that p.
(2) We answer that the actual world is not such that p because we are rationally
committed by our current beliefs to not believing that p.
(3) We withhold judgment because our current beliefs are not strong enough
to commit us one way or the other.
For those like us who understand imagining as at least partly constituted by
supposing, the strong parallels between belief and imagining should not be
surprising. When we suppose some proposition for the sake of argument, we
(rightly) draw the same sorts of conclusions from that supposition that we
would were we to believe the proposition in question. It is precisely for this
reason that we can generally test the coherence of a supposition as proxy
for testing the coherence of a potential belief of the same proposition we
supposed.
Our intention is to use rational commitments to infer in imagination
in order to characterize conceptual entailment. Of course, not all rational
commitments to infer in imagination correspond to conceptual entailment.
The rational commitment to infer from imagining that it was raining in Las
Vegas to imagining that the streets in Las Vegas were wet does not coincide
with an entailment relation between the proposition that it was raining in
Las Vegas and the proposition that the streets in Las Vegas were wet. The
former proposition obviously does not entail the latter in any sense. We can
see as much by remembering how rational commitment can be defeated by
further imaginings. As we already indicated, one might, for instance, imagine
that the streets of Las Vegas are covered. If the streets of Las Vegas are
covered, then they may not be wet even if it rains there.
Perhaps though, indefeasible rational commitments to infer in imagination coincide with conceptual entailments? If someone has an indefeasible
rational commitment to infer from imagining that p to imagining that q,
they’re rationally committed to imagining that q by imagining that p, and
that rational commitment persists in any possible case in which the subject
continues to imagine that p—including cases in which one imagines various
other things (like that the streets are covered). Note that if the proposition
that p does not at least metaphysically entail the proposition that q, then
there is some metaphysical possibility such that p and not-q. If it is imagined that this possibility obtains, this imagining ought to defeat the inference
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from imagining that p to imagining that q—but then, that inference cannot
have been indefeasible. From this argument we can see that an indefeasible
rational commitment to infer does at least entail metaphysical entailment.
Unfortunately, almost no rational commitments to infer in imagination
are in this sense indefeasible.22 Remember that rational commitments to infer
in imagination share their basis with rational commitments to infer in belief.
Our rational commitment to infer from imagining that p to imagining that
q (if the question is raised) is explained by whatever explains our rational
commitment to infer to believing that q (if the question is raised) so long as we
might continue to believe that p. Consequently, rational commitments to infer
in imagination are indefeasible only if corresponding rational commitments
to infer in belief are indefeasible. However, it is quite plausible that no rational
commitments to infer in belief are indefeasible.
Indeed, almost any rational commitment to infer can be defeated due to
a subject’s rational limitations. Rational limitations may arise from limitations in one’s conceptual repertoire, limitations in computational capacity
(e.g. in the time it takes to draw an inference), and tendencies to make performance errors in drawing inferences, or, for that matter, any other sorts
of proclivities the subject has to make or exhibit confusions in attempting
to execute in accordance with what he has reason to think. (This list may
not be exhaustive, but it indicates that the term ‘rational limitations’ is not
a catchall; rational limitations contrasts with limitations in experience that
result specifically in a paucity of evidence, which might limit the subject’s
ability to competently infer in a wholly different way.23 Rational limitations
are limitations concerning the processing of evidence.) Testimony from a
panel of expert logicians can defeat John’s rational commitment to infer in
accordance with modus ponens, but only because of John’s rational limitations vis-à-vis logic. If John were an acknowledged über-logician, he would
have no reason to kowtow to the panel of “expert” logicians any more than
we have reason to defer to elementary school children on matters of basic
arithmetic.
Similarly, almost any rational commitment to infer can be defeated due to
evidence regarding a subject’s (current) rational limitations. Evidence to the
effect that Jane has taken a pill that inhibits rational capacities can defeat
Jane’s rational commitment to infer in accordance with modus ponens as can
evidence to the effect that Jane is crazy even if in fact Jane has not taken
such a pill and is not crazy.
Nevertheless, despite the defeasibility of almost all rational commitments
to infer, we maintain that conceptual entailment can still be characterized in
terms of rational commitments to infer in imagination. We suggest that what
is distinctive of rational commitments to infer in imagination that coincide
with conceptual entailment is that they are defeasible only due to a subject’s
rational limitations or due to evidence regarding a subject’s (current) rational
limitations. More precisely:
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CE: A set of propositions { , , . . ., } conceptually entails
, imagines , . . ., and imagines must be due at least
partly to either (a) the subject’s rational limitations or (b) the subject’s
having evidence concerning his (current) rational limitations.
One can prove that, by CE, conceptual entailment implies metaphysical entailment, and hence is necessarily truth-preserving, as any respectable entailment relation ought to be. Proof: Suppose that the set, S, of propositions
{ , , . . ., } conceptually entails , , . . ., and ought to defeat the rational commitment to infer in imagination from , , . . ., to , , . . ., } conceptually entails
, imagines , . . ., and imagines must never be wholly
due to further imaginings.
The implication from CE to CE∗ is pretty clear. If defeat of a rational
commitment must be due to either conditions (a) or (b), then it cannot be
wholly due to further imaginings. The implication from CE∗ to CE is less
clear, but it is difficult to see what else could defeat a rational commitment
if further imaginings cannot do so by themselves.
It’s worth highlighting that CE and CE∗ are merely characterizations of
conceptual entailment, not explanations of it. For the purposes of showing
that conceptual entailment is a legitimate relation, nothing more than a characterization is required. It is entirely possible, for instance, that conceptual
entailment relations between propositions explain our rational commitments
to infer, rather than the reverse. What’s more, conceptual entailment could
be characterized just as well without invoking imaginings. An alternative
characterization might be offered using belief and knowledge. We outline
this characterization in footnote 25.
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CE is perhaps best understood through considering examples:
• If one imagines that Stephen knows that p, what could possibly defeat one’s
rational commitment to infer (should the question arise) to imagining that
p? Our contention is that defeaters arise only due to rational limitations or
evidence concerning rational limitations. If so, then by CE, .
• Suppose that in imagining the events of a story, the question arises as to
whether is true. Presumably, you have a rational commitment
to infer (on the basis of no particular previous imagining) to the imagining
that p or not-p. Under what circumstances can this rational commitment be
defeated? We might suppose it is only due to your rational limitations or
evidence concerning your rational limitations. If so, then by CE the null set
conceptually entails .
Examples of conceptual entailment are bound to be controversial, but we
must take care to make challenges on the appropriate grounds. For instance,
the proposed conceptual entailment from
is not threatened by the mere existence of Stu, a sophisticated thinker with
complex theoretical reasons for thinking the rational commitment to make
that inference might be defeated in other ways. Of course, if Stu is correct,
then . Nevertheless, so long as it is the case that Stu’s rational capacities might be further
improved upon so as to see through these misleading complex reasons, the
fact that Stu is, in some sense, rational for rejecting that inference does not
imply that .24
Stu’s rationality in this sense and his cognitive sophistication are compatible
with his rational limitations helping explain the defeat of his rational commitment. Likewise, we may have reasons to doubt an instance of excluded
middle, but as long as these reasons are misleading in that an über-rational
logician would see through them, it makes no difference when it comes to
conceptual entailment because the defeat of this inference is explained by
our own rational limitations.
Why can’t the rational commitment to infer from be defeated by further imagining that Stephen knows that p even
though not-p? If , the
proposition . We
parenthetically made note of this phenomenon earlier; further imagining an
absurdity never defeats a rational commitment to infer.
The following examples emphasize that, plausibly, not all a priori inferences with belief coincide with conceptual entailment.
• Some have argued that an inference on the basis of no previous premise to
the belief that one is not a brain in a vat is a priori warranted. Suppose so.
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Even still, does this imply that the null set conceptually entails that one is
not a brain in a vat? Obviously not. To be sure, one probably is rationally
committed to imagining that one is not a brain in a vat if one is imagining
anything about oneself at all. After all, when one imagines that one is having
certain sensory experiences, it is natural also to imagine that these sensory
experiences are veridical. Nevertheless, the rational commitment to infer in
this way is clearly defeated by further imagining that people have kidnapped
you, extracted your brain, and put it in a vat that keeps it alive while they
feed it electrical signals that mimic incoming sensory signals. This further
imagining wholly explains the defeat of our rational commitiment to infer, so
by CE, the null set does not conceptually entail that one is not a brain in a
vat.
• Very plausibly, an inference on the basis of no previous premise to the belief
that one is here now (if one exists, now exists, and one is anywhere at all now)
is a priori warranted. Does this imply that the null set conceptually entails
that one is here now? Obviously not. One might just as well imagine that one
is somewhere else—in Fiji, say. Indeed, it is not obvious in this particular case
that there is a corresponding rational commitment to infer in imagination to
the conclusion that one is here now. (Patterns of rational commitment to infer
in imagination evidently largely but do not entirely parallel those in belief.)
This example shows that conceptual entailment does not coincide with
metaphysical entailment.
• By CE, conceptual entailment presupposes a rational commitment to infer
in imagination. In the event that one does not know that Phosphorus is
Hesperus, there may well be no rational commitment to infer to the imagining
that Hesperus is a planet from the imagining that Phosphorus is a planet.
This would lead us to conclude that conceptually
entails is conceptually necessary.
We have already suggested that a proposition is conceptually possible just
in case the proposition does not conceptually entail an absurdity. But what
is an absurdity? The paradigm instances of absurdities are contradictions,
but we can use conceptual entailment to clarify what an absurdity is as
well. Absurdities conceptually entail any proposition.26 This understanding
of absurdity allows us to simply our definition of conceptual possibility: a
proposition is conceptually possible just in case the proposition is not an
absurdity.
Because we explain conceptual possibility in terms of conceptual entailment and conceptual entailment is characterized in terms of rational commitments to infer, our grasp on conceptual possibility comes through our
apprehension of these rational commitments, i.e. through exercising our rational capacities.
Indeed, our grasp on conceptual possibility is through rational capacities
that track wholly a priori rational commitments, i.e. rational commitments
with no empirical basis. Rational commitments to infer that coincide with
conceptual entailments must not depend upon any empirical basis. Any rational commitment to infer in imagination that depends upon an empirical
basis can be wholly defeated merely by imagining that the relevant empirical discoveries away. This is effectively illustrated by recalling the rational
commitment to infer in imagination from conceptually entails
something about the actual world that is in fact not the case, then is
metaphysically impossible. Using symbols we get FAMI.
FAMI: ∃( ) ⊃ ∼∃( implies that there isn’t
a conceptually entails that in the actual world, q even
though it is not the case that in the actual world, q. This necessary condition
for metaphysical possibility is not met by conceptual possibility. This is
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unsurprising, since we’ve asserted all along that conceptual possibility is
insufficient for metaphysical possibility—SMIH is false. However, we see no
reason to think that the right-hand side of FAMI∗ isn’t, in addition to being
a necessary condition for ’s metaphysical possibility, also a sufficient
condition, in conjunction with ’s conceptual possibility. Call this claim
moderate modal rationalism (MMR):
MMR: ♦ m ( ) ≡ (♦ c ( ) & ∼∃( .) Is there some such is a metaphysically necessary mathematical truth. In
this way, we can explain the metaphysical necessity of mathematical truths
even if they are not conceptually necessary.
An example that often raises concern in the modality of mathematics is the
continuum hypothesis (CH), which is provably independent from the ZFC
axioms of set theory. There is a mistaken tendency to take the independence
results for CH as a clear indication that CH and its negation are both conceptually possible. No such consequence follows; myriad conceptual necessities
(e.g., doesn’t conceptually entail anything at all, much less anything false,
about the actual world. If we can recognize a priori that imagining that a
green square has six-inch sides does not conceptually entail anything about
the actual world, then the second MMR condition—the usually-a-posteriori
one—is trivially met. Insofar, then, as we can recognize the relevant facts
about conceptual possibility and necessity a priori, we can know a priori
that it is metaphysically possible that there is a green square with six-inch
sides.32
To what extent, then, are facts about conceptual necessity, possibility, and
entailment—facts about what can and can’t be coherently imagined and what
we are rationally committed to infer in imagination—knowable a priori?33
It is not at all difficult to see that we can often recognize conceptual
impossibilities a priori. We can know a priori that some imagining is incoherent by finding an obvious reductio ad absurdum using inferences that
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151
correspond to conceptual entailments. Doing so merely requires exercising
rational capacities whose basis survives further imaginings. (As we saw in §5,
such rational capacities cannot depend upon an empirical basis.) Whether we
are capable of this depends on how smart we are—but we are smart enough
often to find them. Imaginings of blatant contradictions are incoherent; likewise with imaginings that there are green apples with no color. (A one line
reductio is sufficient for these propositions; a world where contradictions are
true, or where green apples have no color, is a world where anything goes!)
Other conceptual impossibilities are less transparent, but still recognizable in
this fashion. Some propositions, such as ’ we are indicating a mention of some proposition; when we write
‘p’ we are indicating a use.
8 We are not first to have pointed out that MR is untenable. See, for instance, Bealer (2004),
§5.
9 Byrne (2007) argues that that interpreting Kripke as embracing the MR is a mistake.
10 Peacocke (1999), Chapter 4. Gendler and Hawthorne (2002).
11 Gendler and Hawthorne (2002).
12 Stalnaker (1984) thinks sets of possible worlds are the objects of belief, and that it is
therefore impossible to believe the impossible. If it is impossible to believe the impossible on
a possible-worlds approach, so much the worse for possible-worlds approaches. (Suppose that
Stalnaker is right, contrary to our professed belief: it is impossible to believe impossibilities.
Then when we believe that someone believes an impossibility, we believe the impossible.) (See
Sorensen (1996).) King (2007) argues that Stalnaker can and should admit that we can believe
the impossible.
13 See Currie and Ravenscroft (2002), Chapters 1–2. Goldman (2006) is also a clear proponent of this approach. It’s worth noting that at least one of us thinks that propositional
imagining/supposing does not simulate belief; instead, propositional imagining/supposing that
one believes simulates beliefs. Even so, HPT1 is overwhelmingly plausible.
14 Nichols & Stich (2000).
15 Apparently, Nichols intends to draw a contrast between beliefs and imaginings on one
hand, and, for instance, desires on the other when he says that beliefs and imaginings are “in
the same code.” It is unclear what this contrast could be other than merely that beliefs and
imaginings have similar functional roles. After all, accepting the cognitive box picture implies
that desires and beliefs are in “the same code” as well at least in the sense that both beliefs and
desires involve tokens of Mentalese.
16 Cf. the distinction Chalmers (2002) makes between primary and secondary conceivability.
17 Bealer (2002); van Inwagen (1998).
18 As we point out later, a characterization of conceptual entailment is not the same as
an analysis (or definition) of it. In offering a characterization, one merely gives necessary and
sufficient conditions. In giving an analysis, one is typically suggesting that the analysans is
conceptually or explanatorily prior to the analysandum. In putting forward a characterization,
we intend to make no such suggestion. We leave open the possibility, for instance, that conceptual
entailment should be understood as a primitive relation between propositions.
19 Quine (1936) and Quine (1962). See also Peacocke (2004), especially p. 27.
20 Two different anonymous referees have expressed doubts about whether rational commitment to infer can really be made sense of. We are not moved by these doubts largely because the
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155
notion of rational commitment to infer in belief is so closely tied to the notion of propositional
justification, a notion in epistemology that is not likely to be dislodged. The notion of rational
commitment to infer in imagination is just the analogue of rational commitment to infer in
belief. That there must be some such analogue is mandated by the uses to which we put our
imaginative faculties. Cf. Currie and Ravenscroft (2002).
These points also make it clear why rational commitment to infer is not likely to be supplanted by counterfactual reasoning as one of these anonymous referees suggested might be
the case. Counterfactual reasoning antecedently requires a grasp on what is evidence for what;
establishing any counterfactual requires having a grasp on whether we would be entitled to infer
that counterfactual given the experiences we have had.
21 We distinguish scenarios from possibilities in that scenarios need not be genuinely possible
in any sense.
22 We intend to use ‘rational commitment’, so that if someone is rationally committed to
infer and they so infer because they are rationally committed, then the resulting mental state is
rational. In other words, if someone is rationally committed to infer, they are not irresponsible
for so doing. In this sense of ‘rational commitment’, it will be possible to defeat someone’s
rationally commitment to infer by raising concerns about the inference, even if these concerns
ultimately prove to be the result of confusion, which through more capable reasoning, might be
alleviated. Defeasibility of “rational commitment” in this sense coincides with what Peacocke
(2004), p. 30 terms ‘defeasibility of identification’.
One might alternatively use ‘rational commitment’ so that a person’s rational commitment to
infer can never be defeated by concerns about the inference that, upon further and more capacitated rational scrutiny, ultimately prove to be the result of confusion. Defeasibility of “rational
commitment” in this sense coincides with what Peacocke (2004), p. 30 terms ‘defeasibility of
grounds’.
23 Here we effectively rely on a principled distinction between experience in its role as enabler
and in its role as the provider of propositional warrant. We acknowledge that Williamson (2007)
challenges whether this distinction can be made out in a principled way. Although we engage
with that challenge in ongoing work, we will ignore it here.
24 We therefore avoid the critique of conceptual modality in Williamson (2007), Chapter 4.
25 It is also possible to characterize conceptual entailment in epistemic terms, relating inferences and knowledge, instead of as commitments to imagine. We focused on imagination in
the main text above because our direct interest, for purposes of modal epistemology, was in
commitments of imaginings. A characterization in epistemic terms could be given by reference
to the property of a knowledge-preserving inference. If there is a knowledge-preserving inference from to conceptually entails that , , . . ., } conceptually entails , ,
. . ., } to .
That there are such parallel characterizations of conceptual entailment, one in terms of
rational commitments of imaginings, and the other in terms of preservation of knowledge in
belief, should not be surprising. As we emphasized above, beliefs and imaginings are similar
in a number of respects. And no one should be surprised to find tight connections between
rationality and knowledge.
26 A referee worries that this explanation of absurdities cannot be reconciled with many
(putatively) paradigm cases of absurdities, for instance, the proposition that something is simultaneously pink and turquoise all over. Why think that imagining this proposition rationally
commits one to imagining anything? Of course, an analogous skeptical question could be raised
for any proposed absurdities including an outright contradiction that p and not p. Generally,
there can’t be any demonstration that any putative absurdity is an absurdity that does not rely
on rules of inference that the skeptic is contending. A dialetheist isn’t going to be satisfied by a
classical logician’s deployment of classical rules, but that hardly shows that the classical logician
isn’t right. (In the pink-turquoise case the relevant rules, of course, concern the “logic” of color.
Add the right axioms of color (or equivalent rules of inference) with a strong enough logic and
the desired result will follow.)
We’re not particularly concerned to defend any particular proposition as an absurdity; if
it turns out that the proposition that something is simultaneously pink and turquoise all over
is not an absurdity as we’ve explained it, that’s fine by us. We can show how these sorts of
propositions are impossible on other grounds. See §7.
27 Cf. the view discussed, with citation, in Jackson (1998), p. 69.
28 ‘Settled’ obviously here means something stronger than ‘conceptually entailed’. So likewise is the provable ‘independence’ of CH from ZFC weaker than conceptual independence.
29 Even if we had conclusive reason for thinking that the matter could not be settled, this
may constitute conclusive reason for thinking that although one of CH and its negation is true
in every model of ZFC, neither is true simpliciter. Far from showing that CH and its negation
are both conceptually possible, this might show that neither is conceptually possible, for both
might be indeterminate as a matter of conceptual necessity.
30 This is an epistemic claim rather than a metaphysical claim about fundamentality. For the
purposes of this paper, we need not decide whether conceptual necessity is more fundamental
than metaphysical necessity—it’s enough that they are related in the way MMR claims they are.
31 Compare with Thesis (II) and Thesis (III) of Peacocke (1999), pp. 168–171.
32 Williamson (2007) argues that there is no principled distinction between the a priori and
the a posteriori. We are here presupposing him to be incorrect.
33 Again, we do not assume that a priori knowledge is empirically indefeasible. We might
say that a priori knowledge is weakly a priori. Kitcher (2000); Field (2000).
34 Obviously, we are rejecting the insistence of Yablo (2002), p. 457–61 that “peeking” is
by nature a method of inquiry that is a posteriori. He rejects “peeking” as a priori in the
first place because discerning features of imagined situations is too close to introspecting that
one has a headache. We do not see the connection. To be sure, learning something from a
mental simulation requires, in some sense, being aware of what is going on in the simulated
scenario just as learning something from supposing requires being aware, in some sense, of
what is supposed. We do not see, though, that this sort of “awareness” should constitute any
serious form of introspection that is incompatible with learning a priori in either case. After all,
learning from a simulation need not depend on one’s consciously realizing that one is simulating
Rational Imagination and Modal Knowledge
157
just as learning from supposing need not depend on one’s consciously realizing that one is
supposing.
Yablo rejects “peeking” as a priori in the second place because it requires exercising a “perceptual faculty rather than a cognitive one.” To the extent that modeling requires exercising a
perceptual faculty rather than a cognitive one, we do not see that it is done in a way that is
incompatible with a priority. There is no incoherence in the idea of a priori knowledge being
gained via the supposition of some empirical proposition, so long as the conclusion of the
argument does not ultimately depend on the empirical proposition’s truth, or on one’s having supposed that the empirical proposition was true. Likewise, judging about some particular
scenario using perceptual faculties can lead to knowledge a priori so long as the truth of the
conclusion does not ultimately depend on the scenario’s obtaining or on one’s having exercised
perceptual faculties. What matters for a priority is not whether a perceptual or cognitive faculty
is exercised, but whether experience plays a justificatory role, and if it does, whether the role is
merely hypothetical or not.
Yablo rejects “peeking” as a priori in the third place because the recognitional capacities one
uses to determine what is true in a simulation have an empirical basis. The rational relations
between perceptual experience and beliefs show that there can be (and frequently are) rational
commitments to infer that need not have any empirical basis. One does not need to do any empirical research to know what propositions are true if one’s perceptual experiences are veridical.
Obviously, some recognitional capacities will have an empirical basis, but not all.
35 For one (rather extreme) way of guaranteeing coherence, we could stipulate only microphysical facts; that which those microphysical facts conceptually entail would certainly be
coherent. Cf. Chalmers (1996), pp. 76–77; Jackson (1998), pp. 81–84.
36 For this reason, we take “objectual imagining” or simulation of metaphysical possibility
to be subject to the criticisms of Byrne (2007), §§6–7 in a way that simulation of conceptual
possibility is not.
37 For helpful comments and discussion, we are grateful to Björn Brodowski, Melissa
Ebbers, Richard Heck, Carrie Jenkins, Jason Stanley, Ernest Sosa, Brian Weatherson, Timothy
Williamson, and three anonymous Noûs referees.
References
Bealer, G. (2002). Modal epistemology and the rationalist renaissance. In T. Gendler, & J.
Hawthorne (Eds.), Conceivability and possibility New York: Oxford University Press.
(pp. 71–126).
Bealer, G. (2004). The origins of modal error. Dialectica, 58(1), 11–42.
Byrne, A. (2007). Possibility and imagination. Philosophical Perspectives, 21, 125–144.
Chalmers, D. (1996). The Conscious mind. New York: Oxford University Press.
Chalmers, D. (2002). Does conceivability entail possibility? In T. Gendler, & J. Hawthorne (Eds.),
Conceivability and possibility (pp. 145–200). New York: Oxford University Press.
Currie, G. & Ravenscroft, I. (2002). Recreative minds. New York: Oxford University Press.
Field, H. (2000). A priority as an evaluative notion. In P. Boghossian, & C. Peacocke (Eds.),
New essays on the a priori (pp. 117–49). New York: Oxford University Press.
Gendler, T. (2000). The puzzle of imaginative resistance. Journal of Philosophy, 97(2), 55–81.
Gendler, T. & Hawthorne J. (2002). Introduction: conceivability and possibility. In T. Gendler,
& J. Hawthorne (Eds.), Conceivability and possibility (pp. 1–70). New York: Oxford
University Press.
Goldman, A. I. (2006). Simulating minds: The philosophy, psychology, and neuroscience of mindreading. New York: Oxford University Press.
Harman, G. (1986). Change in view. Cambridge, MA: MIT Press.
Jackson, F. (1998). From metaphysics to ethics. New York: Oxford University Press.
158
NOÛS
King, J. (2007). What in the world are the ways things might have been? Philosophical Studies,
133(3), 443–453.
Kitcher, P. (2000). A priori knowledge revisited. In P. Boghossian, & P. Benacerraf (Eds.), New
essays on the a priori (pp. 65–91). New York: Clarenden Press.
Kripke, S. A. (1980). Naming and necessity. Cambridge, MA: Harvard University Press.
Nichols, S. (2004). Imagining and believing: The promise of a single code. Journal of Aesthetics
and Art Criticism, 62(Special issue on Art, Mind, and Cognitive Science), 129–139.
Nichols, S., & Stich, S. (2000). A cognitive theory of pretense. Cognition, 74(115–47)
Peacocke, C. (1999). Being known. New York: Oxford University Press.
Peacocke, C. (2004). The realm of reason. New York: Oxford University Press.
Quine, W. V. O. (1936). Truth by convention. Reprinted in P. Benacerraf and H. Putnam (Eds.),
Philosophical of Mathematics (pp. 329–354). New York: Cambridge University Press.
Quine, W. V. O. (1962). Carnap and logical truth. Reprinted in P. Benacerraf and H. Putnam
(Eds.), Philosophical of Mathematics (pp. 355–376). New York: Cambridge University
Press.
Sorensen, R. (1996). Modal bloopers: Why believable impossibilities are necessary. American
Philosophical Quarterly, 33(1): 247–61.
Sosa, E. (2007). A virtue epistemology. Oxford: Oxford University Press.
Stalnaker, R. (1984). Inquiry. Cambridge, MA: MIT Press.
Tye, M. (1995). The problems of consciousness. Cambridge, MA: The MIT Press.
van Inwagen, P. (1998). Modal Epistemology. Philosophical Studies, 92, 67–84.
Williamson, T. (2007). The Philosophy of Philosophy. Malden, MA: Blackwell Publishing.
Yablo, S. (1993). Is conceivability a guide to possibility? Philosophy and Phenomenological
Research, 53(1), 1–42.
Yablo, S. (2002). Coulda, woulda, shoulda. In T. Gendler, & J. Hawthorne (Eds.), Conceivability
and possibility (pp. 441–492). New York: Oxford University Press.
just in case any defeat of the rational commitment to infer to
imagining
(at least should the question arise) when one imagines
, but it is metaphysically
possible that the members of S are true while
is not true. Imagining
this metaphysical possibility (that nevertheless
is not true) in addition
to imagining
in and
of itself unless this metaphysical possibility is a genuine absurdity. (Imagining a genuine absurdity rationally commits one to imagining anything at
all—it leads to an imaginative explosion, so to speak. A scenario in which
an absurdity is true is one in which anything goes.) Presumably, metaphysical possibilities are not absurdities—because they are genuine possibilities, a
rational agent can make sense of them. But then, by CE, S does not conceptually entail
, for there is a way to defeat the rational commitment to
infer that does not essentially involve (a) or (b).
So far as we can tell, CE is equivalent to CE∗ :
CE∗ : A set of propositions {
just in case any defeat of the rational commitment to infer to
imagining
(at least should the question arise) when one imagines
just in case
)[∼A(
) & c (p ⊃ A(
)] ⊃ m (<∼p>)
Here, ‘ c ’ means “it is conceptually necessary that”, ‘ m ’ means “it is metaphysically necessary that,” and ‘A(
)’ means “the actual world is such
that q.” The contrapositive of FAMI expresses a necessary condition for
metaphysical possibility:
FAMI∗ : ♦ m (
)[∼A(
) & c (p ⊃ A(
))]
FAMI∗ says that the metaphysical possibility of
such that
)[∼A(
) & c (p ⊃ A(
))])
To deny MMR right-to-left is to assert that there are some propositions
that are conceptually possible, but metaphysically impossible, and for which
imagining them true does not necessitate imagining anything false about the
actual world. This is the claim that metaphysical possibility requires something more than either conceptual possibility or the condition exploited by
Kripke-Putnam thought experiments. What could this mystery ingredient to
metaphysical possibility be? The fact that a proposition meets the necessary
conditions expressed by the right-hand side of MMR is at least generally
thought to settle the question as to whether the proposition is metaphysically possible.
Anyone defending the mystery ingredient view must show either that we
do make an additional distinction that figures into our conclusions about
metaphysical possibility, or defend the view that metaphysical possibility
has necessary conditions about which we’re entirely in the dark. Neither
alternative looks particularly plausible. Certainly the standard examples of
the necessary a posteriori do not motivate any such mystery ingredient. We
conclude that MMR is true.
§7. Examples, Moral and Mathematical
In order to substantiate our conclusion, it helps to see how MMR accommodates the metaphysical necessity of basic moral principles and mathematical
truths.
Basic Moral Principles
Plausibly, (NoPain) is metaphysically necessary:
NoPain: We ought not cause others to feel excruciating pain merely for the
purposes of superficial entertainment.
If NoPain is also conceptually necessary, then MMR easily explains why it
is metaphysically necessary as well: conceptual necessity entails metaphysical
necessity. However, even if NoPain is metaphysically necessary, some version
of G. E. Moore’s open question argument might make us doubt whether
it is conceptually necessary. Perhaps it is not incoherent to suppose this
conclusion false. Suppose NoPain is conceptually contingent.
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NOÛS
According to MMR, NoPain can still be necessarily true if there is some
that is actually false even though NoPain’s being false in some scenario
(real or imagined) conceptually entails
is actually true. (To see that this
follows from MMR, negate both sides of the biconditional, and substitute
? Yes.
Before we point to the
, let us try to explain why there should
be one. It can be settled merely by rational reflection that the normative
strongly supervenes on the non-normative. This, even if it cannot be settled
by such means what the bridge principles of supervenience specifically are.
The specifics of the bridge principles, of course, constitute the correct moral
theory (perhaps it will be a general theory, or perhaps, as the particularist
thinks, it will be only a collection of truths). In supposing that moral principles like NoPain are not conceptually necessary, we are supposing that our
discovery of the correct moral theory does not proceed via purely rational
reflection; perhaps there is a quasi-perceptual or even constructivist aspect
to this discovery. Whatever the basis of this discovery, though, it is clearly a
matter of conceptually necessity that these discoveries project to non-actual
scenarios in the same way that discoveries of say, the material composition
of natural kinds, project to non-actual scenarios. This is enough to establish
the metaphysical necessity of NoPain.
How? Let basic moral principles be moral principles that follow from the
correct moral theory. Let
be the proposition that NoPain is not a basic
moral principle. That NoPain is false (in some scenario) conceptually entails
that actually, NoPain is not a basic moral principle. But actually, NoPain is
a basic moral principle, so it follows by MMR that NoPain is metaphysically
necessary.
In other words, MMR allows that the metaphysical necessity of NoPain
may be conclusively settled by the fact that 1) it is conceptually necessary
that if it is false (in some scenario), then NoPain does not actually follow
from the correct moral theory and 2) whatever actually makes it the case
that some moral theory is correct and NoPain follows from it. Obviously,
this result generalizes for any basic moral principles. The upshot is we can
recognize that basic moral principles are metaphysically necessary simply by
combining our knowledge of conceptual necessity with the knowledge we
gain through moral inquiry (however that works).
Mathematical Truths
There is a longstanding debate in the philosophy of mathematics over whether
our warrant for believing mathematical truths has a purely rational basis, or
whether it is gained via exercising, for instance, quasi-perceptual or constructivist faculties. This debate is largely analogous to the debate just considered
over whether our warrant for believing basic moral principles has a purely
rational basis, or whether it is gained in some other way. Our treatment here
will be the same as in the previous case.
Rational Imagination and Modal Knowledge
149
If our warrant for believing mathematical truths has a purely rational
basis—if it is just incoherent to suppose them false—then they are generally
conceptually necessary, and hence metaphysically necessary. We could, of
course, learn that these mathematical truths are metaphysically necessary by
learning that they can be established on a purely rational basis.
If it is not generally incoherent to suppose mathematical falsehoods (because of their existential commitments, for instance), then they are not conceptually necessary. Still, what is conceptually necessary is that whatever settles mathematical truth in actuality projects to non-actual scenarios. More
specifically, that
, then someone, if she knows that p, and infers that q on that basis,
while continuing to know that p, will come to know that q. (Harman (1986) emphasizes the
importance of the ‘continuing to know’ clause.) This feature of inference is roughly analogical
with the rational commitments discussed above. As in the case with rational commitment in
imagination, that an inference is knowledge-preserving does not imply that it corresponds to a
conceptual entailment. The same counterexample suffices; the inference from
, could someone know
that p, and infer on this basis that q, continuing to know that p throughout the process, and
yet fail to know that q? Only, as above, by virtue of rational limitations, or by having evidence
concerning one’s rational limitations. In generality:
CE k : A set of propositions {
just
in case, for any subject, there is a knowledge-preserving inference from {
that can be defeated only due at least partly to (a) the subject’s
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NOÛS
rational limitations, or (b) the subject’s having evidence concerning his (current) rational
limitations.
Our new CE k delivers the same verdicts about conceptual entailment as did CE. For example,
if one knows that Stephen knows that p, and infers to the belief that p, this latter can only fail
to constitute knowledge by virtue of the (a) or (b) conditions above, so