Knowledge and Subjunctive Conditionals
Juan Comesaña
Paper intended for the Philosophy Compass.
1
Introduction
A recent development in epistemology is the claim that there is a constitutive
connection between knowledge and the truth of some subjunctive conditional.
More precisely, the claim is that for a subject to know a certain proposition,
some subjunctive conditional related to that subject and that proposition has
to be true. In this paper I present and evaluate the main proposals of this type.
2
Subjunctive Conditionals
Subjunctive conditionals are usually marked in English by the presence of verbs
in the subjunctive mood, as in the constructions “. . . were (not) . . . would (not),”
(“If it were the case that kangaroos have no tails, then it would be the case that
they topple over”) and “. . . had (not) . . . would (not)” (“If it had not rained,
then the yard would have been dry”), and we will represent them as follows:
A → B.
1
1 As
David Lewis noted, however, there are shortened conditionals that have no verb (and,
a fortiori, no verb in the subjunctive mood), such as “No Hitler, no A-bomb,” and which
should still receive the same semantic treatment as subjunctive conditionals, and there are
also subjunctive conditionals about the future, such as “If our troops invade Iran next year,
there would be trouble,” which behave rather like indicative conditionals (see Lewis (1973), p.
4). Iatridou (2000) argues that what distinguishes a subjunctive conditional is the presence
1
The groundwork for giving a semantics for that kind of conditionals was laid
down by work on possible world semantics for modal logic.2 The main idea of
such a semantics is that a necessity operator ‘’ can be defined as a restricted
universal quantifier over a domain of possible worlds, as follows:
φ is true at a world w if and only if φ is true at every world
accessible from w,
where different restrictions on the accessibility relation give rise to different
modal logics. For instance, if every world in the domain is accessible to every
other world, then the resulting logic is the familiar S5. In what follows I will
not explicitly mention the restriction to accessible worlds, because it does not
matter for our purposes.
From the definition of ‘’ and the usual understanding of the material conditional, we can get the following definition of a strict conditional :
(A ⊃ B) is true at a world w if and only if A ⊃ B is true at every
world (in other words, if and only if every world where A is true is
a world where B is true).
A subjunctive conditional does not have the same truth-conditions as a strict
conditional, for a subjunctive conditional can be true even if there are some
worlds where the antecedent is true and the consequent false, provided that
those worlds are different enough from the actual world (for instance “If Mike
Tyson were to fight David Letterman, then Mike Tyson would win” is certainly
true, even though there surely are possible worlds where Letterman wins). But
if we assume that there is an overall similarity ordering of the possible worlds,
then we can capture that difference between subjunctive and strict conditionals
in this definition:
of past morphology in both the antecedent and the consequent clause.
2 Cf. Kripke (1963).
2
A → B is true at a world w if and only if all the worlds that are most
similar to w where A is true are worlds where B is true as well.3
3
Nozick’s Account I: Sensitivity
The most influential part of Nozick’s book Philosophical Explanations 4 is the one
where he gives and defends an interesting definition of propositional knowledge.
The definition is the following:
A subject S knows that p via method M if and only if:
1. S believes that p via M;
2. p is true;
3. If p were false, then S wouldn’t believe that p via M;
4. If p were true, and S were to use M to arrive at a belief whether
(or not) p, S would believe that p via M.5
As can be seen, besides belief and truth Nozick imposes two further conditions on knowledge, and both of them are subjunctive conditionals. Condition
3 (which has come to be called the “sensitivity” condition) has been widely
discussed in the literature.6 Condition 4 has been less widely discussed, but it
raises an important issue that we will address.
3 The definition is similar to the one put forward by Stalnaker (1968) (and differs from the
one put forward by Lewis (1973)) in that it incorporates the assumption that, for any given
world w, there is a set of worlds whose members resemble w more than any world not in
the set, but it differs from it (and, in that respect, it resembles the one in Lewis (1973)) in
allowing that set to contain more than one member (that is, it allows for ties).
4 Nozick (1981).
5 Cf. Nozick (1981), p. 178. The definition in the text is a slightly revised version of
Nozick’s.
6 The sensitivity condition, as well as the claim (also made by Nozick) that knowledge is not
closed under known logical implication, were anticipated by Fred Dretske—see. Dretske (1971)
and Dretske (1970).
3
3.1
Problems for Sensitivity: Counterexamples and Closure
Let us begin, then, with the sensitivity condition. Is it true that, if I know
that p via method M, then if p were false then I wouldn’t believe that p via
method M? Or are there cases where I know that p via some method M and
yet it is not the case that if p were false then I wouldn’t believe that p via
that method? Virtually every philosopher (besides Nozick) that has written on
the topic believes that condition 3, as it stands, is false. Some philosophers,
though, believe that it is on the right track, and that the correct reaction to the
counterexamples shouldn’t be to abandon the sensitivity condition altogether,
but rather to refine it.
One main reason for thinking that the sensitivity condition is false as it
stands stems from a family of counterexamples that can be traced back to
Vogel (1987). One of the counterexamples runs as follows:
GARBAGE CHUTE: I throw a trash bag down the garbage chute of
my condo. Some moments later I believe, and know, that the trash
bag is in the basement. If the trash bag were not in the basement,
however, that would be because it is stuck somewhere in the chute,
and I would still believe that it is in the basement.7
My belief that the trash bag is in the basement is not sensitive, and yet it does
amount to knowledge.
Another reason for dissatisfaction with the sensitivity requirement is that it
doesn’t respect a very plausible closure principle. Notice first that it is not true
that if one sensitively believes that p and competently deduces that q from p
without ceasing to sensitively believe that p, then one sensitively believes that q.
To take one extreme example (also due to Vogel (1987)), take the propositions
7 The
counterexample is taken from Sosa (2000).
4
that there are cookies in the jar and that I do not falsely believe that there are
cookies in the jar. I sensitively believe that there are cookies in the jar (if there
were none, then I wouldn’t believe that there are). I can competently deduce
from that proposition that I don’t falsely believe that there are cookies in the
jar (without ceasing to sensitively believe that there are cookies in the jar). And
yet I do not sensitively believe that I don’t falsely believe that there are cookies
in the jar (if I did falsely believe that there are cookies in the jar, then I would
still believe that there are cookies in the jar, and I would still deduce from that
proposition that I don’t falsely believe that there are cookies in the jar).
Now, As Vogel (1987) noticed,8 the fact that the sensitivity condition is not
closed under competent deduction doesn’t mean that any account of knowledge
that incorporates the sensitivity condition is similarly not closed—in any case
where a proposition is sensitively believed but a consequence of it is not, it
might happen that the proposition that is sensitively believed doesn’t satisfy
some other condition that the account posits as necessary for knowledge. Nevertheless, on Nozick’s account knowledge does fail to be closed under competent
deduction, and this failure can be traced back to the sensitivity condition.
This failure of the sensitivity condition of being closed under competent deduction was welcomed by Nozick, because it afforded him an explanation of both
the allure and the ultimate failure of skeptical arguments. Skeptical arguments
often appeal to “skeptical hypotheses:” propositions that claim that most of
my beliefs are undetectably false. One such hypothesis is the brain-in-a-vat hypothesis: the proposition that the world is such that I am a brain in a vat being
fed experiences as if I were a normal human being in a normal environment,
and that not much more goes on in the world (let’s call this proposition “biv”).
If biv were true, then most of my beliefs would be false, but I would have no
way of detecting that they are. One powerful skeptical argument uses that (or
8 see
also Warfield (2004).
5
similar) skeptical hypothesis in the following way:
1. I do not know that biv is false.
2. If I do not know that biv is false, then I do not know that I have
hands.
Therefore,
3. I do not know that I have hands.
Armed with his account of knowledge, Nozick can explain the argument’s appeal
by noting that it is a valid argument (it is an instance of Modus Ponens) and
its first premise is true. I do not know that biv is false, according to Nozick,
because if it were true then (given that I would be a brain in a vat being fed
experiences as if I were a normal human being in a normal environment) I would
still believe that it is false, and so I fail the sensitivity condition with respect to
that proposition. On the other hand, the argument’s second premise is false. I
do know that I have hands according to Nozick, because my belief that I have
hands satisfies all the clauses of his definition of knowledge. In particular, that
belief of mine is sensitive: if I didn’t have hands, then I would not believe that
I do. Therefore, premise 2 is a conditional with a true antecedent and a false
consequent, and so it is false.9
But although Nozick (as well as Dretske) welcomed the fact that their accounts of knowledge don’t respect a closure principle, most philosophers think
that this constitutes a very serious problem for those accounts. Even setting
aside the question of whether I can know that I have hands even if I don’t know
that I am not a biv, Nozick’s account of knowledge licenses particularly egre9 The
fact that my belief that I have hands is sensitive whereas my belief that biv is false
is not is underscored by the fact that subjunctive conditionals are variable strict conditionals
and not any kind of fixed strict conditionals. When we evaluate the truth-conditions of the
proposition that if biv were true then I would not believe that it is false we have per force to
consider worlds that are much more dissimilar to the actual world than when we evaluate the
truth-conditions of the proposition that if I didn’t have hands then I wouldn’t believe that I
did.
6
gious failures of closure. For instance, according to Nozick’s account, knowledge
doesn’t distribute over conjunction. I can know that I am writing and I am not
a brain in a vat (in particular, notice that that conjunction satisfies sensitivity,
because if it were false that would be because I am not writing, in which case I
wouldn’t believe it), but, as explained above, I can never know that I am not a
brain in a vat.10
3.2
Defending Sensitivity
Despite the counterexamples and the fact that it violates a very plausible closure
principle, some philosophers think that the condition of sensitivity is sufficiently
on the right track as to be worthy of refinement—as opposed to rejection. With
respect to the problem that sensitivity is not closed under competent deduction,
it is interesting to note that Nozick himself considered (in a few sentences) the
possibility of incorporating the sensitivity condition in a recursive account that
has the consequence that knowledge is closed under competent deduction. Say
that if S satisfies all the conditions of Nozick’s original account with respect to
a proposition p, then S tracks that p. The new account can then be formulated
as follows:
S knows that p if and only if either:
1. S tracks that p; or
2. S knows that q and S competently deduces that p from q.
Under this recursive account, a proposition is non-inferentially known if and only
if it is tracked (and is not inferred from another proposition that is tracked),
but propositions can also be inferentially known by being competently deduced
10 See
Nozick (1981), p. 228.
7
from propositions that are tracked.11,12
With respect to the counterexamples to sensitivity, Keith DeRose has made
(in passing, and without committing himself to its ultimate adequacy) a proposal
that has the potential to handle some of them. DeRose says that some beliefs
that are insensitive nevertheless strike us as known when their negations entail
something that we take ourselves to know to be false, without explaining how
we came to falsely believe it.13 If we follow DeRose’s suggestion and amend the
sensitivity condition accordingly, the result is the following:
DeRose-style sensitivity condition: S knows that p via M only
if either:
1. if p were false, then S wouldn’t believe that p via M; or
2. ¬ p entails some q, S takes himself to know that ¬ q (and S
would continue to believe that ¬ q if p were false), and ¬ p
doesn’t explain why S would falsely believe that ¬ q if p were
false.14
This version of the sensitivity condition has the consequence that my belief that
I don’t falsely believe that I have hands is sensitive. For the hypothesis that
11 For a development of this idea in the framework of a probabilistic interpretation of Nozick’s
subjunctive conditions, see Roush (2006).
12 Inductive knowledge presents a problem for Nozick’s own account, who claims (implausibly) that you can know that the sun will come out tomorrow only if, if it weren’t the case that
the sun will come out tomorrow, then there would have been signs of that (a “back-tracking”
counterfactual, where the consequent refers to a time that comes before the time referred to
by the antecedent)—see Nozick (1981), pp. 222-223. The modified version of Nozick’s account
under consideration should also deal with inductive knowledge: presumably, one would want
to allow for knowledge of propositions that are neither tracked nor deduced from propositions
tracked, but inferred from tracked propositions according to sound inductive cannons.
13 See DeRose (1995), p. 23.
14 The parenthetical qualification is my addition, but it seems clear that is needed. Also,
DeRose’s proposal is that we tend to judge that S knows that p only if either S believes that p
sensitively or we take it that there is some q such that . . . This avoids the difficulty that S may
know anything as long as he takes himself to know the right proposition. At the same time,
however, it means that there is no easy translation from DeRose’s proposal to a condition on
knowledge (as opposed to knowledge attribution). In the text I ignore this complication by
assuming that S takes himself to know only propositions that we would take him to know.
8
I falsely believe that I have hands doesn’t explain why I falsely believe that I
have hands, and I take myself to know that I have hands. In this example, we
let p be the proposition that I don’t falsely believe that I have hands, and q the
proposition that I have hands.15
However, the new condition seems to be of no help in dealing with other
kinds of counterexamples. Recall, for instance, the garbage chute case: I know
that the trash bag is in the basement, despite the fact that if it were not in the
basement I would still believe that it is. What we need to find if the DeRose style
sensitivity condition is going to fare better with respect to this counterexample
is a proposition q such that: (i) the trash bag is not in the basement entails that
¬ q; (ii) I take myself to know that q (and I would continue to believe that q if
p were false); and (iii) that the trash bag is not in the basement doesn’t explain
why I would falsely believe that q. A plausible candidate is the proposition
that the trash bag is in the basement itself. That proposition certainly satisfies
conditions (i) and (ii). But is it the case that if the trash bag were not in
the basement that would not explain why I still believe that the trash bag is
in the basement? Well, we judge that my belief that the trash bag is in the
basement is insensitive (as the case is described) because if it were not in the
basement it would, unbeknownst to me, be stuck in the chute on its way to the
basement. So, the closest situation were the trash bag is not in the basement is
one that does explain why I would still falsely believe that it is in the basement
(because it is a situation where the trash bag miseladingly appears to be in the
basement). Therefore, unless more is said about what it takes for a proposition
to explain another, it is natural to conclude that the DeRose style sensitivity
condition fails to account for this kind of cases.
15 For a development of the DeRose-style sensitivity condition, see Black and Murphy (forthcoming).
9
4
Nozick’s Account II: Adherence
Remember that Nozick’s account of knowledge requires not only that if the
proposition believed were false then the subject wouldn’t believe it (via the
method by which he actually believes it), but also that, if the proposition believed were true (and the subject were to use the method that he actually uses
in order to arrive at a belief) the subject would still believe it. This condition, known as the “adherence condition” hasn’t been as widely discussed as
the sensitivity condition, but it does raise interesting issues.
Perhaps the most interesting issue raised by the adherence condition is
whether or not it is a trivial condition. After all, it is a subjunctive conditional
whose antecedent and consequent are guaranteed to be true by the account of
which the condition is a part. Subjunctive conditionals with true antecedent
and true consequent (“true-true conditionals” in what follows) are hard to evaluate. Consider the true-true conditional: If Bush were President, he would
have invaded Iraq. Our first reaction upon hearing such a conditional might
well be: “Whaddaya mean, ‘If Bush were President? He is the President!,” and
we might well be at a loss to judge its truth-value. Now, under the semantics for
subjunctives introduced in section 2, any true-true conditional is trivially true,
because in the actual world both the antecedent and the consequent are true,
and any world is closer to itself than any other world.16 So there are two related
tasks that a friend of the adherence condition must undertake: first, he must
explain why it is legitimate to impose a condition that strike us as unassertible;
second, he must provide a semantics that doesn’t make true-true conditionals
trivially true.
With respect to the second task, Nozick did offer a sketch of a semantics
that doesn’t have the consequence that all true-true conditionals are trivially
16 This
is the assumption that Lewis calls “centering”.
10
true. One suggestion starts by defining the p-neighborhood of a world, and then
defines subjunctives in terms of neighborhoods, as follows:
For any worlds w1 and w2 , w2 is in the p neighborhood of w1 if
and only if p is true in w2 and there are no worlds wp and w¬p such
that:
1. p is true in wp and false in w¬p ;
2. w¬p is closer to w1 than w2 is to w1 ;
3. wp is at least as close to w1 as w¬p is to w1 .
A → B is true at w if and only if B is true in the A neighborhood
of w.17
Roughly speaking, the p neighborhood of a world w is the largest stretch of
worlds where p is true that is unninterrupted by any world where p is false
that is closest to w. If p is true in w, then w will be in the p neighborhood of
w, but if p is false in w (and possibly true), then w’s p neighborhood will not
include itself. Those definitions do have the consequence that not all true-true
conditionals are trivially true.18 But the difficulties with true-true conditionals
are not over. Remember our first problem with such conditionals: they strike us
as unassertible, and we are at a loss to judge their truth-value.19 The Nozickian
semantics under consideration assures us that not all true-true conditionals will
be trivially true, but in order to know which true-true conditionals are true and
which are false we would now need to know, for any conditional A → B, which
17 See Nozick (1981), pp. 680-681, n. 8. Nozick goes on to consider a further refinement to
allow for not-p worlds that are just as close to the world in which the conditional is evaluated
as are some of the worlds in the p neighborhood. I ignore that complication.
18 A different theory that allows for non-trivially true (and false) true-true conditionals is the
one put forward in von Fintel (2001)–although only in contexts where other counterfactuals
have been previously asserted.
19 Or at least, conditionals that we know to be true-true conditionals strike us as unassertible
and we are at a loss to judge their truth-values. That is the kind of conditional in play in
Nozick’s adherence condition.
11
are the worlds in the A neighborhood of the actual world. But this construes
the relationship between the formal semantics and our pre-theoretic judgments
about the truth-values of conditionals exactly backwards: the closeness relation among worlds in the model should be construed so that it delivers the
truth-values that we pre-theoretically judge different conditionals to have, and
it shouldn’t be the case that the model introduces distinctions where we don’t
find any (or, of course, that it obliterates distinctions that we do find).20 We
find all conditionals that we know to be true-true equally unassertible, and we
are equally at a loss to judge their truth-values. Unless this pre-theoretic reaction of ours is massaged to lead us to accept differences between conditionals
that we know to be true-true, no amount of formal semantics is going to rescue
the adherence condition from this problem.
Besides this problem with true-true conditionals, the adherence condition is
also subject to potential counterexamples. Consider, for instance, the following:21
BIRD IN THE YARD: There is a pelican in the yard. I take a glance
at the yard and form the belief that there is a bird in the yard. There
is also a canary behind the pelican, which is too small for me to see
from where I am standing.
It seems clear that in the situation described I know that there is a bird in the
yard. But there are worlds in the bird-in-the-yard neighborhood of the actual
world where I do not believe that there is a bird in the yard (namely, those
worlds where the pelican is gone but the canary is still there). Therefore, I do
not satisfy the adherence condition.22
20 The traditional semantics also finds truth-values where we don’t (clearly) see any, but at
least it doesn’t introduce any distinctions that we don’t see.
21 Taken from Sosa’s “Replies” in Greco (2004).
22 The adherence condition could be defended by claiming that my method of belief formation is different if I see a pelican than if I don’t see anything. This is true, but it just
highlights the need to say much more about method-individuation than Nozick ever said.
12
5
Sosa’s Account: Safety
Under the standard semantics for subjunctives, those conditionals are not equivalent to their contrapositives. Thus, suppose that we flip a coin to decide
whether you or I will struck this match, heads you strike it, tails I strike it. The
coin comes up heads, you strike the match and it lights. In this situation, it is
true that if I had struck the match, then it would have lit. But it need not be
true that if the match hadn’t lit then I wouldn’t have struck it. If the match
hadn’t lit, then that could have been because it was wet (although it actually
wasn’t), and either of us could have struck it. In the possible worlds terminology, the closest possible world where I struck the match is a world where it
lights, but there are possible worlds where the match doesn’t light and I strike
it that are as close to actuality as are worlds where the match doesn’t light and
you strike it.
After noticing the failure of subjunctives to contrapose, Ernest Sosa had
proposed that we should replace Nozick’s sensitivity condition with its contrapositive, which Sosa calls a “safety” condition. The following formulation seems
to capture Sosa’s intent:
Safety: S’s belief that p based on e is safe if and only if S would
not easily believe that p based on e without it being so that p (in
symbols, S believes that p on basis e → p).23
Given that the safety condition is offered as a necessary condition on knowledge, and given that belief and truth are also necessary for knowledge, Sosa’s
safety condition will always be a true-true conditional. Because of this, it seems
clear that Sosa (like Nozick) cannot accept the standard semantics for subjunctives, on pain of making the safety condition trivial. Let us suppose, then, that
23 See Sosa (2002). Williamson (2000) also proposes what he calls a “safety” condition on
knowledge, and he cites Sosa approvingly. However, Williamson might not be adverse to
understanding safety in terms of knowledge, which goes against Sosa’s project.
13
in assessing the safety condition we are to assume some other semantics for
subjunctives, perhaps the one sketched in the previous section.
One advantage of the safety condition over sensitivity is that my belief that
I am not a brain in a vat (and, in general, any belief that I am not the victim
of undetectable deception) is safe. Throughout the worlds that are in the Ibelieve-that-I-am-not-a-biv neighborhood of the actual world, I am not a brain
in a vat.24 Thus, the safety condition is a crucial ingredient in Sosa’s “Moorean”
response to skepticism: it is true that we know that we are not brains in a vat,
but we might be fooled into thinking that we don’t know it because that belief
of ours is not sensitive, and whereas it is safety, and not sensitivity, that is
required for knowledge, the two conditions are easily confused (because one is
the contrapositive of the other).
Despite these advantages of the safety condition over its contrapositive, several counterexamples to safety have appeared in the literature. One of them
runs as follows:25
Halloween Party: There is a Halloween party at Andy’s house,
and I am invited. Andy’s house is very difficult to find, so he hires
Judy to stand at a crossroads and direct people towards the house
(Judy’s job is to tell people that the party is at the house down the
left road). Unbeknownst to me, Andy doesnt want Michael to go to
the party, so he also tells Judy that if she sees Michael she should tell
him the same thing she tells everybody else (that the party is at the
house down the left road), but she should immediately phone Andy
so that the party can be moved to Adam’s house, which is down the
24 Another advantage may be that safety respects plausible principles of closure, but whether
that is so or not depends on details of the individuation of bases of belief formation.
25 The example is taken from Comesaña (2005), p. 397. See also Neta and Rohrbaugh (2004).
It is interesting to note that, under the assumption that p is truly believed, if p is sensitive then
it is safe (under the revised semantics offered in the previous section). Therefore, counterexamples to safety as a necessary condition on knowledge are also (further) counterexamples to
sensitivity.
14
right road. I seriously consider disguising myself as Michael, but at
the last moment I don’t. When I get to the crossroads, I ask Judy
where the party is, and she tells me that it is down the left road.
In the case as described, I know that the party is down the left road, and yet
I could have easily believed the same thing without its being true (because I
could have easily have come disguised as Michael, in which case Judy would
have lied to me). In other words, I have knowledge but my belief is not safe.
6
Conclusion
Accounts of knowledge that incorporate subjunctive conditionals are seen by
many as promising developments of an “externalist” approach to epistemology
(whether the subjunctive holds or not is not determined entirely by factors
internal to the subject in question). It is fair to say that these accounts must face
important obstacles. In particular, the standard semantics for subjunctives will
have to be replaced, and there are counterexamples to every proposed condition.
If the subjunctive conditionals approach falls to these problems, however, it
would be premature to conclude that externalism is thereby compromised. All
that the failure of the subjunctive conditionals account would show is that
these particular externalist theories are not satisfactory, just as many particular
internalist theories are not satisfactory.26
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26 Many
thanks to Carolina Sartorio and Andy Egan for very helpful comments.
15
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16
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17