This paper raises a problem for contrastivist accounts of knowledge. It is argued that contrastivism fails to succeed in providing a modest solution to the sceptical paradox—i.e. one according to which we have knowledge of a wide range of ordinary empirical propositions whilst failing to know the various anti-sceptical hypotheses entailed by them—whilst, at the same time, retaining a contrastivist version of the closure principle for knowledge

Kelp, Christoph

Philosophical Studies

English

This paper raises a problem for contrastivist accounts of knowledge. It is
argued that contrastivism fails to succeed in providing a modest solution to the sceptical paradox—i.e. one according to which we have knowledge of a wide range of ordinary empirical propositions whilst failing to know the various anti-sceptical hypotheses entailed by them—whilst, at the same time, retaining a contrastivist version of the closure principle for knowledge.status: Publishe

Lirias

A Problem for Contrastivist Accounts ofKnowledgeChristoph Kelp∗AbstractThis paper raises a problem for contrastivist accounts of knowledge. It isargued that contrastivism fails to succeed in providing a modest solutionto the sceptical paradox–i.e. one according to which we have knowledgeof a wide range of ordinary empirical propositions whilst failing to knowthe various anti-sceptical hypotheses entailed by them–whilst, at the sametime, retaining a contrastivist version of the closure principle of knowledge.1 ContrastivismContrastivism in epistemology is the view that knowledge is not a binary relationbetween a knower and a proposition but a ternary relation between a knower, S,a proposition known, p, and contrast proposition, q. To know a proposition, p,according to contrastivism, really is to know that p rather than q.1 Knowledgepropositions are represented thus:(C) Ks pq2One of the chief motivations for contrastivism is its ability to offer a certain kindof response to the sceptical paradox. The sceptical paradox threatens to showthat we do not know most of the things we take ourselves to know because, forinstance,(S1) I do not know that I am not a brain in a vat artificially stimulated to havedeceptive experiences as of a physical world.(S2) If I know that I have hands, then I know that I am not such a brain in avat.(S3) So, I do not know that I have hands.3Contrastivists believe that the first premise, the closure principle which validatesthe second premise and the negation of the conclusion are highly intuitive. In∗Institute of Philosophy, University of Leuven, Dekenstr. 2, #3220, B–3000 Leuven, Email:christoph.kelp@hiw.kuleuven.be1fact, they are considered so intuitive that on a satisfactory analysis of the scep-tical paradox each one has to come out true. The response to the scepticalparadox must be what Jonathan Schaffer, one of the main proponents of con-trastivism, calls ’modest’. The analysis of knowledge as contrastive makes sucha modest response to scepticism viable by, first, making explicit the contrastivestructure of the premises and the negation of the conclusion and thereby render-ing them compatible and, second, modifying the closure principle so as to allowextensions of knowledge while not falling prey to the sceptic’s fatal conclusion.The explicit contrastive structure of (S1), (S2) and the negation of (S3) is this:(S1*) I do not know that I am handed rather than envatted.(S2*) If I do not know that I am not envatted rather than envatted then I donot know that I am handed rather than envatted.(S3*) I know that I am handed rather than amputated.4By contrastivist lights, all of these propositions are true. This is the first stepthe contrastivist makes to make possible a modest response to the scepticalparadox. I will, for the purposes of this paper, grant the contrastivist that all of(S1*)-(S3*) are true. What I am interested in rather is the contrastivist accountof the closure principle, which, recall, is to be preserved by contrastivism. In arecent paper, Jonathan Schaffer, has taken upon himself the task of providinga detailed account of contrastivist closure. He claims that the following fourprinciples capture the sense in which contrastive knowledge is closed.(Expand-p) (Ks p1q & (p1 → p2) & {p2}⋂{q} = {}) → Es p2q5This principle licenses expansion of knowledge. The idea is that if one knowsa proposition p1 vis-a-vis a contrast proposition q, if p1 entails p2, and if theintersecting set of the set containing p2 and and the set containing q is theempty set, one is in a position to know p2 rather than q.6The second principle mimics the classical principle of closure under conjunc-tion introduction. The idea is that if one knows a proposition p1 vis-a-vis acontrast proposition q and one knows another proposition p2 rather than q thenone is in a position to know both p1 and p2 rather than q.(Intersect-p) (Ks p1q &Ks p2q) → Es (p1 & p2) q7The third principle is a principle that preserves knowledge under contractionof the contrast proposition. Here, the idea is that if one knows a propositionp vis-a-vis a contrast proposition q1, if q1 is entailed by another proposition q2and if the set containing q2 is not the empty set, one is in a position to know prather than q2.(Contract-q) (Ks pq1 & (q2 → q1) & {q2} 6= {}) → Es pq28Finally, the contrastivist endorses a principle that preserves knowledge underunion of contrast propositions. The idea is that if one knows a proposition pvis-a-vis a contrast proposition q1 and one knows p vis-a-vis another contrastproposition q2 then one is in a position to know p rather than q1 or q2.2(Union-q) (Ks pq1 &Ks pq2) → Es p (q1 ∨ q2)92 A Problem for Contrastivist Accounts of Knowl-edgeConsider the following case:(Square 1) I know that the object before my eyes is a square rather than atriangle.(Square 2) If I am deceived by a malign genius into believing that the objectbefore my eyes is a square, while, in fact, it is a triangle, then it is atriangle.(Square 3) Therefore, I am in a position to know that the object before myeyes is a square rather than that I am deceived by a malign genius intobelieving that it is a square while, in fact, it is a triangle.Note that the new contrast proposition entails the old one. Moreover, the setcontaining the new contrast proposition does obviously not equal the emptyset.10Therefore, by Schaffer’s own lights, (Square 1)-(Square 3) is a valid in-stance of Contract-q. But things are worse. For this line of thought can begeneralized in the following way:(P1) One knows that p rather than q.(P2) If one is deceived by a malign genius into believing that p while as amatter of fact q, then q.(P3) Therefore, one knows that p rather than that one is deceived by a maligngenius into believing that p while as a matter of fact q.Since, at least for a large number of propositions, p and q, the set containing theproposition that one is deceived, by a malign genius, into believing that p whileas a matter of fact q does not equal the empty set, (P1)-(P3) is a template forgenerating valid instances of Contract-q. This result is unacceptable for Schaffer,though. After all, it shows that, on his premises, we can have a wide range ofanti-sceptical knowledge. In this way the results of Contract-q fly in the face ofcontrastivists’ commitment to a modest approach to the sceptical paradox—anapproach, that is, according to which we lack anti-sceptical knowledge. Insofaras contrastivists motivate their position by appealing to the need of a modestapproach to the sceptical paradox this result undermines the very motivationfor their position.Can Schaffer do without Contract-q? It seems that the answer to this ques-tion is ’no’. After all, cases like the following seem to be perfectly fine ways ofacquiring knowledge: Sandra knows that Paul was born in Germany rather thanin Asia. However, Sandra does not know very much about Asia except that it’sa different continent than the one she and Paul inhabit, which is Europe. Now,3Sandra learns that China is a country in Asia. From the fact that Paul was bornin Germany rather than in Asia and the fact that China is a country in Asia,she competently deduces and thereupon comes to believe that Paul was born inGermany rather than in China. Intuitively, when Sandra acquires her belief inthis way, her belief also qualifies as knowledge. The problem for contrastivistsis, of course, that once Contract-q is given up, they can no longer explain thisintuition. Contrastivism thus appears to fall prey to a pattern of failure thatJohn Hawthorne has diagnosed as common for accounts of knowledge that denyor otherwise restrict closure: It fails to restrict the closure principle in such away that it succeeds in predicting that the subject acquires closure-based knowl-edge in all cases in which, intuitively, she does, whilst avoiding to predict thatthe subject acquires closure-based knowledge in all cases in which, intuitively,she doesn’t.11In personal communication Schaffer has offered the following response to thisobjection. First, he points out that whether, by contrastivist lights, one standsin a given knowledge relation to a target proposition and a contrast propositiondepends on what error possibilities are in play. Either a world in which thescenario depicted in the antecedent of (P2) is among the error possibilities inplay or it isn’t. If it is, then since one cannot eliminate this possibility, (P1)turns out to be false.12 If, on the other hand, such an error possibility isn’tin play, then one also cannot access it via Contract-q and so (P3) does notfollow. So, in neither case Contract-q generates the problematic anti-scepticalknowledge. In order to explain how contrastive knowledge attributions can stillbe true in some contexts, Schaffer goes on to embrace contextualism about thecontent of that-clauses: Which scenarios are denoted by a given that-clausedepends in part on the domain of quantification. In consequence, there will becontexts in which the clause “that q” at issue in (P1) denotes a set of possibilitiesthat includes the scenario depicted in the antecedent of (P2). In such contexts,the relevant contrastive knowledge attributions will turn out false. On the otherhand, there will also be contexts in which the very same clause denotes a set ofpossibilities that is restricted to non-deception scenarios. In such contexts, asthe above argument shows, the relevant contrastive knowledge attributions cancontinue to be true.By way of rejoinder to this response, let us first go back to the case ofSandra who knows that Paul was born in Germany rather than in Asia. Sinceshe knows so very little about Asia, before she acquires the information thatChina is a country in Asia, Sandra is unable to eliminate the possibility thatPaul was born in China.13 By the lights of Schaffer’s response, it follows thatwe can truly attribute to Sandra knowledge that Paul was born in Germanyrather than in Asia only in contexts in which scenarios in which Paul was bornin China are not amongst the scenarios denoted by the clause “that Paul wasborn in Asia”. That, however, is rather implausible. Thus suppose that theepisode is embedded in the following case: In order to ascertain the extent ofhis students’ geographical knowledge, a teacher designs a multiple choice testincluding questions such as “Which, if any, of the following sentences are true: A)Paul was born in Germany rather than in Bonn, B) Paul was born in Germany4rather than in China, C) Paul was born in Germany rather than in Asia, D)Paul was born in Germany rather than in the Black Forest”.14 When evaluatinghis students’ answers to this question he may, for instance, truly say somethinglike: “While Peter knows that Paul was born in Germany rather than in China,Sandra only knows that he was born in Germany rather than in Asia.” It is clearthat, in the teacher’s context, the scenario in which Paul was born in China isdenoted by the clause “that he was born in Asia”. By the lights of Schaffer’sabove response, however, since Sandra cannot eliminate the possibility that Paulwas born in China, it follows that, in the present context, she cannot be trulyattributed knowledge that Paul was born in Germany rather than in Asia. Onceagain, contrastivism passes the wrong verdict.We thus see that contrastivism’s conception of closure runs into serious prob-lems. Initially we found that there is reason to believe that contrastivism fallsprey to a pattern of failure common amongst conceptions of knowledge thatdeny or restrict closure, viz. of restricting closure in such a way that, accordingto the principle, the subject acquires closure-based knowledge when and onlywhen intuitively she does. The failure of Schaffer’s attempted solution to thisproblem highlights that the problem actually has yet another dimension. It isthe problem not only of matching our intuitive verdicts regarding closure-basedknowledge but also of doing so whilst continuing to match our intuitive verdictsregarding knowledge of the bases of closure-based knowledge. Like the lot of pro-posals that venture to deal with scepticism by restricting closure, contrastivismfails to do the trick.15ReferencesM. Blaauw. 2004. Contrastivism: Reconciling Sceptical Doubt with OrdinaryKnowledge. PhD thesis, Free University Amsterdam.J. Hawthorne 2005. ‘The case for closure.’ In M. Steup and E. Sosa, editors,Contemporary Debates in Epistemology. Blackwell, Oxford.A. Karjalainen and A. Morton. 2003. ‘Contrastive knowledge.’ PhilosophicalExplorations, 6:74–89.J. Schaffer. 2004. ‘From contextualism to contrastivism.’ PhilosophicalStudies, 119:73–103.J. Schaffer 2005. ‘Contrastive knowledge.’ In J. Hawthorne and T. Gendler,editors, Oxford Studies in Epistemology, Volume 1. OUP, Oxford.J. Schaffer. 2007. ‘Closure, contrast, and answer.’ Philosophical Studies,133:233–55.W. Sinnot-Armstrong. 2004. Pyrrhonian Skepticism. OUP, Oxford.Notes1Versions of contrastivism have been defended in e.g. Sinnot Armstrong [2004], Blaauw[2004], Karjalainen and Morton [2003] as well as Schaffer [2004, 2005, 2007].2Schaffer [2007, p. 234].53Schaffer [2005, pp. 259-60].4Cf. Schaffer [2005, p. 263].5Schaffer [2007, p. 243].6One might wonder why Schaffer requires that the intersection of the set containing theproposition entailed by the proposition known and the set containing the contrast propositionbe the empty set. The answer to this is that he construes knowledge as a relation between aknower, a target proposition and a contrast proposition where the contrast proposition andthe target proposition are pairwise exclusive, that is, if the target proposition is true, thenthe contrast proposition must be false. If the intersection between these two sets were notthe empty set, then the resulting relation would not be a relation between a knower, a targetproposition and a contrast proposition where the target proposition and the contrast propo-sition are pairwise exclusive. As a consequence, the relation would, on contrastivist premises,not be the knowledge relation. The requirement that the intersection of the set containing theproposition entailed by the target proposition and the set containing the contrast propositionbe the empty set is thus vital for Schaffer’s expansion principle.7Schaffer [2007, p. 245].8Schaffer [2007, p. 244]. Again, the requirement that the set containing the new contrastproposition, q2, which entails the original contrast proposition, q1, must not equal the emptyset is a natural consequence of contrastivists’ construal of knowledge as a ternary relationbetween a knower, a target proposition and a set of contrast propositions. If the set containingthe new contrast proposition were the empty set, then the knowledge obtained by the closureprinciple would specify a binary relation between a knower and a target proposition. By thelights of contrastivism, however, that relation would not be the knowledge relation. Thus,the requirement that the set containing the new contrast proposition, q2, which entails theoriginal contrast proposition, q1, must not equal the empty set is vital for the contrastivist’scontraction principle.9Schaffer [2007, p. 246].10Perhaps Schaffer wants to say that a set containing an inconsistent proposition equals theempty set. Notice, however, that it is quite plausible that the anti-sceptical proposition is notinconsistent. It seems entirely possible that one be so deceived.11Hawthorne [2005, p. 34].12What is meant by ’elimination’ of an error possibility? For present purposes it will sufficeto note that Schaffer countenances the following conceptual relation between elimination oferror possibilities and the ability to answer questions: “A third point of connection betweencontrastive knowing and answering is that the elimination of the relevant alternatives consti-tutes the ability to answer. That is . . . the evidential component of contrastive knowledge isthe elimination of the alternatives. Which is what it takes to be able to answer.” [Schaffer2007, p. 241] Moreover, makes the following claim about abilities to answer: “’able to answer’denotes an epistemic capacity. It is epistemic in that one may guess rightly without havingthe requisite ability.” [Schaffer 2005, p. 236]13Notice that this is supported by the conceptual relation between the elimination of errorpossibilities and the ability to answer questions Schaffer countenances (cf. n. 12). Since beforeshe gets the information about China Sandra knows next to nothing about it—for instance, shedoes not know whether ’China’ names a country, a continent, or a city or region in Germany—she cannot correctly answer questions such as whether Paul was born in China or whetherPaul was born in Germany rather than in China except by guessing. By Schaffer’s lights, then,she is unable to answer such questions. And given the conceptual relation between eliminationof error possibilities and ability to answer questions countenanced, she cannot eliminate thepossibility that Paul was born in China. (Of course, we can ask Sandra questions that, inconjunction with what she already knows, will enable her to correctly answer such questionswithout having to guess. This will be the case, for instance, if we put to her the question:“Exactly one of the following two sentences is true: which one? A) Paul was born in Germanyrather than in China. B) Paul was born in Germany rather than in Europe.” However,what enables her to correctly answer this question without having to guess is the additionalinformation contained in the question, viz. that exactly one of the two sentences is true. Itis only with the help of this information that Sandra can eliminate the China possibility. Tosee this notice that she would not have been able to correctly answer the following question6without guessing: “Which, if any, of the following sentences is true: A) Paul was born inGermany rather than in China. B) Paul was born in Germany rather than in Europe.” Giventhat this is so, it is plausible that, where Sandra has not received the crucial additionalinformation, she is unable to answer questions such as whether Paul was born in China orwhether he was born in Germany rather than in China and so cannot eliminate the possibilitythat Paul was born in China.)14Notice that this question does not contain the crucial information that would enableSandra tick off B) as a correct answer without guessing. So, by the conceptual relationbetween ability to answer and elimination of error possibilities, here too she cannot eliminatethe possibility that Paul was born in China.15Acknowledgements: Jonathan Schaffer, Duncan Pritchard, Jake Chandler and the audi-ences at the International Conference on Linguistics and Epistemology at the University ofAberdeen as well as the Albritton Society at UCLA.7

A Problem for Contrastivist Accounts of Knowledge

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Kelp, C. (2011) A problem for contrastivist accounts of knowledge. Philosophical 
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http://eprints.gla.ac.uk 
A Problem for Contrastivist Accounts of
Knowledge
Christoph Kelp∗
Abstract
This paper raises a problem for contrastivist accounts of knowledge. It is
argued that contrastivism fails to succeed in providing a modest solution
to the sceptical paradox–i.e. one according to which we have knowledge
of a wide range of ordinary empirical propositions whilst failing to know
the various anti-sceptical hypotheses entailed by them–whilst, at the same
time, retaining a contrastivist version of the closure principle of knowledge.
1 Contrastivism
Contrastivism in epistemology is the view that knowledge is not a binary relation
between a knower and a proposition but a ternary relation between a knower, S,
a proposition known, p, and contrast proposition, q. To know a proposition, p,
according to contrastivism, really is to know that p rather than q.1 Knowledge
propositions are represented thus:
(C) Ks pq2
One of the chief motivations for contrastivism is its ability to offer a certain kind
of response to the sceptical paradox. The sceptical paradox threatens to show
that we do not know most of the things we take ourselves to know because, for
instance,
(S1) I do not know that I am not a brain in a vat artificially stimulated to have
deceptive experiences as of a physical world.
(S2) If I know that I have hands, then I know that I am not such a brain in a
vat.
(S3) So, I do not know that I have hands.3
Contrastivists believe that the first premise, the closure principle which validates
the second premise and the negation of the conclusion are highly intuitive. In
∗Institute of Philosophy, University of Leuven, Dekenstr. 2, #3220, B–3000 Leuven, Email:
christoph.kelp@hiw.kuleuven.be
1
fact, they are considered so intuitive that on a satisfactory analysis of the scep-
tical paradox each one has to come out true. The response to the sceptical
paradox must be what Jonathan Schaffer, one of the main proponents of con-
trastivism, calls ’modest’. The analysis of knowledge as contrastive makes such
a modest response to scepticism viable by, first, making explicit the contrastive
structure of the premises and the negation of the conclusion and thereby render-
ing them compatible and, second, modifying the closure principle so as to allow
extensions of knowledge while not falling prey to the sceptic’s fatal conclusion.
The explicit contrastive structure of (S1), (S2) and the negation of (S3) is this:
(S1*) I do not know that I am handed rather than envatted.
(S2*) If I do not know that I am not envatted rather than envatted then I do
not know that I am handed rather than envatted.
(S3*) I know that I am handed rather than amputated.4
By contrastivist lights, all of these propositions are true. This is the first step
the contrastivist makes to make possible a modest response to the sceptical
paradox. I will, for the purposes of this paper, grant the contrastivist that all of
(S1*)-(S3*) are true. What I am interested in rather is the contrastivist account
of the closure principle, which, recall, is to be preserved by contrastivism. In a
recent paper, Jonathan Schaffer, has taken upon himself the task of providing
a detailed account of contrastivist closure. He claims that the following four
principles capture the sense in which contrastive knowledge is closed.
(Expand-p) (Ks p1q & (p1 → p2) & {p2}
⋂ {q} = {})→ Es p2q5
This principle licenses expansion of knowledge. The idea is that if one knows
a proposition p1 vis-a-vis a contrast proposition q, if p1 entails p2, and if the
intersecting set of the set containing p2 and and the set containing q is the
empty set, one is in a position to know p2 rather than q.6
The second principle mimics the classical principle of closure under conjunc-
tion introduction. The idea is that if one knows a proposition p1 vis-a-vis a
contrast proposition q and one knows another proposition p2 rather than q then
one is in a position to know both p1 and p2 rather than q.
(Intersect-p) (Ks p1q &Ks p2q)→ Es (p1 & p2) q7
The third principle is a principle that preserves knowledge under contraction
of the contrast proposition. Here, the idea is that if one knows a proposition
p vis-a-vis a contrast proposition q1, if q1 is entailed by another proposition q2
and if the set containing q2 is not the empty set, one is in a position to know p
rather than q2.
(Contract-q) (Ks pq1 & (q2 → q1) & {q2} 6= {})→ Es pq28
Finally, the contrastivist endorses a principle that preserves knowledge under
union of contrast propositions. The idea is that if one knows a proposition p
vis-a-vis a contrast proposition q1 and one knows p vis-a-vis another contrast
proposition q2 then one is in a position to know p rather than q1 or q2.
2
(Union-q) (Ks pq1 &Ks pq2)→ Es p (q1 ∨ q2)9
2 A Problem for Contrastivist Accounts of Knowl-
edge
Consider the following case:
(Square 1) I know that the object before my eyes is a square rather than a
triangle.
(Square 2) If I am deceived by a malign genius into believing that the object
before my eyes is a square, while, in fact, it is a triangle, then it is a
triangle.
(Square 3) Therefore, I am in a position to know that the object before my
eyes is a square rather than that I am deceived by a malign genius into
believing that it is a square while, in fact, it is a triangle.
Note that the new contrast proposition entails the old one. Moreover, the set
containing the new contrast proposition does obviously not equal the empty
set.10Therefore, by Schaffer’s own lights, (Square 1)-(Square 3) is a valid in-
stance of Contract-q. But things are worse. For this line of thought can be
generalized in the following way:
(P1) One knows that p rather than q.
(P2) If one is deceived by a malign genius into believing that p while as a
matter of fact q, then q.
(P3) Therefore, one knows that p rather than that one is deceived by a malign
genius into believing that p while as a matter of fact q.
Since, at least for a large number of propositions, p and q, the set containing the
proposition that one is deceived, by a malign genius, into believing that p while
as a matter of fact q does not equal the empty set, (P1)-(P3) is a template for
generating valid instances of Contract-q. This result is unacceptable for Schaffer,
though. After all, it shows that, on his premises, we can have a wide range of
anti-sceptical knowledge. In this way the results of Contract-q fly in the face of
contrastivists’ commitment to a modest approach to the sceptical paradox—an
approach, that is, according to which we lack anti-sceptical knowledge. Insofar
as contrastivists motivate their position by appealing to the need of a modest
approach to the sceptical paradox this result undermines the very motivation
for their position.
Can Schaffer do without Contract-q? It seems that the answer to this ques-
tion is ’no’. After all, cases like the following seem to be perfectly fine ways of
acquiring knowledge: Sandra knows that Paul was born in Germany rather than
in Asia. However, Sandra does not know very much about Asia except that it’s
a different continent than the one she and Paul inhabit, which is Europe. Now,
3
Sandra learns that China is a country in Asia. From the fact that Paul was born
in Germany rather than in Asia and the fact that China is a country in Asia,
she competently deduces and thereupon comes to believe that Paul was born in
Germany rather than in China. Intuitively, when Sandra acquires her belief in
this way, her belief also qualifies as knowledge. The problem for contrastivists
is, of course, that once Contract-q is given up, they can no longer explain this
intuition. Contrastivism thus appears to fall prey to a pattern of failure that
John Hawthorne has diagnosed as common for accounts of knowledge that deny
or otherwise restrict closure: It fails to restrict the closure principle in such a
way that it succeeds in predicting that the subject acquires closure-based knowl-
edge in all cases in which, intuitively, she does, whilst avoiding to predict that
the subject acquires closure-based knowledge in all cases in which, intuitively,
she doesn’t.11
In personal communication Schaffer has offered the following response to this
objection. First, he points out that whether, by contrastivist lights, one stands
in a given knowledge relation to a target proposition and a contrast proposition
depends on what error possibilities are in play. Either a world in which the
scenario depicted in the antecedent of (P2) is among the error possibilities in
play or it isn’t. If it is, then since one cannot eliminate this possibility, (P1)
turns out to be false.12 If, on the other hand, such an error possibility isn’t
in play, then one also cannot access it via Contract-q and so (P3) does not
follow. So, in neither case Contract-q generates the problematic anti-sceptical
knowledge. In order to explain how contrastive knowledge attributions can still
be true in some contexts, Schaffer goes on to embrace contextualism about the
content of that-clauses: Which scenarios are denoted by a given that-clause
depends in part on the domain of quantification. In consequence, there will be
contexts in which the clause “that q” at issue in (P1) denotes a set of possibilities
that includes the scenario depicted in the antecedent of (P2). In such contexts,
the relevant contrastive knowledge attributions will turn out false. On the other
hand, there will also be contexts in which the very same clause denotes a set of
possibilities that is restricted to non-deception scenarios. In such contexts, as
the above argument shows, the relevant contrastive knowledge attributions can
continue to be true.
By way of rejoinder to this response, let us first go back to the case of
Sandra who knows that Paul was born in Germany rather than in Asia. Since
she knows so very little about Asia, before she acquires the information that
China is a country in Asia, Sandra is unable to eliminate the possibility that
Paul was born in China.13 By the lights of Schaffer’s response, it follows that
we can truly attribute to Sandra knowledge that Paul was born in Germany
rather than in Asia only in contexts in which scenarios in which Paul was born
in China are not amongst the scenarios denoted by the clause “that Paul was
born in Asia”. That, however, is rather implausible. Thus suppose that the
episode is embedded in the following case: In order to ascertain the extent of
his students’ geographical knowledge, a teacher designs a multiple choice test
including questions such as “Which, if any, of the following sentences are true: A)
Paul was born in Germany rather than in Bonn, B) Paul was born in Germany
4
rather than in China, C) Paul was born in Germany rather than in Asia, D)
Paul was born in Germany rather than in the Black Forest”.14 When evaluating
his students’ answers to this question he may, for instance, truly say something
like: “While Peter knows that Paul was born in Germany rather than in China,
Sandra only knows that he was born in Germany rather than in Asia.” It is clear
that, in the teacher’s context, the scenario in which Paul was born in China is
denoted by the clause “that he was born in Asia”. By the lights of Schaffer’s
above response, however, since Sandra cannot eliminate the possibility that Paul
was born in China, it follows that, in the present context, she cannot be truly
attributed knowledge that Paul was born in Germany rather than in Asia. Once
again, contrastivism passes the wrong verdict.
We thus see that contrastivism’s conception of closure runs into serious prob-
lems. Initially we found that there is reason to believe that contrastivism falls
prey to a pattern of failure common amongst conceptions of knowledge that
deny or restrict closure, viz. of restricting closure in such a way that, according
to the principle, the subject acquires closure-based knowledge when and only
when intuitively she does. The failure of Schaffer’s attempted solution to this
problem highlights that the problem actually has yet another dimension. It is
the problem not only of matching our intuitive verdicts regarding closure-based
knowledge but also of doing so whilst continuing to match our intuitive verdicts
regarding knowledge of the bases of closure-based knowledge. Like the lot of pro-
posals that venture to deal with scepticism by restricting closure, contrastivism
fails to do the trick.15
References
M. Blaauw. 2004. Contrastivism: Reconciling Sceptical Doubt with Ordinary
Knowledge. PhD thesis, Free University Amsterdam.
J. Hawthorne 2005. ‘The case for closure.’ In M. Steup and E. Sosa, editors,
Contemporary Debates in Epistemology. Blackwell, Oxford.
A. Karjalainen and A. Morton. 2003. ‘Contrastive knowledge.’ Philosophical
Explorations, 6:74–89.
J. Schaffer. 2004. ‘From contextualism to contrastivism.’ Philosophical
Studies, 119:73–103.
J. Schaffer 2005. ‘Contrastive knowledge.’ In J. Hawthorne and T. Gendler,
editors, Oxford Studies in Epistemology, Volume 1. OUP, Oxford.
J. Schaffer. 2007. ‘Closure, contrast, and answer.’ Philosophical Studies,
133:233–55.
W. Sinnot-Armstrong. 2004. Pyrrhonian Skepticism. OUP, Oxford.
Notes
1Versions of contrastivism have been defended in e.g. Sinnot Armstrong [2004], Blaauw
[2004], Karjalainen and Morton [2003] as well as Schaffer [2004, 2005, 2007].
2Schaffer [2007, p. 234].
5
3Schaffer [2005, pp. 259-60].
4Cf. Schaffer [2005, p. 263].
5Schaffer [2007, p. 243].
6One might wonder why Schaffer requires that the intersection of the set containing the
proposition entailed by the proposition known and the set containing the contrast proposition
be the empty set. The answer to this is that he construes knowledge as a relation between a
knower, a target proposition and a contrast proposition where the contrast proposition and
the target proposition are pairwise exclusive, that is, if the target proposition is true, then
the contrast proposition must be false. If the intersection between these two sets were not
the empty set, then the resulting relation would not be a relation between a knower, a target
proposition and a contrast proposition where the target proposition and the contrast propo-
sition are pairwise exclusive. As a consequence, the relation would, on contrastivist premises,
not be the knowledge relation. The requirement that the intersection of the set containing the
proposition entailed by the target proposition and the set containing the contrast proposition
be the empty set is thus vital for Schaffer’s expansion principle.
7Schaffer [2007, p. 245].
8Schaffer [2007, p. 244]. Again, the requirement that the set containing the new contrast
proposition, q2, which entails the original contrast proposition, q1, must not equal the empty
set is a natural consequence of contrastivists’ construal of knowledge as a ternary relation
between a knower, a target proposition and a set of contrast propositions. If the set containing
the new contrast proposition were the empty set, then the knowledge obtained by the closure
principle would specify a binary relation between a knower and a target proposition. By the
lights of contrastivism, however, that relation would not be the knowledge relation. Thus,
the requirement that the set containing the new contrast proposition, q2, which entails the
original contrast proposition, q1, must not equal the empty set is vital for the contrastivist’s
contraction principle.
9Schaffer [2007, p. 246].
10Perhaps Schaffer wants to say that a set containing an inconsistent proposition equals the
empty set. Notice, however, that it is quite plausible that the anti-sceptical proposition is not
inconsistent. It seems entirely possible that one be so deceived.
11Hawthorne [2005, p. 34].
12What is meant by ’elimination’ of an error possibility? For present purposes it will suffice
to note that Schaffer countenances the following conceptual relation between elimination of
error possibilities and the ability to answer questions: “A third point of connection between
contrastive knowing and answering is that the elimination of the relevant alternatives consti-
tutes the ability to answer. That is . . . the evidential component of contrastive knowledge is
the elimination of the alternatives. Which is what it takes to be able to answer.” [Schaffer
2007, p. 241] Moreover, makes the following claim about abilities to answer: “’able to answer’
denotes an epistemic capacity. It is epistemic in that one may guess rightly without having
the requisite ability.” [Schaffer 2005, p. 236]
13Notice that this is supported by the conceptual relation between the elimination of error
possibilities and the ability to answer questions Schaffer countenances (cf. n. 12). Since before
she gets the information about China Sandra knows next to nothing about it—for instance, she
does not know whether ’China’ names a country, a continent, or a city or region in Germany—
she cannot correctly answer questions such as whether Paul was born in China or whether
Paul was born in Germany rather than in China except by guessing. By Schaffer’s lights, then,
she is unable to answer such questions. And given the conceptual relation between elimination
of error possibilities and ability to answer questions countenanced, she cannot eliminate the
possibility that Paul was born in China. (Of course, we can ask Sandra questions that, in
conjunction with what she already knows, will enable her to correctly answer such questions
without having to guess. This will be the case, for instance, if we put to her the question:
“Exactly one of the following two sentences is true: which one? A) Paul was born in Germany
rather than in China. B) Paul was born in Germany rather than in Europe.” However,
what enables her to correctly answer this question without having to guess is the additional
information contained in the question, viz. that exactly one of the two sentences is true. It
is only with the help of this information that Sandra can eliminate the China possibility. To
see this notice that she would not have been able to correctly answer the following question
6
without guessing: “Which, if any, of the following sentences is true: A) Paul was born in
Germany rather than in China. B) Paul was born in Germany rather than in Europe.” Given
that this is so, it is plausible that, where Sandra has not received the crucial additional
information, she is unable to answer questions such as whether Paul was born in China or
whether he was born in Germany rather than in China and so cannot eliminate the possibility
that Paul was born in China.)
14Notice that this question does not contain the crucial information that would enable
Sandra tick off B) as a correct answer without guessing. So, by the conceptual relation
between ability to answer and elimination of error possibilities, here too she cannot eliminate
the possibility that Paul was born in China.
15Acknowledgements: Jonathan Schaffer, Duncan Pritchard, Jake Chandler and the audi-
ences at the International Conference on Linguistics and Epistemology at the University of
Aberdeen as well as the Albritton Society at UCLA.
7


A problem for contrastivist accounts of knowledge

Enlighten

      Kelp, C. (2011) A problem for contrastivist accounts of knowledge. Philosophical Studies, 152(2), pp. 287-292.     There may be differences between this version and the published version. You are advised to consult the publisher’s version if you wish to cite from it.    http://eprints.gla.ac.uk/140941/            Deposited on: 15 May 2017                       Enlighten – Research publications by members of the University of Glasgow http://eprints.gla.ac.uk A Problem for Contrastivist Accounts ofKnowledgeChristoph Kelp∗AbstractThis paper raises a problem for contrastivist accounts of knowledge. It isargued that contrastivism fails to succeed in providing a modest solutionto the sceptical paradox–i.e. one according to which we have knowledgeof a wide range of ordinary empirical propositions whilst failing to knowthe various anti-sceptical hypotheses entailed by them–whilst, at the sametime, retaining a contrastivist version of the closure principle of knowledge.1 ContrastivismContrastivism in epistemology is the view that knowledge is not a binary relationbetween a knower and a proposition but a ternary relation between a knower, S,a proposition known, p, and contrast proposition, q. To know a proposition, p,according to contrastivism, really is to know that p rather than q.1 Knowledgepropositions are represented thus:(C) Ks pq2One of the chief motivations for contrastivism is its ability to offer a certain kindof response to the sceptical paradox. The sceptical paradox threatens to showthat we do not know most of the things we take ourselves to know because, forinstance,(S1) I do not know that I am not a brain in a vat artificially stimulated to havedeceptive experiences as of a physical world.(S2) If I know that I have hands, then I know that I am not such a brain in avat.(S3) So, I do not know that I have hands.3Contrastivists believe that the first premise, the closure principle which validatesthe second premise and the negation of the conclusion are highly intuitive. In∗Institute of Philosophy, University of Leuven, Dekenstr. 2, #3220, B–3000 Leuven, Email:christoph.kelp@hiw.kuleuven.be1fact, they are considered so intuitive that on a satisfactory analysis of the scep-tical paradox each one has to come out true. The response to the scepticalparadox must be what Jonathan Schaffer, one of the main proponents of con-trastivism, calls ’modest’. The analysis of knowledge as contrastive makes sucha modest response to scepticism viable by, first, making explicit the contrastivestructure of the premises and the negation of the conclusion and thereby render-ing them compatible and, second, modifying the closure principle so as to allowextensions of knowledge while not falling prey to the sceptic’s fatal conclusion.The explicit contrastive structure of (S1), (S2) and the negation of (S3) is this:(S1*) I do not know that I am handed rather than envatted.(S2*) If I do not know that I am not envatted rather than envatted then I donot know that I am handed rather than envatted.(S3*) I know that I am handed rather than amputated.4By contrastivist lights, all of these propositions are true. This is the first stepthe contrastivist makes to make possible a modest response to the scepticalparadox. I will, for the purposes of this paper, grant the contrastivist that all of(S1*)-(S3*) are true. What I am interested in rather is the contrastivist accountof the closure principle, which, recall, is to be preserved by contrastivism. In arecent paper, Jonathan Schaffer, has taken upon himself the task of providinga detailed account of contrastivist closure. He claims that the following fourprinciples capture the sense in which contrastive knowledge is closed.(Expand-p) (Ks p1q & (p1 → p2) & {p2}⋂ {q} = {})→ Es p2q5This principle licenses expansion of knowledge. The idea is that if one knowsa proposition p1 vis-a-vis a contrast proposition q, if p1 entails p2, and if theintersecting set of the set containing p2 and and the set containing q is theempty set, one is in a position to know p2 rather than q.6The second principle mimics the classical principle of closure under conjunc-tion introduction. The idea is that if one knows a proposition p1 vis-a-vis acontrast proposition q and one knows another proposition p2 rather than q thenone is in a position to know both p1 and p2 rather than q.(Intersect-p) (Ks p1q &Ks p2q)→ Es (p1 & p2) q7The third principle is a principle that preserves knowledge under contractionof the contrast proposition. Here, the idea is that if one knows a propositionp vis-a-vis a contrast proposition q1, if q1 is entailed by another proposition q2and if the set containing q2 is not the empty set, one is in a position to know prather than q2.(Contract-q) (Ks pq1 & (q2 → q1) & {q2} 6= {})→ Es pq28Finally, the contrastivist endorses a principle that preserves knowledge underunion of contrast propositions. The idea is that if one knows a proposition pvis-a-vis a contrast proposition q1 and one knows p vis-a-vis another contrastproposition q2 then one is in a position to know p rather than q1 or q2.2(Union-q) (Ks pq1 &Ks pq2)→ Es p (q1 ∨ q2)92 A Problem for Contrastivist Accounts of Knowl-edgeConsider the following case:(Square 1) I know that the object before my eyes is a square rather than atriangle.(Square 2) If I am deceived by a malign genius into believing that the objectbefore my eyes is a square, while, in fact, it is a triangle, then it is atriangle.(Square 3) Therefore, I am in a position to know that the object before myeyes is a square rather than that I am deceived by a malign genius intobelieving that it is a square while, in fact, it is a triangle.Note that the new contrast proposition entails the old one. Moreover, the setcontaining the new contrast proposition does obviously not equal the emptyset.10Therefore, by Schaffer’s own lights, (Square 1)-(Square 3) is a valid in-stance of Contract-q. But things are worse. For this line of thought can begeneralized in the following way:(P1) One knows that p rather than q.(P2) If one is deceived by a malign genius into believing that p while as amatter of fact q, then q.(P3) Therefore, one knows that p rather than that one is deceived by a maligngenius into believing that p while as a matter of fact q.Since, at least for a large number of propositions, p and q, the set containing theproposition that one is deceived, by a malign genius, into believing that p whileas a matter of fact q does not equal the empty set, (P1)-(P3) is a template forgenerating valid instances of Contract-q. This result is unacceptable for Schaffer,though. After all, it shows that, on his premises, we can have a wide range ofanti-sceptical knowledge. In this way the results of Contract-q fly in the face ofcontrastivists’ commitment to a modest approach to the sceptical paradox—anapproach, that is, according to which we lack anti-sceptical knowledge. Insofaras contrastivists motivate their position by appealing to the need of a modestapproach to the sceptical paradox this result undermines the very motivationfor their position.Can Schaffer do without Contract-q? It seems that the answer to this ques-tion is ’no’. After all, cases like the following seem to be perfectly fine ways ofacquiring knowledge: Sandra knows that Paul was born in Germany rather thanin Asia. However, Sandra does not know very much about Asia except that it’sa different continent than the one she and Paul inhabit, which is Europe. Now,3Sandra learns that China is a country in Asia. From the fact that Paul was bornin Germany rather than in Asia and the fact that China is a country in Asia,she competently deduces and thereupon comes to believe that Paul was born inGermany rather than in China. Intuitively, when Sandra acquires her belief inthis way, her belief also qualifies as knowledge. The problem for contrastivistsis, of course, that once Contract-q is given up, they can no longer explain thisintuition. Contrastivism thus appears to fall prey to a pattern of failure thatJohn Hawthorne has diagnosed as common for accounts of knowledge that denyor otherwise restrict closure: It fails to restrict the closure principle in such away that it succeeds in predicting that the subject acquires closure-based knowl-edge in all cases in which, intuitively, she does, whilst avoiding to predict thatthe subject acquires closure-based knowledge in all cases in which, intuitively,she doesn’t.11In personal communication Schaffer has offered the following response to thisobjection. First, he points out that whether, by contrastivist lights, one standsin a given knowledge relation to a target proposition and a contrast propositiondepends on what error possibilities are in play. Either a world in which thescenario depicted in the antecedent of (P2) is among the error possibilities inplay or it isn’t. If it is, then since one cannot eliminate this possibility, (P1)turns out to be false.12 If, on the other hand, such an error possibility isn’tin play, then one also cannot access it via Contract-q and so (P3) does notfollow. So, in neither case Contract-q generates the problematic anti-scepticalknowledge. In order to explain how contrastive knowledge attributions can stillbe true in some contexts, Schaffer goes on to embrace contextualism about thecontent of that-clauses: Which scenarios are denoted by a given that-clausedepends in part on the domain of quantification. In consequence, there will becontexts in which the clause “that q” at issue in (P1) denotes a set of possibilitiesthat includes the scenario depicted in the antecedent of (P2). In such contexts,the relevant contrastive knowledge attributions will turn out false. On the otherhand, there will also be contexts in which the very same clause denotes a set ofpossibilities that is restricted to non-deception scenarios. In such contexts, asthe above argument shows, the relevant contrastive knowledge attributions cancontinue to be true.By way of rejoinder to this response, let us first go back to the case ofSandra who knows that Paul was born in Germany rather than in Asia. Sinceshe knows so very little about Asia, before she acquires the information thatChina is a country in Asia, Sandra is unable to eliminate the possibility thatPaul was born in China.13 By the lights of Schaffer’s response, it follows thatwe can truly attribute to Sandra knowledge that Paul was born in Germanyrather than in Asia only in contexts in which scenarios in which Paul was bornin China are not amongst the scenarios denoted by the clause “that Paul wasborn in Asia”. That, however, is rather implausible. Thus suppose that theepisode is embedded in the following case: In order to ascertain the extent ofhis students’ geographical knowledge, a teacher designs a multiple choice testincluding questions such as “Which, if any, of the following sentences are true: A)Paul was born in Germany rather than in Bonn, B) Paul was born in Germany4rather than in China, C) Paul was born in Germany rather than in Asia, D)Paul was born in Germany rather than in the Black Forest”.14 When evaluatinghis students’ answers to this question he may, for instance, truly say somethinglike: “While Peter knows that Paul was born in Germany rather than in China,Sandra only knows that he was born in Germany rather than in Asia.” It is clearthat, in the teacher’s context, the scenario in which Paul was born in China isdenoted by the clause “that he was born in Asia”. By the lights of Schaffer’sabove response, however, since Sandra cannot eliminate the possibility that Paulwas born in China, it follows that, in the present context, she cannot be trulyattributed knowledge that Paul was born in Germany rather than in Asia. Onceagain, contrastivism passes the wrong verdict.We thus see that contrastivism’s conception of closure runs into serious prob-lems. Initially we found that there is reason to believe that contrastivism fallsprey to a pattern of failure common amongst conceptions of knowledge thatdeny or restrict closure, viz. of restricting closure in such a way that, accordingto the principle, the subject acquires closure-based knowledge when and onlywhen intuitively she does. The failure of Schaffer’s attempted solution to thisproblem highlights that the problem actually has yet another dimension. It isthe problem not only of matching our intuitive verdicts regarding closure-basedknowledge but also of doing so whilst continuing to match our intuitive verdictsregarding knowledge of the bases of closure-based knowledge. Like the lot of pro-posals that venture to deal with scepticism by restricting closure, contrastivismfails to do the trick.15ReferencesM. Blaauw. 2004. Contrastivism: Reconciling Sceptical Doubt with OrdinaryKnowledge. PhD thesis, Free University Amsterdam.J. Hawthorne 2005. ‘The case for closure.’ In M. Steup and E. Sosa, editors,Contemporary Debates in Epistemology. Blackwell, Oxford.A. Karjalainen and A. Morton. 2003. ‘Contrastive knowledge.’ PhilosophicalExplorations, 6:74–89.J. Schaffer. 2004. ‘From contextualism to contrastivism.’ PhilosophicalStudies, 119:73–103.J. Schaffer 2005. ‘Contrastive knowledge.’ In J. Hawthorne and T. Gendler,editors, Oxford Studies in Epistemology, Volume 1. OUP, Oxford.J. Schaffer. 2007. ‘Closure, contrast, and answer.’ Philosophical Studies,133:233–55.W. Sinnot-Armstrong. 2004. Pyrrhonian Skepticism. OUP, Oxford.Notes1Versions of contrastivism have been defended in e.g. Sinnot Armstrong [2004], Blaauw[2004], Karjalainen and Morton [2003] as well as Schaffer [2004, 2005, 2007].2Schaffer [2007, p. 234].53Schaffer [2005, pp. 259-60].4Cf. Schaffer [2005, p. 263].5Schaffer [2007, p. 243].6One might wonder why Schaffer requires that the intersection of the set containing theproposition entailed by the proposition known and the set containing the contrast propositionbe the empty set. The answer to this is that he construes knowledge as a relation between aknower, a target proposition and a contrast proposition where the contrast proposition andthe target proposition are pairwise exclusive, that is, if the target proposition is true, thenthe contrast proposition must be false. If the intersection between these two sets were notthe empty set, then the resulting relation would not be a relation between a knower, a targetproposition and a contrast proposition where the target proposition and the contrast propo-sition are pairwise exclusive. As a consequence, the relation would, on contrastivist premises,not be the knowledge relation. The requirement that the intersection of the set containing theproposition entailed by the target proposition and the set containing the contrast propositionbe the empty set is thus vital for Schaffer’s expansion principle.7Schaffer [2007, p. 245].8Schaffer [2007, p. 244]. Again, the requirement that the set containing the new contrastproposition, q2, which entails the original contrast proposition, q1, must not equal the emptyset is a natural consequence of contrastivists’ construal of knowledge as a ternary relationbetween a knower, a target proposition and a set of contrast propositions. If the set containingthe new contrast proposition were the empty set, then the knowledge obtained by the closureprinciple would specify a binary relation between a knower and a target proposition. By thelights of contrastivism, however, that relation would not be the knowledge relation. Thus,the requirement that the set containing the new contrast proposition, q2, which entails theoriginal contrast proposition, q1, must not equal the empty set is vital for the contrastivist’scontraction principle.9Schaffer [2007, p. 246].10Perhaps Schaffer wants to say that a set containing an inconsistent proposition equals theempty set. Notice, however, that it is quite plausible that the anti-sceptical proposition is notinconsistent. It seems entirely possible that one be so deceived.11Hawthorne [2005, p. 34].12What is meant by ’elimination’ of an error possibility? For present purposes it will sufficeto note that Schaffer countenances the following conceptual relation between elimination oferror possibilities and the ability to answer questions: “A third point of connection betweencontrastive knowing and answering is that the elimination of the relevant alternatives consti-tutes the ability to answer. That is . . . the evidential component of contrastive knowledge isthe elimination of the alternatives. Which is what it takes to be able to answer.” [Schaffer2007, p. 241] Moreover, makes the following claim about abilities to answer: “’able to answer’denotes an epistemic capacity. It is epistemic in that one may guess rightly without havingthe requisite ability.” [Schaffer 2005, p. 236]13Notice that this is supported by the conceptual relation between the elimination of errorpossibilities and the ability to answer questions Schaffer countenances (cf. n. 12). Since beforeshe gets the information about China Sandra knows next to nothing about it—for instance, shedoes not know whether ’China’ names a country, a continent, or a city or region in Germany—she cannot correctly answer questions such as whether Paul was born in China or whetherPaul was born in Germany rather than in China except by guessing. By Schaffer’s lights, then,she is unable to answer such questions. And given the conceptual relation between eliminationof error possibilities and ability to answer questions countenanced, she cannot eliminate thepossibility that Paul was born in China. (Of course, we can ask Sandra questions that, inconjunction with what she already knows, will enable her to correctly answer such questionswithout having to guess. This will be the case, for instance, if we put to her the question:“Exactly one of the following two sentences is true: which one? A) Paul was born in Germanyrather than in China. B) Paul was born in Germany rather than in Europe.” However,what enables her to correctly answer this question without having to guess is the additionalinformation contained in the question, viz. that exactly one of the two sentences is true. Itis only with the help of this information that Sandra can eliminate the China possibility. Tosee this notice that she would not have been able to correctly answer the following question6without guessing: “Which, if any, of the following sentences is true: A) Paul was born inGermany rather than in China. B) Paul was born in Germany rather than in Europe.” Giventhat this is so, it is plausible that, where Sandra has not received the crucial additionalinformation, she is unable to answer questions such as whether Paul was born in China orwhether he was born in Germany rather than in China and so cannot eliminate the possibilitythat Paul was born in China.)14Notice that this question does not contain the crucial information that would enableSandra tick off B) as a correct answer without guessing. So, by the conceptual relationbetween ability to answer and elimination of error possibilities, here too she cannot eliminatethe possibility that Paul was born in China.15Acknowledgements: Jonathan Schaffer, Duncan Pritchard, Jake Chandler and the audi-ences at the International Conference on Linguistics and Epistemology at the University ofAberdeen as well as the Albritton Society at UCLA.7

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A problem for contrastivist accounts of knowledge

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