International Phenomenological Society

On the ObviousAuthor(s): Robin JeshionSource: Philosophy and Phenomenological Research, Vol. 60, No. 2 (Mar., 2000), pp. 333-355Published by: International Phenomenological SocietyStable URL: http://www.jstor.org/stable/2653489Accessed: 13/07/2009 23:35

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/action/showPublisher?publisherCode=ips.

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.

JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with thescholarly community to preserve their work and the materials they rely upon, and to build a common research platform thatpromotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org.

International Phenomenological Society is collaborating with JSTOR to digitize, preserve and extend access toPhilosophy and Phenomenological Research.

http://www.jstor.org

Philosophy and Phenomenological Research Vol. LX, No. 2, March 2000

On the Obvious*

ROBIN JESHION

University of Southern California

Infallibilism about a priori justification is the thesis that for an agent A to be a priori justified in believing p, that which justifies A's belief that p must guarantee the truth of p. No analogous thesis is thought to obtain for empirically justified beliefs. The aim of this article is to argue that infallibilism about the a priori is an untenable philosophical posi- tion and to provide theoretical understanding why we not only can be, but rather must be, a priori justified in believing some false propositions. The argument develops notions of obviousness and conceptual understanding as a means of affording insight into the conditions for having a priori justification and, consequently, into why infallibilism cannot stand.

Can one be a priori justified in believing a false proposition, and if so, why? Many have thought that the answer is "no". A priori justifications are infalli- ble. Sometimes people have maintained infallibility because they stipulate- work into their definition of a priority-that any a priori justified beliefs must be true. There would, of course, be little point of even raising the ques- tion on such a conception. But I think that the infallibilist view is rather per- vasive, even for those who, like myself, regard the essential mark of a priori justifications to be their non-empirical epistemic basis. A priori justifications are justifications that do not depend upon or make any reference to sensory experiences; they depend upon and are constituted by or refer only to reason- ing, conceptual understanding, or rational intuition. The infallibility require- ment for a priori justifications may be formulated as follows: for a subject S to be a priori justified in believing p, that which justifies S's belief that p must guarantee the truth of p. No analogous requirement is thought to obtain

* I have presented material from ??2,3 in colloquia at University of Southern California, University of Chicago, University of Illinois at Urbana, and University of California at Santa Barbara, and presented a short paper, essentially ?2, by the same name at the Pacific APA in Berkeley in March 1997. I thank my audiences and the students in my graduate seminar on a priori knowledge for stimulating discussions. I would also like to thank Frank Arntzenius, Janet Levin, Leonard Linsky, Steve Peterson, Philip Robbins, Nathan Salmon, Josef Stern, Gregg Ten Elshof, and Kadri Vihvelin for helpful comments. Two anonymous referees for Philosophy and Phenomenological Research offered excellent criticisms that helped improve this paper. Very special thanks to Albert Casullo and Michael Nelson for challenging constructive critical discussion from which I learned a great deal.

ON THE OBVIOUS 333

for empirically justified beliefs. This asymmetrical position regarding fallibil- ism with respect to a priori and empirical justifications has been predominant within epistemology.

In recent years, several philosophers have argued that it is a mistake to maintain that a priori justified beliefs must be immune to all rational doubt (indubitable),' that they are not rationally revisable, i.e., would not be rationally given up in any epistemically possible circumstance (unrevisable),2 and that the grounds for the belief entail the truth of the proposition believed (infallible).3 While some have advanced the debate by giving cogent grounds for dispensing with indubitability and unrevisability,4 considerable confusion remains with regard to the infallibility requirement. Many of the arguments for rejecting infallibilism would not be compelling to one who is not antecedently opposed to the view. Moreover, there currently exists no theoret- ical understanding of why we can (if we can) be a priori justified in believing false propositions.

My objective in this essay is to argue that infallibilism is an untenable philosophical position and to provide an explanation as to why we not only can be, but rather must be, a priori justified in believing some false proposi- tions. In this essay, I shall focus primarily on beliefs that are grounded on conceptual understanding alone. I argue that infallibilism regards as unjustified reasoning with one's most precise conceptual understanding of concepts. Yet such reasoning is necessary for the belief correction which affords the only rational means of attaining correct conceptions of concepts. But any epistemic theory must ensure the possibility of the non-accidental

For contemporary proponents of indubitability, see especially Philip Kitcher's The Nature of Mathematical Knowledge (Oxford: Oxford University Press, 1984). Hilary Putnam at times identifies a priori truths with those statements that it would never be rational to doubt. See Realism and Reason: Philosophical Papers, Volume 3 (Cambridge: Cambridge University Press, 1983).

2 Kitcher, ibid., and Putnam., ibid, both advocate conceptions of a priority that entail unrevisability.

3 Roderick Chisholm links understanding required for a priori justification with a guarantee of truth: "...an a priori proposition is one such that, if you accept it, then it becomes certain for you. (For if you accept it, then you understand it, and as soon as you under- stand it, it becomes certain for you.)." See "The Truths of Reason" in Theory of Knowl- edge (Englewood Cliffs, Prentice Hall, Inc., 1977), 2nd edition, pp. 34-61.

Kitcher's conception of a priority also requires that a priori justificatory processes guarantee that the proposition believed is true.

4 Cf. Albert Casullo "Revisability, Reliabilism, and A priori Knowledge", Philosophy and Phenomenological Research, 49, pp. 187-213, and Donna Summerfield, "Modest A priori Knowledge", Philosophy and Phenomenological Research, 51, pp. 39-66. In "Proof Checking and Knowledge by Intellection", Philosophical Studies, 92, pp. 85-112, I advance grounds for regarding as illegitimate an indubitability requirement pertaining specifically to knowledge of theorems of long proofs. Since long proofs are among the hardest cases, if my argument against this indubitability requirement holds, it holds for most cases of a priori knowledge.

334 ROBIN JESHION

attainment of correct conceptions of concepts without reliance on unjustified beliefs. So infallibilism cannot stand.

The discussion breaks down into three sections. In ?1, I critically evaluate recent arguments that have been advanced against infallibilism, concluding that they fail to establish fallibilism. The results are, however, not wholly negative. Because the criticisms expose the primary rationales underlying infallibilism, they afford insight into conditions on a successful argument against infallibilism. In ?2, I give what is, I hope, such a successful argu- ment. In ?3, I detail the notion of obviousness and conceptual understanding employed in the argument so as to afford insight into why infallibilism is wrong.

?1 Infallibility

The infallibility requirement for a priori justifications says that if agent A is a priori justified in believing p, that which justifies A's belief that p must guarantee the truth of p. The requirement is often thought to be apparent because it seems to be borne out when we reflect on the canonical examples of justifications grounded on reason and understanding alone, namely proofs. When an agent's basis for believing a proposition p is a proof, the agent possesses truth-entailing reasons for believing p. Reflection on such exam- ples tends to encourage directly connecting a priori justifications with truth, for it seems that there must be something defective about an individual's understanding or reasoning if the proposition believed on the basis of that intellection is false. So the individual would not have been justified in believ- ing the proposition in the first place.

One problem with the infallibility requirement, one which has been noticed by many, is that it is plausible only if the individual's basis for belief is conceptual understanding alone or conceptual understanding plus deductive reasoning. If the proposition believed is grounded on inductive reasoning, infallibility is highly questionable.

Of course, historically, mathematical and philosophical propositions taken as justified a priori were almost always thought to rest entirely upon deduc- tive reasoning from self-evident propositions recognized on the basis of conceptual understanding alone. In the twentieth century, several mathemati- cians and philosophers emphasized the widespread use of inductive reasoning for the justification of axioms and plausibility arguments. We can have strong inductive grounds for believing non-self-evident propositions by recognizing their necessity for deriving other (possibly self-evident) proposi- tions known a priori.5 We can also have strong inductive grounds for believ-

In his 1908 paper "A New Proof of the Possibility of a Well-ordering", Zermelo argued that we can be justified in believing an axiom because of its necessity for deriving other, perhaps more basic or obvious, mathematical propositions. See From Frege to Glidel, van Heijenoort, ed. (Cambridge, Massachusetts: Harvard University Press, 1967), pp. 183-89.

ON THE OBVIOUS 335

ing certain mathematical theorems because we know that they obtain for, say, all numbers or functions heretofore considered. It is extremely doubtful that there is anything epistemically inadequate, much less defective, about such reasoning.

One might think we could bypass criticism of this premise altogether on the grounds that inductive reasoning automatically makes the justification empirical. This would be a mistake. There is nothing about inductive reason- ing per se that makes beliefs supported by it empirically based. Inductive reasoning, like deductive reasoning, is a style of reasoning. Justifications involving nothing more than inductive reasoning from other propositions known a priori are themselves a priori, not empirical.

These points merit appreciation. But there is another infallibility principle that is not refuted by them and that deserves serious critical discussion:

Infallibility: if agent A is a priori justified in believing p, and A's basis for belief involves no inductive reasoning, that which justifies A's belief that p must guarantee the truth of p.

In recent years, several philosophers have claimed that this infallibility requirement ought to be rejected. Why should it be?

George Bealer, Albert Casullo, and Donna Summerfield have all argued that infallibilism is incorrect. Their primary basis for this claim is that the standards for epistemic evaluation of the deliverances of our intellectual facul- ties ought to be the same as for the deliverances of our perceptual faculties.7 Since most everyone upholds fallibilism with respect to empirically justified beliefs, symmetrical standards on justification will ensure fallibilism with respect to the a priori. This point that we ought to uphold symmetrical stan- dards is quite significant. To be sure, many have upheld an infallibilist line solely because their standards on evaluation are more stringent for a priori justification. The common complaint, "what good is the a priori if it doesn't guarantee truth?" often comes from those who think that justificatory stan- dards should differ. Now, it seems to me that if this is the infallibilist's sole basis for his position, the point about symmetrical standards ought to suffice to at least place the burden of proof on the infallibilist. Absent an indepen-

Polya emphasized the use of inductive methods in mathematics in Mathematics and Plausible Reasoning, Volumes 1 and 2 (London: Oxford University Press, 1958). Cf. also Lakatos, "A Renaissance of Empiricism in the Recent Philosophy of Mathematics?" in Philosophical Papers, Volume 2, J. Worrall and G. Currie, eds. (Cambridge: Cambridge University Press, 1978); Putnam "What Is Mathematical Truth?" in Philosophical Papers, Volume I (Cambridge: Cambridge University Press, 1975).

6 I develop these points in more detail in "Proof-Checking and Knowledge by Intellection", op. cit. Cf. also Casullo, op. cit.

7 Bealer, "The Incoherence of Empiricism", The Aristotelian Society, Supplementary Vol- unme 66, pp. 99-138, Casullo, op. cit., Summerfield, op. cit. Bealer also advances other considerations to support fallibilism.

336 ROBIN JESHION

dent rationale for maintaining stricter standards for a prior justification, symmetrical standards ought to obtain. If the attraction of infallibilism rests only on a philosophical predisposition or tendency to uphold higher standards on understanding and reason than on perception, the view is easily defeated indeed.

But, of course, it is not. Acceptance of symmetrical standards on justification does not necessitate fallibilism. It need not even incline an infal- libilist to an alternative position. To see how alternative rationales bolster infallibilism, I will evaluate Casullo's argument against infallibilism and show that, contra Casullo, the assumption of symmetric standards does not necessitate fallibilism.

Casullo's argument against the infallibilist conjoins the symmetry of standards assumption with claims about the following two cases, one involv- ing a priori basis for belief, the other perceptual.

A priori Case: Suppose that Mary wonders whether [*] 'p->q' entails -p->-q'. She reflects upon the statements in question and on the

basis of this reflection concludes that the former entails the latter. Later, a counterexample to the alleged entailment occurs to her. On the basis of recognizing the counterexample, she comes to believe that her initial belief is mistaken and that [**] 'p-?q' entails ' q-4p'.

Perceptual Case: Suppose Mary has normal vision and is a reliable discriminator of shapes. She sees a sheet of paper and on that basis forms the belief that the paper is square. On closer examination, she recognizes that two of the sides are longer than the two sides to which they are perpendicular. Because of this Mary comes to reject her initial belief that the paper is square and comes to believe that it is rectangular.

Casullo argues for the Fallibilist thesis that (F) Mary's initial false belief that [*] is a priori justified. Although Casullo does not spell it out, his argument for (F) may be summarized as follows:

(1) We should uphold the same standards on justification for a priori and empirical cases.

(2) In the perceptual case, the agent is justified in believing the false proposition that the paper is square.

(3) The a priori case is in all relevant respects analogous to the percep- tual case.

ON THE OBVIOUS 337

So, (F) the agent is a priori justified in believing [*].

Since we are aiming to show that the central point of disagreement with the infallibilist is not necessarily over the first premise, let us grant it. And let us also grant (2) that our subject is initially justified in believing that the paper is a square. Does Casullo succeed in establishing that (3) the a priori case is in all relevant respects analogous to the perceptual case?

To decide the issue, the first thing to reflect upon is how the agent's hav- ing later formed true beliefs is supposed to bear on the epistemic evaluation of her initial belief. Casullo is not clear about this. In some places, he seems to be assuming a reliabilist framework. More specifically, he seems to be assuming that the agent's beliefs that [*] and [**] are both based on the same type of belief forming process and that, like perception, this process is one which is "reliable but not infallible".8 The subject's coming to correct her initial belief and form a true belief functions solely to illustrate the reliabilist framework and these assumptions. But if this is what Casullo is doing, his argument (as it stands) will not be persuasive to one with infallibilist instincts. For Casullo has simply assumed a way of type-individuating belief forming processes which classifies both [*] and [**] as being caused by a process having reliability sufficient for justification. He is right, of course, that there is a belief forming process upon which [*] and [**] are both based. However, the infallibilist will not allow him to assume without argument that this sort of type-individuation is the relevant sort for justification. On other ways of type-individuating processes, [*] and [**], or [*] alone, would come out as being caused by an unreliable process, and so would not be justified. I want to emphasize that I am not here suggesting that Casullo is incorrect to type-individuate in the way he does. I am only suggesting that it is ad hoc to identify a given type as the relevant type, in the absence of a general theory of relevance for reliabilism. To make a persuasive case, Casullo needs an independently motivated means of classifying processes as the relevant ones for reliabilism.

In personal correspondence, Casullo says that he regards this case as stand- ing independent of any reliabilist assumptions. So let us leave these behind and reconsider the way in which the agent's later true beliefs are supposed to bear on our assessment of the initial false beliefs. Casullo places much emphasis on the parallel between Mary's having reflected more carefully in the a priori case and her having viewed more carefully in the empirical case. It appears that he intends to use Mary's later true empirical belief to illustrate that we allow justified belief in false propositions even if the agent could

8 Casullo writes that some of the salient features of the case are that "Mary's initial belief is based on a nonexperiential process which is reliable but not infallible" and that "a process of the same type leads Mary to conclude that the initial belief is mistaken and to arrive at the correct conclusions."

338 ROBIN JESHION

have avoided having a mistaken belief. Casullo's strategy is to show that we allow justification in empirical cases in which the agent could have avoided making a mistake, and so we ought to allow a priori justification in the same circumstances.

The problem here is that the infallibilist can regard the a priori and percep- tual cases as disanalogous in a certain crucial respect. He may plausibly maintain that in the a priori case, at the time at which Mary judges [*], she possesses all the evidence, all the intellectual information and resources, to avoid having made a mistake. One can see this by recognizing that no new information is rationally responsible for her coming to believe [**]. (Casullo says that her recognition of the counterexample to [*] is her basis for believ- ing [**], but this is rather odd. If it is, why should we accept that her belief is well-grounded? It isn't as if believing [**] because one recognizes a counterexample to one's belief that [*] is a good method of belief formation.) The infallibilist is not straight-away incorrect in regarding the subject's belief that [**] as grounded on logical knowledge that she already possesses, and so ought, if she is justified, to have employed. By contrast, in the perceptual case, when Mary judged that the piece of paper is a square, she does not already possess all the perceptual evidence required for avoiding the mistake. Mary's initial belief that the paper is square is based on her having a visual experience of the paper appearing to her squarely. It is only later, once she takes another closer look-has a new visual experience of the paper as having two parallel sides that are longer than the sides to which they are perpendicu- lar-that she acquires additional perceptual evidence, evidence which consti- tutes a rational basis for Mary to correct her belief that the paper is square and also to form the belief that it is rectangular.9 The infallibilist may then hold that since she does not already possess evidence for avoiding mistake, she may be justified. So Casullo's argument does not succeed because (3) is false; the a priori and perceptual cases are in a crucial respect disanalogous.

The same point may be developed in a way that affords insight into a possible rationale backing infallibilism. On this interpretation of Casullo, the argument suggests and depends upon the claim that the infallibilist upholds his position because he thinks that if mistake is avoidable, one is unjustified, and all a priori, but not all empirical, mistake is avoidable. We can regard Casullo's perceptual case as a challenge to the inference from avoidably being mistaken to being unjustified.

Now, suppose that the infallibilist upholds his position because of the mistake avoidance rationale. Casullo's perceptual case fails as a counter- example to the inference from avoidable mistake to being unjustified because

9 One might think that Mary does possess all the information needed to avoid making a mistake. Perhaps she knows that the paper is on an angle and that when objects are on an angle, her shape-discriminating abilities are less reliable. But if this is so, the case will not help Casullo, for then premise (2) will be false.

ON THE OBVIOUS 339

his perceptual case involves a modal notion of mistake avoidance that differs from that which is employed in the infallibilist's rationale. To see this, distinguish the following two notions of avoidable mistake:

Avoidable Mistake 1: Agent A's false belief that p held at time t is avoidable if and only if at t A possesses information I, and use of I is sufficient for recognizing that p is false.

Avoidable Mistake 2: Agent A's false belief that p held at time t is avoidable if and only if at t A does not possess information I, yet is in position to acquire I, and use of I is sufficient for recognizing that p is false.

The infallibilist's contention that if mistake is avoidable, then one is unjustified construes the modal notion as Avoidable Mistake 1 (or something like it). The infallibilist's claim is surely not based on understanding "avoidable" in the sense of Avoidable Mistake 2. The premise that if mistake is avoidable, then one is unjustified would be wholly implausible on that reading. Moreover, it would make most all empirically grounded beliefs unjustified-in conflict with the infallibilist's second premise, which, together with the first, is supposed to reveal an asymmetry between a priori and perceptual justification. Yet Casullo's perceptual case only works if we take Avoidable Mistake 2 as the relevant modal notion. As noted above, the subject must have a new perceptual experience if she is to avoid mistakenly believing that the paper is square. At the time at which Mary believes the paper is square, she does not possess the information required for her to recognize her belief as mistaken. So Casullo's case cannot stand against the infallibilist's contention that if mistake is avoidable, then one is unjustified.

I am inclined to think (but will not try to defend the claim) that any argument launched against this premise of the infallibilist's avoidable mistake rationale will be, if not unsuccessful, at least extremely contentious. (The premise is not wholly implausible.) What seems to me a more promis- ing line against such an infallibilist is this: establish a case in which the agent does not possess information which is sufficient for recognizing the belief as mistaken, but nevertheless must be a priori justified. The challenge is directed to the other premise of the infallibilist's rationale, namely that all a priori mistake is avoidable. And this, after all, is the natural point of attack since it expresses the a priori/empirical asymmetry.

Casullo is saddled with a further problem, one that is logically indepen- dent of those already advanced. The a priori and empirical cases are disanalogous in another pertinent respect. The infallibilist may hold that there is something inherently confused or unclear about the cognitive state which prompts Mary to believe [*]. Mary judged that [*] because it seemed to her

340 ROBIN JESHION

that 'p-4q' entails '-p-4-q'. Since her belief is false, her intellection must be in some way confused or unclear. Yet nothing analogous obtains in the perceptual case. Mary's belief that the paper is square is based on her having had the visual experience of the paper being a square. There need not be any- thing unclear or, better, blurred in her perceptual state. The visual appearance of the rectangular piece of paper as a square may be every bit as clear as a square paper's appearance as a square. The upshot is that in the empirical case, if the subject has a false belief based on perception, we cannot conclude that there is anything inherently unclear or blurred about the agent's percep- tual state. Yet the opposite holds for the a priori case. Notice that this criticism sidesteps Casullo's points about Mary's later belief states. The infallibilist may regard them as irrelevant to whether the subject was initially justified in believing [*].

The foregoing helps expose another rationale underpinning infallibilism. The infallibilist may hold that if something intrinsic to an agent's cognitive state is epistemically amiss, if it is confused, unclear, or blurred, we ought to regard it as unjustified. He may hold this across the board, for both intellec- tion and perception. The infallibilist's asymmetrical position is generated from the claim that if the proposition believed is false, then for intellection, but not perception, there must be something intrinsic to the agent's cognitive state that is confused or unclear. This latter point, though not entirely uncontroversial, enjoys support from fallibilists and infallibilists alike."' The infallibilist will maintain that confusion and unclarity are signs of irrational- ity-common ways of being irrational, but irrational nevertheless. Confused and unclear cognitive states are unwarranted cognitive states. The result, then,

For example, according to Laurence BonJour, "a mistake in an a priori intuitive appre- hension can only result from some sort of confusion or unclarity intrinsic to the cognitive state itself rather than, say from something external to the state such as the way in which it was produced." The Structure of Empirical Knowledge (Cambridge: Cambridge University Press, 1985), p. 208.

In "The Justification of A priori Intuitions", Philosophy and Phenormenological Research, 56, Paul Tidman criticizes BonJour's assumption that all reasons for having a mistaken belief have to do with an unclarity or confusion in the agent's understanding or reasoning. Tidman thinks that mistakes can occur for reasons that are external to the agent. Consider this case (which is a variant on one originally given by Alvin Plantinga): Suppose you are transported to another environment in which elephants give off radiation which will "cause its subject to affirm the next a priori proposition" that the subject considers. As a result of the radiation, the subject comes to believe that p, where p is a necessary truth. And suppose that if apart from the radiation, the subject would have been agnostic about p. This case does not substantiate Tidman's thesis that external factors are relevant. To see this, consider whether the agent believes p on the basis of her understanding of the proposition. If the belief is simply caused by radiation, it is far from clear that the epistemic basis of the belief is a priori. (That the proposition is a necessary truth is irrelevant.) Yet, if the radiation prompts the agent to have the concep- tual understanding which makes it the case that just from reflecting on p, the agent accepts p, then the belief has an a priori basis. But then what is responsible for the agent's belief seems to be internal to the agent.

ON THE OBVIOUS 341

is that Casullo's argument fails because cases of error in intellection and the symmetry of standards thesis, by themselves, make no headway against this infallibilist rationale.

Let us turn to consider Summerfield's attack on infallibilism. Summer- field's central points are built on a case involving a capable and careful mathematician who believes a false proposition on the basis of an argument involving a subtle flaw. Summerfield claims it is gratuitous to insist that she merely appears to have warrant. This claim, reasonable as it may sound to one antecedently committed to fallibilism, is not an argument and, by itself, will be unconvincing to the opponent. Summerfield does not, however, leave the matter there. She embeds her case in two background theories that, she maintains, provide the resources for thinking her case stands against the infallibilist.

One background theory is reliabilism. Suppose that the mathematician's proof-following abilities are normally extremely reliable. Then, says Summerfield, she is warranted in believing the results of all her intellection, even in those instances in which it leads to error. Leaving aside general prob- lems with reliabilism, there remains the issue (already noted in connection with Casullo) of type-individuating processes of belief-formation. Summerfield recognizes this difficulty as is evident from the fact that she considers various ways of type-individuating. In the end, however, she only suggests that she finds "reasonable" Ernest Sosa's proposal to type-individu- ate "dependable source[s] of information over a certain field in certain circum- stances".1' The infallibilist can just deny this claim. In any event, it is surely worthwhile to seek stronger grounds for rejecting infallibilism.

The other background theory is some variety of a deontological episte- mology. Summerfield maintains that if the agent who follows the flawed mathematical argument has done everything she could reasonably be expected to do in the situation, she may be entirely blameless. And so, on a deonto- logical theory, she would be justified in believing the false proposition. The problem here is that, even if we leave aside difficulties with deontological theories, Summerfield still needs to establish that the agent has done every- thing that can reasonably be expected of her to do in the situation. Summerfield assumes, but does not argue for the claim, that her case fits the bill. Since, as we saw above, the infallibilist may maintain the agent possesses the resources to avoid mistake, he may contend that the subject has not done everything that can reasonably be expected of her to do in the situa- tion. The infallibilist's ground is unshaken until this position is definitively ruled out.

11 Summerfield, op. cit., pp. 55-56.

342 ROBIN JESHION

The upshot of this critique is that none of the above arguments against infallibilism completely succeeds.'2 The traditional infallibilist position has more resources than its critics have recognized. Our critique is nevertheless fruitful. We have exposed what appear to be the roots of infallibilism and so will be in better position for nailing down an argument against it, one which might offer a theoretical explanation of why fallibilism must reign. Let me summarize our results. Infallibilism has been upheld because it is thought that:

(X): Standards for justification for beliefs based on deductive reasoning or conceptual understanding alone ought to be more stringent than standards for beliefs based on perception.

(Y): (yl) If at t one has a false belief that p yet possesses all the informa- tion needed for avoiding believing p, one is unjustified in believing p, and (y2) all cases of false beliefs based on deductive reasoning and conceptual understanding alone are such that at the time of belief one possesses all the information needed for avoiding believing the false proposition.

(Z): (zl) If one's belief in a false proposition is based on deductive reasoning or conceptual understanding alone, one's basis for belief must involve a confusion or unclarity, and (z2) if a belief is based on deductive reasoning or conceptual understanding that is confused or unclear, one's belief is unjustified.

The point about symmetry of justificatory standards, while not a knock- down response to infallibilism based on (X), at least very definitely shifts the burden of proof. And perhaps that is all that need be said to infallibilists who

12 These seem to me the most fully developed arguments in the literature. A paper by Tyler Burge might be mistakenly regarded as containing a successful argument against infalli- bilism. In "Content Preservation", Philosophical Review, 102, pp. 457-88, Burge argues that one could be a priori justified in believing a proposition on the basis of testimony. If he is correct, it may seem that he has given a cogent argument for why there can be cases in which an agent is a priori justified in believing a false proposition (and Burge sometimes speaks as if this is so): an agent comes to believe, on the basis of testimony, a false mathematical proposition. But the infallibilist's position is, however, untouched. For, according to Burge, the full justification of the recipient of the testimony includes the justification of the source (Cf. pp. 485-87.). Since Burge gives no argument as to why the source is justified, the infallibilist may retain his position that the source is not justified, and, by invoking Burge's own assumption about the transference of justification, may infer that the recipient is not justified. So Burge has not established any case in which an agent is a priori justified in believing a false proposition. On the assumption that the recip- ient is justified only if the source is, the epistemic status of testimony is logically indepen- dent of the debate with the infallibilist, and so will contribute nothing to settling these issues.

ON THE OBVIOUS 343

hold their view solely because of (X). We are still in need of an argument against infallibilists whose position is based on (Y) or (Z).

?2 Infallibility: a Critique

I will be attempting to argue against infallibilists whose positions are rooted in rationales (Y) or (Z). While my argument assumes symmetry of standards, it also assumes as true a premise of each of the rationales (Y) and (Z) motivating infallibilism. I will assume (yl) that if at t one believes a false proposition p yet also possesses all the information needed for avoiding believing p, one is unjustified in believing p;'3 and I will assume (zI) that for all cases of believing false propositions based on deductive reasoning or conceptual understanding alone, it is not incorrect to regard the agent's intel- lection as, in some sense, unclear. If my argument is correct, then even if (yl) and (zi) are true, infallibilism still fails.

The argument is this: [1] For any true proposition p that someone S can know, S can believe p

with the services of only justified beliefs, and, in particular, without the services of beliefs that are accidentally attained.

[2] If infallibilism is true, then [1] is false.

So infallibilism is incorrect.

I shall have a few brief words to say about [1] below. But I take this premise as fairly uncontroversial. One thing seems clear: it begs no question against the infallibilist as it plays no special role in any motivation backing the asymmetrical view. In large measure, the remainder of this section is devoted to arguing in support of [2]. My strategy is to isolate a case in which an individual can know a certain true proposition p, and to demonstrate that if infallibilism is true, then it is not possible for that individual to believe p using only the services of justified beliefs. That will be sufficient to establish [2].

13 I will here assume the premise, but nothing I say turns on it. I do, however, hold that it is not implausible and that the infallibilist's asymmetrical position is not rooted in the premise. Its formulation is "basis-neutral". An infallibilist who upholds symmetrical stan- dards on justification ought to regard it as applicable to empirical as well as non-empirical cases. The specific empirical version of the premise is this: if one possesses all the empir- ical evidence and cognitive resources for avoiding a mistaken belief based on percep- tion, then one is unjustified in the belief that results. The plausibility of the premise is partly brought out by the following example. Suppose one sees a hummingbird at rest drinking from the nearby feeder. One knows all the information relevant to distinguishing Anna's Hummingbirds from Ruby-Throated Hummingbirds and birds of both types are typical residents of the region. If the bird's distinguishing marks are in one's plain sight, conspicuous and clear to one's naked eye-one sees and notices them as such-and nevertheless one makes a mistake in identifying the bird, it is not implausible that one is unjustified in one's empirical belief.

344 ROBIN JESHION

It should be noted that in the case I isolate to establish [2], an individual believes a proposition on the basis of conceptual understanding alone. But the argument for [2] carries over in a fairly straightforward way to mistakes resulting from deductive reasoning. So it is generally applicable to defeat the version of infallibilism identified above.

Below I will present two cases. The second of the two is the case I will use for demonstrating [2]. The first case shall serve as a useful foil for estab- lishing fundamental points about the latter case. I shall initially present an intuitive analysis of the cases and shall follow this with an argument in support of [2]. In the next section, I shall provide the theoretical machinery underpinning my analysis of these cases. For now, a few preparatory remarks are needed prior to the presentation of the cases. I shall later refine and expand upon them.

Throughout this paper, I shall be taking obviousness to be a three-place relational notion between an individual, a proposition, and a time. A proposi- tion p is obvious to an agent A at time t (or, as I will sometimes say, A finds p obvious at t) if and only if at t A finds p true on the basis of her conceptual understanding alone. Obviousness manifests an agent's conceptual understanding, at a given time, of the concepts in p. Finding p true on the basis of conceptual understanding alone is direct, non-inferential acceptance of p as true. It is based on no inductive or deductive reasoning, no sense percep- tual experience, and no insight or imagination.

Now to our cases. Here's the first one. Suppose that Lena, a rational, responsible agent, is given an exam in which she must prove those proposi- tions that require proof (i.e., that require proof, given the conceptual resources and standards of proof in her number theory class14), and ignore those that do not require proof. She considers the proposition that [P] there does not exist a greatest prime number. Initially, she finds [P] obvious. It seems to her necessary and so she judges that it does not require proof; she moves on to the next question. Later, upon checking her work, she reconsiders the propo- sition and this time, she finds [P] non-obvious, and so sets out to prove it.

Lena's initial judgment was occasioned by her conceiving of the primes as integers which have special properties-are primes-but, in her initial consideration of the proposition, she failed to exercise full control on her conceptual understanding. In reflecting on the proposition [P], she did not make fully articulate that special essential property and ended up associating it with other properties. She thought of primes as continuing on ad infinitum, and so, just "just saw" [P] as true solely on the basis of her

14 The qualification is needed because "require proof' is, in an important sense, contextual. For any proposition, there is an axiomatic system from which the proposition is derivable. The contextual feature extends beyond niceties about deductive systems, as the paren- thetic remark above suggests. Here "require proof' is vague, but surely definite enough for its illustrative purpose.

ON THE OBVIOUS 345

initially unsharpened, semi-inchoate conceptual understanding. When she took greater care, she employed her full and sharper conception of primes as natural numbers that are divisible only by themselves and the number 1, and realized that [P] stands in need of proof.

The salient feature of this case is that at the time that our subject believed that [P] because she found it obvious, she possessed and had available the conceptual resources that enabled her to recognize and correct her belief. The fact that she actually did correct her belief without engaging in any reasoning or conceptual analysis, and without attaining new insights demonstrates this fact."5 She initially found [P] obvious because she failed to exercise control on her conceptual thinking, and so it was unclear, blurred by the association of non-essential properties within her conception. She possessed a sharp con- ception of the concept prime, yet in thinking about primes, she did not exercise her sharpest way of thinking of the concept. Because she possessed- had available for use-the conceptual resources needed for avoiding believing that [P] stands without proof, we may regard her first judgment as unjustified, and thereby countenance (yl). Intuitively, our subject's initial judgment was hasty and hastiness in judgment embodies a type of failure of rationality, albeit a weak one. Nothing in the upcoming argument turns on this epis- temic evaluation, however. The main point is just that here we have a fairly clear sense in which our subject possesses and has access to a fuller, more precise conception of the concept prime.

The second case is rooted in mathematical history. 16 Before the middle of the last century, the concept continuity lacked a precise analytical definition. Eighteenth century mathematicians considered it a basic concept, one which did not stand in need of formal definition. They thought our grasp of it was intuitive, achieved with the assistance of physical or geometrical examples that serve to "trigger" our understanding. The concept continuity was usually thought to be inextricably bound to the notions of motion and change in magnitude. Knowledge of the concept derivative was less widespread. Never- theless, most mathematicians viewed it as a fairly well- though far from perfectly-understood notion, mathematically secure because of its enormous success in helping solve outstanding theoretical problems and explain the physical world.

At the time, mathematicians commonly believed that [C] the continuity of a function is a sufficient condition for the existence of a derivative (except at isolated points). They frequently relied on this assumption implicitly and

15 That she actually does correct her belief is otherwise inessential to the case. It is impor- tant only because it helps illustrate that our subject has the conceptual resources for such correction.

16 I have relied on Morris Kline's Mathematical Thought from Ancient to Modern Times, especially chapter 40 (New York: Oxford University Press, 1972), for an historical overview of the development of the concepts of the calculus.

346 ROBIN JESHION

sometimes used it explicitly in proofs. They made the inferential transition from noting the continuity of the function to the existence of a derivative. Some may have believed the proposition on inductive grounds. The more common view was that it is self-evident. We know now that [C] is false. In an unpublished work written in 1834, Bolzano discovered a function that is continuous at every point through an interval and differentiable at none. The discovery went unnoticed and unappreciated for years. Further work in analy- sis revealed numerous different types of counterexamples.

During the years in which the discoveries of the counterexamples were made, nineteenth century mathematicians, including Bolzano, Cauchy, Abel, and Weierstrass, were working toward the rigorization of analysis. Studies of new functions and paradoxes-many of which arose independent of the counterexamples to [C]-forced mathematicians to attempt to give analytical definitions of the notions of function, continuous, differentiable, and so on. Even while the concept continuity was recognized as standing in need of a rigorous definition, many of the mathematicians of the time still regarded [C] as self-evident. Cauchy and Ampere initially regarded it in this way. In their later attempts toward ultimate rigor, they actually tried to furnish [C] with a proof.

The subject for our case is a leading mathematician of the early part of the last century who, at time t, finds p obvious. Although there is good reason for taking, say, the actual Cauchy prior to his attempt to prove [C] as our subject, books on the history of analysis do not, alas, document their subjects' cognitive states. So let's be clear that the case is to be understood as hypothetical, but still call our subject "Cauchy". So our man, Cauchy, believes [C] solely on the basis of his conceptual understanding of the concepts in [C].

Now, this case bears certain similarities to the previous case. The concep- tual understanding that our subject Lena initially judged with was unclear and confused. The same may be said here. Cauchy's understanding is not maxi- mally clear. It is not wholly inappropriate to regard it as marred by confu- sion. That, at least, is what the infallibilist proponent of (zl) will say, and it will not hurt our argument to grant it.

But there remain striking differences between the two cases. Although our mathematician's conception of continuity may have been unclear, it was the best, or among the very best, conceptual understanding on the market. The best mathematical minds of the time found [C] obvious. Not so in the Lena case. Moreover, it seems that in finding [C] obvious, Cauchy was exercising the finest control on his conceptual thought, drawing on his fullest clearest conceptual understanding.' At an intuitive level, it seems that unlike the

17 The fact that the real Cauchy (and Amp6re) tried to prove [C] is evidence that they were judging with their fullest, sharpest conceptual understanding. For in order to attempt to

ON THE OBVIOUS 347

subject of the first case (and unlike Mary in Casullo's case), our mathemati- cian does not possess and have available for use conceptual resources for avoiding the mistaken belief. And, again at the intuitive level, it seems his mistake cannot plausibly be attributed to mere hastiness or another failure of rationality.

Let us leave the intuitive level behind and move to arguing in support of [2]. That premise says that if infallibilism is true, then it is not the case that for all propositions p knowable by an agent S, S could truly believe p with the services of justified beliefs alone. We need to find a proposition p and an agent S such that S could know p, yet could not truly believe p using only beliefs the infallibilist takes as justified. The agent here is our Cauchy and the proposition is [C*], the correct analytical ?-6 definition of continuity.

Could Cauchy have non-accidentally come to know the correct analytical definition of continuity using only the services of beliefs regarded as justified by the infallibilist? He could do so only if he were in some way endowed with the correct conceptual understanding of continuity or could recognize his conceptual understanding of continuity as standing in need of analysis with- out making use of beliefs the infallibilist claims to be unjustified.

The first disjunct is immediately ruled out. Our minds are not imbued with perfectly articulate correct mathematical knowledge from their inception. We are not, as Frege said, given concepts "in their pure form". To be sure, we are not endowed with knowledge of the ?-6 definition of continuity.' Discursive thinkers must discover correct conceptions by reasoning.

One might object to this point on the grounds that we do, in some sense, possess knowledge of correct conceptions of concepts. After all, Cauchy and his fellow mathematicians possessed the intellectual resources to recognize the proposition as false upon seeing the counterexamples. Therefore, they must possess tacit knowledge of the correct conception-or so one might reason. Leaving aside the cogency of this reasoning to the existence of tacit knowledge, we can still rule out the first disjunct. Let us assume that we

prove what one finds obvious, one must aim to explicitly articulate the properties of the concepts in the proposition one finds obvious. In articulating the properties of a concept, one self-consciously thinks with the conception of the concept that one judges with when one judges the proposition self-evident, drawing on most of one's relevant cognitive repertoire. It is worth noting that the fact that one is justified in finding a proposition to be obvious is fully compatible with one's aiming to provide a proof of that proposition. Aiming to prove what one takes to be obvious is, I believe, normally a sign of epistemic virtue; it is not in itself grounds for thinking one is not rational in accepting what one finds obvious.

lx The definition is: F is continuous at a, a point in the domain D(f), if and only if for e>O, there exists a number d(e)>0 such that if xCED(F) and llx-all<d(e), then Ilf(x)-f(a)II<e. If, by some miracle, an agent were simply "endowed" with such understanding, an understanding which was not in any way connected to its discovery through reasoning, then, for rational agents like us, this would be accidental.

348 ROBIN JESHION

possess tacit knowledge of the c-6 conception of continuity.19 The basic problem is not ameliorated by this assumption. The mere existence of tacit knowledge of a correct conception per se does not shield us from error; and it does not, by itself, get us reasoning with correct conceptions. Even if the correct conception is, in some way, known by us, it is our unclear (semi- inchoate) and incomplete conceptions of concepts that we draw upon in our reasoning. To avoid mistakes, we need to be able to possess it so that we can employ it in our reasoning. Yet we simply cannot access it for use in our reasoning by carefully surveying the mind or by introspecting. So even if tacit knowledge "is there", it would not, by itself, enable Cauchy to know [C*].

This leads us to consider the second disjunct. Could our subject come to know [C*] by recognizing his conceptual understanding of continuity as standing in need of correction without employing the services of propositions the infallibilist will rule as unjustified? There are two ways one might think he could do so. First, he might identify his unclear conception as unclear directly. But this will not work. Unclear conceptual understanding is not somehow marked in thought as unclear. To see it as unclear, we need to recognize its inadequacies. Such recognition requires coming to know counterexamples to propositions that we find obvious.2" Yet acquiring such knowledge of counterexamples requires mathematical theorizing-in particu- lar, the exercising of insight, imagination, and reason. So, the recognition of unclear conceptions as unclear is possible only by means of theorizing.

This leads us to the second, more promising alternative. Instead of directly identifying unclear conceptual understanding as such, one might think that a sufficiently cautious thinker could do so indirectly, by exercising reasoning, insight, and imagination, all the while withholding from believing proposi- tions the infallibilist would rule as unjustified. Perhaps a thinker such as Cauchy could come to identify problems with his conceptual understanding by reasoning to the counterexamples to his unclear conceptual understanding. But this will not do either. The suggested scenario requires that one recognize a counterexample as a counterexample to the proposition one finds obvious. But recognizing a counterexample as a counterexample to the proposition one finds obvious entails judging-hence believing-that such-and-such is a counterexample to the proposition one finds obvious. Such a judgment must itself be grounded on one's conceptual understanding alone, indeed, normally,

19 Of course, the exact nature of such tacit knowledge needs to be explicated. For the sake of argument, I am assuming a fairly rich conception, one modeled on something like Plato's account of geometrical knowledge.

20 Knowledge of paradoxes involving propositions containing concepts will also enable us to recognize unclear conceptual understanding as such. The points I make in the text about knowledge of counterexamples also apply to cases in which one recognizes one's understanding as inadequate from appreciation of paradoxes.

ON THE OBVIOUS 349

on the same unclear conceptual understanding that one initially thought with in finding the false proposition obvious. Therefore, correction of false beliefs based on one's best, yet still unclear conceptual understanding requires reliance on-belief in propositions grounded on-one's best yet still unclear conceptual understanding alone.

How would infallibilists evaluate Cauchy's belief that, say, Bolzano's function is a counterexample to [C]? The infallibilist proponent of the (Z) rationale will automatically regard such beliefs as unjustified, for they are based on conceptual understanding that is confused or unclear. An infallibilist who rests his position solely on the (Y) rationale should also take such beliefs as unjustified. For if he does otherwise, he needs a principled and non- ad hoc way of accounting for why such beliefs are justified yet beliefs like [C] are unjustified. He cannot appeal to haste in judgment or possession of a clearer conceptual understanding. In our case, the beliefs are on a par in these respects. And there is of course nothing about beliefs that something is a counterexample that sets them apart as epistemically special. After all, if one is judging with one's best but still clouded conceptual understanding, one can be mistaken in thinking something constitutes a genuine counterexample. The source of error would be the same as in [C]-the unclear conceptual understanding. Therefore, the infallibilist ought to evaluate these beliefs just as he does other beliefs grounded on one's clearest yet still clouded conceptual understanding. Since some are false, and so according to the infallibilist unjustified, these must be as well. So infallibilists of any stripe ought to regard Cauchy's belief that Bolzano's function is a counterexample to [C] as unjustified.

But now we have established [2]: if infallibilism is true, premise [1] is false. For we have canvassed all the ways for our subject to rationally correct his false belief and so non-accidentally come to know the correct definition. As far as I can see, there are no more. And yet surely our subject can come to non-accidentally believe the correct analytical definition of continuity using only the services of justified beliefs.

I have argued that our mathematician cannot non-accidentally attain knowledge of the correct analytical definition of continuity without believing a proposition that the infallibilist will regard as unjustified. In non-empirical inquiries aimed at discovering correct analytical definitions of concepts, it simply is not always possible to avoid having beliefs grounded on one's clouded conceptual understanding of concepts. While it is clear that the fore- going argument in support of this point rests heavily on the given example, it should be equally clear that it is in no way atypical. With only a little reflection, we could amass a list of cases. For now, a small sample will do: our conception of knowledge, Frege's conception of extensions of concepts, conceptions of infinity before Cantor. Each one produced false beliefs grounded on clouded conceptual understanding alone. It is doubtful in the

350 ROBIN JESHION

extreme that all such beliefs could have been avoided by subjects who were aiming to think with the correct conception.

Our first premise, that any proposition capable of being known can be believed with the services of only justified beliefs, and, in particular, without the services of beliefs that are accidentally attained, should be acceptable. It begs no question against infallibilism and seems a natural constraint on any epistemic theory. For any epistemic theory that did not ensure the possibility of the attainment of true beliefs without the use of unjustified assumptions would effectively break down the widely accepted connection between being rational and being justified. The attainment of true conceptual beliefs ought to be regarded as paradigmatically rational.

The result is that traditional infallibilism is not merely implausibly or unreasonably strong. It is rather an untenable philosophical view. The view fails even if it is conceded that all a priori error based on deductive reasoning and conceptual understanding is in some way due to confusion or unclarity and that one's belief is unjustified if one possesses all the cognitive resources for avoiding mistake.

?3 Obviousness and Conceptual Understanding

I now want to make more precise my notion of obviousness. Doing so will tighten our arguments and will offer theoretical understanding as to why infallibilism must be rejected.

As I said above, I take obviousness to be a three-place relational notion obtaining between a person, a proposition, and a time: a proposition p is obvious to an agent A at time t if and only if at t A finds p true on the basis of her conceptual understanding alone. Conceptual understanding is here taken to be what we would think of as our ordinary semantical notion of under- standing. And an agent's finding a proposition obvious is always to be construed de dicto; that which the agent finds true is always a certain senten- tially expressed content.2

Finding a proposition p to be true on the basis of one's conceptual under- standing alone is non-inferential. It involves neither inductive nor deductive reasoning. Suppose I find it obvious that all even natural numbers are divisi- ble by 2. My finding the proposition true on the basis of conceptual under- standing alone is direct, involving no reasoning. This feature of obviousness does not exclude the possibility that one possesses inferential grounds for believing a proposition that one finds obvious. We assumed above that Cauchy found it obvious that continuity entails differentiability. Yet he may have also possessed inferential, inductive, grounds for believing the proposi-

21 Cases of non-empirical non-inferential acceptance of propositions, conceived de re, need separate, delicate, handling. The same goes for the understanding of sentences involving indexicals and demonstratives.

ON THE OBVIOUS 351

tion (e.g., induction over all known continuous functions, all of which were differentiable). Inferential bases for belief are, however, necessarily separate, distinct bases for belief from those rooted in conceptual understanding alone. Likewise, if one finds p obvious, one might have perceptually based support for believing p. The latter type of support is necessarily distinct from the former.

Finding a proposition obvious differs from acceptance of a proposition on the basis of insight or imagination. A philosopher's or a mathematician's ability to "see" a conclusion immediately, or to produce a proof, a construc- tion, or a philosophical argument is not always (not even normally) attributable to having special, deeper, conceptual understanding of the concepts in the proposition. Think about Gauss's famous method for arriving at the sum of the first 100 natural numbers. When instructed by a grade school teacher to give the sum-apparently an assignment to busy students with practicing addition-Gauss immediately recognized that it is equal to 101 multiplied by 50. The following construction brings out the ingenuity that enabled him to recognize the equality:

1 2 3 ... 48 49 50 100 99 98 ... 53 52 51

The sum of the numbers in each column is 101. Since there are 50 columns, the sum of the first 100 positive numbers is 101 multiplied by 50. Gauss's knowledge that the sum of the first 100 positive natural numbers is 101 times 50 was not grounded just on his understanding of the concepts in the proposition. The ingenuity in the proof is a mark of his mathematical insight. Conceptual understanding is more basic. It is what one reasons, thinks, and imagines with.

There is, in a greatly reduced sense, a "phenomenology"-an intellectual phenomenology-that is associated with, but should not be identified with, one's finding p obvious. On reflecting on an arbitrary proposition p, p will either strike one as necessary or fail to strike one as necessary.22 The intellec- tual phenomenology of a proposition p striking one as necessary ordinarily prompts one to judge that one finds p obvious. But such an "intellectual

22 There are no doubt cases in which it is unclear or undetermined whether something seems necessary to one. All this shows is that, like most concepts, seems necessary has areas of vagueness.

What then is the status of apparently a priori knowledge of contingent propositions like Kripke's example of "Stick S is a meter long at t" or Kaplan's "I am here now"? These cases need and deserve special treatment. I discuss them in "Ways of Taking a Meter", forthcoming in Philosophical Studies. But cf. footnote 21.

352 ROBIN JESHION

seeming" is not itself the basis, or source, of one's belief. The basis, if one finds p obvious, is one's conceptual understanding alone.23

We now face an important question. The Lena case illustrated that we sometimes do not draw upon our full or most precise conception of a concept. In consequence, we can find a proposition obvious at one time and fail to find it obvious at a later time even if our conceptual resources have not changed at all, i.e., even if we have neither learned nor forgotten any concep- tual or empirical facts. We think with a less full or less precise conception of a concept than we actually possess. So we have a situation in which a subject finds p to be true on the basis of her conceptual understanding alone at t and fails to find p true on the basis of her conceptual understanding alone at t', indeed, finds that p stands in need of proof. How are we to make sense of what it is to find p true on the basis of conceptual understanding alone if such a change can occur from t to t', even if the subject's conceptual resources are constant during the interval t'-t ?

What we need to do is draw a distinction that reflects this feature of con- ceptual thought. Distinguish what I call occurent conceptual understanding from comprehensive conceptual understanding. Roughly speaking, occurent conceptual understanding is the understanding one actually uses in particular judgment. Comprehensive conceptual understanding is characterized disposi- tionally. It is the understanding one would use in making a particular judg- ment if one were intellectually at, or close to, one's best. One has at one's disposal one's conceptual repertoire and one employs it with precision. A somewhat more refined analysis goes as follows:

For a subject S at time t, S's Occurent conceptual understanding at t is that conceptual under-

standing S in fact employs in making judgment J at t.24

Comprehensive conceptual understanding at t is that conceptual understanding S would employ at t, if S were to make judg- ment J with S's fullest most precise conceptions of the relevant concepts.

23 Contrast with George Bealer's views as spelled out in his interesting papers "The Philo- sophical Limits of Scientific Essentialism", Philosophical Perspectives, 1987, pp. 289-365 and "The Incoherence of Empiricism", op. cit. Bealer introduces a notion of intuition which, for him, is supposed to be the basis of our non-inferential non-empirical beliefs. This notion is specifically phenomenological. According to Bealer, having an intuition is the having of a conscious episode in which something seems to you to be the case.

24 Notice that, on this view, for all times t, unless one in fact makes a judgment involving concepts C-Cn, one's occurent conceptual understanding of C-Cn does not exist. This follows definitionally from the fact that occurent conceptual understanding is that under- standing one in fact employs in making a judgment. Yet one's conceptual resources and one's comprehensive conceptual understanding nevertheless exist in absence of one's actually presently making any judgments.

ON THE OBVIOUS 353

When we speak about S's belief that p being based on S's conceptual under- standing alone, should we be speaking about S's occurent or comprehensive conceptual understanding? From the cases in ?2, it should already be apparent that I regard occurent conceptual understanding as what is relevant for deter- mining the basis of an agent's belief. On my view, S finds a proposition p obvious at t if and only if at t S finds p true on the basis of her occurent con- ceptual understanding alone. While I will not attempt to supply a full argu- ment as to why we ought to understand obviousness in terms of occurent conceptual understanding, two (related) points are worth noting. First, one test of any analysis is its capacity to explain the cases as naturally and as well as its competitors. I think that our characterization best accommodates the cases.25 Alternative positions have highly undesirable consequences. Consider what results if we take an agent's comprehensive conceptual under- standing or an agent's conceptual resources as that which determines the basis of that agent's belief. We must say that at both t and t' Lena finds p non- obvious. We would then have the ostensibly paradoxical situation in which a rational, responsible agent finds p non-obvious, yet judges that p does not need to be proved. Such a view would, I think, entail a disunification of an agent and her conceptual understanding, a situation I regard as entailing the agent's irrationality, in conflict with our supposition of her rationality. So such a view is at least prima facie implausible.

Second, understanding obviousness in terms of occurent conceptual under- standing makes sense of our ordinary assumption that if one judges that one finds a proposition p obvious, one finds p obvious. To see that we make this assumption, consider the following situation. Suppose that you judge that p is not self-evident and I judge that it is. Self-evidence is here taken to be the objective correlate of the subjective notion of obviousness: a proposition p is self-evident if and only if understanding the concepts in p provides sufficient and compelling basis for recognition of p's truth. We judge as we do because you judge that you find p non-obvious and I judge that I find p obvious.26 We attempt to resolve our difference regarding p's self-evidence. Suppose you convince me that p is not self-evident, that it requires proof. If I claimed that I initially maintained that p is self-evident not because there was something deficient about my conceptual understanding when I made the judgment, but rather because I wrongly identified what my conceptual understanding was, you would be on sturdy grounds in thinking me highly irrational or, more

25 Understanding obviousness in terms of occurent conceptual understanding also offers a natural account of one's present belief that p being grounded on one's conceptual understanding alone even if one is not presently making a judgment involving any concepts in p. One's present belief that p is grounded on one's conceptual understanding if, at some earlier time t*, one found p true on the basis of one's (then, at t*) occurent conceptual understanding. In the absence of defeating evidence, one's belief retains its a priori backing over time.

26 Nothing I say here turns on whether there are any genuinely self-evident propositions.

354 ROBIN JESHION

probably, insincere. This indicates that we regard one's judgment that one finds p obvious as grounds that one finds p obvious. The assumption seems a correct one. Explicating obviousness in terms of occurent conceptual under- standing enables our theory to reflect this natural assumption. If we chose to analyze obviousness in terms of comprehensive conceptual understanding or conceptual resources, we would have to reject the assumption. Other things equal, preference goes to the theory that captures ordinary assumptions.

Armed with a more detailed analysis of obviousness, we are in position to offer a more precise account as to why infallibilism is wrong. Let us return one last time to our cases. In the Lena example, in making her initial judgment that [P] does not need proof, our subject's occurent conceptual understanding does not "match" her comprehensive conceptual understanding. Were she to have employed her most precise conception of the concepts in that proposition, she would have judged as she did on the second round, that it needs to be proved. Infallibilism may well be wrong in taking her initial (false) judgment as unjustified. But it is not entirely clear to me that such a stand is wrong, or, better, if it is, why it is. (It is an interesting and impor- tant issue.) After all, our subject was judging with only part of her available conceptual resources.

But matters are different in the historical example. Cauchy's comprehen- sive conceptual understanding did not outstrip the conceptual understanding he in fact judged with. Yet, as was previously argued, he needed to reason with his comprehensive conceptual understanding in order to learn the new concep- tual information necessary for a rational alteration in his conception of the concept continuity. He needed to reason with his partly incorrect comprehen- sive conceptual understanding at t in order to have a correct, more precise comprehensive conceptual understanding of the very same concept at t'. We have shown that (one reason) infallibilism is wrong is because it regards as unjustified the very reasoning with one's comprehensive conceptual under- standing that is necessary for the attainment of sharper, more precisely delimited conceptions of concepts, and hence for correct conceptual knowl- edge.

Any rationalist theory must reflect the rationality in judging and reason- ing with our comprehensive conceptual understanding. It is, I suppose, a sad fact about us that we cannot (non-accidentally) avoid believing what is false even while reasoning at our best. But it is for this very reason that fallibilism must reign.

ON THE OBVIOUS 355