The A Priori-A Posteriori Distinction

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The A Priori--A Posteriori Distinction David W. Benfield Philosophy and Phenomenological Research, Vol. 35, No. 2. (Dec., 1974), pp. 151-166. Stable URL: Philosophy and Phenomenological Research is currently published by International Phenomenological Society.

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THE A PRIOR1 - A POSTERIORI DISTINCTION Although quite familiar to most philosophers the a priori-a posteriori distinction has never been clearly drawn. Further confusion has resulted from the fact that philosophers have termed 'a priori' entities of very different ontological types. Each of the following has been said to be a priori: knowledge, truths, evidence, sources of knowledge, propositions, judgments, facts, necessities, ways of knowing, intuitions, and laws of thought. Given this collection of philosophical troublemakers, surely it is not surprising that there is some difficulty in finding a property, namely the property of being a priori, which characterizes them all. This, combined with the belief that if an entity is a priori, then it cannot also be a posteriori, is the main source of the difficulty and unclarity. Any adequate analysis of, knowledge should suffice for both a priori and a posteriori knowledge. This has been challenged recently. Ungerl, Goldman2, and Swain3 have all provided analyses specifically restricted to a posteriori knowledge. The assumption they all tend to operate under is that a posteriori knowledge requires a special analy'sis whereas a priori knowledge can be analyzed in some reasonably standard manner such as the justified true belief approach. I believe that once the a priori-a posteriori distinction is properly and clearly drawn the temptation to demand a separate anaylsis for a posteriori knowledge will diminish. So, in this paper I will present an account of how the a priori-a posteriori distinction should be drawn. Using this account I will then try to argue that a single analysis should suffice for both sorts of knowledge. I shall also briefly discuss a proof that counterexamples to the justified true belief anaylsis of knowledge arise in connection with a priori propositions.

1 P. Unger, "An Analysis of Factual Knowledge," The Journal of Philosophy, LXV, 6 (March 21, 1968): 157-170.

2A. Goldman, "A Causal Theory of Knowing," The Journal of Philosophy, LXIV, 12 (une 22, 1967): 357-372. 3 M. Swain, "Knowledge, Causality, and Justification," The Journal of Philosophy, LXIX, 11 (une 1, 1972): 291-300.


It is extremely important to avoid confusing the a priori-a posteriori distinction with the necessary-nonnecessary distinction. Kant fostered the confusion when he remarked, "Necessity and strict universality are thus sure criteria of a priori knowledge . . ."4 The a priori distinction is an epistemological distinction whereas the necessarynonnecessary distinction is a metaphysical distinction. Even if the extension of the two distinctions should turn out to be the same, there would still be two distinctions, Quine and the set theorists to the contrary. I shall argue that the distinctions are not coextensive. Indeed, it would be a philosophical surprise if they were. For why should one think that our: capacities for knowing should coincide precisely with certain meltaphysical categories? In order to state my account of the a priori, it is necessary first to define something I call 'intuitive knowing.' The definition is as follows: (1) S knows p intuitively = Using only ordinary human epistemic capacities S knows p directly and not in virtue of any other knowledge S has. I do not regard knowledge of the external world which comes via the senses as intt~itiveknowledge. The argument from illusion tends to support this position since one would need some evidence that one was not the victim of an illusion, that is, one would need this evidence if one were to know that what one seemed to see is really there. However, this evidence would then keep the person from knowing directly since direct knowing must be independent of any other knowledge. It is far from certain that this argument is correct, and it may ultimately be difficult to show that ordinary perception is not an instance of direct knowing as defined above in (1). Using the concept of knowing intuitively, one can define the notion of a person's being able to construct an a priori proof. The definition is as follows: (2) S can construct an a priori proof of p = S can construct a deductive proof of p such that S knows intuitively that the premises are true and that the inferences employed are deductively valid. 4 I. Kant, Critique o f Pure Reason, translated by N . K. Smith, (New York; St. Martins, 1963), B-4, p. 44. .

The definition is intended to count as a priori provable all and only the deductive consequences of what can be known intuitively. Using this definition it is possible to define the crucial concept of knowing a priori. The definition is the following: (3) S knows p a priori = S knows p, S can construct an a priori proof of p, and S believes p on the basis of the existence of the proof. Assorted complications arise concerning what it is for someone to believe a proposition on the basis of the existence of a proof. In particular, what does one say about the case of a person who believes the proposition in question for some other reason and has done so prior to his coming to be able to construct an a priori proof of the proposition, but who also would believe it on the basis of the existence of the proof, if he did not believe it for the other reason? Does such a person believe it on the basis of the proof or not? It is no easy matter to settle this. Philosophers of science are still puzzled about how to analyze partial causation and one of the difficulties they must overcome is precisely this problem of overdetermination or multiple causation. So it is unrealistic to expect a solution to the problem about overdetermination of belief when a general solution is totally lacking. My own opinion is that the person does believe it on the basis of the proof, and he does this so long as he would not feel epistemically satisfied in rejecting the proposition while he accepted the proof. I realize that this is not conclusive, but it is probably better not to pursue the matter here. In order to implement ( 3 ) in the desired manner, it is necessary to countenance as proofs, derivations of a statement from itself. That is, suppose a person knows intuitively that the law of contradiction is true; he will know this a priori provided he can construct an a priori proof of it, etc. However, it is unlikely that he can construct a nontrivial proof of it; thus, he will only be able to construct a proof of it from itself. So, if he is to know it, then such single line proofs must be accepted. Using the concept of knowing a priori, it is then possible to define what it is for a proposition to be a priori. ( 4 ) p is an a priori proposition = It is logically possible that someone knows p a priori. Definition ( 4 ) is designed so that not every proposition whatever is classed as a priori. Probably it is logically possible that there could be a person who had the capacity to know everything knowable and to do so in an intuitive manner. God has been alleged to be such a being. However, such a being surely has an intuitive capacity quite different from that of ordinary mortals. Hence, such a being would not know

intuitively in the sense defined in ( I ) , for in (1) it is specifically required that only the ordinarily available epistemic capacities be employed. Surely for ordinary humans many, if not all, so-called empirical propositions are beyond the capacity for intuitive knowing. Therefore, there will be many propositions which are not a priori. Using the notions thus far defined, it is possible to define several other concepts, some of which are crucial to Kantian-style transcendental philosophy. The definitions are rather similar, and so I shall present them all at once and then comment on them subsequently.

(5) S judges a priori that p is true = S asserts p on the basis of S's ability to construct an a priori proof of p. = p is an a priori proposition. ( 6 ) p is an a priori judgment (7) x is an a priori judgment by = x is an event consisting of S'S judging a priori that p is true. S that p is true = x is a type of intuition used in (8) x is an a priori source of

knowing intuitively knowledge

= If someone knows a proposi(9) x is an a priori way of

tion in way x , he knows it a knowing

priori. (10) x is an a priori law of thought = It is a true a priori proposition, that anyone who thinks correctly, thinks in accord with x . = p is a true a priori proposition. (11) p is an a priori truth = Someone could know a priori (12) x is an a priori concept of an object that x applies to it. (13) x is an a priori form of intui- = Someone could know a priori that x is a form of intuition. tion = Someone could know a priori (14) x is an a priori condition of that if there is experience, then the possibility of experience condition x obtains. I shall now comment on the above definitions beginning with (5). When it is said that someone judges a priori, what is meant is that the person is making his assertion on a priori grounds. That is, the person either does not have o r is not employing any non-(a priori) grounds or evidence. It is the type of grounds on which a person bases his judgment which determines whether or not it is a priori. That is, one and the same assertion might very well be both a priori, and assuming an appropriate definition, a posteriori also, since a person might be asserting it both on the basis of a priori grounds and on the basis of empirical or a posteriori grounds. This is often

the case when we assert a familiar mathematical proposition; not only can we construct a proof of it, but we also can cite many experts who think that it is correct. The problem one encounters in defining the notion of an a priori judgment is that there are two distinct notions involved. Sometimes an a priori judgment is nothing more than an a priori proposition; but on other occasions an a priori judgment is an action, namely the action of asserting a proposition on a priori grounds. (6) and (7) are intended to reflect these two different senses of 'a priori judgment.' Now (6) will be as good or as bad as the definition of an a priori proposition, since it is totally parasitical on that definition. (7) is actually quite different from (6); not only are there relativizing terms, but it is events rather than propositions which are being characterized. Roughly (7) asserts that an a priori judgment is a certain kind of judging, namely the a priori kind. (7) has the advantage of explaining how an action can be a priori. Unfortunately (7) runs into the standard problems confronting any analysis which involves reference to events; however, except for these problems (7) seems to be acceptable. It may well be that very few philosophers ever speak of a priori sources of knowledge or ways of knowing. However, it seems that in a sense it is these which are the primary objects to which the modifier 'a priori' ought to apply. In my approach to the a priori I did not take them as fundamental notions. They do have the virtue of emphasizing the basically epistemological character of the a priori. (9) and (8) are not totally felicitous, but at least they do not seem to raise any new problems, and they will probably be as satisfactory as the other concepts they are defined in terms of. Given the evidence that exists concerning deviant intellectual behavior, it would be very surprising if there were any empirical laws of thought. There may be normative laws of thought, particularly in the area of logic. Logical rules seem to be a priori propositions which are true. Hence, (10) requires that an a priori law of thought be like the rules of logic, that is, an a priori proposition such that if anyone is to think correctly (here is the normative element), then he must think in accord with that proposition. There could be nonlogical laws of thought; indeed certain synthetic a priori propositions may be such. However, there is no reason to think that they would not conform to (10). Quite obviously many controversial issues are buried in (11). In particular there is the question of what is true, that is, the question of what sort of entity is the bearer of truth. Indirectly this raises the

question of whether nominalism is correct and so on. In order to avoid these philosophical hornets' nests, I have decided that it is propositions which are true and false, and the variable 'p' is intended to range over propositions. In (12), (13), and (14) definitions of traditional Kantian terms are proposed. In each case the modifier 'a priori' is eliminated in favor of the previously defined term 'knows a priori.' Someone may want to object that this fails to reveal the essence of the terms in question, an essence which has to do with the constituting of experience by the subject. While this may be true, I suspect that for Kant and for others who have followed him, it is true that one could know a priori the propositions used in (12)-(14).Further it is likely that the equivalences would hold. One might, nonetheless, want to search for better definitions, definitions which would explain why (12)-(14) are true. The foregoing discussion of (5)-(14) may not have proven that the definitions are totally acceptable; however, it does provide good evidence that they are in the correct spirit, and that with suitable modifications, they could be made to work. This shows that the real problem centers around giving an adequate account of the primitive concepts, the concepts defined in (1)-(4). The account offered is quite unusual, and it is likely to be rather violently rejected by most philosophers. However, it is not without its merits. Its virtues will be made more apparent after a discussion of its apparent fatal defects. So, I now turn to a series of objections, each of which at first sight seems to be overwhelming. It is a consequence of definitions (1)-(4) that basic propositions about one's mental states would be knowable a priori. As a paradigm of such propositions let us take the proposition expressed by the sentence 'I have a headache.' This proposition will be knowable intuitively, hence an a priori, albeit trivial, proof of it can be constructed, and hence if someone knows it on the basis of such a proof, then he will know it a priori. Therefore, it is an a priori proposition. So far as I can see, it is this aspect of the theory which is the most problematic. For, here we have a proposition which is made true in virtue of certain events which involve essentially human experience, which is contingent, not knowable by others in the same a priori manner; yet according to my theory the proposition is knowable a priori. To many this will seem absurd. Let me formulate precisely the various grounds on which someone might wish to object.

Objection 1: All a priori propositions are necessary. The theory implies that there are contingent a priori propositions. Hence the theory is false. Objection 2: Every a priori proposition is knowable completely independently of sense experience. It would be impossible to know that one has a headache without the experience of having a headache. The theory counts the proposition that someone has a headache as knowable a priori by that person. Hence the theory is false. Objection 3: All a priori propositions are knowable without the use of any experience of this world (rather than other possible worlds). So, all a priori propositions are knowable without the use of any evidence as to which of all possible worlds is the actual world. Therefore, a priori propositions must be true in all possible worlds, hence, necessary. The proposition that I have a headache is not necessary. Therefore, the theory is false. Objection 4: All a priori propositions are such that if they are knowable by one person a priori, they are knowable by any other person (who is smart enough) a priori. Since it is not because others are not smart enough that they cannot know a priori about one's headaches, the theory must be mistaken in counting propositions about one's headaches as a priori for the person having the headache. I shall now attempt to reply to this battery of objections. Merely to claim that all a priori propositions are necessary and that the theory must be wrong since it sanctions contingent a priori propositions, as does Objection 1, is to raise no real objection. Surely one must give an argument for the view that all a priori propositions are necessary. One could cite the authority of Kant, but that will be of little help. The property of being a priori, however it be characterized, is an epistemological property, whereas the property of being necessary is a metaphysical property. Unless one conflates these two properties, there is a need for an argument that all a priori propositions are necessary. There is some fairly convincing evidence that there are necessary propositions which are unknowable to humans at least. If they are unknowable, then they are unknowable a priori and hence not a priori propositions. That there are such propositions seems quite likely; Goldbach's conjecture may well be one. If we limit our method of mathematical knowing to what can be proved within a given system, then there will be, relative to that system, true but

unprovable propositions. In any event it seems to require quite a bit of hubris to think that humans are capable of knowing every true proposition whatever. Things might just be such that man is rather limited. So, it is far from obvious that every necessary proposition is knowable a priori. Hence, the claim that the necessary is coextensive with the a priori is, contrary to Kant, false.5 The dialectic can continue here. The enthusiastic or diehard defender of the extensional equivalence of the two notions can modify his account of the a priori and claim that a proposition, in order to be a priori, need only be capable of being known by an epistemic agent of roughly the same sort of abilities as an ordinary human. These modified agents might be imagined to be rather like humans only smarter. They would be able to know propositions humans were too limited to know. Using this notion of the a priori, there would no longer be necessary propositions which were not a priori due to human epistemic frailty. At least two problems arise in connection with these modified epistemic agents. First, it is not obvious that they will be able to know all necessary truths. What guarantee is there that they too will not be unable to prove some very difficult mathematical proposition? Of course, they could be supposed, by hypothesis, to be capable of knowing everything. However, under that assumpltion what guarantee is there that they will be anything like humans? Further the claim that all necessary propositions are a priori becomes rather trivial; namely, all necessary propositions are such that they can be known by an epistemic agent who is capable of knowing all necessary propositions. So, this move either encounters the same problem that the original definition encountered or else it renders the extensional equivalence hypothesis trivial. There is a second problem. If we allow these more perfect than we epistemic agents to determine conceptual matters for us, how are we to know in advance that they will not also possess the ability to know clearly non-(a priori) propositions intuitively and directly? If 5 Recently several philosophers have challenged the Kantian dogma linking the a priori and t h e necessary. T h e most extended discussion occurs i n Ed Erwin's "Are t h e Notions o f ' a priori Truth' and 'Necessary Truth' extensionally Equivalent?" ( T h e Canadian Journal o f Philosophy, V o l . 3, January 1974, Pp. 591-602. Alvin Plantinga discusses several examples o f necessary truths which are not knowable a priori i n chapters 1 and 7 o f his The Nature o f Necessity (Oxford: Clarendon, 1974). Probably all o f the recent discussion stems f r o m Kripke's original and provocative papers o n identity: "Identity and Necessity," i n Identity and Individuation, edited b y M. K. Munitz ( N e w Y o r k : NYU Press, 1971) and "Naming and Necessity" i n Semantics o f Natural Language, edited b y G . Harman and D. Davidson (Dordrecht: Reidel, 1972).

such agents either possessed this ability or evolved so that they came to possess it, then they would know empirical propositions about the world in the same way that normal humans now know propositions about the foundations of mathematics and logic - they would just "see" that they were true. Thus, there is a problem; of course, one could try to say that such agents could not exist, since it is impossible that a person should know a contingent proposition in the same way that he knows an a priori proposition. This is far from evident. To be sure, most a priori propositions are known on the basis of other propositions which deductively imply them. However, there are those a priori propositions which serve as starting points. These propositions, on my account, are known intuitively. It is somewhat vague how they are known, but one thing is clear, and that is that they are not knowable without being reflected on or thought about. That is, in order to know them, one must consider them; at least one must do so in order to know them a priori. This act of reflecting on the proposition does not seem radically different from what one does when one reflects on propositions about one's inner mental states, nor does it seem all that different from what an evolved epistemic agent might do with respect to any "empirical" proposition whatever. That is, the agent reflects on the proposition, it seems true, so he believes it and thereby knows it. This seems both coherent and possible. If so, and if we are allowing for the evolution of an epistemic agent, then is it not possible that any proposition whatever (except for trick propositions such as "Nothing is known a priori") could be known a priori? The answer seems to be in the affirmative; hence, it is a mistake to try to define the a priori in terms of such evolved agents, however initially tempting it might be. Objections 2 and 3 both involve assertions about the way in which a priori propositions are supposed to be knowable. These assertions agree that the a priori way of knowing is a way of knowing which is in a crucial sense independent of certain other ways of knowing. Objection 2 locates the independence in the area of sense experience whereas objection 3 locates it in the area of contingent propositions. In both objections there is a certain confusion concerning the form this independence is to take. When traditional philosophers insisted that the a priori was what could be known completely independently of sense experience, they did not mean that a person who had never had any sense experience could know every, or for that matter any a priori proposition. They realized all along that sense experience was necessary in order that the person develop sufficient mental ability to comprehend the con-

cepts in question. While they may not have been terribly clear on this matter, surely what they meant to say was that a priori propositions could be known without appealing to sense experience as evidence or grounds. That is, a priori propositions could be known by someone to be true, and that knower would not need any propositions about sense experience as evidence. The area of independence was the area of grounds; the grounds for an a priori proposition need not be propositions about sense experience (objection 2) nor need they be contingent propositions (objection 3). Propositions which are known intuitively, by nature, are not known on the basis of other propositions; that is, no other propositions serve as their grounds. Therefore, these propositions whatever they might be about, satisfy the requirements of independence. Since they have no grounds whatever, they have no grounds which are about sense experience o r which are contingent propositions. Hence, all intuitively known propositions, whether they are about the foundations of logic or about one's mental states, are adequately independent. Thus, both objections 2 and 3 are obviated. The reason philosophers are tempted to offer objections 2 and 3 is the contingent feature of propositions about one's inner experience. However, surely one should not conflate the character of propositions about one's inner experience with the character of possible grounds for them. It is precisely this mistake which leads to the objections. To turn now to the final objection, note that it is based on the presupposition that an a priori proposition must be knowable a priori by anyone smart enough to understand the subject matter. However, there is little justification for this presupposition. The rationale for it goes something like this: all a priori propositions are necessary propositions; if a person can know a necessary proposition, then he can prove it from premises he knows intuitively; the proof could just as easily be known by anyone else smart enough to think it up or to understand it after he was told it by someone else; therefore, a priori propositions are knowable by everyone in the a priori manner. This argument is fairly convincing. It does seem to be true that if someone cannot understand an a priori argument involving only necessary propositions, then the difficulty is that he is not smart enough. This is not entirely evident, however. There may be many necessary propositions which are not publicly accessible. Those philosophers who agree with Kripke might be willing to cite many identity statements which are of this sort. But, in general, one is justified in


thinking that if Smith can know a certain argument involving only necessary propositions and if Brown cannot, then the problem is that Brown is not as talented as Smith. Fortunately without deciding the matter of whether all a priori necessary propositions are equally knowable by those intelligent enough to compete, it is possible to dismiss objection 4. Objection 4 depends entirely on the presupposition that all a priori propositions are equally publicly knowable and that presupposition is itself plausible only if one assumes that all a priori propositions are necessary. This last assumption is surely unjustified and, in a sense, is precisely what is at issue. In effect, objection 4 reduces to objection 1 and hence can be dismissed for the same reason. Until there is an acceptable argument that all a priori propositions must be necessary, it is to be assumed that they need not be necessary. Thus, my theory survives the objections. Of course, if someone does prove that all a priori propositions are necessary, then the theory will stand refuted. In defining the a posteriori, at least the following two points need to be kept in mind: the definition of a posteriori knowing ought not to make it impossible that a person know a proposition both a posteriori and a priori. And the definition of the a posteriori ought to be such that if a person knows a proposition, then he knows it either a'priori or a posteriori. Quite frequently we can prove a proposition from a priori premises, and yet we also have in our possession the testimony of the experts to the same effect. When we are in such an epistemologically fortuitous condition, we surely know the proposition a priori since we can prove it. But equally, surely we know it a posteriori since we have the word of reliable experts. So any definition of the a posteriori of the following sort would be highly undesirable: (15) S knows p a posteriori = S knows p and S does not know p a priori. For (15) would force us to say that the person who has the testimony of the experts does not know a posteriori since he also knows a priori. While we want to allow for the possibility of a person's knowing a single proposition in both manners, we do not want to allow that he knows it but does not know it in either manner. The natural place to take up the slack is in the definition of knowing a posteriori; that is, we will define knowing a posteriori so that any way of knowing which is not precisely the a priori way of knowing will be classed as knowing a posteriori.

We make use of the notion of intuitive knowing defined above in (1). Using this notion we define a concept of a posteriori proof construction as follows: = S can construct an argument for p (2') S can construct an a from premises S knows intuitively posteriori proof of p to be true. The argument must be essentially inductive and must employ inferences which S knows to be deductively valid or inductively reliable. Thus, the concept of proof construction for a posteriori knowledge closely parallels that for a priori knowledge. The difference being that a posteriori proofs are essentially inductive, that is, they are arguments which contain an inference which is justifiable only on inductive grounds. Once we have this notion of an a posteriori proof construction, we can define the central concept of knowing a posteriori. The definition contains two parts, one is a clause to catch all forms of knowing which are not a priori, the other is the genuine definition of the a posteriori.

(3') S knows p a posteriori = S knows p but does not know p a priori OR S can construct an a posteriori proof of p and S knows p on the basis of this proof. On this definition a person who knows something but does not know it a priori, knows it a posteriori, no matter in what manner he knows it. This is so in virtue of the first disjunct in the analysans. However, a person who does know a priori could also know a posteriori provided he could construct an a posteriori proof. There remains the following problem. Suppose there is a third way of knowing which does not involve constructing either an a priori proof or an a posteriori proof. Suppose further that there was a person who knew a poposition a priori and also in this third way. On this definition it would not be the case that he knew the proposition a posteriori. But if he were to lose his a priori knowledge of the proposition and yet continue to know it in the third manner, then he would be said to know it a posteriori. This is a defect. I can see no way around it. One is tempted to avoid talking in any detail about the a posteriori manner of knowing by the following variation on (15):

(16) S knows p a posteriori = S knows p and does not know p a priori OR S knows p and would continue to know p even if S were no longer to know p a priori. The problem with (16) is that it contains a subjunctive conditional. Consider the following case: a man does know p both a priori and a posteriori, but he is such that whenever he loses his a priori knowledge of a proposition, he also loses his a posteriori knowledge also. Perhaps he has some peculiar disease of the brain which affects his memory. Such a man shows that (16) fails to provide a necessary condition for knowing a posteriori, since neither clause in the analysans of (16) would be satisfied; yet by hypothesis he does know a posteriori. Most of the remaining definitions directly parallel their a priori counterparts. I shall list all of them and then comment briefly on some of the more interesting ones. (4') p is an a posteriori proposi- = It is logically possible that tion someone knows p a posteriori. (5') S judges a posteriori that p = S asserts p on the basis of S's is true ability to construct an a posteriori proof of p. (6') p is an a posteriori judgment = p is an a posteriori proposition. (7') x is an a posteriori judgment = x is an event consisting of S's by S that p is true judging a posteriori that p is true. (8') x is an a posteriori source of = x is a source of knowledge knowledge which is essentially inductively related to what is known. (9') x is an a posteriori way of = If anyone knows something in knowing way x, then he knows it a posteriori. (10') x is an a posteriori law of = It is a true a posteriori propothought sition that anyone who thinks correctly, thinks in accord with x. (11') p is an a posteriori truth = p is a true a posteriori proposition. (12') x is an a posteriori concept = Someone could know a posteriori that x applies to an object.

(13') x is an a posteriori form of intuition

= Someone could know a poster-

iori that x is a form of intuition. (14') x is an a posteriori condition = Someone could know a posteriori that if there is experience, of the possibility of experience then condition x obtains. While it is desirable that if someone knows a proposition, then he ltnows it either a priori or a posteriori, it is not desirable that all propositions be either a priori or a posteriori. There may very well be propositions which cannot be known. These propositions should be excluded from the categorization. What sense would it make to hold that a proposition which was unknowable was also a priori? Of course, one could just mean by calling such a proposition a priori that it was necessary. However, as I have argued, this is a mistaken use of the notion of the a priori. It is simply wrong to conflate a metaphysical category with an epistemological category. Once one decides to avoid systematically this conflation, one is no longer shocked by cases where the a priori-a posteriori distinction does not divide the category into two mutually exclusive but jointly exhaustive subcategories. It is quite likely that (4) together with (4') does leave some propositions unclassified; namely, they leave the unknowable propositions unclassified. In the case of the last three definitions it may well be a mistake to allow one and the same entity to be classed as both a priori and a posteriori. If so, this is easily remedied by adding to each of the definiens the requirement that the entity in question not be knowable a priori For example, (14') would become: (14") x is an a posteriori condition = Someone could know a posterof the possibility of experiiori that if there is experience, ence then condition x obtains and no one could know this a priori. I11 If the foregoing definitions are satisfactory, then it is possible to use an analysis of knowledge which includes both a priori and a posteriori knowledge and then to conjoin that analysis with certain other conditions and thereby distinguish between a priori and a posteriori knowledge. Thus, an analysis of knowledge which did not distinguish between the two kinds of knowledge could nonetheless be used to make the distinction. Still someone might want to claim that two separate analyses are needed since Gettier problems arise only in the area of a poster-

iori propositions. However, this claim is false. This can be shown in at least two ways. One can envision an expert mathematician who makes a mistake and thinks he has a proof when he does not. Since he is usually careful, he is justified in believing what he thinks is a proof. If we suppose that the conclusion of his n o n p r d is true, then he has a justified true belief which is not knowledge. Or, one can imagine a person who asks all the experts about some proposition in mathematics. They all tell him that it is true. However, it is true only as a matter of luck since all the experts were right but for the wrong reason. The man does not know but he does have a justified true belief. This establishes that the traditional anaylsis is subject to Gettier cases even when a necessary, a priori proposition is involved. The sort of difficulty which occurs seems to the same for both necessary and contingent propositions, namely, something goes wrong with the evidence on which the knowledge is based. It seems quite reasonable to believe that once this difficulty is correctly isolated and removed, both contingenlt and noncontingent propositions alike will be free of the Gettier difficulties. If so, there seems to be little reason to look for separate analyses of knowledge. There remains the question of whether Gettier cases can still be construc~tedgiven the analyses of a priori and a posteriori knowledge provided in (3) and (3') respectively. In one sense of the question, the answer is that such problems cannot arise since both (3) and (3') require in the definiens that the person in question have know ledge. The substantive issue is whether (3) and (3') without the requirement that the person have knowledge suffice to avoid Gettier cases. Clearly (3') is susceptible to such cases since even the very best inductive arguments are subject to them. ( 3 ) also is not immune, since various tricks can be played with the notion of the construction of an a priori ppoof. That is, a person might construct a proof in accord with certain rules of inference which he knows intuitively but fail to get them in the right order. If luck were with him, he would still end up with a true conclusion. So, unless one can make proof construction foolproof, there still remains trouble. To be sure, the trouble is now located in a different place from where it was before. This may constitute progress. I have attempted to present a coherent, systematic account of the a priori-a posteriori distinction. Even if this attempt is successful, there will remain the fundamental problem of how to define knowledge. Also, much more will need to be said about the unanalyzed notion of direct knowing. Nonetheless, it is encouraging to see

that once an adequate analysis of knowledge is discovered, there will not exist significant further obstacles to distinguishing the a priori from the a p o s t ~ i o r i . ~ DAVID W. BENFIELD. MONTCLAIR STATE COLLEGE.

6 1 would like to express my appreciation to Ed Erwin, Fred Feldman, and Michael Slote for their valuable criticism of earlier versions of this paper.