Abstract

In "Discrimination and Perceptual Knowledge", Alvin Goldman presents a theory of non-inferential, perceptual knowledge that involves the putative knower's ability to differentiate between "relevant alternatives" to what he claims to know. This paper is an attempt to extend this notion to knowledge in general, and to explore further the concept of epistemic relevance.

Goldman's "perceptual equivalence" will be extended to a more general "cognitive equivalence," and some attempt will be made to define this concept explicitly. Epistemic relevance will be seen to be a property of alternative circumstances (states of affairs), and some rough rules will be given as to which states will be relevant under what circumstances. From these concepts, a theory of knowledge will be presented which assigns knowledge only when, roughly, where is no relevant circumstance in which the knower would have the evidence he has now (or some cognitive equivalent), and yet be mistaken.

The theory will be compared to some other accounts of knowledge (including Fred Dretske's "Conclusive Reasons" and Gilbert Harman's "undermining evidence one does not possess"). It will be claimed that these theories are already very like the one presented here, and that by studying them in its light, their faults and virtues may be made more evident.

Under the theory as presented, determining whether an individual knows becomes more complex than it is under previous theories. To determine whether T is correct in believing that S knows P, not only must we be omniscient about S and P, we must also know who T is, and the circumstances he is in. It will be argued that this is not a weakness, but a strength, as it more accurately reflects our intuitions about the nature of actual knowing.

Introduction

What are the truth-conditions for knowledge statements? When I attribute knowledge of some proposition to some person, what do I mean; how can my statement be usefully paraphrased in a way that will shed some light on the function of knowledge statements in my speech community, and on what I expect from my fellows before I am willing to label their beliefs knowledge?

In this paper, I will present and attempt to defend a theory which addresses this sort of question. In origin, the theory is an extension of Goldman's account of non-inferential, perceptual knowledge, as set out in his "Discrimination and Perceptual Knowledge"(1976). It is an attempt to extend the notions of that paper to apply to knowledge in general, and at the same time to remove the need for the rather awkward "appropriate genesis" clause in Goldman's account of knowing.

The theory I will propose is not a complete analysis of knowledge in terms of already well-defined concepts. The interpretation (and hence the truth) of any particular utterance of the form "S knows that p" will be analyzed in terms of (among other things) the "epistemic relevance" of various alternative states of the world. No formal analysis of epistemic relevance itself will be given, however, independent of the basic characterization of knowledge; this relevance will be described largely by analogy and parable.

Why, it might well be asked, bother? If we are only solving one old familiar characterization problem (knowledge) at the cost of adopting a new one ("epistemic relevance"), what have we gained? I will try to answer this objection below by actually displaying a benefit or two, but I will at least comfort the reader here.

First, the notion of epistemic relevance, once accepted, clarifies a good deal of the murkiness of the knowledge-characterization debate. The fact that it is relativized to persons and times, and that, as a matter of psychological fact, what is relevant for one member of a particular community will only usually be relevant for another, explains on the one hand various differences in intuition that occur in the literature, and on the other, the temptation of various sorts of skepticism.

Second, in getting from knowledge to epistemic relevance, a good deal of unpacking will have gone on; even with relevance only fuzzily defined, we will be able to say a number of new things about knowledge statements, their logical relations to other statements, when they may be validly uttered, etc. In bringing the problem down a level, we will find ourselves with several new facts.

Why is there a problem with characterizing knowledge? The legacy of Russell and Gettier is well-known, but I will sketch its outlines here. With Pappas and Swain(1978), I will refer to a "traditional analysis" of knowing (although tradition no longer favors it). This analysis, typically blamed on Plato's Theaetetus, identifies knowledge with justified true belief(1). A person S, that is, knows a proposition p if and only if

        1) S believes that p
        2) p is true, and
        3) S's belief that p is justified
            (under some appropriate characterization
             of "justified")

This analysis of knowledge thrived for an age or two, in forms as diverse as Plato's, and Ayer's "right to know". This idyllic period ended with Edmund Gettier's "Is Justified True Belief Knowledge"(1963), which presented some situations in which, although the main character has justified belief in some true proposition, the situation is (roughly) strange enough that we do not want to grant him knowledge.

The simplest of Gettier's examples concerns two men who have applied for the same job. I will call them Smith and Jones. While waiting for the Boss to decide who will be hired, Smith finds out (because the two men are passing the time with recreational mathematics or the like) that Jones has exactly ten coins in his pocket. Subsequently, Smith is told by the prospective employer's secretary (whom he knows to be a reliable source), that Jones is the man who will get the job. It is generally uncontroversial that reliable testimony can justify belief of a proposition, so it seems that Smith has justified belief in the proposition (a) "The man who will get the job has ten coins in his pocket."

As it turns out, however, the secretary was in this instance mistaken; Smith himself will actually get the job. Also coincidentally, when Smith grabbed a handful of coins off his dresser that morning, he took precisely ten coins, and still has them in his pocket (a fact of which he is not aware). So, as it turns out, (a) is true, Smith believes it, and his belief is justified. However, we do not want to grant Smith knowledge in this situation; it might as well have been the case that he drowsily picked up nine, or twelve coins. Speaking pre-theoretically, Smith believes (a) for the wrong reasons(2).

Since Gettier's originals, the literature has spawned a few hundred similar examples, most designed specifically to weigh against some new attempt to replace the much-mourned traditional analysis. These examples range from the slightly unlikely to the trully bizarre, and employ numerous Martian hypnotists, holograms, cardboard sheep, mad neurophysicists and mysterious new types of radiation. This last observation is not simply idle; I shall suggest below that the multiplicity of "Gettierized" examples is a point in favor of my treatment of epistemic relevance.

The principle reactions of the philosophical community to Gettier's questions are nicely summarized in a long unpublished paper by R. Shope(1978)(3). Some tried to save the traditional analysis by finding loopholes in the Gettier examples; more tried to replace it with analyses of their own. For every new set of truth-conditions proposed, at least two examples appeared designed to show it either too restrictive or too lax. Appeal to intuition, as a method of determining the validity of a theory's results, showed its limitations: with no accepted theory to fall back on, what do you do when two authors disagree about whether a particular true belief counts as knowledge? Even if we were to agree that a pre-theoretic consensus would do as the correct judgement, there is no guarantee that such a consensus exists; the situations hypothesized are usually so far from everyday experience that intuition, unbolstered by a favorite theory, recoils.

Alvin Goldman's "Discrimination and Perceptual Knowledge" presents a theory of non-inferential perceptual knowledge, and expresses the hope that it will "lay a foundation for a general theory of knowing." Stripped of its fine detail, the theory grants knowledge only when the subject has true belief, based on some percepts which are such that there is no relevant situation where functionally the same percepts occur, but the proposition believed is false.

As an example of this, Goldman gives us a man (Henry) driving through the countryside, pointing out various objects to his small son. At one point, he indicates a barn, saying "that's a barn." Now under normal circumstances, we are willing to grant Henry the knowledge that what he is pointing at is indeed a barn. If, however, we are also told that there are several ingenious barn-facades in the area, set up so as to look just like barns from the road, we will not. In Goldman's words,

"Given that the district Henry has entered is full of barn facsimiles, there is a relevant alternate hypothesis about the object, viz., that it is a facsimile. Since, by assumption, a state of affairs in which the alternate hypothesis holds is indistinguishable by Henry from the actual state of affairs (from his vantage point on the road), this hypothesis is not 'ruled out' or 'precluded' by the factors that prompt Henry's belief. So... we are inclined to deny that Henry knows."

The proposal bears some relation to Fred Dretske's "conclusive reasons" analysis(Dretske, 1971) (where S knows when, were p false, S would not have his reasons for believing it), and other analyses making essential use of some sort of counterfactual.

Anticipating his colleagues, Goldman comes up with his own heavily Gettierized example, suggesting that his analysis is too weak in this form, granting non-inferential perceptual knowledge in certain cases where the true belief in question has a particularly strange and dubious origin.

The problem stems from the details of Goldman's formulation; for something to be a perceptual equivalent to a given situation, there must be some object in the equivalent case which causes the subject to believe of it that it has some property. Goldman's example:

"S truly believes something to be a tree, but there is a relevant alternative in which an electrode stimulating S's optic nerve would produce an equivalent percept, which would elicit the same belief. Since this is assumed to be a relevant alternative, it ought to disqualify S from knowing. But it doesn't satisfy our definition of a perceptual equivalent, first because the electrode would not be a perceptual cause of the percept (we would not say that S perceives the electrode), and second because S would not believe of the electrode (nor of anything else) that it is a tree. A similar problem arises where the alternative state of affairs would involve S's having a hallucination."

Shope also cites some examples which seem to suggest the same conclusion, in less anomolous circumstances. His example E30, for instance, is designed especially to show Goldman's analysis too weak:

"The Two Nurses: S is a patient who is regularly but separately attended by identical twins, Judy and Trudy. Unsuspected by S, Trudy's duties, but not Judy's, include the responsibility of immediately administering to S a drug which has the side effect of almost instantly making S highly attentive to differences in his percepts. At the moment, S looks and forms the true belief p: 'Judy is present.' But he does not know p since he is very dulled and inattentive to details of his percepts; had he remained so, he would have identified Trudy as Judy, while still being able to tell that at least one of them is present. It happens that the difference in dress and behavior of the twins is so subtle that it takes a certain period of close scrutiny even for their close acquaintances to tell from their percepts which one is present.

Goldman's conditional is satisfied in this example because Trudy's presence would lead her to administer the drug, which would, in turn, lead S to be so alert during the period of scrutiny typically required for discrimination that S would indeed notice the difference."

I shall attempt to show how my proposed extension of Goldman's theory accounts for his own suggested problem-example, and that Shope's examples do not apply under a careful construal of what may count as an "alternative situation" (Shope seems to be denying that there is a relevant alternative in which S, senses dulled, sees a blurry image of Trudy. If we allow conceivable worlds, however, this will not be the case).

Proposal

I propose the following:

A person S knows a proposition P if and only if:

1. S believes P for reasons R
2. In every relevant alternative situation in which S believes P for reasons cognitively equivalent to R, P is true.

Stated less rigorously, S knows a proposition only when his reasons for believing it "narrow down" the set of relevant alternative situations enough to exclude those in which it is false. This analysis includes the traditional account: by (1), S believes P. By (2), and assuming that the situation which actually obtains is relevant, P is true. And I will assert below that whenever (1) and (2) are satisfied, S is justified in believing that P (although the converse decidedly does not hold).

The parallels with Goldman's account of perceptual knowledge are obvious. My "cognitive equivalence" is an extension of his "perceptual equivalence," and my "relevant alternative situation" corresponds roughly with his "relevant perceptual equivalent."

Attempts to define epistemic relevance and cognitive equivalence will be the concern of much of this paper; before we get that far, however, we will need at least a general notion of what they are.

Cognitive equivalence is a relation that holds between sets of internal reasons that a believer has for believing. Roughly, two sets of reasons are cognitively equivalent if and only if they differ in no way that is relevant to their bearer's belief. If reasons R lead S to believe that p, and (all other things being equal), reasons R' (had S held them) would have led him to believe that p in the same way, then R and R' are cognitively equivalent reasons.

Epistemic relevance is a quality of alternative situations. Just what an alternative situation is will be touched on below, but it is essentaily a state of affairs which, in some sense, might have obtained. One of the major activities of the human mind is the imagining of such counterfactual states of affairs, in pondering might-have-beens and may-yet-bes. It is important to note that these alternative states of affairs are not possible worlds in the usual sense; they are perhaps better called "conceivable worlds." There are (for me now) conceivable alternative states in which Fermat's Last Theorm is true, and states in which it is false. These are both alternative states of affairs in the sense in which I mean the term, yet only one set is logically possible.

Epistemic relevance is a property of those alternative states of affairs which are somehow similar enough to the actual state to merit consideration. If I go on a camping trip, I take a rain fly, because it might rain. I do not, however, take a French ten-franc piece because a madman with a revolver might demand one of me on a lonely hillside. The latter alternative (although logically possible) lacks relevance (unless such a madman is know to be in the area, in which case I am well advised to take the coin). As we shall see, relevance will have to be relativized to persons and times, as will cognitive equivalence. I will later attempt to use this relativity to account for various disagreements in the literature, and for the attraction of skepticism (as a desire for absolutes).

On Denying Knowledge

To see how this characterization of knowledge works, and how it repairs the defects of the traditional analysis, it will be helpful to look at the reasons for which we commonly deny someone knowledge. Neither these considerations nor those in the next section are intended to demonstrate the truth of my proposal; that will stand or fall on its handling of various Gettier-like examples. I hope, however, that these sections will give the reader some intuitive grasp of how the proposal works, and incline him to be more charitable if he encounters apparent contradictions farther along.

It is generally agreed (with various exceptions, some of which I note below), that the conditions imposed by the traditional analysis are necessary for knowledge; any replacement account will therefore have to deny knowledge wherever the traditional analysis does. The Gettier examples show that these conditions are not sufficient for knowledge; so any new account will have to impose some further condition.

Belief

Both the traditional analysis and the proposed replacement will deny knowledge in the absence of belief. This seems quite plausible, but if, with Merril Ring (1977), we wish to use "belief" to denote only a state of assent weaker than knowledge, we can easily rewrite our condition (1) to read: "S is willing to affirm p for reasons R," "S gives assent to p for reasons R," or "S takes p to be the case for reasons R." The important point here is not the precise level of credence that S grants p, but merely that he acknowledges it as a fact. Speaking sincerely, S would claim to know p(4).

Cases where the belief-condition is violated are numerous, but relatively uninteresting. I have excellant evidence for some proposition p, but still I do not believe p, either because I have never thought through the evidence I have, or because p is a proposition so distasteful to me that I have chosen to ignore its connection to that evidence. In these cases, I will not affirm p, nor will I base plans or actions upon its truth. Despite my evidence, then, I do not know p.

Truth

Although this facet of the traditional analysis seems even less problematic than that of belief, it is not explicitly mentioned in my account of knowledge. If we assume, however, that the situation which actually obtains is always a relevant alternative situation (a sort of degenerate form), my account contains it implicitly. If I believe a false proposition, the actual state of affairs will be a relevant alternative situation in which, obviously, my reasons are cognitively equivalent to my actual reasons, but the proposition is false; so I will not know.

The fact that the truth condition is not explicit in my formulation, however, means that it is not strictly necessary for knowledge; under a sufficiently strange assignment of epistemic relevance, it will not hold. Allowing knowledge of even false propositions is a relatively rare sort of anti-skepticism, generally encountered only in the small hours of the night, in solipsist discussion groups. I will claim further along that its origin is the inverse of the origin of a certain kind of skepticism: where this skepticism proceeds by requiring us to consider every logically or conceivably possible alternative as epistemic relevance, this solipsism does not even require us to consider the actual world beyond our line of sight.

Justification

This is the thorniest clause of the traditional analysis. Precisely what it is for a belief to be justified is by no means a well-settled question. There is not even a consensus as to what it is that may be justified (a belief, a person, a proposition), or by what justification occurs (is a belief justified by circumstances, the believer's sence-experience, the truth of the proposition believed...?).

Since justification plays no role in my account of knowledge, I will not give a precise characterization of it here. I will, however, attempt to give a coherent description of it, as it functions in the traditional analysis of knowledge.

I will assume that what is justified (in the epistemological sense) is always a belief, and that what justifies a particular belief for a particular person is the set of reasons he has for holding to that belief, where by "reasons" here I mean pieces of information actually in the believer's posession. (For the sake of brevity, I will call these "internal reasons." This terminology is not intended to imply any claims about the objectivity of experience, the location of meaning, or other tangential issues. I merely wish to exclude various facts of which the believer is unaware, which might be "reasons" for his believing in some other sense). Justification, then, will be a function only of persons, beliefs, and internal reasons, without reference to the truth or falsehood of the proposition believed, or to any other external considerations, or circumstances to which the agent has not had access.

How do we determine whether a given belief is justified for an individual? In essence, we examine the believer's reasons, and the way in which they led to the belief, and decide whether or not the believer has made any fundamental errors or oversights, or in any way violated the requirements of epistemic responsibility. If the believer's reasons actually do (given only the information he posesses), eliminate to within a reasonable doubt the possibility that the believed proposition is false, we will grant that the belief is justified for him. If, on the other hand, the believer has been in some way irresponsible, we will deny justification. If he has overlooked some possibility which (had he thought of it) might have made the falsity of the belief relatively likely, or ignored an entire body of evidence for inappropriate reasons (such as the desire to protect cherished opinions), he has not fulfilled the requirements for justification.

With justification so construed, any true, but unjustified, belief will fail to be knowledge under the proposed analysis (as well as the traditional). For if the subject's reasons, or reasoning, fail to effectively rule out some situation which he should have considered, and in which the belief is false, then that situation will be a relevant alternative, and the subject will not meet condition (2). Not having a precise characterization of justification, I cannot conclusively prove this, but I will give two general examples to illustrate how it works.

The most obvious case of true belief without justification occurs when a belief is formed on inadequate evidence. Presented with a few examples (or even only one) of a class of object, and observing that all possess some property, I form the belief that all objects of this class have that property. In time, I come to regard this belief as a bit of knowledge. Because I have made an induction on such scanty grounds, however, the belief is not justified. There is a relevant alternative in which I encountered precisely the same specimens, but my unwarranted conclusion was false. So I fail to know under both accounts of knowledge, and for a similar defect. My reasons fail to adequately guarantee the truth of the proposition that I believe.

If the number of cases is high enough to be representative (as far as the believer can tell) induction can lead to justified belief. In my terms, if an adequate sample is observed (and no other factors apply), the alternative where the sample is actually biased will be irrelevant for purposes of justification.

Unjustified true belief can also occur when some important body of evidence, currently in the believer's posession, is ignored in forming the belief. If, for whatever reason, I do not consider some pertinent information which I have, and which might show the proposition to be unlikely, there will be a relevant alternative situation in which the believed proposition was false, this falsehood was reflected in the evidence that I ignored, but I came to believe the proposition anyway. So my account also denies knowledge to this sort of unjustified belief.

It should be noted that simply ignoring some body of evidence in forming a belief will not always render the belief unjustified. If the evidence already considered shows the chances of the proposition's being false to be vanishingly small, we are not obliged to consider all possibly pertinent evidence, just on the off-chance that it might prove important. Only when there is still a significant chance that the unexamined data will be pivotal, only when (despite evidence already examined) the alternative in which those data cast doubt on the truth of the proposition is still relevant, does leaving some evidence out of consideration lead to unjustified belief. This is an important point: we are not normally obliged to go to infinite pains to verify our beliefs. If we have narrowed the possibilities to within a reasonable doubt, we can be justified in our beliefs. If we have narrowed the possibilities to within epistemic relevance (something very like 'reasonable doubt'), we can have knowledge.

On Granting Knowledge

I have shown how the traditional analysis fits into my proposal, and given some reason to think that my analysis will deny knowledge whenever the traditional one does. It remains to show that the conditions of my analysis, unlike those of the traditional, are actually sufficient for knowledge. In this section I will describe how my analysis imposes an additional restriction on knowledge; in the next I will more fully treat epistemic relevance, and deal with some examples from the literature, to illustrate the conditions in operation, and to clarify the notions of cognitive equivalence and epistemic relevance.

We have said that justification depends only on information the believer possesses, and the way that information leads to his belief. In all the Gettier examples, and other instances of justified true belief that does not qualify as knowledge, there is some circumstance in the outside world of which the believer is unaware, and which, from the viewpoint of us omniscient observers, is epistemically relevant to that belief. Despite the fact that the subject has considered all the possibilities that his information (and permissable assumptions about the state of the world) oblige him to, we will not grant him knowledge, because there are possibilities which, all things considered, he should have taken into account.

This use of "should" and "obliged" is somewhat metaphorical. To put the point more literally, we will need some picture of the requirements of justification and of knowledge.

Take as an example, Smith (of Gettier's Smith-and-the-Ten-Coins). His important internal reasons for believing (a) are as follows: he has seen Jones turn his pocket lining out, and then restore it, and put in ten coins. He has also heard the Boss's secretary tell him that Jones will get the job; and he remembers several incidents which make it reasonable to suppose that the secretary is a trustworthy man. Because these reasons eliminate, to within a reasonable doubt, the possibility of this world being any in which the man who will get the job does not have ten coins in his pocket, Smith's belief in (a) is justified. Note that worlds in which Jones will not actually be hired are not judged impossible (logically, causally, or otherwise), but only unlikely enough that Smith is correct in dismissing them.

From his point of view, then, the alternatives in which Jones will not get the job are not relevant, and need not be considered. For the better-informed philosopher, however, who is viewing the situation from the outside, this is not the case. The secretary was mistaken; those alternatives in which Smith (or any other likley applicant) is hired are therefore epistemically relevant to his knowing that (a), and we must see whether his evidence guarantees, to within a reasonable doubt, that (a) is true in those worlds as well. Does Smith know that every person who might get the job has ten coins in his pocket? Hardly; he probably does not even know that he does. Given that the secretary was mistaken, then, there is a relevant alternative situation in which Smith has cognitively equivalent reasons for believing (a), but (a) is false. One such alternative is that in which Smith himself will be hired, and his half-awake gropings this morning picked up eleven coins from the dresser(5).

We have seen, then, how the traditional analysis is sometimes overgenerous in granting knowledge. The reasons we have for forming a belief justify us (in one sense) in ignoring certain possible or conceivable states of the world. The traditional analysis will grant knowledge whenever the proposition believed is true in all the states which we are not justified in ignoring. My analysis, on the other hand, acknowledges the fact that some alternative may actually be relevant, despite the justification we have for believing that it is not.

The conclusion of the previous section was that the proposed analysis is at least strong enough; this section should suggest that it is not too strong. The only cases where the proposal denies knowledge which the traditional analysis grants, are those in which the subject is in a crucial way wrong about the epistemic relevance of certain situations, and his internal justification will thus not lead to knowledge.

This sort of circumstance is typical of the Gettier examples and their kin, some of which we will examine later on.

Epistemic Relevance

We have gotten this far on a purely intuitive notion of epistemic relevance, heavily dependent on our ideas about knowledge. I will now try to show that it is one of a group of properties which play an important role outside the explication of knowledge-statements, and which thus may be used here without circularity.

In this section, I will argue for two theses: first, that "relevance" as a property of conceivable worlds is useful in various fields (and that "epistemic relevance" refers to the special case applicable to ascription of knowledge), and second, that the characterization of relevance of worlds is largely an empirical endeavor.

Some consideration of alternatives, of possibilities, is involved in most conscious human activities. We are always imagining what might happen in the future of a world in which we perform some action, as compared to a world in which we do something else.

At every instant, there are an uncountable number of conceivable futures for any given action I perform. There are also an infinite number of worlds I might, conceivably, be in now. I can obviously base my expectations for the future, and my opinions as to the appropriatness of my beliefs and actions, on only a small subset of broadly characterized conceivabilities. That subset which is, in whatever sense is appropriate to the specific problem we are considering, the correct subset for me to take into account, is the subset of worlds which are, in this instance, relevant. So the epistemically relevant worlds are those in which my belief must be true if I am to have knowledge; in other fields, the relevant worlds might be those I must consider if my decision is to count as rational or safe or morally praiseworthy, or those in which my action must succeed in order for my success to count as intentional. I expect that, in a given circumstance and for a given person, the same (or nearly the same) worlds will be picked out by all these "relevance"s, but whether this is in fact true will only be determined by further investigation.

By way of illustration, I will briefly discuss a term which is relatively free of theoretical dispute: the idea of "safe action." Now we will generally call an action safe if, to within a reasonable doubt, it does not tend to lead to undesired consequences. The unpacking of "reasonable doubt" brings out a certain sort of relevance. Is an action unsafe because there is some infinitesimally slight chance that it might cause some unintended harm? Hardly; we are always allowed to leave sufficiently unlikely worlds out of consideration. Is, on the other hand, an action safe whenever, as far as the agent can tell, there is no possibility of harm? Again no; it is always unsafe to walk across a mine field, no matter how good one's evidence is that it is not a mine field at all. Thirdly, is it safe to walk a tightrope across what one is convinced is a thousand-foot drop, because there is a transparent net just below you? No; we will say "You were safe all along" but not "You certainly have been acting safely today."

My suggestion is that there is something very like epistemic relevance at work here. In the first instance above, there are indeed conceivable worlds in which your action has a catastrophic result, but they are so unlikely as to merit no consideration; they are not relevant. In the second case, despite the fact that you walk unerringly between the mines that you are convined are not there, there is a relevant alternative situation in which you are blown to bits. And in the third, there is the relevant alternative in which you fell, and there was no net.

The kinship between the relevance employed in this model of safe action and what I am calling epistemic relevance is highlighted by the fact that either concept may be defined in terms of the other: a safe action is one which the doer knows will cause no undesirable result, and (if we assume that a false belief is undesirable) knowledge is any belief which it is safe to hold.

Another, more problematic, example comes up in the study of intention. It has been argued that an act is intentional only if it is not accidental that the agent succeeds. Gilbert Harman(1976) writes "...at the firing range the sniper intentionally shoots a bulls-eye only if that is something he can do at will. If it is just a lucky shot, he does not intentionally shoot a bulls-eye." It is not the case, however, that we may intentionally perform only those acts at which we are utterly infallible; we must only be sufficiently likely to succeed. We must, that is, succeed in every relevant conceivable world.

In another of Harman's examples, the agent sets out to kill her enemy and, in backing the car out of the driveway, runs him down. Since she did not even know that he was there, she has done what she intended, but she has not done it intentionally. Here there is a relevant alternative in which the victim did not choose to walk just there just then, and the killing did not take place.

It is possible to construct intention-analogues to most of the common theories of knowledge explication, and to demonstrate their inadequacy through analogous Gettier-like examples. In answer to a simple causal theory (an act is intended iff its result was intended, and this intention led to the result), we may cite Harman's third situation: "If [the killer's] intention makes her nervous and nervousness causes her to pull the trigger, her intention leads her to pull the trigger but not in the intended way; so she does not do what she intends and does not kill... intentionally."(p. 445) The intention did lead to the killing, so a causal explanation erroneously grants intentionality to the act. A properly fleshed-out relevance account would not: there is a relevant alternative in which her nervousness caused her to pull the trigger a moment too early, and she did not kill.

This sort of relevance is not as obviously close to my epistemic relevance, but it serves to illustrate the utility of relevance of alternatives further afield(6).

I have shown how epistemic relevance may be one example of a kind of property which has roots well outside the explication of knowledge. I will now present some thoughts on how relevance might operate in a community of speakers, and why I think that the characterization of relevance is largely an empirical matter.

Epistemic relevance, and therefore knowledge, are concepts which are most useful on an interpersonal level. I want to determine whether someone else's belief is actually knowledge not merely to decide whether to believe it myself (for then I would only want to know if it were true), but also to determine how reliable the person is as a source of true information. If his belief is not knowledge, there are relevant alternatives in which it is false, but he affirms it just the same. The next time he tells me something, it may well be false.

What we want to determine about our own beliefs is often just whether they are true. When we do inquire as to their status as bits of knowledge, we are inquiring (roughly) into the reliability of our sources.

When we praise someone, then, as "knowing a lot," we are saying more than just that he believes a lot of true propositions. We are also claiming that his ways of forming beliefs are generally good, and that he considers the proper alternatives before giving credence to a proposition.

Just which alternatives are the proper ones, which ones will be relevant in ascribing knowledge, will differ between persons, even between functionally omniscient persons. It will not usually differ much (non-philosophers in ordinary circumstances have no major problems in ascribing knowledge), but in odd situations or borderline cases it may differ noticeably, and not only because of a difference in the information possessed by the disagreeing parties.

Take a hypothetical situation, for which all important details are completely specified. If the situation is problematic enough, it will be possible to find two epistemologists who will make different knowledge ascriptions to some individual in the situation. And yet both have exactly the same information(7). If my proposed analysis of knowledge is correct, the epistemologists are assigning relevance to different sets of conceivable worlds. If one of them is the sort of skeptic who denies that anyone in fact has knowledge, he will grant relevance to such a large set of worlds that there is always one where a given proposition is false, though the evidence still exists. If the other is the sort of solipsist described above, he will allow us to ignore any conceivable world we like (including the actual one) and still grant knowledge. If both are more moderate, however, they may only disagree on the relevance of a few small classes of worlds, whose status seldom matters in everyday life. The reasons for this sort of dispute are not mysterious; as children, we are not taught any explicit rules for which worlds we ought to consider, we only have certain unpleasant experiences as a result of considering the wrong ones. Relevance is thus learned by experience: because we are all in the same (broadly-defined) culture, we have approximately equivalent experiences about relevence. But no two lives are identical.

Which epistemic relevance do we want to employ in the analysis of knowledge? If we rephrase "In every relevant alternative situation..." to read "In every alternative situation which is relevant under standard of relevance SR...", how are we to choose the standard? For theoretical purposes, we will probably want to define an "ideal" standard of relevance; one which, if universally employed, would lead to the maximum possible efficiency in the community of speakers and knowers, with the maximum number of bits of knowledge, and the minimum number of false beliefs thought to be knowledge. This is probably the correct standard to substitute for "SR" in my rephrased analysis; I do not mean, however, to imply that everyday use of the term "knowledge" in any way implies beliefs about ideal standards of relevance.

If this account of epistemic relevance and its function in a community of knowers is correct, investigating the rules for which alternatives are relevant in which circumstances would require the skills of the psychologist and sociologist as much as those of the philosopher. Determining the ideal or correct standard of relevance would require a rather detailed study of how the community as a body works, the role of knowledge in that working, and undoubtedly a host of important questions that would not even arise until the investigation was well under weigh. This is not to suggest, however, that we can say nothing about the relevance of worlds without a major undertaking; there are a few rough rules which seem likely to be close to the mark. We will consider some of these in the next section.

Guidelines for Epistemic Relevance

The suggestions presented here constitute rough rules which may have some part in a correct standard of relevance. I will make no particular attempt to justify them, and my analysis of knowledge does not depend upon their validity. I give them here primarily to give the reader a taste of what a standard of relevance might look like. In the next section, when we treat some standard test cases from the literature, an attempt will be made to apply them.

These rules will generally state that some conceivable world, and all worlds sufficiently similar to it, will be epistemically relevant in a particular situation. The notion of "similarity" of worlds is by no means a simple one, but I will not attempt to formalize it here. I will only note that the "similarity" I want is not strictly physical, but rather depends upon the question at issue, and the way we would describe the situation. For instance, the world in which Mount Everest is one centimeter to the north of where it actually is presumably involves more physical differences than the one in which I am about to be rendered unconscious by a cerebral blood clot, yet in judging my knowledge of my immediate future we want to say that the latter case is in the appropriate sense more different (or "farther") from the actual world than is the former.

With these disclaimers in mind, I will present these tentative rules:

1) A neighborhood of the actual world is always relevant. If a putative knower does not have reasons which guarantee his proposition's truth in all worlds sufficiently like the real world, he will not have knowledge. Those worlds sufficiently like the actual world are thus epistemically relevant. Some factors which influence the magnitude of "sufficiently like" will be touched on below.

2) A neighborhood of the agent's "rationally expectable alternatives" is always relevant.

The rationally expectable alternatives for a given person at a given time are those alternatives which, given only the information in that person's possession at that time, the agent may reasonably assume the actual world to be like(8). If the world were always in the apparently most likely state, the actual world would always be a rationally expectable alternative. Unfortunately, there is invariably something unlikely going on.

3) The farther the agent's rationally expectable alternatives are from the real world, the larger these neighborhoods become.

Roughly, the more peculiar states of affairs there are that actually apply, the more scrupulous the agent must be in forming beliefs if he is to obtain knowledge. If I am surrounded by conspiracies to deceive me, I will have to have more complete evidence before I can have any knowledge (even in areas where there is in fact no conspiracy).

4) All alternatives between the actual world and the agent's rationally expectable alternatives are relevant.

I will attempt no quasi-geometrical interpretation of this "between." The idea is something like this: If some circumstance in the actual world is different from the way the agent, making reasonable assumptions about the world, would expect it to be, then every alternative which differs from the actual world only in that that circumstance (and its necessary connections) is in a "compromise" or "half-way" state, is also relevant. If, in normal circumstances, I am justified in believing that it is pouring rain, but it is in fact sunny, then every alternative like the actual world except in regard to degree of rain is relevant.

This rule is more difficult to apply than the first two. It is seldom easy to say what constitutes a "compromise" between two states of affairs; something besides physical facts must be involved. If, in the example above, I am also justified in believing "If it is not pouring, it is sunny," then the alternative in which it is drizzling is not between the actual (sunny) world and the rationally expectable alternatives. The metric which determines the betweeness involves the oddness or unexpectedness of worlds, not their physical descriptions as such.

5) The testimony and beliefs of persons in the actual world has some effect on the relevance of the worlds which they claim or believe to be the actual one.

I awaken with justified true belief that my congressman is Herman Hacking. The local paper (which I have not yet read, but all my neighbors have) has run an erroneous story stating that Hacking has resigned. My neighbors no longer believe that Hacking is congressman, and if I had read that paper I wouldn't either. There is some question as to whether the alternative in which he really has resigned is thus relevant; at any rate, it is not obvious that it is not.

It is important to note that neither rule three nor rule four assigns relevance to every world which is at least as close to the agent's rationally expectable alternatives as is the actual state of affairs. Rule three stipulates that when actual circumstances are unusually odd (i.e. far from the rationally expectable conditions), alternatives a bit odder than usually do will count as relevant. Rule four, on the other hand, says roughly that when the actual world is odd in some respect, worlds which are any less odd in that same respect will be relevant.

Individuals' standards of relevance will generally conform to these rules; differences of opinion will usually be found only in the settings of "sufficiently like," in judgements of the betweenness of worlds, and in the degree to which testimony can make worlds relevant. If, for example, an individual has just had a series of very unusual expeiences (or has heard about someone who has), he will probably have a broader notion of "sufficiently like." If he has just heard several news stories he knows to be false, he will be less likely to allow knowledge on the basis of the testimony of newsmen(9).

Some Examples

Unjustified True Belief

When an agent has true belief without knowledge, it is because of the relevance of some world in which he has cognitively equivalent reasons, but the proposition believed is false. When that world is relevant under my rule (2) above (i.e. it is like the agent's rationally expectable worlds) the agent fails to have knowledge because he fails to have justified belief. He has failed to take into account some possibility which he ought to have realized was relevant. If I claim to know you have a cold simply because I dreamed that you did (and my dreams are as fallible as the next man's), I have neither justified belief nor knowledge. Given only the information that I have, it is not reasonable for me to assume that you have a cold; my rationally expectable worlds are not ones in which you have a cold; in the expectable worlds, your health is not determined (conceivable worlds are not, after all, complete specifications of the universe, only somewhat detailed sets of circumstances).

When an agent has justified true belief without knowledge, it is because of the relevance of some world which is relevant for some other reason. These are the more controversial, and usually the more interesting, cases.

Justified True Belief

We have already seen how the proposed analysis correctly handles Gettier's example of Smith and the ten coins, and Goldman's barn example. In both these cases, the worlds which led to a denial of knowledge were relevant under rule (1) above. We will next examine a more controversial case, where the correct ascription of knowledge is not so clear.

Tom Grabit

To deny knowledge as we wish to in this case, we need to find a relevant conceivable situation in which S has the same blurred, indistinct Judy-or-Trudy shaped percepts as his reasons for believing "Judy is present," and yet she is not. Can we find such a situation? The obvious candidate is that in which Trudy is in fact present, and the situation is otherwise just like that which actually obtains. S's evidence does not rule out this situation, and in it his belief is false.

But, says Shope, "Unsuspected by S, Trudy's duties, but not Judy's, include the responsibility of immediately administering to S a drug which has the side effect of almost instantly making S highly attentive to differences in his percepts." In some sense, then, it could not have been the case that S had equivalent reasons, but Trudy was actually present.

What is this sense? It is surely not a logical or physical impossibility that Trudy is present, nor is it inconceivable that she should be present and not administer the drug. It is only that, in worlds very like the actual one, whenever Trudy is present, the drug is administered. If we allow only very nearby worlds to count as relevant alternatives, the proposal naturally does not work: in the case of Smith and the ten coins there is (in this sense) no alternative in which "the man who will get the job has ten coins in his pocket" is false. After all, either Smith or Jones will get the job, and both men's pockets have ten coins.

The point here is that there is no reason to limit relevant alternative situations to those so close to the real world. As the next example will show, there may be relevant alternatives which are in fact not even logically possible.

The Mistaken Mathematician

A mathematician constructs a long and involved proof of some theorem of arithmetic T. The theorem is true, and his proof-making skill is such that he is justified in believing that it is true. On this occasion, however, he has committed a subtle error, and his argument does not in fact prove T. So, despite justified true belief, he does not know that T(10).

Since we deny knowledge here, there must be a relevant alternative situation where the mathematician constructs the same specious proof, but T is false. Now since T is presumably true in every possible world, this alternative situation, despite being epistemically relevant, is logically impossible.

This is actually no problem for the proposal. Relevant alternative situations are those which you may not ignore when forming beliefs if your beliefs are to count as knowledge. You may not ignore an alternative merely because the alternative is impossible; you must have a valid reason to believe that it is impossible (or at least that it is not actual). If you leave a logically impossible world out of consideration for the wrong reasons, you will attain true belief, but not knowledge.

No Brain Damage

The following example is similar to Shope's E30 and to the case of the mistaken mathematician, but it illustrates some peculiarities of (at least this author's) intuitions about which alternatives may count as relevant.

A victim of a car accident awakens on the operating table just long enough to glimpse his own exposed brain reflected in the surgeon's mirror. Before he goes under again, he forms the belief (solely on the basis of his visual percepts and background beliefs about what intact brains look like) the belief "my brain is not smashed." His vision if actually fuzzy, though, and his percepts are not strongly related to the actual image in the mirror. We want to deny the patient knowledge in this case. There must, therefore, be a relevant alternative situation in which the brain actually is smashed, but he believes it is not.

I admit that I am more reluctant to allow an alternative in which someone with a smashed brain has beliefs, than I am to allow one which is logically impossible because of some abstruse theorem of arithmetic. Rather than merely letting the impossiblilty stand (as we did in the case of the mistaken mathematician), I tend to tell myself stories about synthetic brains and matter duplicators.

I give this example not so much to pose a problem for my analysis (a correct standard of relevance would presumably tell us which alternative is precluding knowledge here), as to point up the subjective nature of our intuitions: because brains and matter are more familiar entities, I am more disturbed by a biological impossibility than I am by a logical one (which is in some sense even less possible).

Brain Damage

This example is presented to illustrate the need for something like rule (3) above.

I fall on my head, sustaining a minor concussion whose only effect is that I come to believe p: "I have brain damage." Now we certainly want to deny knowledge here: beliefs caused solely by blows to the head are generally not justified. Yet I definitely have true belief, and in every "nearby" conceivable world in which I believe p, p is true, because my believing it is caused by the condition it describes. If we are to deny knowledge here, we must find a relevant world further afield(11).

The first important point is that the situation here is wildly, hideously improbable. It is almost invariably the case that none of one's beliefs are caused solely by knocking one's head on the pavement. Thus in this case the actual world is much further than usual from my rationally expectable worlds. By rule (3), we may then look further from the actual world for our knowledge-precluding alternatives.

There are numerous conceivable worlds, no more improbable than the actual world above, in which I come to believe p, but p is false: sudden encounters with electromagnetic fields, strange drugs, hypnotists practicing their sneak-up-behind-someone-and-make-him-think-he-has-brain-damage techniques, and others my imagination is not currently up to. None of these are eliminated by my reasons for believing p (I have none), and the great difference between the actual world and my rationally expectable worlds makes some of them relevant. Thus I do not know.

Note that the mere fact that something unlikely is going on somewhere in the world is not enough to expand the set of relevant worlds this much; there is invariably some unlikely circumstance around. For rule (3) to operate with this much effect, the peculiarity involved must actually be in the local situation in which we are making knowledge ascriptions.

The Lottery-Testimony Paradox

In speaking of the relevance of alternative situations, I have referred several times to the probability or likelihood of an alternative. Why, it might be asked, not define epistemic relevance solely in terms of the likelihood of worlds, given various information-sets? Aside from difficulties inherent in the concept of likelihood, there is convincing evidence that relevance is not just probability. The following examples are from Harman (1968):

"In the testimony case a person comes to know something when he is told about it by an eyewitness or when he reads about it in the newspaper. In the lottery case, a person fails to know he will lose a fair lottery, even though he reasons as follows: 'Since there are N tickets, the probability of losing is (N-1)/N. This probability is very close to one. Therefore, I shall lose the lottery.' A person can know in the testimony case but not in the lottery case...

For some N, the likelihood that a person will lose the lottery is higher than the likelihood that he witness has told the truth or that the newspaper is right. Our ordinary, natural judgements thus seem almost contradictory."

For some N, the alternative in which you win the lottery is less likely than that in which the testimony is false, and yet the former is relevant while the latter is not. Epistemic relevance, then, must not be simply a matter of likelihood.

In the testimony case, when the testimony is indeed false, there is in an important sense something odd or unusual going on. We would say that newspapers don't usually lie, that eyewitnesses are usually correct. In the lottery case, when the agent wins, we will not say quite the same thing. It is not "People don't usually win lotteries," but rather "S doesn't usually win lotteries." When the newspaper lies, we are in a peculiar or unexpected state of the world in a way that we are not when someone wins a lottery (after all, we knew someone would win). Although the alternatives may be equally likely, there is some sense in which the lying newspaper is odder; a sense which is not captured by the notion of probability.

This sort of consideration also applies to various non-epistemic relevances, and a complete investigation of relevance in general would need some rules to account for it. It is not covered by my rough rules above, because it is very difficult to specify just what is odd in a world where "the Times was wrong" that is not odd in one where "Trudy won the lottery!"

Cognitive Equivalence

"The relation of perceptual equivalence must obviously be relativized to persons (or organisms). The presence of Judy and the presence of Trudy might be perceptual equivalents for Sam, but not for the twins' own mother (to whom the twins look quite different). Similarly, perceptual equivalence must be relativized to times, since perceptual discriminative capacities can be refined or enhanced with training or experience, and can deteriorate with age or disease." (Goldman, 1976)

Goldman's remarks on perceptual equivalence apply equally to our more general relation of cognitive equivalence. Two sets of reasons may be correctly said to be cognitively equivalent only to a given person, at a given time, and, although Goldman does not mention it, relative to a particular belief or set of beliefs.

Take as an example a tourist in Spain, standing at a crossroads trying to determine which route leads back to his lodging. There is a sign at the crossroads indicating the proper direction, but it is in Spanish and our tourist speaks no Spanish. He has studied the sign, but in vain; the hotel's name is there (so he correctly infers that it must be close by), but he has no idea as to the proper route. Relative to a belief about the direction in which the hotel lies, then, the actual appearance of the sign (which says "Hotel Colonar to the left" in Spanish) is cognitively equivalent to the way it would appear if it read "Hotel Colonar to the right." Relative to the belief "The word 'izquierda' appears on that sign," however, the two signs are not cognitively equivalent.

For another tourist (or our original at a later time), in just the same situation, but with a knowledge of Spanish, the sets of reasons are cognitively equivalent for neither belief. The appearance of the sign "Hotel to the right" would either not lead to the same belief as the other, or would lead to it in a different way (e.g. through a superstitious belief that all signs in Spanish about things to the right are misleading).

The relativity of cognitive equivalence does not lead to the sort of complications that that of epistemic relevance does. In evaluating ascriptions of knowledge, we need only look at cognitive equivalence relative to the putative knower, at the instant of putative knowledge, relative to the belief which may be knowledge; we need not concern ourselves with ideal standards or with the psychological state of the individual doing the ascribing. Cognitive equivalence is on the whole a simpler notion than epistemic relevance.

Some Final Notes

Now that our proposed theory of knowledge has been presented in some detail, a brief examination of some implications and side issues is in order.

On Knowing that One Knows

Does "S knows that p" entail "S knows that S knows that p"? In general, no. S may know (under our analysis) q: "That building is a bank," and his knowledge may be based on perfectly valid reasons. In claiming to know that q, however, he may irrationally ignore the validity of his original reasons, and believe that q is a bit of knowledge solely because q is something he believes; S is the sort of person who assumes that all of his beliefs represent knowledge. In this case, S knows q, but merely has true belief that he knows it. It is also possible for S to know p, but to be agnostic on the subject of his knowing; he may never have thought about it.

In the more ordinary case, where the agent has considered the matter, it may be that the entailment holds. First, if I know (and thus believe) that p, I typically come to believe that I believe it by simple introspection. I further come to believe that this belief is a bit of knowledge by considering my reasons for believing it in the first place; if my reasons rule out the proposition's falsehood to within a reasonable doubt, I will conclude that I indeed have knowledge. If, on the other hand, my reasons do not seem that good, I presumably will not(12). We should then examine the case where S knows p, S believes (and would claim to know) that q:"S knows p," and S's belief that q is based on his justified conclusion that his reasons for believing p eliminate to within a reasonable doubt the possibility of its falsehood. In this sort of case, is it always true that S knows that S knows that p?

Even with these further specifications, the answer is not clear. What relevant alternative situation could preclude knowledge that one knows without eliminating knowledge in the first place? I will give one concrete example which suggests that the answer lies in a more thorough investigation of the actual nature of epistemic relevance.

Take the Tom Grabit example above, in which no one hearing Mrs. Grabit's false tesimony believes her. Let us assume that in this case one succeeds is knowing that p: "Tom stole the book," because the alternative in which the world is the way Mrs. Grabit described it is not relevant. If, however, we further assume that there is a relevant alternative in which her testimony, (although false) is generally believed, we may fail to know that we know; in that alternative we have precisely the same reasons for believing that q: "We know that Tom stole the book," and yet (it is at least possible to argue) although we have true belief of p in that case, we do not know. That is to say, there is no relevant alternative in which we have equivalent reasons for believing p, but p is false, but there is a relevant alternative in which we have the same reasons for believing q, but q is false.

This example is by no means unproblematical; whether the gullibility of Mrs. Grabit's audience actually affects our knowledge is open to dispute, as is the possibility that the alternatives above could be relevant in the ways described. If, for instance, relevance of alternatives turns out to be a transitive relation (if situation A is relevant in situation B, and B is relevant in C, then A is relevant in C), the above conditions could not obtain; the alternative which precludes knowledge in the case where Mrs. G. is believed would also be relevant in the case where she is not. It is clear, however, that even under reasonable assumptions about the knower's belief-structures, knowing that p does not trivially imply knowing that one knows it.

Dretske's "Conclusive Reasons"

Fred Dretske's analysis of knowledge (as presented in "Conclusive Reasons") may be outlined as follows:

a) S knows that P on the basis of reasons R entails

b) R would not be the case unless P were the case.

Rephrasing (b) in terms of alternative situations, we seem to get something like:

c) There is no alternative situation in which not P, but R.

Now (c) is obviously too strong; our reasons are almost never absolute guarantees. From the rest of the paper, it appears that Dretske means something like

c') In the alternative most like the actual world except that not P, not R.

where the alternative meant "includes those circumstances prevailing on the occasion [i.e. in the actual world] which are logically and causally independent of the state of affairs" P.

Although at first glance this seems simple enough, it is actually rather difficult to say what circumstances are in the proper sense "dependent" upon which states of affairs. In, for instance, Goldman's barn example, which circumstances are we to hold fixed in the alternative where what Henry sees is not a barn? If, in this case, P is "that object is a barn" and R is "Henry sees something there that looks like a barn," we cannot preserve "that object is not a barn-facade," for this is not independent of P. And yet, if there are no facades anywhere about, we do not want the alternative where the object is a facade to keep Henry from knowing.

Perhaps it is "there are no barn-facades in the county through which Henry drives" that we are to preserve. In that case, if the object had not been a barn, and there were still no facades in that county, then the object would have been a silo, or a house, and Henry would have had cognitively distinct reasons for his beliefs about it. But this also seems unfair; if we may preserve "there are no facades in this county" why not "there are no Q's on this lot"? (where "Q" is whatever the object would have been, were it not a barn.) And this leads to contradiction; in this alternative, the object is neither a barn, nor whatever it would be if it were not a barn.

If we cannot preserve something like these circumstances, then it seems that even if there are no barn-facades anywhere, the situation where Henry sees a facade may count as precluding knowledge at the wrong time. For it is very difficult to see how we can choose our notion of "independence" to deny knowledge when there are many barn-facades in the area, and grant it when there are not.

I mention this analysis because it has the same structure as my proposed one; it requires that in certain worlds in which the proposition believed is false, the believer's evidence reflect that fact. In Dretske's formulation, that world is (in some sense) the nearest one in which the proposition is false. In the current proposal, the worlds in question are those epistemically relevant worlds in which it is false. Both formulations may be roughly expressed by "if it were not that p, it would not have been the case that (I had reasons) r." For Dretske, the antecedent is "if it were not the case that p, and everything else were as unchanged as physically possible..."; for my analysis it is roughly "if it were not the case that p, and other circumstances were not unduly strange..." The latter, I think, more fully captures our responsibilities as knowers. Our evidence must be an accurate indicator, not only in the most similar world where the proposition we believe is false, but in a large set of worlds which, in the appropriate sense, "might have been" the actual world. These are the worlds I call epistemically relevant.

Harman's "Undermining Evidence"

Gilbert Harman's Thought is not primarily concerned with the Gettier problem as such, but it does contain some ideas which are relevant here. One is prevented from knowing, it is suggested, when there is some undermining evidence one does not possess. Harman notes that "undermining" evidence cannot simply be evidence which, were we to come across it, would lead us to stop believing some proposition (if it were, all belief would be undermined); but he does not analyze it any further.

If the current proposed analysis of knowledge is correct, truly undermining evidence is evidence that some particular relevant alternative is (unbeknownst to the believer) in fact relevant. Evidence which only seems to undermine (i.e. which would keep us from believing if we possessed it, but does not keep us from knowing if we do not) is evidence for the relevance of some alternative which is in fact not relevant. In the Tom Grabit example, when Mrs. Grabit is generally believed, it may be that an account of her testimony would be genuinely undermining evidence, because it is evidence for the relevance of the relevant alternative in which what she says is true, and so one does not know. When her pathological lying is generally known, however, the same account of her testimony would not be undermining, because here the alternative whose relevance it suggests is in fact not relevant.

If this presentation is correct, we may usefully characterize truly undermining evidence (historically a thorny concept) in terms of epistemic relevance, which already serves a purpose in the explication of knowledge.

Some Benefits of the Proposal

The current proposal provides an analysis of knowledge, but leaves us with the notion of epistemic relevance as a primitive property of alternatives, defined ostensively at best. I have tried to show above how this sort of relevance might fit into a larger class of philosophically useful relevances, sharing various broad qualities, but varying in fine tuning between different fields of application. While this membership in an interesting class does nothing to directly enlighten the nature of epistemic relevance itself, it does suggest that there may be ways of exploring it besides the trivial one of observing under which circumstances we are willing to grant knowledge.

The notion of epistemic relevance, and its relativity to persons and times, can also account for the proliferation and controversial nature of Gettier examples. Because a developing knower learns how to judge relevance only implicitly, with experience, the judgements of different persons have the highest probability of agreeing only under fairly normal sorts of circumstances, which most people have encountered at one time or another. To find interesting or problematic examples on which to test various theories of knowledge, it is necessary to go beyond the bounds of the usual, into those areas where our ideas of relevance are as yet largely unformed. And in such odd circumstances, it is not surprising that judgements of relevance, and thus of knowledge, sometimes differ.

Even as an unanalyzed property, the way that epistemic relevance functions can cast some light on the way that knowledge operates within a community of believers and actors. Although this is not the place for it, with a better understanding of relevances in general, the responsibilities of a knower (or a moral agent, or an actor) could be more fully examined; which possibilities the individual is obliged to take into account to remain in good standing, how much investigation one is obliged to do before forming various opinions, and pehaps even how the community's expectations differ according to the role of the agent, all seem to be questions which are much more accessible if we can phrase them in terms of relevance, instead of unanalyzed knowledge.

Influences on Epistemic Relevance

We have seen some of the factors that probably influence epistemic relevance; I will here offer some speculations as to why these factors function as they do. A good standard of relevance tends to maximize the number of true propositions counted as knowledge, and minimize the number (or perhaps the importance) of false ones thought to be knowledge. Any element of a standard should somehow contribute to these ends.

The relevance of alternatives similar to the agent's rationally expectable alternatives is obviously desirable; if the agent's reasons do not even guarantee the truth of his beliefs in circumstances very like those he expects (or should expect) to hold, his belief (even if true) is not justified, and we do not want to label such irresponsibly formed beliefs as knowledge.

As the intuitive appeal of the traditional analysis suggests, the roles of the other rules of epistemic relevance are less obvious. The rule granting relevance to a neighborhood of the actual world has the result that, as well as being responsible as regards situations of which he is aware, the agent must, if he is to have knowledge, also be correct about situations of which he is not aware. The prima facie unlikely circumstance that the secretary misinformed Smith keeps him from knowing, despite the fact that, given only the information available to him, he was justified in ignoring the (non-zero) possibility of that occurrence. What does this imply for the long-term behavior of knowledge-ascriptions employing this rule? In general, one will not tend to claim knowledge for one's beliefs unless one is relatively sure that no important ends are loose: the more information one gathers, the closer one's rationally expectable alternatives cluster around the actual state of affairs, and the less likely it is that some belief, although justified, will turn out not to be knowledge. This rule, then, discourages the willfully deluded, and denies knowledge to the involuntarily deluded. If, for one reason or another, one's picture of the world is particularly distorted, one's beliefs may be justified relative to that picture, but they may still fail to be knowledge, because of the requirement that one's evidence function correctly around the real world as well.

These two rules are the most important determiners of relevance that I have mentioned; the others serve similar but more restricted purposes. We generally want people in environments where strange things happen to be more careful of their evidence, hence rule three, "The farther the agent's rationally expectable alternatives are from the real world, the larger these neighborhoods become." In particular, when the world is odd in some specific way, we want believers to be especially careful about evidence which involves that peculiarity; hence rule four.

The function of rule five ("The testimony and beliefs of persons in the actual world has some effect on the relevance of worlds which they claim or believe to be the actual one") is still less obvious, and indeed there seem to be differing opinions in the literature as to whether or not it actually holds. The motivation for including it, however, is probably something like this: if the community, or some significant part of it, has a particular belief, there is usually some evidence for it. And unless our reasons for belief are sufficient in every alternative for which there is good evidence, we are in danger of error, and should not be granted knowledge.

Conclusion

A theory of knowledge is only as good as the phenomena it illuminates, and the interesting questions it can raise. I have tried to show that the proposed theory accounts for the way we ascribe knowledge both in ordinary circumstances where the judgement is relatively uncontroversial, and in stranger Gettierized cases, where there may be either uncertainty or significant disagreement.

To accomplish this end, the concept of epistemic relevance was necessary. It may well be that this raises more questions than it answers, but I doubt that this is a fault of the theory. If the new questions prove interesting and productive in the solving, then they were in an important sense there all along. And if the introduction of relevance as an epistemological notion brought the questions to our attention, the same notion will most likely be important in answering them. Outside of knowledge-ascription, the other sorts of relevance suggested in this paper might well prove useful in their respective fields, if anyone were to examine them closely.

I hope that this paper represents one more move in the direction that Goldman set for his original theory, to "lay a foundation for a general theory of knowing." With knowledge explained in terms of relevance, and thus tied to other endeavors of cognitive society, it may be easier to take the next steps, whatever they prove to be.

Bibliography