Hauptli's Introduction to Epistemology Lecture Supplement

Epistemology is the theory of, or study of knowledge. Amongst its most central topics are:

Epistemologists (and philosophers generally) are usually concerned with what is called propositional knowledge—knowledge claims which may be expressed by affirming a proposition (a sentence capable of being either true or false—note that not all sentences are propositions: questions and commands, for example, don’t make assertions). It is important to note that there are other sorts of knowledge, and epistemologists usually distinguish two fundamental kinds of non-propositional knowledge:

knowledge by acquaintance (e.g., knowing your Uncle Fred, French, your migraine headaches, your best friend, etc.); and

know-how (sometimes called “competence” knowledge or “procedural” knowledge—e.g., knowing how to ride a bike, to amend a motion, to play a piano, to sail, etc.).

In his Problems of Knowledge: A Critical Introduction to Epistemology, Michael Williams does an excellent job of distinguishing propositional knowledge from acquaintance or familiarity, and practical know-how.[1] In this regard, his contextualism provides a valuable corrective to the tendency to draw hard-and-fast lines here:

for a contextualist, there cannot be a sharp distinction between knowing-that and knowing-how because being able to make judgements—the precondition of any knowing-that—involves know-how essentially. This is why propositional knowledge and certain kinds of know-how are acquired together. Propositional knowledge is not self-contained: not because it rests on some pre-propositional knowledge-by-acquaintance, but because it is embedded in the practical mastery of forms of discourse and inquiry.[2]

knowing-why (having an explanation as to why some thing, event, etc., came about—e.g., knowing why you must go to bead without supper). Of course, quite often, such knowledge may be fully propositional (scientific explanations, for example), and at other times it may be “acquaintance knowledge” (acquaintance with the rules of the house-hold), but it seems to me that it is sometimes neither of these, nor is it a species of know-how.

Moreover, given the talk of some educators, there may be another sort of knowledge called knowing-how-to-learn (or know).

In the above citation, Williams is evoking Ludwig Wittgenstein’s contention that philosophers can come to confuse propositional knowledge with the other forms. Wittgenstein recommends that we compare knowing

how many feet high Mount Blanc is,
how the word ‘game’ is used,
how a clarinet sounds.
If you are surprised that one can know something and not be able to say it, you are perhaps thinking of a case like the first. Certainly not one like the third.[3]

Wittgenstein is drawing our attention to the fact that following Plato many epistemologists presume that all knowledge is propositional, and our ordinary concept is not well-captured by this presumption. In a similar vein, in his Return To Reason, Stephen Toulmin maintains that:

I have distinguished here the conceptual grasp of a theory; the techniques we master as ways of dealing with practical problems; and the private perceptiveness needed to put such techniques to use in a variety of situations. Aristotle liked to insist that all these different kinds of knowledge—episteme, techne, and phronesis[4]—were orchestrated by the broader wisdom he called sophia. Yet they all take for granted a certain articulateness, and thus ignore the special skills of those who master their crafts to good effect without saying much about them.[5]

Like Wittgenstein, Toulmin wants to remind us that there are many types of knowledge, and warn us that an over-emphasis upon one kind may lead to a false conception of what knowledge is.

In his “The Pragmatic Dimension of Knowledge,” Fred Dretske contends that propositional knowledge is not a matter of degree, while knowledge by acquaintance (for example, “knowing Boston” or “knowing Russian”) may be susceptible to differences in degree.[6] We need to recognize, then, that saying that epistemology is concerned with propositional knowledge, means that discussion of the first core epistemic question, “What is knowledge?”, as it is traditionally asked, rests on a premise—that there is a single uniform nature of knowledge. This appears clearly fallacious!

That is, one should not automatically assume that “knowledge” is a “natural kind” but, rather, note that it may be a “nominal” one—that a “unitary analysis” may not be the right way to go.[7] Later in the course, we will have more to say about this, but, at least at first, simplifying assumptions may be not only helpful, but necessary.

On the other hand, we should not instantly conclude that the different sorts here belie an underlying unity. In his Experience and Nature, for example, John Dewey maintains that:

the difference between acquaintance and “knowing about” or “knowing that” is genuine, but is not a difference between two kinds of knowledge, one immediate and the other mediate. The difference is an affair of accompaniments, contexts, and modes of response. The greater intimacy and directness that marks acquaintance is practical and emotional not logical. To be acquainted with anything is to have the kind of expectancy of its consequences which constitutes an immediate readiness to act, an adequate preparatory adjustment to whatever the thing in question may do. To know about it is to have a kind of knowledge which does not pass into direct response until some further term has been supplied.[8]

Whatever conclusion one reaches regarding the “types of knowledge,” in this sense of the distinction, since propositional knowledge is distinct from belief (there are, after all, lots of statements which we claim to believe but would not claim to know), and since knowledge claims are distinct from truths (there are lots of truths which are not known), discussions of epistemology also find themselves strongly focused upon the concepts of truth and justification—both seem central to distinguishing between statements of belief and genuine propositional knowledge claims.

Skepticism is the philosophical orientation which holds that there is little or nothing for epistemologists to study. Many contemporary epistemologists treat skepticism as a position which no one really adheres to—it is often considered only as vehicle for raising challenges to our knowledge and justificatory claims, rather than as a viable position in its own right. In ancient philosophy (that is in Greek and Roman philosophy from about 400 B.C.E. to 200 C.E.), there were two distinct sorts of skepticism which were recognized—and they were actual philosophical positions (indeed “schools”), championed by real individuals: Academic skepticism and Pyrrhonian skepticism. As Louis Pojman notes, the former

...builds on Socrates’ confession in the Apology, “All that I know is that I know nothing.” It argues that the only thing we can know is that we know nothing. The Academics argued that there is no criterion by which we can distinguish veridical perceptions from illusions and that at best we have only probable true belief.[10]

The Pyrrhonians rejected Academic skepticism and dogmatism, the view that we could have knowledge, and set forth “tropes,” skeptical arguments leading to equipollence: the balancing of reason on both sides of an issue that led to epoche, or the suspension of judgment. Whereas the Academics claimed to know one thing (that they didn’t have any other knowledge), the Pyrrhonians denied that we could know even that. The Greek Pyrrhonist, Sextus Empiricus (second century C.E.), said that Pyrrhonism was like a purge [laxative] that eliminates everything, including itself—of course, he also held, this treatment left the patient in good health (the search for unattainable knowledge (that is any knowledge) was conceived by these skeptics as an illness.[11]

Traditionally, skeptics hold that once you make our traditional distinction between belief and knowledge, it turns out that there are no cases (or only one case) of the latter. As I noted, few epistemologists take a skeptical position, however. Instead, for most epistemologists, skepticism expresses the epistemologists’ conscience—it helps ensure that we will not accept a pale substitute where we seek claims which, truly, are knowledge!

The challenge posed by skepticism is at the core of the epistemological enterprise. One thing which seems to separate us from the other creatures is our rational ability—indeed, some characterize us as rational animals (though they must be considering an ideal group of human beings—our actual practice requires that we accept, at best, that we are partially rational). It is usually held that rationality is an advantage—it aids us in discovering what our world is like and allows us to survive, prosper, and, perhaps, attain the good life. Let’s consider this ability a moment—what justifies our reliance upon (and our praise of) our (alleged) rationality?

One model of rational procedure consists of equating it to mathematics—we engage in deductive argumentation. There are two problems which the skeptic may point to right away. First, there is always the possibility that in endeavoring to provide a deductive justificatory argument one will fall prey to a logical error. Secondly, all such argumentation proceeds by drawing consequences from premises. The skeptic simply asks: “Where do these get their authority?” Note that each of the available alternative answers to this question seems to leave us with a problem:

a priori, or self-evident truths (or innate knowledge, or intuition)—the actual claims which various philosophers claim have such status do not garner anything like universal agreement. Moreover, it sometimes appears that the claims selected for such a special status are arbitrarily selected.

Another model of rational procedure consists of equating it to science. On this model, we engage in inductive argumentation—we learn from experience. Again there are two problems which the skeptic may point to in trying to show that our beliefs lack inductive justification. First, as was the case with deductive argumentation, there is the possibility that one makes a mistake in our reasoning. Secondly, since all such arguments appeal to the senses (or, more generally, to human experience), and since we dream, there is a serious question as to whether we will be able to offer empirical justifications for our claims—dream reports do not provide the requisite intersubjective justification so that we may have clear arguments; and it is difficult to point to distinguishing marks between awakened and dreaming experience.

Now, if we don’t have secure deductive or inductive premises from which we may reason, what can reason establish? We seem lead to skepticism! The skeptic, then, seems to show us that the usual distinction between knowledge and belief is not well-drawn, and that we need to clarify our underlying conceptual scheme. The “enduring problem” here is our fallibility. In the first part of this course we will more carefully examine the skeptical challenge.

Another important distinction regarding skepticism may be that between the Pyrrhonian skepticism and the more modern (“Cartesian”) variety. In his “Scepticism,” Peter Klein maintains that:

assuming that knowledge is some form of sufficiently warranted true belief, it is the warrant condition, as opposed to the truth or belief condition, that provides the grist for the sceptic’s mill. The Pyrrhonists will suggest that no non-evident, empirical proposition is sufficiently warranted. A Cartesian sceptic will argue that no empirical proposition about anything other than one’s own mind and its contents is sufficiently warranted because there are always legitimate grounds for doubting it. Thus, an essential difference between the two views concerns the stringency of the requirements for a belief’s being sufficiently warranted to count as knowledge. A Cartesian requires certainty. A Pyrrhonist merely requires that the proposition be more warranted than its negation.[12]

In his Pyrrhonian Reflections On Knowledge and Justification, Robert Fogelin distinguishes these views saying that:

...Cartesian skepticism seems to rely on an antecedent philosophical commitment to the way of ideas—a commitment that a Pyrrhonian skeptic would not make. To the Pyrrhonist, the Cartesian-style skeptic is not skeptical enough. More to the point, it does not take radical—globally dislocating—scenarios to introduce suspension of belief. It is quite sufficient to note—and dwell on—the fact that our empirical claims are made in the face of unchecked, though checkable, defeators. This is an important point to make, because it may be possible to bring forth arguments showing that skepticism based on skeptical scenarios is conceptually incoherent.....The skeptical problems raised by checkable but unchecked defeators cannot be dealt with in a parallel fashion.....Dwelling on uneliminated defeators can produce skeptical doubts no less strong than those produced by skeptical scenarios. If anything, the situation is worse with uneliminated but eliminable defeators. With respect to them, no transcendental style of argument will work; the only way to eliminate these defeators is actually to eliminate them. The recognition that we make knowledge claims without doing so gives one as robust a skeptical challenge as one would like.

It is the fragility of our common epistemic practices that leads philosophers into justificational programs....Justificationalism in both its foundationalist and nonfoundationalist modes is an attempt to secure a suitably wide range of knowledge against skeptical challenges. But, as we have seen, such justificatory programs inevitably raise the Agrippa problem....no justificatory program seems to show any prospect of solving the Agrippa problem....We have thus arrived at the following result: Reflection on our ordinary epistemic practices reveals their fragility, and when we turn to epistemologists for help, we are disappointed.[13]

In the background here we can, perhaps, distinguish four core “arguments for skepticism:” (a) the appearance/reality distinction, (b) the problem of the criterion, (c) the regress problem, and (d) the problem of the nature of “adequate” justification.”

In his Theaetetus, Plato gives the example of a jury which rightly convicts an individual of a crime although the jury lacks sufficient evidence. Though they have true belief, they lack knowledge. This leads to the “Justified True Belief” [JTB] Thesis at 201d.[14] This traditional analysis of the nature of [propositional] knowledge came under intense critical scrutiny in the last half of the Twentieth Century. In 1963, Edmund Gettier’s “Is Justified True Belief Knowledge?” showed that this traditional analysis was insufficient.[15] In his “The Analysis of Knowledge,” Jack Crumley maintains that:

the traditional analysis does not place any restrictions on how the truth and justification conditions...are satisfied. More precisely, the truth and justification conditions can be satisfied independently of one another. The reasons why the belief is justified might have nothing to do with why the belief is true.[16]

We will examine Gettier’s argument, and several responses to it in the second part of the course. We will see that it is not easy to specify what, exactly, the nature of propositional knowledge is!

The skeptical challenge and the Gettier problem have led many contemporary epistemologists to an intense study of justification, and this study will occupy us during the third (and longest) part of the course. Of course there are other forms of justification than those relevant to epistemology: moral justification, legal justification, business justification, theological justification, etc.

Epistemic justification can’t simply be thought of as justification dealing with beliefs: for example, there could be a “moral” justification for some beliefs (e.g., the belief that one should stand up for one’s friend); there could be a “religious” justification for some beliefs (e.g., Pascal’s wager). Epistemic justification is centrally concerned with (or tied to) the “non-accidental truth” of our beliefs. In the third part of the course we will get an overview of the problems which arise as one attempts to provide an account of epistemic justification by engaging in a study of one contemporary account—Lawrence BonJour’s The Structure of Empirical Knowledge. In the process of studying his account of empirical knowledge and its justification, we will come to understand the challenges which arise for most of the contemporary positions.

In his Problems of Knowledge: A Critical Introduction to Epistemology, Michael Williams maintains that:

more generally, ‘know’ is a ‘success-term’ like ‘win’ or ‘pass’ (a test). Knowing is not just a factual state or condition but a particular normative status. Such statuses are related to appropriate factual states: winning depends on crossing the line before any other competitor. But they also depend on meeting certain norms or standards which define, not what you do do, but what you must or ought to do. To characterize someone’s claim as expressing or not expressing knowledge is to pass judgement on it. Epistemic judgements are thus a particular kind of value-judgement.[17]

Williams’ point here is important for us because the normative aspect of epistemology has been an important element in its concern with justification (and in its response to the other central problems to be addressed). While many theorists emphasize the connection between justification and truth in order to talk about knowledge, Williams also places emphasis upon understanding:

In Plato’s ideal republic, the members of the military caste do not have knowledge, only true belief. But if justification can supervene on a belief’s deriving from a reliable source, they have justified true belief. After all, they are educated by the philosopher-kings, who know everything there is to know. So why do the soldiers not have knowledge? Because the kind of justification they possess has no connection with understanding.[19]

It should be noted, however, that all this talk of justification at the center of epistemology falls on deaf ears in the case of those who follow the views of the Austrian/English 20th century philosopher Karl Popper. In his Teachers Without Goals: Students Without Purposes, Henry Perkinson maintains that:

the antidote to authoritarianism is fallibilism—the acceptance of human fallibility. If human beings accept their fallibility, then they will realize that they can never have perfect knowledge.[20]

If knowledge does grow through trial-and-error elimination, then attempts to justify knowledge, to strengthen commitment to it—as the progressive educators attempt to do—will actually hinder or curtail the growth of knowledge. Nevertheless, the notion that teachers should insist that students accept only justified knowledge is deeply implanted in educational thought.[21]

We will not be studying Popper’s epistemic theory, nor can we discuss all the varied orientations which philosophers have offered on the questions noted above.

Epistemologists are also concerned with the question of how extensive our knowledge is—what are the broad areas of knowledge (or, what are the broad sorts of [propositional] knowledge which we can have)? Clearly there is some sort of difference between the knowledge we have in calculus and that which we have in geology. In their Contemporary Theories of Knowledge, John Pollock and Joseph Cruz maintain that there are six “areas” of knowledge in epistemology:”

the problem of perception is that of explaining how perceptual knowledge is possible.[22]

In contrast to perceptual knowledge, even the very basic psychological facts about other areas of knowledge tend to be obscure. It is clear that [i] sense perception is the source of perceptual knowledge, but for some areas of knowledge the source is quite mysterious. [ii] A priori knowledge comprises one of the most problematic areas. A priori knowledge is usually defined as “what is known independently of experience”, or perhaps as “what is known on the basis of reason alone”. But it must be acknowledged that these are not very helpful definitions and they should not be taken too seriously. Rather, we recognize that there is a certain class of knowledge that seems importantly different from other kinds of knowledge....[23]

A priori knowledge is not the only area in which the psychological facts are obscure. Moral knowledge is at least a problematic. There is not even a consensus that moral knowledge exists. Although some moral philosophers are convinced that there is such a thing as [iii] moral knowledge, at least as many are adamant that there is not.[24]

Pollock and Cruz also list the problems of [iv] other minds, [v] memory, and [vi] induction as other areas. As we pursue the readings in this course, we will have to look at the different sorts of knowledge which we might have.

As our inquiries progress, we should attend to the diversity of the sources of knowledge which include at least the following as clear contenders:

It will be helpful, at this early stage, to note a number of distinctions which will become important for us as we proceed. I will not try to offer definitive characterizations of the alternative orientations in each case, but, instead, want to provide an introductory overview at this stage. As the discussion demonstrates, these distinctions are interrelated in a complex manner. As we begin to employ these distinctions, we will come to seen the need for yet more careful distinctions in each case. An excellent secondary source which is well worth consulting in regard to these distinctions (and is very useful generally for this course) is A Companion to Epistemology, ed. Jonathan Dancy and Ernest Sosa.[25]

Rationalists hold that some (or all) of our knowledge must be a priori,[26] while empiricists hold that our knowledge (most, or all, of it) depends upon our contingent experiences. As I have distinguished the positions, they represent not so much contradictory orientations as differing areas of a broad spectrum.

The distinction is an epistemological one—between propositions (or knowledge claims) whose justifications depend upon evidence derived from sensory experience and those which do not depend upon such evidence. As long as a non-empirical procedure of validation exists, we are said to be confronted with an a priori proposition.

In his In Defense of Pure Reason, BonJour distinguishes what he calls the negative conception of a priori justification (justification independent of appeal to experience) from the positive conception of a priori justification (appeal to reason or “pure thought” alone).[27] Neither sort of characterization, however, is without problems.

It is worth noting that this distinction may not offer an exhaustive breakdown of the class of propositions. Consider what J.W.N. Watkins and Karl Popper call “all and some propositions” (others refer to them as “doubly general” propositions): like (x)($y)Fxy (e.g.: every event has a cause)—they are unverifiable (because universal) and unfalsifiable (because existential). Warnock says such propositions are vacuous (because unfalsifiable). Kant holds that such propositions (or at least this one) are necessary. Note that it does not seem that such propositions can be known a posteriori! But can they be known at all? D.W. Hamlyn maintains that “such propositions certainly could not be known a posteriori; if true, they must be known a priori if they are to be known at all. The difficulty is just this—how are they to be known at all? Thus, it may be better to distinguish between a priori propositions and non-empirical propositions of this kind. A priori propositions are those which can be known to be true and whose truth is ascertainable by a procedure that makes no reference to experience; non-empirical propositions of the kind in question are not like this, for their truth is, strictly speaking, not ascertainable at all. If we accept them, it must be as mere postulates or as principles whose force is regulative in some sense.”[28]

Lawrence BonJour maintains that the distinction between the a priori and the a posteriori is an epistemological distinction regarding the way in which a claim is justified; while the distinction between the necessary and the contingent is a metaphysical distinction regarding the status of a proposition in relation to the ways the world might have been.[29] Necessary truths, it is held, are those which must be true—their opposites are contradictions (and, hence, impossible). Contingent propositions, then, are those whose opposites are not contradiction and, therefore, are possible.

Here we should consider whether all a priori propositions necessarily true. Phillip Kitcher maintains that “frequently...it is maintained that only necessary truths can be known a priori. Behind this contention stands a popular argument. Assume that a person knows a priori that p. His knowledge is independent of his experience. Hence he can know that p without any information about the kind of world he inhabits. So, necessarily p.”[30] Kitcher maintains, however, that “...there are propositions which could not both be false and also be believed by us in particular, definite ways. Obvious examples are propositions about ourselves and their logical consequences: such propositions as those expressed by tokens of the sentences “I exist,” “I have some beliefs,” “There are thoughts,” and so forth. Hence the...[argument above]...breaks down and...[we must allow] for the possibility of a priori knowledge of some contingent propositions.”[31] Consider, also, the “doubly general” propositions mentioned above.

The distinction between analytic and synthetic propositions is best made in terms of an alleged connection between meaning and truth: analytic propositions are supposed to be such that when one understands their meaning, one sees that they must be true. Frege puts this in terms of “identity”—analytic propositions are either simple identity statements or are “transformable” into such by substitution of “synonyms for synonyms.” Note that the way this is phrased is important—we can not simply say that the “analytic” is a function of meaning. We need to appeal to logic (substitution of phrases equivalent in meaning leaves an identity statement), and this raises a question of whether the logical truths are analytic—especially given the question of the meaning of such statements! Frege avoids a problem with a definition of ‘analyticity’ which says that such propositions are logical or transformable into such. Of course, a lot now rides upon “transformable!” Note, also, that it is a mistake to consider analytic propositions as merely “definitional” truths. Definitions are about words and the analytic propositions are taken to be about things: “All bodies are extended things” as an analytic truth is not to be taken as a truth about ‘bodies’ and ‘extended things’ but, rather, about bodies and extended things!

In her “Contextual Implication,” Isabel Hungerland notes that “our ordinary discourse contains quite often sentences of the form p and not-p which we employ and take quite readily in sensible non-standard ways, for example, “It is and it isn’t.””[32] She also notes that “a man caught in the complexities of the divorce laws of California, Nevada, and Mexico, might appropriately be described as a bachelor, but still married.”[33]

Must a priori propositions be analytic? Synthetic a priori truths are supposed to depend for their validation on a priori argument but they can not be given a deductive proof from logical truths. Kant wants this class to include the truths of mathematics (arithmetic and time, geometry and space) and the presuppositions of experience and science (every event has a cause, nothing can be red and green all over at the same time and in the same respect, etc.).

The competing theories of truth contend that what truth is either the correspondence of our beliefs (propositions, statements, etc.) with the world (forms, etc.), or that it is the coherence of our beliefs (propositions, statements, etc.) with one another.

The competing theories of justification hold that what justification lies in the nature of either the connection of our beliefs (propositions, statements, etc.) with the world, or that in the coherence of our beliefs with one another.

The distinction between necessary and sufficient conditions may be made in a number of ways. Necessary conditions may be described as “those which must be there for an event to occur” (thus paying your parking fines is necessary for graduation), while sufficient conditions are conditions such that the event must occur (thus a direct double shotgun blast to the head is sufficient for death). Note that conditions may be sufficient without being necessary (as in the example), and that necessary conditions need not be sufficient (as in the example). An alternate way of drawing the distinction is to say that “p is a necessary condition for q” means “if q is true, then p is true” (symbolically q®p), while “p is a sufficient condition for q” means “if p is true, then q is true” (symbolically: p®q).

Notes: (click on note number to return to text for that note)

[1] Michael Williams Problems of Knowledge: A Critical Introduction to Epistemology (N.Y.: Oxford U.P., 2001), p. 15.

[2] Ibid., p. 166.

[3] Ludwig Wittgenstein, Philosophical Investigations, trans. G.E.M. Anscome (N.Y.: Macmillan, 1953), I 58.

[4] That is, “judgment,” or “wise and virtuous thinking.”

[5] Stephen Toulmin, Return To Reason (Cambridge: Harvard U.P., 2001), p. 179.

[6] Cf. Fred Dretske, “The Pragmatic Dimension of Knowledge,” Philosophical Studies v. 40 (1981), pp. 363-378, esp. p. 363.

[7] As philosophers use the term generally, a “natural kind” would be a type of thing which is capable of being correctly and concisely characterized, where as a “nominal kind” would be the sort of thing which is not so characterizable. Gold, for example, is generally taken to be such a kind—it has a unique physical/chemical characterization and “things” are generally clearly golden or not. It is not clear that “American” can designate a natural kind (and if you think that it is, recognize that the first question might be how many continents you are considering, and how many countries if you are considering only one. Philosophical questions abound here, but the one in the foreground is, clearly, whether “knowledge” is a natural kind. By the way, philosophers use single quotes to surround a word when they are mentioning it rather than using it. For example, in the sentence "`Long' is a short word," the word `long' is mentioned (discussed) while the word `short' is used!

[8] John Dewey, Experience and Nature [1929] (N.Y.: Dover, 1958), pp. 329-330.

[9] There are two spellings (‘skeptic’ and ‘sceptic’), but they do not distinguish different positions.

[10] Louis Pojman, “Skepticism,” in The Theory of Knowledge: Classical and Contemporary Readings (third edition), ed. Louis Pojman (Belmont: Wadsworth, 2003), pp. 19-21, p. 19. Emphasis is added to the passage.

[11] Ibid., pp. 19-20

[12] Peter Klein, “Scepticism,” in A Companion to Epistemology, eds. Jonathan Dancy and Ernest Sosa (Oxford: Blackwell, 1992), pp. 457-458, p. 457. Emphasis added to the passage twice.

[13] Robert Fogelin, Pyrrhonistic Reflections On Knowledge and Justification (N.Y.: Oxford U.P., 1994), pp. 192-193.

[14] Cf., Plato’s Theory of Knowledge: Theaetetus and Sophist, trans. Francis M. Cornford (Indianapolis: Bobbs-Merrill, 1957).

[15] Cf., Edmund Gettier, “Is Justified True Belief Knowledge?” Analysis v. 23 (1963), pp. 121-123.

[16] Jack Crumley, “The Analysis of Knowledge,” in Readings in Epistemology, ed. Jack Crumley (Mountain View: Mayfield, 1999), pp. 128-130, p. 129.

[17] Michael Williams, Problems of Knowledge: A Critical Introduction to Epistemology, op. cit., p. 11.

[18] Ibid., p. 42.

[19] Ibid., p. 43.

[20] Henry Perkinson, Teachers Without Goals: Students Without Purposes (N.Y.: McGraw-Hill, 1993), p. 41.

[21] Ibid., p. 46.

[22] John Pollock and Joseph Cruz, Contemporary Theories of Knowledge (second edition) (Lanham: Rowman & Littlefield, 1999), p. 15.

[23] Ibid., p. 16.

[24] Ibid., p. 17.

[25] A Companion to Epistemology, ed. Jonathan Dancy and Ernest Sosa (Oxford: Basil Blackwell, 1992).

[26] Rationalists also, importantly, hold that our knowledge should be organized in a deductive, or axiomatic, system of truths whose most basic truths are self-evident and certain.

[27] Cf., Laurence BonJour, In Defense of Pure Reason: A Rationalist Account of A Priori Justification (Cambridge: Cambridge U.P., 1998), p. 7.

[28] D.W. Hamlyn, “A Priori and A Posteriori,” The Encyclopedia of Philosophy, ed. Paul Edwards (N.Y.: Macmillan, 1967) v. 1, p. 142.

[29] Cf., Laurence BonJour, In Defense of Pure Reason, op. cit., p. 11.

[30] Phillip Kitcher, “A Priori Knowledge” in Naturalizing Epistemology, ed. Hilary Kornblith (Bradford Books: New York, 1985), p. 139.

[31] Ibid.

[32] Isabel Hungerland, “Contextual Implication,” Inquiry v. 4 (1960), pp. 211-258, p. 214.

[33] Ibid., p. 232.