Introduction to Theory of Knowledge

UC Davis Philosophy 102

Theory of Knowledge

Spring, 2014

Instructor: G. J. Mattey, Senior Lecturer

Version 2.6.1, April 9, 2015


The subject of this course is what has come to be called “theory of knowledge” or “epistemology.” The two names are interchangeable in common use. (A similar pair of terms for philosophical disciplines is ‘theory of value’ (or ‘value theory’) and the little-used ‘axiology.’) Until the nineteenth century, there had been no special term to indicate the study of knowledge as such, even though knowledge had been studied from the very beginning of Western philosophy. The word “epistemology” was coined by James Ferrier in his 1856 book Institutes of Metaphysics. The root word ‘episteme’ in Greek means ‘knowledge,’ while the ‘-ology’ suffix signifies, roughly, ‘study of.’ Similar constructions are ‘biology’ (study of life), ‘geology’ (study of the earth), etc. Shortly after Ferrier, Eduard Zeller in 1862 introduced the German word ‘Erkenntnistheorie’ in Ueber Aufgabe und Bedeutung der Erkenntnistheorie. This word is translated into English as ‘theory of knowledge.’

Theory of Knowledge Today

All the great philosohers in the Western tradition (e.g. Plato, Aristotle, Descartes, Hume, and Kant) were deeply engaged in epistemology. In modern Anglo-American universities, theory of knowledge is considered to be one of the “core” sub-disciplines of philosophy. It is frequently linked to metaphysics, the general study of reality, as a component of the center of philosophy, “M & E” (metaphysics and epistemology). In our own numbering system in the UC Davis philosophy department, Metaphysics is Philosophy 101 and Theory of Knowledge is Philosophy 102. Virtually every philosophy department in the English-speaking world has at least one person who teaches and does research in theory of knowledge.

Each year, numerous articles and a fair number of books on the topic appear in print. Other pieces are posted on Web sites. Papers on the theory of knowledge are given at all meetings of the American Philosophical Assocation, as well as at many general philosophical conferences. There are frequent special conferences on the theory of knowledge, including a major conference offered every year at Rutgers University, which is one of the leading departments in the field. A blog devoted to epistemology was established in 2004. Another blog hosted by Duncan Pritchard at the University of Sterling is centered on epistemic value.

The Projects of Epistemology

There are many distinguishable projects that make up the study of knowledge. These projects overlap with one another in various ways, as we will see throughout the course. There are at least seven projects which comprise the heartland of epistemology.

Each of these projects will be described briefly in this introduction. First, however, we would do well to consider what it is that knows (or can know) and what it is that is known (or can be known).

The Epistemic Subject

It seems that all knowledge must be attributed to something that knows, which we will call an “epistemic subject.” What this subject might be is a matter of great controversy. Knowledge has been attributed to human beings, gods, animals, computers, and probably other things as well. Some epistemologists think that knowledge is confined to a relatively small class of beings, perhaps to mature, rational human beings. Others are willing to attribute knowledge to a broad class of beings. It is also common to consider knowledge on the part of groups of people or of other beings.

There is pretty general agreement that any knowing subject must be capable of somehow representing reality. That is, knowledge is said to be knowledge of what is the case in the world. One way of expressing this is to say that knowing is “intentional,” in the commonly accepted sense that the knower’s knowledge is supposed to be “about” what is the case in the world.

The Object of Knowledge

Just what it is that knowledge is about can be understood in different ways. The kind of knowledge most commonly studied by epistemologists is knowledge that is about states of affairs—ways the world is or might be—and it is generally held that states of affairs are represented by propositions. Consider the state of affairs that there is a ticking clock above my desk. The proposition that there is a ticking clock above my desk represents the state of affairs it describes. (Explicit reference to propositions using English will be made using an italicized phrase beginning with ‘that’ followed by an English sentence.)

Besides states of affairs, knowledge can be about concrete things. I may be said to know my parents, my wife, my car, my golf course, etc. This kind of knowledge gets relatively little treatment by epistemologists. Related forms of knowledge that are not widely examined are “knowing who” or “knowing what.” A very different kind of knowledge is “knowing how” (sometimes called “procedural knowledge”), which has attracted some interest among epistemologists. Here, we shall direct our attention to “knowing that,” which is the subject of most of the epistemological literature.

The Methodological Project

It seems that the study of knowledge ought to be undertaken in an orderly way, but there is widespread disagreement among epistemologists about how to study knowledge. Some of the disagreement is based on differences in their general approaches to philosophical investigation. We shall here call attention to several such differences.

Descriptive versus Normative Approaches

Many philosophers make a fundamental distinction between questions of fact and questions of value. One way of making this distinction is in terms of what is on the one hand, and what is permitted to be or what ought to be, on the other. Here is an example from ethics. It is a question of fact whether a person A has killed person B. But even if it is established that A killed B, there is a further question as to whether it was morally permissible or morally impermissible (or indeed, even morally obligatory) for A to have killed B. In questions of value, it is standard practice to invoke and try to defend the use of standards or norms by which these questions may be judged (hence the use of the word ‘normative’). In the example from ethics, one might argue that inflicting harm on other persons is morally impermissible, that taking the life of another inflicts harm, and therefore that taking the life of another is morally impermissible. The issue for epistemology is whether the study of knowledge is a purely descriptive discipline, a purely normative discipline, or a discipline with both descriptive and normative components.

It is possible to take any of the three positions. A purely descriptive approach would take it that the task of epistemology is to discover and explain the ways in which representations of states of affairs are processed by those systems (living or mechanical) which are capable of processing such representations. To be sure, such processing of representations is subject to rules by which the representations are processed by the system. In itself, this does not make epistemology a normative discipline, because the sole task of the purely descriptive epistemologist would be simply to describe the rules or procedures of the system which uses them, rather than to try to determine whether they are “correct” or “proper.”

A second position would be that the task of epistemology is solely to establish which set or sets of norms are adequate (or perhaps optimal) for knowledge. Potential standards for knowledge differ in how demanding they are. Historically, philosophers (such as Descartes) have set a very high bar for knowledge, making absolute certainty the standard for knowing, and relegating all else to probability. In ordinary life, we tend to set lower standards. For example, it is common to allow that a person can gain knowledge solely on the basis of what someone else has told him or her, despite the uncertainties of testimonial evidence. We can characterize the strength of standards in terms of how strong an epistemic position a subject must be in, in order to know. Then a purely normative approach to epistemology would be concerned with establishing how strong one’s epistemic position must be in order to know. For example, as Plato suggested, one might hold that being an eye-witness puts one into a strong enough epistemic position for knowledge, while merely hearing testimony does not.

At its most abstract level, a purely normative approach would consider rules that apply to any possible knowing being. If the norms are to govern a specific kind of being (for example, adult human beings), some description of the capacities of those beings would have to be given. Then the project would be to study the norms applying to that kind of being.

It seems that either of these two “pure” approaches would leave out much of interest to the student of knowledge. Even if we know how a system processes its representations, we surely would wish to discover whether it is processing the representations well—well enough for knowledge. And even if we are able in a “pure” way to set down a set of norms that are appropriate to knowledge, we surely would want to find out whether and how the norms fare when applied to the relevant epistemic subjects. Historically, most work in epistemology has been of a mixed variety. Unfortunately, there has been little agreement as to the precise nature of the mix.

In early modern philosophy of the seventeenth and eighteenth centuries, epistemologists tended to work with very minimal assumptions about the cognitive powers of human beings. For example, the “British empiricists” Locke, Berkeley and Hume, gave accounts of perceptual knowledge yet explicitly steered clear of describing the physiology of perception. Locke, whose purpose was “to inquire into the original, certainty, and extent of human knowledge,” declined to “trouble [him]self to examine . . . by what motions of our spirits or alterations of our bodies we come to have any sensation by our organs, or any ideas in our understandings” (An Essay Concerning Human Understanding, Introduction, Section 2). Traditional epistemology has tended to follow Locke’s lead and minimize the descriptive element in its treatments of knowledge.

Particularism versus Methodism

A different kind of deep disagreement about how to study knowledge has to do with the starting-point of the investigation. Probably the majority view these days is that we should take as a given datum that people have knowledge and then go on to discover what its characteristics are. This kind of investigation is suggestive of the methodology of the empirical sciences, which try to provide explanations of empirical data. But others think that we must begin with a prior conception of the characteristics knowledge has and then go on to investigate whether or not we have any knowledge. Roderick Chisholm has called the first kind of investigation “particularism” and the second “methodism.” (“The Problem of the Criterion,” The Aquinas Lecture, 1973, reprinted in Chisholm, The Foundations of Knowing, 1982.)

Chisholm recognized that it is not easy to see how this disagreement could be resolved in a principled way (that is, resolved other than by dogmatically asserting that one’s own approach is the correct one). For how, he asked, can we identify items of knowledge unless we already have a prior conception of what knowledge is? This consideration seems to favor methodism. But we can ask as well how we can get a conception of what knowledge is if we have not already determined what items are to count as items of knowledge. Now, particularism seems to have the advantage. Yet to motivate the choice of items that count as knowledge, one would seem to require a prior conception of what knowledge is. This takes us around again to methodism, and we seem to be on a “wheel.”

A particularist might claim that there is a satisfactory way to pick out cases of knowledge without a prior conception of what it is. We can simply observe what people are willing to identify as cases of knowledge. This strategy avoids “the wheel,” but it should be noted that it must deal with the obvious variability in which cases are identified as knowledge by different people, or by the same person in different circumstances. The methodist might also claim that there is some external source for his conception of knowledge. For example, one might cite the ways in which philosophers have traditionally conceived of knowledge. But here again, there is variability that must be accounted for.

Analysis versus Use

In the twentieth century, the study of language has played a much more important role in philosophy than it had before. This has led philosophers to investigate the meaning and use of ‘know’ in language. Once again, there is room for dispute about how to proceed. The most familiar way of approaching the meaning of ‘know’ is to give an analysis of sentences containing the word ‘know.’ The analysis is supposed to express necessary and sufficient conditions for knowing. Generally, the conditions proposed by epistemologists do not contain the word ‘know’ itself, and so it is concluded that if the analysis is successful, knowledge is “reducible” to something more fundamental that is revealed by the analysis.

The analytic approach, which will be discussed in detail in this course, has to some extent fallen out of favor in recent times. A different way of investigating the meaning of ‘know’ is to try to discover the ways in which the word is used by speakers of the language in various contexts. This approach has special appeal to philosophers of language, many of whom have “crossed over” to epistemology in trying to determine the conditions of the use of sentences containing the word ‘know.’ This method of investigation is largely descriptive in nature, since it concerns how users of language actually behave. It may uncover linguistic rules that govern the use of the word, but it does not pronounce on the propriety of usage.

It is apparent that there have been, and still are, fundamental disputes about epistemological method. It is not so clear as to whether these disputes can be resolved satisfactorily. The approach taken here will be to give descriptions of each side, as well as of their strengths and weaknesses (as with the brief discussion above of the “wheel”). If neither side can claim superiority over the other, there may be a temptation to be skeptical about epistemological method.

The Formal Project

A second project can be called “formal,” in that it applies formal techniques to epistemology. In the last couple of decades, this project of the theory of knowledge has come to be known as “formal epistemology.” Perhaps the best-known area of formal epistemology applies probability theory to belief in order to represent it formally. Here, we shall be concerned instead with the use of symbolic logic as a tool for representing ways in which propositions about knowledge (as opposed to the propositions which represent the objects of knowledge) are logically related to one another.

Since the 1950s, philosophers have been developing what has come to be called “epistemic logic.” The most widely-studied type of epistemic logic is based on what is generically called “modal logic.” There are are many systems of modal logic on which to base epistemic logic, and there have correspondingly been different systems of epistemic logic proposed by epistemologists. (Modal logic is also the basis for logics of belief, called “doxastic logics.”) The symbolism of epistemic logic will prove to be useful in representing the analysis of knowledge. And what are called “closure” principles of epistemic logic will figure importantly in some varieties of skepticism.

Representing Knowledge

It will be helpful to have a compact way of symbolizing attributions or denial of knowledge of a state of affairs to a subject. Our symbolization should make reference both to the knowing subject and to the proposition which represents what is said to be known or not known. Accordingly, we will use the variable ‘S’ to stand for a possible knowing or ignorant subject. Propositions will be symbolized with variables such as ‘p’ or ‘q,’ with or without numeric subscripts. Finally, we will use the letter ‘K’ as an “operator,” which forms from a proposition p a new proposition that indicates the relation of knowledge between a subject and p. To represent that a subject S knows that p, we shall place a subscripted ‘s’ after the ‘K’ and before the ‘p.’ Thus we schematically represent S’s knowing that p as:

Since there may be times when a subject knows that p and others when he does not, as for example when we learn, we may add a second subscript, ‘t,’ to indicate that time at which S knows that p. Thus we may write, for S’s knowing that p at time t:
Some epistemologists think that some features of S’s circumstances at t are also relevant to whether S knows that p. (For example, whether S knows that p in a given circumstance c might be thought to depend on how important it is for S’s belief that p to be true in that circumstance.) Since the time at which it exists is a component of any circumstance, we can replace the ‘t’ with a ‘c’ and write:
to indicate that S knows that p in circumstances c (which includes time t at which S is said to know that p).

The symbolism introduced thus far does not enable us to represent S’s lack of knowledge, or ignorance, that p. To do this, we may use a symbol that represents denial or negation, ’~.’ Thus, we can write:

to indicate that S does not know that p in circumstances c. This notation also allows for the representation of knowledge that something, say p, is not the case:
Further useful symbols are ‘∧’ for the “and” of conjunction, ‘∨’ for the “or” of disjunction, and ‘⊃’ for the conditional “if ... then ---.” The left-hand proposition in the conditional is the “antecedent,” and the right-hand proposition is the “consequent.” To represent that S knows in c that p and q, we would write:
Ks,c(p ∧ q).
Parentheses will be used to group symbols to prevent ambiguity. In the present case, the parentheses indicate that the knowledge is of a conjunction. Without the parenthesis, what would be represented is that both S knows in c that p and that q is also the case.
Ks,cp ∧ q.
This symbolism, though perhaps unfamiliar at first, greatly facilitates the representation of principles of logic.

Principles of Implication

Now that we have in place symbolism for representing knowledge, we may turn to its use in epistemic logic. One of the fundamental relations studied by logicians is that of implication between propositions. In the simplest case, we say that a proposition p implies a proposition q. In more complex cases, we say that a set of propositions p1, . . ., pn implies q.

There is a great deal of philosophical dispute about the nature of implication. One way of viewing it is that the relation of implication holds when the truth of a proposition or set of propositions is sufficient for the truth of another proposition. Much of the debate revolves around how to understand sufficiency. For example, if q is true independently of p, should we say that the truth of p is sufficient for the truth of q? If so, then the relation is generally referred to as “material” implication. Another example is the case where it is not possible for p to be true unless q is true, a relation called “strict” implication.

To keep our account of epistemic logic close to the standard way of representing implication in epistemic logic, we shall take an approach that is independent of semantics, that is independent of any notion of truth and falsehood. Instead, we will say that p implies q in case q can be derived from p using purely logical rules. (Note that there is much dispute about which logical rules should be the basis of the derivation relation. Here, we will use the standard “classical” rules of modal logic.) For classical implication we will write:

p turnstile q
to indicate that q follows from p. (The symbol is frequently referred to as the “turnstile,” and it will be called by that name in what follows.)

The limiting case is one in which q follows from “nothing”, so to speak. We say then that q is “provable” on its own and write:

turnstile q.
(Provable propositions are also called “theorems” of the system of logical rules.) An example of a provable proposition is one that has the form:
~(p ∧ ~p),
the so-called “principle of non-contradiction,” that it is provably not the case that both p and not p.

Here are some principles of implication that hold in classical non-modal logic. The first is that the proposition (p ∧ q) implies the proposition p. The principle of logic is sometimes referred to as “Simplification.”

Simplification: (p ∧ q) turnstile p.
For example, the proposition that Davis is in California and California is in the United States implies the proposition that Davis is in California. (Semantically, the basis of the implication is supposed to be that the truth of the former proposition is sufficient for the truth of the latter, and so for the other cases of implication discussed here.)

In the other direction, the set of propositions p, q implies (p ∧ q). This implication conjoins two separate propositions and hence is knowns as Conjunction.

Conjunction: p, q turnstile (p ∧ q).
The pair of proposition, that Davis is in California and that California is in the United States implies the conjunctive proposition that Davis is in California and California is in the United States.

Disjunction works in only one direction. From p, one may infer (p ∨ q), an implication known as “Addition.”

Addition: p turnstile (p ∨ q).
The proposition that Davis is in California implies the proposition that Davis is in California or Bob Dylan wrote ‘Idiot Wind’.

A further principle of implication is that the two propositions, p and (p ⊃ q), together imply the proposition q. We shall call this principle “Detachment.” (It is also known as “modus ponens.”) The consequent q of the conditional p ⊃ q is “detached,” so to speak, from the conditional in the presence of the antecedent p.

Detachment: p, (p ⊃ q) turnstile q.
For example, the propositions that Davis is in California and that if Davis is in California, then Davis is in the United States imply the proposition that Davis is in the United States.

The System K

Thus far, we have looked at examples of implication relations or provable propositions that do not contain the knowledge operator ‘Ks,c.’ In what follows we will develop some features of systems of epistemic logic which do involve that operator. We will begin with the system K, which is very “weak,” relative to other “stronger” systems that are based on K. That is, they employ all of the rules of K but also allow for provable propositions and implications which do not hold in K. Because of this variability in what can be proved, we must attach a subscript to the turnstile to indicate the system at hand.

The first principle of K is that every provable proposition is provably known by any subject in any circumstances. The subject is, so to speak, omniscience with respect to the theorems of logic, and so we can call the principle one of Logical Omniscience.

Logical Omniscience: If turnstileK p, then turnstileK Ks,cp (for any s and c).
(Hereinafter, we will take it as understood that the principles apply to all subjects and all circumstances in which they might find themselves.) The principle of Logical Omniscience is clearly an idealization, in that there are infinitely many provable propositions in S4, so that no actual epistemic subject in no actual circumstance is aware of them all. One way of describing the idealization is to say that epistemic subjects always have “implicit” knowledge of everything that is provable.

A second principle is a form of detachment that is adapted to epistemic logic. This is a kind of “closure” principle, that we will call “Closure Under Detachment.” The principle is that if S knows in c that p and knows in c that if p then q, then s knows in c that q.

Closure Under Detachment: Ks,cp, Ks,c(p ⊃q) turnstileK Ks,cq.
According to Closure under Detachment, my knowing in my present circumstances that Davis is in California and also knowing that if Davis is in California, then Davis is in the United States implies that I know in my present circumstances that Davis is in the United States. Here, there once again is an idealization. It may be that S in c knows that p and S knows that if p then q but has not “detached” the antecedent from the conditional, that is, has not made the inference to q from premises p and if p then q.

Closure Under Detachment is typical of a whole class of closure principles of epistemic logic. Such principles begin with implications in non-epistemic logic and apply them to epistemic logic. For illustration, we will apply closure to the other three kinds of implication described above. Simplification gives us an implication: (p ∧ q) turnstileK Ks,c p. Now affix the knowledge operator to both (p ∧ q) and p. This gives us a specific instance of closure under implication.

Closure Under Simplification: Ks,c(p ∧ q) turnstileK Ks,cp.
Suppose I know in my present circumstances that Davis is in California and California is in the United States. Then one might want to say that this knowledge implies that I know in my present circumstances that Davis is in California (as well as that I know in my present circumstances that California is in the United States). It is not open, so to speak, for me not to know that Davis is in California or for me not to know that California is in the United States, given that I know the conjunction.

Closure Under Simplification, like all other versions of closure, involves an idealization. It may be that S has always thought of p and q together, but never separately, in which case it could be asked whether S really knows the conjuncts individually. The idealization can be seen more clearly in the case in which S knows that p and S knows that q, in the same circumstance. Since by the principle Conjunction p and q together imply (p ∧ q), closure dictates that S thereby knows that (p ∧ q).

Closure Under Conjunction: Ks,cp, Ks,cq turnstileK Ks,c(p ∧ q).
Now perhaps p and q are unrelated propositions that S has never considered in relation to one another. It seems an idealization to say that S knows the conjoined proposition.

Closure under the rule Addition, the principle that p turnstileK (p ∨ q), works in the same way as the other cases:

Closure Under Addition: Ks,cp turnstileK Ks,c(p ∨ q).
This type of closure seems even more of an idealization than is Closure Under Conjunction. Suppose S knows (in some circumstances) that Davis is in California. The proposition that Davis is California implies the proposition that either Davis is in California or Bob Dylan wrote “Idiot Wind.” But if S has never heard of the song “Idiot Wind” (or Bob Dylan, for that matter), do we want to say that S knows that either Davis is in California or Bob Dylan wrote “Idiot Wind?” Perhaps not. If we are inclined not to attribute knowledge, we must give up closure for this specific form of logical implication.

Each of the cases of Closure given above are instances of a more general principle, that of Closure Under Implication.

Closure Under Implication: If p1, . . ., pn turnstileK q, then Ks,cp1, . . . , Ks,cpn turnstileK Ks,cq.
If a set of propositions p1 through pn implies q according to the rules of K, then knowledge of p1 through pn implies knowledge of q. Once again, this principle is best regarded as an idealization, as real epistemic subjects presumably are not aware of all of the infinitely many implications of the system.

Before leaving system K, we will consider briefly an issue regarding Closure Under Detachment. Although the principle itself seems quite plausible, especially as an idealization, epistemologists are deeply divided about its acceptability. This issue will be discussed at length later in the course, but for now an example will do. Suppose that you know that you are looking at your two hands and that if you are looking at your two hands, then you are not asleep. Do you thereby know that you are not asleep? Some would say that you must know this, and others that in fact you do not know this. One reason for the denial of knowledge is that you have had vivid dreams in which you apparently were looking at your hands but were not doing so, and you could not tell at the time that you were deceived. And if you cannot tell whether you are deceived by a dream, you do not know that you have two hands. (A version of this case was originally raised by Descartes in his First Meditation in the seventeenth century.)

One might wonder whether there is a further principle of K which is a modification of Closure Under Detachment, where the conditional whose antecedent is detached may not be known. The principle would look like this:

Ks,cp, (p ⊃q) turnstileK Ks,cq.
The answer (which will not be proved here) is that there is no such implication in K. One may know that p and not know that q even though it is a fact that if p then q. We might say that this principle would require more than merely logical omniscience on the part of the subject, but rather omniscience with respect to matters of fact.

On the other hand, there is a version of this principle that does hold in K, that is, when (p ⊃ q) is itself provable. What gets detached is a strong, logically provable, conditional, so we may call this principle one of Strong Detachment.

Closure Under Strong Detachment: If turnstileK (p ⊃ q), then Ks,cp, (p ⊃q) turnstileK Ks,cq.
The reason this principle holds is that the knowing subject is presumed (by Logical Omniscience) to have knowledge of all provable conditionals. Since both the antecedent and the conditional are known, the consequent is known as well (by the Principle of Detachment). Again we see the idealization embodied in Logical Omniscience and Closure Under Implication that is required to make the system at all plausible.

The System D

A plausible epistemic principle is that S’s knowing in c that p implies that S does not know in c that not-p. The addition of this principle to the system K results in a stronger system D.

D: Ks,cp turnstileD ~Ks,c~p.
Thus, if I know that Davis in California, I do not know that Davis is not in California.

The System T

Another plausible principle, which will be discussed in more detail later, is that S’s knowing in c that p implies that p. ()In semantic terms, the principle states that if proposition p is known, then it is true.)

T: Ks,cp turnstileT p.
If I know that Davis is in California, then Davis is in California. The addition of this principle to system D yields as system generally known as T, though some call it M. Note that the principles generating systems D and T do not seem to be idealizations as much as descriptions of what is required for any subject to have knowledge in any circumstances.

The System S4

A much more controversial principle is that S’s knowing in c that p implies that S knows in c that S knows in c that p. This has come to be known at the “KK” Principle, or sometimes just as “KK.”

S4: Ks,cp turnstileS4 Ks,cKs,cp.
The system resulting from adding KK to T is known as S4. The motivation for the S4 principle is that if one is in a strong enough epistemic position with respect to p, then one is in a strong enough epistemic position to tell that one is in a strong enough epistemic position with respect to p.

The S4 or KK principle has been contested throughout the history of epistemology. It has been asked why the strength of the epistemic position with respect of a state of affairs about the world (for example) must be automatically available to the knower. It seems, for example, that we know many things about which we have not reflected. I might know that the color of my computer is black but never have given the matter a second thought. I might not know how or why it is that I know it: I just know it because I see it. But then can I be said to know, in the same circumstances, and hence without reflection, that I know that my computer is black?

Some systems even stronger than S4 have been suggested as the best systems for the representation of knowledge, but we will end our presentation of the systems here.

A final, and very important, point is that it is not at all clear whether there is a “logic” of the kind of knowledge that ordinary people have. It seems that no matter how “logical” a person is, there are times when he or she does not make use of logic or even thinks illogically, in which case the principles would not apply to him or her. As noted above, one might know that p and that (p ⊃ q), but never have bothered to use detachment to draw the conclusion that q. Worse, one might illogically believe that ~q, in which case it seems wrong to say that one knows that q. This is another reason that most epistemic logicians think that the principles apply only to “idealized” knowers rather than real-world knowers.

The subject of epistemic logic is worthy of a great deal more discussion. It will not be pursued further, except with respect to the questions that arise regarding Closure Under Detachment. For a sophisticated discussion of closure principles in epistemology, see the entry in the Stanford Encyclopedia of Philosophy. A very sophisticated treatment of epistemic logic in general can be found on this Stanford Encyclopedia page.

The Linguistic Project

Investigations into the way in which ‘know’ is used were carried out in the 1940s by the British philosopher J. L. Austin, who was strongly influenced by the Austrian philosopher Ludwig Wittgenstein. Austin was concerned with self-attributions of knowledge, such as when a person utters sentences like, “I know that you will like this wine.” According to Austin (“Other Minds,” 1946), making an attribution of this kind is similar to making a promise. In uttering the words ‘I promise,’ one has created a new reality (so to speak), a commitment to do what one has promised. Similarly, when one utters the words ‘I know,’ one is giving one’s word that what he has said to know is actually the case. The speaker is indicating that he may be held responsible if he turns out to be incorrect.

More recently, much attention has been devoted to the context of knowledge attribution. It has been pointed out by contextualists that different speakers, armed with exactly the same information about a given person, are inclined to differ in their attributions or denials of knowledge. This is taken as a datum to be explained. The contextualist explanation for the difference is to be found in variability of epistemic standards (or the strength of epistemic position required for warrant) based on the context of attribution or denial. It seems that certain contextual factors, such as the practical consequences of being wrong, affect the strength of the epistemic position that people require for attributing knowledge. As will be seen, there is a good deal of disagreement about which contexts are crucial in knowledge attribution and exactly what role the context plays.

The Analytic Project

Thus far, almost nothing has said about what knowledge is, except that it is something that meets some standards or other, or that it requires that the knower be in an epistemic position of some strength or other. Since the beginnings of epistemology in Plato, philosophers who think there is such a thing as knowledge have been inquiring into its nature. As will be seen, it is not easy to determine what knowledge might be (or even whether there might be different kinds of knowledge that must be understood differently from one another).

It is not even clear what one is doing in trying to determine what knowledge is. Most would say that the epistemologist is giving an “analysis” of knowledge. The traditional approach follows Aristotle and consists in attempts to give a definition of knowledge. One might say, inspired by Descartes, that knowledge is belief that is certain and unshakable. Here we specify a “genus,” belief, which is differentiated from other beliefs by its being certain and unable to be dislodged, while other beliefs are uncertain and vulnerable to being given up. F. P. Ramsey in 1929 defined knowledge as belief that is true, certain, and obtained by a reliable process. More recently, Timothy Williamson defines knowledge as a specific kind of non-belief mental state. (This account will be discussed in a later module.)

The standard approach, however, is to attempt to give a set of necessary and sufficient conditions for knowing. One finds this approach turning up in the mid-1950s in the writings of A. J. Ayer (The Problem of Knolwedge, 1956) and Roderick Chisholm (Perceiving: A Philosophical Study, 1957). Edmund Gettier in 1963 criticized what he called the “traditional” analysis of knowledge, which gave rise to myriad attempts at providing necessary and sufficient conditions for knowledge that could withstand the kind of counter-examples he gave to the “traditional” analysis.

According to this approach, if one knows, he must satisfy each of the conditions, and if one satisfies all the conditions, then one does know. We will understand necessary and sufficient conditions in terms of a kind of implication that we will call analytic implication, symbolized the the operator. If A is a necessary condition for B, then B → A, and if A is a sufficient condition for B, then A → B. The kind of implication that is characteristic of an analysis may be stronger than logical implication. That is to say, it may be logically possible but perhaps “conceptually” impossible for what is analyzed to lack one or both of its necessary or sufficient conditions.) Thus, we will use a different symbol to indicate it.

If C is a condition thought to be necessary for S to know that p, we may express this by writing:

Ks,cp → C
Conversely, if C is a condition (perhaps consisting of more than one component) which is thought to be sufficient for S to know that p, we indicate this by:
C → Ks,cp.
We will now begin considering some widely-accepted necessary conditions for knowledge.

Conditions for Knowing

It is generally, though not universally, agreed that in order for any subject to know that p, it must be true that p, or it must be the case that p, or there must be an existing state of affairs represented by the proposition p. This kind of necessary condition was endorsed by Plato, the first philosopher to investigate the conditions for knowing (see Plato’s Theaetetus). But even this condition can be controversial, particularly because there is substantial disagreement about what it is for a proposition to be true. Others dispute the condition itself. These philosophers (and some non-philosophers as well) generally tie knowledge to social practice and consider it primarily in terms of being “authoritative” rather than “true.”

We can symbolize the truth-condition, using ‘T’ as a truth operator, in the following way:

Ks,cp → Tp.
Since it is generally acknowledged that:
Tp → p,
(For example, that it is true that Serena Williams is a famous tennis-player, implies that Serena Williams is a famous tennis-player), we will simply write:
Ks,cp → p.
This condition is captured in epistemic logic by the T principle: Ks,cp turnstileT p.

A second widely-accepted condition for knowledge is that S believe or accept that p. Broadly speaking, the idea is that for S to have knowledge that p, S must in some way be committed to the truth of p. For example, Descartes required that when one knows, one’s conviction must be unshakable. Yet despite the widespread agreement that there must be some kind of strong commitment for there to be knowledge, there is a good deal of disagreement about the exact nature of the commitment that is required for knowledge. One area of dispute concerns the kind of cognitive activity that is required for knowledge. Some hold that one must be committed intellectually to the truth of p, while others hold that that one need only be committed in a way that disposes him to act as if p were true. A person talking on a mobile phone while driving might be too distracted to make an intellectual commitment to the truth of the proposition that there is a car in front of him in his lane. Yet in some way he is really committed to its being there, as evidenced by the fact that he maintains a uniform distance behind that car, etc.

A further complication is the fact that we often conceive of belief as coming in degrees. That is, one may believe more or less strongly that p, and if so, then the degree of belief required for knowledge becomes an issue. Moreover, it also must be asked how it is that the degree of belief is to be measured.

The symbolization of the belief condition can be carried out the same way as with knowledge. We will use the symbol ‘B’ to indicate belief, and we will index this symbol with a reference to the epistemic subject and the circumstances of belief.

Ks,cp → Bs,cp.
We could take the matter one step further and stipulate that in order to know, S must have a belief at least to the degree n. Then we could write:
Ks,cp → Bns,cp.
Although this complication will not be pursued further here, the symbolic notation will be exploited shortly. (Note that the epistemic logic developed earlier would have to be enriched with a ‘B’ operator in order to represent this condition. Such an operator would be subject to its own special rules. For example, it might be based on K and allow the D and S4 implications, but not the implication characteristic of T.)

Although there is pretty broad consensus that S’s knowing that p requires that p be true and that S believe that p, further conditions in the analysis are quite controversial. Since Plato’s Theaetetus, it has been generally accepted that knowledge is more than mere true belief. A belief that is formed on the basis of third-hand gossip might be true, but it seems that this source of information is not good enough, does not put the subject in a strong enough epistemic position, to allow us to attribute knowledge to a person who forms a true belief on the basis of gossip that turns out to be true.

So what must be added to the truth of p and S’s belief that p to yield the result that S knows that p? In most of the literature of contemporary epistemology, it is said that S must be “justified” in believing that p. However, we will here follow Alvin Plantinga and use the term ‘warranted,’ in place of ‘justified,’ so that in order to know that p in circumstances c, S must be warranted in believing that p in those circumstances.

Warrant (as well as belief and justification) comes in degrees. An eye-witness is generally more warranted or justified in belief about what he has seen than is the recipient of testimony. So the condition for knowing must be that there is enough, or sufficient, warrant in order for there to be knowledge. (Be careful not to confuse the notion of sufficient warrant with that of a sufficient condition for knowledge, as sufficient warrant is only understood here as a potential necessary condition for knowledge.)

One approach to describing sufficient warrant is to decide in advance, so to speak, on the degree n of warrant required for knowledge.

Ks,cp → Wns,cp.
We fix a value for the n and then plug it into the analysis, which in turn determines what knowledge is. One might, for example, be tempted to take n to denote a high degree of probability, in which case knowledge that p requires that that probability of p be n. (But this temptation should be tempered by infamous “lottery paradox”.) It should also be noted that the term ‘degree’ is here used rather loosely, with no presumption that it be a numerical quantity. It may be that different types of warrant are required jointly for sufficiency.

Plantinga’s alternative approach was that the addition of sufficient warrant to true belief is exactly what is needed to convert true belief to knowledge. (Compare the use of the variable ‘x’ in the equation: 2 + 3 + 4 + x = 14. The value of x is whatever is needed to be added to 2, 3 and 4 to get 14.) Thus, in trying to understand what warrant is, we need only examine our concept of knowledge, and not be concerned about what it is that makes a subject ‘justified’ in believing. We might try to understand justification independently, as some epistemologists do, but that is not our central concern in analyzing the concept of knowledge (if indeed there is a single such concept). As we shall see, Plantinga thought that ‘justification’ brings with it some undesirable baggage.

Here is how Plantinga describes warrant:

Initially then, and to a first approximation, warrant is a normative, possibly complex quantity that comes in degrees, enough of which is what distinguishes knowledge from mere true belief (Warrant: The Current Debate, 1993, p. 4).
We can use this notion to say that a necessary condition for S’s knowing that p is that S is warranted to a sufficient degree in believing that p. We will let ‘Wk’ stand for this notion of sufficient warrant (where k is whatever degree of justification required for knowledge. Then we can write:
Ks,cp → Wks,cp.
Clearly, the bulk of the work to be done is to understand what sufficient warrant is, besides being something which meets a standard (or norm) for evaluating belief, which comes in degrees, and which may be complex in nature. (Adding a warrant operator to the epistemic logic that is already enriched with the belief operator would require yet another specification of rules. It should be noted that Closure under Conjunction is an important component of the lottery paradox.)

One way to think of warrant is as a measure of the strength of S’s epistemic position relative to p. In order to know that p, S must be in a relatively strong epistemic position with respect to p. Someone whose belief depends on third-hand gossip is in a rather weak epistemic position, we might say, and lacks warrant sufficient for knowledge, while a first-hand witness is in a strong epistemic position and may be sufficiently warranted. It remains to specify what gives strength to one’s epistemic position, and to specify how strong that epistemic position must be in order to amount to knowledge. These are the central questions to be answered in order for sufficient warrant to be understood.

The questions of what is relevant to the strength of S’s epistemic position and what the standard of strength ought to be are highly controversial. Some common ways of understanding sufficient warrant are that S’s belief that p be based on “good reasons” or on “good evidence” for believing that p is true. There is much debate about the nature of reasons and evidence, how their strength is to be measured, how strong they must be in order to constitute sufficient warrant, etc.

Internalism and Externalism

Many philosophers think that the having of good reasons or good evidence is not necessary for knowledge. For the most part, these epistemologists regard the notions of reasons and evidence as too narrow a condition to capture all types of knowledge. Some have proposed that the sufficient warrant condition might not invoke the notions of reasons or evidence at all.

A related question, which deeply divides contemporary epistemologists, is how the epistemic subject must be related to whatever it is that confers sufficient warrant. Many epistemologists insist that in order to have a warranted belief that p, a subject S must be aware, in some way or other, of what it is that makes S warranted in believing that p, and perhaps how it makes S warranted. Such an “awareness requirement” is natural if warrant is thought of in terms of having good reasons. Those who impose this kind of requirement are known as “internalists.” (This way of describing internalism is taken from Michael Bergmann’s Justification without Awareness.)

“Externalists,” on the other hand, impose no such awareness requirement, though there is considerable disagreement about what other requirement should take its place. Two leading candidates are reliability in the process of forming the belief that p (reliabilism) and the exercise of “virtuous” (or excellent) cognitive faculties (virtue epistemology). It is possible for a subject to be reliable in the formation of beliefs or to exercise virtuous cognitive faculties without being aware of the fact. This, according to externalists, does not block the subject from being warranted (or sufficiently warranted) on account of reliablity or virtue.

The term ‘warrant,’ as used here, is vague enough to accommodate internalism or externalism, as it was introduced by Plantinga as a way of being non-committal about what exactly is required, beyond truth and belief, for a subject to have knowledge. The reason for doing this is that the term ‘justification,’ which is frequently treated as a condition for knowledge, is most commonly associated with internalism and not so much with externalism. For example, if one is aware of reasons supporting the truth of p, one can “give a justification” for holding that belief. But if one has merely formed the belief in a reliable way, he may not be able to “give a justification” for holding it. (However, some externalists think that justification is a necessary condition for knowledge. An externalist analysis of justification can be found in Michael Bergmann’s Justification without Awareness.)

Putting the truth, belief, and sufficient warrant conditions together, we arrive at a version of what has been called the “traditional” analysis of knowledge. We will use the symbol ‘↔’ to indicate co-implication, or a condition that is both necessary and sufficient.

Ks,cp ↔ (p ∧ Bs,cp ∧ Wks,cp).
S knows that p (in circumstances c) if and only if p, S believes that p (in circumstances c), and S is sufficiently warranted (in circumstances c) in believing that p. Note that one need not relativize knowledge to circumstances. If one takes knowledge to be “invariant,” then the circumstance index may be replaced by a time-index. (But since a natural subject may have knowledge that p at one time but not another, relativization to at least a time is essential.)

The Gettier Problem

Most people would agree that if a subject’s belief that p is true as the result of luck or accident, the subject lacks knowledge that p. Suppose I flip a coin, and you indicate your belief that it will come up heads by spontaneously calling out “heads.” (Your commitment to its being heads might be reflected in a large wager you have placed on that outcome.) The coin turns up heads. Did you know that it would, or were you just lucky to have made the right call? It appears that you did not in fact know that the coin would come up heads. Knowledge, it seems, cannot be the result of accident or “epistemic luck.”

Since you had a true belief that the coin would come up heads, it follows from the traditional analysis of knowledge that you did not have sufficient warrant for that belief. And as we have been describing sufficient warrant, the problem is that your epistemic position with respect to the outcome was too weak. We might say that the evidence, or your reasons for believing, or whatever else might warrant your belief, is just not sufficient in this circumstance.

But what about a situation where a subject’s reasons or evidence for believing that p are very good—seemingly constituting sufficient warrant—but the truth of the belief is yet merely accidental? One way in which accidentally true belief that p may arise is when the reasons for a belief that p do not reflect what it is that makes p is true. In a short paper published in 1963 by Edmund Gettier (“Is Knowledge Justified True Belief?”), two hypothetical cases are given in which a true belief backed by good reasons apparently fails to be knowledge, because p is true by virtue of circumstances that are not reflected in the reasons. (One example is reproduced here.) The relevant cases have come to be known as “Gettier cases,” and the problem of dealing with them in one’s account of warrant as the “Gettier problem.”

Here is a re-telling of one of the original Gettier cases. Smith has applied for a job, which someone will get. The president of his company tells him that Jones will be get the job. We will suppose that what the president said constitutes good reason for believing that Jones will get the job. Moreover, Smith has counted the coins in Jones’s pocket and found that there are ten. It appears that this is good reason for Smith to believe that he has ten coins in his pocket. Now Smith properly infers from these two beliefs that the man who will get the job has ten coins in his pocket. Presumably Smith has good reasons for believing this as well.

So does Smith know that the man who will get the job has ten coins in his pocket? There is one further circumstance which might prevent us from conceding this. It turns out that it is Smith who will get the job. (Perhaps the president was intentionally misleading Smith, or perhaps he had confused Smith and Jones in his mind.) As it happens, Smith also has ten coins in his pocket, so it is true that the man who will get the job has ten coins in his pocket. So it seems that despite his belief’s being true, Smith does not know this, and hence it seems that Smith was not sufficiently warranted in his belief that the man who will get the job has ten coins in his pocket. The problem is that his belief turns out to be true by accident with respect to what warranted Smith.

Given that Smith lacks knowledge while holding a true belief, he also lacks sufficient warrant. Then the account of sufficient warrant must be of such a nature as to preclude cases of accidentially true belief as being sufficiently warranted. The most obvious approach to preclude cases of accidentally true belief is to require that the subject’s epistemic position be so strong that accidentally true belief is impossible. For example, one might require absolute certainty or impossibility of error in the circumstances. Clearly Smith was not in such a strong epistemic position. Most epistemologists, however, hold that sufficient warrant does not require infallibility.

The Gettier cases seem to be more problematic for internalists than for externalists. Recall that an internalist requires some kind of awareness by the subject of what gives him sufficient warrant (good reasons, good evidence, etc.). What the Gettier cases seem to indicate is that part of what is relevant to sufficient warrant can be circumstances that are not accessible to the subject and so are not objects of awareness. In the case discussed above, the fact that Smith’s boss was not telling the truth is not something of which Smith was aware. (Such a fact is sometimes called a “defeater.”)

These considerations have led some internalists to separate out internal and external components of warrant. The internal component, to which the subject has access, is the reasons or evidence supporting the belief. The external component, to which the subject may not have access, is facts about the world, such as the fact, inaccessible to Smith, that his boss was lying. Most generally, the requirement will be that in addition to a belief’s being “justified,” there must be no external fact about the world that makes the truth of p accidental relative to the subject’s epistemic position. Thus, an internalist might wish to divide warrant into two distinct kinds, which might be called “internal warrant” and “external warrant.”

The externalist, who does not require awareness of what makes warrant for a belief sufficient, is not forced to bifurcate the account of warrant to avoid the Gettier problem. It is possible to build a “no accident” condition into a unified account of warrant. Gettier cases are then treated as cases in which the warrant is simply not sufficiently strong. For example, Alvin Goldman’s initial response to the Gettier cases was to propose an analysis according to which S’s belief that p must be caused in an “appropriate” way by the fact that p (“A Causal Theory of Knowing,” Journal of Philosophy 64 (1967), pp. 357-372). The requirement of “appropriateness” would be spelled out so as to exclude beliefs that are accidentally true. If I see a squirrel right in front of me and believe that there is a squirrel in front of me because I see it, my belief has been formed in an appropriate way, and it is no accident that my belief is true.

The description of Gettier cases given here is very abstract, and only one example of such a case has been discussed. As will be seen in a later module, it is difficult to find a satisfactory way to deal with the Gettier problem. It turns out that there are myriad variations on the original cases. Epistemologists have shown great ingenuity in giving accounts of sufficient warrant that would seem to block all cases, but unfortunately new cases are constantly being invented to show that those accounts are inadequate.

The Normative Project

Trying to discover the standards of knowledge is one of the most prominent projects in epistemology. As has been stated, the standard for S’s knowing that p can be understood abstractly in terms of the strength of S’s epistemic position with respect to p, which determines whether S is sufficiently warranted in believing that p. One normative question is which epistemic positions are such that they make a subject warranted in believing something. A second is what makes S’s epistemic position strong enough is to serve as sufficient warrant. The answers to these questions are determined by appeal to norms. The debate between internalists and externalists, which was discussed in the last section, concerns whether only “internal” norms govern warrant, or whether at least some “external” do. The choice of a set of norms also depends on how strong it is thought S’s epistemic position must be in order to make knowledge possible, so we will now turn to this issue.

Fallibilism and Infallibilism

The traditional standard for sufficient warrant, held by nearly all epistemologists until the twentieth century, is that S be in the optimal epistemic position. The strongest form of the optimality of S’s epistemic position with respect to p is that it be so strong that S could not go wrong in believing that p. This view is known as “infallibilism.” The denial of infallibilism, “fallibilism,” allows that S’s epistemic position may be allow it to be possible that S is wrong about p without excluding the possibility of S’s knowing that p. (A traditional view that to know that p, S must be “certain” that p might or might not be viewed as infallibilist. According to such a view the strength of one’s epistemic position by itself renders S unable to doubt rationally the truth of p, though it does not enable S to rule out the possibility of being wronge. This may have been the view of Descartes in the Meditations.) Virtually all epistemologists today are fallibilists. Yet within fallibilism there is tremendous scope for disagreement, since there are many ways in which a subject’s epistemic position may fall short of perfection.

Epistemic and Ethical Norms

In order to understand, to the extent possible, the nature of the norms governing knowledge (“epistemic” norms), it may be useful to compare them to ethical norms purporting to apply to human action. In one of their applications, ethical norms are the basis for judgments of the following kind:

Thus we might say that it is right for S to honor a promise he has made, or it is good that S is trustworthy.

Correlatively, we often make statements of the following types:

It seems that normative notions such as “rightness” and “goodness” are at least one component of the ordinary way in which we understand of knowledge. If S is not in a strong epistemic position with respect to p, it is natural to think that in some sense it is not “right” for S to believe that p.

One question that arises immediately is whether the kind of “rightness” and “goodness” that is relevant to knowledge is at least partly ethical in character, or whether there is a special kind of epistemic rightness and goodness which has no moral overtones. (Alvin Plantinga has termed the conception of epistemic norms in terms of moral duty a “deontological” approach in his Warrant, the Current Debate.) While most epistemologists do not understand epistemic norms in a way that is explicitly deontological, others do. William K. Clifford once stated that “it is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence” (“The Ethics of Belief,” 1887). If the epistemologist thinks that there is some element of “rightness” or “goodness” of believing that p that involves ethical standards, he must then try to discover the specific standards that would determine whether believing, reasoning, etc. are “right” or “good” for a subject S in a circumstance.

Epistemic Norms

Let us now leave aside the analogy with ethics and turn to the norms themselves. We must first distinguish between the basic norms governing knowledge and norms governing the selection of norms governing knowledge. Most of the investigation in epistemology is directed toward the norms that are said to govern whether one knows or is ignorant. (See especially the work of John Pollock on this subject.) However, there is a higher-level debate about how to choose epistemic norms, as with the question of whether epistemic norms are tied to morality, or whether they must be “internal” or may be “external.” Here we would have to use some higher-level norms to choose the norms that govern knowledge itself. On Pollock’s view, we do not justify the use of the norms we have but can only describe them. A further dispute, typical of Pyrrhonian skepticism, involves whether a higher-level choice of norms can itself be justified.


The internal norms governing knowledge are generally divided into two types, according to the complexity of the cases to which they apply. We may restrict our attention to an individual piece of information about a state of affairs (as expressed through the proposition p), or we may consider the relation between proposition p and a group of propositions p1, . . ., pn that “support” p. For the moment, this notion will remain a mere metaphor, but epistemologists have tried to flesh it out in various ways, as will be seen.

The norms governing the relation between a proposition and a group of one or more propositions generally fall under the heading of “logic.” (This is not to imply that one must engage in logical reasoning in order for the support relation to exist; some epistemologists think that the kind of support needed for knowledge requires explicit reasoning, and others do not.) So a proposition p might meet some standard for knowledge if it follows logically (deductively or non-deductively) from some other propositions. These other propositions may get their standing by following logically from some further propositions. But, to re-phrase a contention Aristotle made in his Posterior Analytics, an infinite regress of logical connections of support cannot put a subject in a strong enough epistemic position for knowledge.

This consideration led Aristotle and many others to hold that some propositions meet the standards of knowledge by themselves, which means that there are standards which apply to individual propositions taken by themselves. If a subject has knowledge or warrant in this way, such knowledge or warrant is typically called “basic.” Some epistemologists think that what provides support for an individual proposition or set of propositions is not itself propositional. It might, for example, be a psychological state of S. The claim that there is something which supports all (other) knowledge or warrant is known in the literature as “foundationalism.” There is much debate about how foundationalism should be fleshed out. For those who think the foundation is propositional, there is the question as to whether foundational propositions are warranted or not. If they are warranted, then do the propositions somehow warrant themselves, or are they warranted in some other way?

We will call potential foundational warranters “basic warranters.” There are two very different kinds of basic warranters investigated in epistemology. One kind deals with abstract propositions, such as simple propositions about numbers or geometrical figures, or about truths of logic. The second kind deals with concrete propositions about existing states of affairs. For example, it is commonly held that people have basic warranted beliefs about their being in intense pain. Whether there is basic warrant at all, and if so what norms apply to it, is controversial, and the controversy is discussed in a later module.

If there turn out to be no foundations for warrant, is warrant then impossible? Some epistemologists have held that there can be warrant without there being basic warrant. One anti-foundationalist account of warrant allows an infinite regress of warrant, something Aristotle thought impossible. Another anti-foundationalist account, known as “coherentism,” claims that warrant can be the product of a relation of mutual support.

The Support Relation

We may think of the support relation in terms of the strength of a subject’s epistemic position with respect to a proposition p. Support is a positive factor affecting epistemic position: the better supported p is for S, the stronger S's epistemic position is with respect to p. There are two ways in which a subject’s epistemic position can be supported. One way is to be in possession of something which provides support, e.g. evidence or reasons. Let us call this the “material” aspect of support. The other way is for there to be some kind of connection between the material aspect of support which allows it to support what it does. This will be called the “formal” aspect of support.

To take one example of formal support, suppose that S is sufficiently warranted in believing q, and moreover, that S is sufficiently warranted in believing that q implies p. And assume, for the sake of argument, that closure under implication applies to sufficient warrant: (SWs,cq, q → p) → SWs,cp. In such a case, it seems that S’s epistemic position with respect to p would be just as strong as it is with respect to what supports p. It is just as strong because of the strength of S’s epistemic position with respect to q and because the relation of implication seems to be the kind of relation that would “transmit” the strength of S’s epistemic position with respect to q to S’s epistemic position with respect to p.

Turning to the formal aspect of the support relation, we find that the most basic division among standards of logic is between deductive and non-deductive norms governing transmission. A deductive norm requires that if each member of the set of initial propositions (the supporting propositions) is true, the proposition they support (the conclusion) must also be true as well. (In terms that we have been using so far, the conjunction of the premises implies the conclusion.) This standard of “deductive validity” is considered by most to be as good a logical standard as there can be, in the sense that the conclusion cannot be supported any better. A deductively valid relation between what supports a proposition and the proposition supported leaves one’s epistemic position with respect to the supporting proposition no weaker than one’s epistemic position relative to the supported proposition. (However, it may be argued that the strength of one’s epistemic position is weakened if the deductive support relation is unrecognized, in which case something like known deductive validity would be required for full preservation of strength.)

The problem with deductive validity as a norm governing the support relation is that it does not, so to speak “get us very far.” Deductive validity merely reveals what is already implicit in the supporting propositions. For example, if I am already warranted in believing p ∧ q, it is not of much interest that I am therefore warranted in believing p. The real interest in epistemic norms lies in those which are not as powerful as deductive validity, but which allow for support of propositions whose content is more extensive than the content of the propositions which support it. The trade-off is that some epistemic strength is lost in the process of transmission, so to speak.

Some non-deductive norms are called “inductive.” Induction begins with particular propositions and takes them to support more general ones. A famous inductive generalization mentioned by David Hume is from the premise that the sun has in the past always been observed to “rise” in the morning to the conclusion that the sun always has risen and will rise in the morning. The most prominent kind of inductive generalization is the kind made in statistics, where information from relatively small samples is generalized to larger populations. As has been noted, one’s epistemic position in the case of inductive support becomes weakened. Hume pointed out that there is always the possibility that even if the sample shows complete uniformity, the population as a whole may not reflect that uniformity. It is at least possible that the sun will not rise tomorrow.

There are well-studied and widely accepted formalizations of rules for deductive and inductive implication: formal deductive logic, and the probability calculus and statistics, respectively. These formalized systems are generally taken to be very useful in formulating our epistemic norms. There is even a relatively recently-named sub-discipline of epistemology called “formal epistemology” which exploits these formal techniques.

A second class of non-deductive norms was called by C. S. Peirce “abductive.” We more typically refer to them as “explanatory” norms. The most prominent kind of support that is studied by epistemologists is inference to the best explanation (often referred to as “IBE”). The idea is that there is a set of data, such as the results of scientific observation, which supports a theoretical claim about the world. The theoretical claim is supported by virtue of explaining the data. The better the explanation, the stronger the support, and the best explanation is the best supported explanation. Thus, the quality of the explanation is the key factor in the strength of our epistemic position relative to the supporting data being transmitted to our position relative to the theoretical claim.

For example, someone might think that the proposition that global warming is occurring now is supported because it best explains various unusual weather patterns, as well as the breakup of the polar ice caps. But sometimes we take a proposition to be supported because it is explained by something else. I might take a loud bang to be a car backfiring (and not gunfire) because an old car is passing nearby, in the direction of the sound. Explanatory norms turn out in practice to be very complicated, as is discussed in another module.

One factor that is important in accounts of explanatory rules is “coherence,” the way in which a proposition “fits” with other propositions in a non-linear way (a way that does not have a tree-structure, with the foundations as the “roots”). Some epistemologists have tried to lay down rules of coherence whose satisfication would be at least a partial standard for knowledge. We shall have more to say about coherence (though not of the explanatory kind) in another module, where we contrast coherentism with foundationalism.

One class of epistemic norms does not fit into the classification that has just been given. Some epistemologists invoke what might be called “non-logical” norms which are specific to certain kinds of warrant. One of several such norms enunciated by Thomas Reid is, “That there is a certain regard due to human testimony in matters of fact” (Essays on the Intellectual Powers of Man, Essay Six, Chapter Five). The twentieth-century philosopher Roderick Chisholm formulated a number of special norms, of which the following is an example: “For any subject S, if S believes, without ground for doubt, that he is perceiving something to be F, then it is beyond reasonable doubt for S that he perceives something to be F” (Theory of Knowledge, second edition, p. 76). Generally, this kind of special norm is adopted by particularists whose aim it is to adapt the norms to the attributions of knowledge that we in fact make.

The Descriptive Project

Earlier in these notes a distinction was drawn between normative and descriptive approaches to the investigation of knowledge. We generally regard knowledge as being the outcome of some process or processes involving the epistemic subject and perhaps the subject’s environment. Examples of such processes are sense-perception and reasoning. A purely descriptive approach would examine how these processes work, but norms can enter the picture when we ask how well, according to some standards, the processes function. Here, we will be concerned with this second kind of descriptive approach to epistemology. We shall call such an approach the “descriptive” project, in contrast to the normative project which focuses on the norms themselves.

In our dicussion of the analytic project, we considered knowledge as sufficiently warranted true belief. This can serve as a framework for understanding the goal of the kind of descriptive project with which we are concerned. More specifically, the project is concerned to describe how it is that a belief on the part of an epistemic subject in various circumstances comes to have a sufficiently warranted belief. Of course, such an investigation presupposes a conception of what sufficient warrant is, and how one regards sufficient warrant can surely influence the course of the investigation.

We have seen that there is a fundamental disagreement over the role of awareness in warrant. Internalists claim that in order to be warranted, an epistemic subject must be at least capable of being aware of what it is that makes him warranted. Externalists reject this requirement.

If it is demanded that what makes one warranted be internally accessible to the epistemic subject, it seems that the investigation of how our beliefs become warranted in this way can be carred out purely internally, or “from the armchair,” as it is often said. On the other hand, if warrant may depend on factors that are not internally accessible, then the investigation would require external input and could take on a very different character from “armchair epistemology.”

Perhaps the most famous case of an internalist descriptive project was that of Descartes in his Meditations of First Philosophy of 1641. Descartes was concerned with discovering which of his beliefs he could count as being certain, and he thought that he could achieve his goal through the process of meditation. He intentionally isolated himself from human company and simply thought about himself and his capacity for knowledge.

Descartes tried to determine determine by a process of self-inspection what his cognitive capacities were. He thought that it was possible for him to use purely internal resources to determine the proper standards for the use of these capacities, as well as whether those standards have been met. He did his epistemology “in the armchair,” or (to use a more high-sounding expression), a priori. Many reject this approach, claiming that the correct description of the capacities of humans must be determined empirically, through physics, physiology, or “cognitive science,” which take an empirical, interpersonal, approach to discovering the facts about knowers that are relevant to their ability to know.

The outcome of Descartes’s investigation was that he had a capacity for purely abstract thinking, and that by exercising that capacity properly, he could attain certainty. The way to certainty, as he saw it, was to remove prejudices from his mind by disregarding the input of his senses and imagination. The next step is to pay full and undistracted attention to his thoughts and only to assent to those which are very clear and distinct. Interestingly, he believed that this rigorous process of meditation requires an intellectual capacity that many people lack. (In the Latin Preface to the Meditations, Descartes notes that he did not give a full account of his method in the French-language Discourse on Method “in case weaker intellects might believe that the ought to set out on the same path.”

The focus of Descartes’s investigations was a special kind of knowledge, which is called “a priori” or independent of sense-experience: for example that 2 + 3 = 5. For Descartes, this knowledge is gained through rational intuition, which yields clear and distinct preception, and deductive reasoning. These seem to be ways of knowing best suited to introspective or “armchair” investigation that can be carried out “a priori.”

Descartes’s successors turned their attention to empirical knowledge, or knowledge which is based on sense-experience. Since this kind of knowledge involves the interaction of the epistemic subject with the external world, it is not so clear that the description of the origin of this knowledge can be given from the armchair. At best, we have internal access only to perceptions in our own mind, so a description based purely on introspection would have to ignore the causes of our perceptions. This seems to be a severe limitation.

The purely introspective approach faces another apparent problem. If it is to be successful, the workings of the mind must be “transparent” to the mind when the mind observes them. However, it is not so clear that we are able to determine from introspection the way the mind really works. For that, we might have to turn to other means of scientific investigation, such as psychological experimentation, studies of the operations of the brain, or simulation of the mind's behavior in artificial intelligence. However, if there are workings of the mind that bear essentially on warrant, but of which we are not aware, then internalism has a major problem. For example, it might be discovered that we are unable to detect prejudices or biases that influence our beliefs in ways that prevent them from being warranted.

Externalists are not bound by the awareness requirement, and so the scope of what makes a subject’s belief warranted is potentially much greater. An externalist description of warranted belief may well include data from introspection, as well as from the various kinds of scientific study of the mind. But it could also include descriptions of how the mind interacts with the world around it. Most importantly, it could concern itself with how the perceptual states of the mind are produced by the transmission of information about physical objects by media such as light and sound waves.

A descriptive project which investigates epistemic subjects as being enmeshed in the natural world is sometimes called “naturalistic,” and the enterprise itself is called (after Quine’s paper “Epistemology Naturalized”) “naturalistic epistemology.” Quine in particular viewed epistemology as a branch of psychology, whose task it was to explain how the mind is able to produce an extensive set of beliefs on the basis of relatively meager sensory input. Such an investigation would be of a kind that we have been calling “purely descriptive.”

If we think of naturalistic epistemology as a scientific investigation of the extent to which our beliefs are warranted, we would wish that the results of the investigation be beliefs that themselves be warranted. We distinguish between good science and “junk” science, and at the very least we should ask ourselves whether given results of naturalistic epistemology meet the norms demanded of good science. And of course, this question raises the normative questions of what the norms of good science are, and what it is about them that makes them good.

Naturalistic epistemology seems to lead to questions about scientific methods and how they are practically carried out. For the most part, science is a social activity, and its product is the result of joint efforts, often by large numbers of scientific investigators. This suggests that there might be a kind of knowledge, scientific knowledge, that is not lodged in any individual epistemic subject, but rather is the joint possession of a social group, perhaps “the scientific community” or some subset of it.

This suggests a further descriptive project. There is the “pure” project which describes how the practices of scientists lead to scientific belief. More generally, the production of beliefs of any social group can be studied. “Sociology of knowledge” is the name of the branch of sociology devoted studies beliefs possessed by groups. There are also more philosophical (or as some might say, less scientific) investigations along these lines. One prominent approach initiated by Nietzsche and popularized by Foucault considers the central role of power relations in the production of belief.

There is considerable disagreement about the norms that govern the production of belief in social groups. This disagreement colors the way in which the processes of belief-generation are described. The traditional philosophical approach has been to look for “objective” norms as the only route to knowledge. But others have held that norms are generated through social practices, and they consequently allow that warranted belief may fall short of objectivity. For example, warrant is often construed relativistically in terms of authoritativeness or general acceptance by a community.

The Validation Project

The last project to be considered in these notes, that of “validation,” is perhaps the most difficult and frustrating of all. At issue is the validation of knowledge attributions: showing that S really does know that p in circumstances c. With respect to individual propositions or large classes of propositions, it is asked whether there are compelling reasons to think that the attribution is correct. Epistemological skeptics answer in the negative, while what we can call “dogmatists” answer in the affirmative.

Before we turn to the dispute between dogmatists and skeptics, it might be best to consider the question of validation in the terms that have been used earlier in these notes. The question may be asked in various ways: Is S sufficiently warranted in believing that p in circumstances c? Does S satisfy, in c, the epistemic norms that govern sufficient warrant? Is S’s epistemic position with respect to p, in c, strong enough?

It is clear that answering these questions presupposes an understanding of the epistemic norms that must be satisfied for there to be knowledge. One approach to epistemic norms that makes validation relatively difficult is to make them very strong and hard to satisfy. At the extreme end, an infallibilist might have a harder time validating knowledge attributions than would a fallibilist. And versions of fallibilism with stricter norms might be more vulnerable to skepticism than versions with looser norms.

The strictness of epistemic norms is not the only factor that can make validation difficult. The other factor lies with the epistemic subject to which the norms apply. Unless the subject is an omniscient being, there will be limitations to its cognitive powers. The effect of these limitations is that the epistemic position of the subject can attain only a limited degree of strength. To see this, we will take a look at some of the tools we humans have to get into a favorable epistemic position with respect to various kinds of objects.

Traditionally, epistemologists have singled out various capacities of the mind as providing warrant for certain of our beliefs. These capacities can be classified with respect to their relation to the objects to which they are directed. One of the most important distinctions is whether their epistemic position with respect to their objects depends on sensory experience. If the epistemic position does depend on sensory experience, it operates “empirically” or “a posteriori.” If it does not so depend, it operates “a priori.” (Descartes’s account of a priori knowledge was described in the last section.) If the epistemic object is detected by one of the five senses, for example, our sense-perception is empirical. If, on the other hand, it is detected by some purely rational faculty, that faculty functions in an a priori way, as may be the case with mathematical knowledge.

Regarding attributions of a priori knowledge to human beings, the Meditations of Descartes affords a good illustration. As we have seen in the last section, Descartes thought that if the human mind is able to remove the prejudices that arise from an over-reliance on the senses, and if it focuses on the clear and distinct perceptions it finds within itself, it can attain knowledge a priori. The epistemic position of a clear-minded, unprejudiced subject contemplating a clear and distinct perception is as strong as is humanly possible, and in Descartes’s view, strong enough to constitute knowledge. One can in fact look at the Meditations as a project of the validation of a priori knowledge.

One kind of attribution of empirical knowledge, to which Descartes called attention, is knowledge of the existence, nature, and contents of one’s own mind. In such cases, the mind is an object of itself, and, it is claimed, a mental operation of “reflection” or “introspection” reveals the mind to itself. It appears that the mind is in a very strong position with respect to itself as an object, and if it is, there is little room for skepticism with respect to attributions of self-knowledge. The skeptical argument would have to be that the mind does not present itself to itself in a “transparent” way. This seems to be the case with respect to unconscious states of mind, for example.

The most contentious attributions concern empirical knowledge of the “external world” existing (or said to exist) “outside” the mind. The epistemic position of the subject with respect to these objects seems weaker than with respect to the objects of introspection, as our access to these objects through the senses is indirect rather than direct. This relative weakness has been a breeding-ground for skepticism.

The ancient skeptics held that sense-perception puts us in a strong-enough epistemic position only with respect to the appearances of things. For the Pyrrhonian skeptics in particular, the strength of an epistemic position is measured by whether there can be any dispute about the object in question. The ancient skeptic Sextus Empiricus writes, “Nobody, I think, disputes about whether the external object appears this way or that, but rather about whether it is such as it appears to be” (Outlines of Pyrrhonism, Book I, Section 11, “The Criterion of the Skeptic Way”).

Modern skepticism begins with Descartes, who in effect questioned the presupposition of the very existence of the external object which is said to appear to be some way or other. Descartes described the human epistemic position derived from sense-perception as being limited to a small, but important, extent. Specifically, we are unable to use sense-perception to rule out the possibility that the entirety of our sense-experience is massively misleading, in that its source is not external objects at all, but rather an evil demon powerful enough to deceive us in this regard. In this way, Descartes set what we now call “the problem of the external world,” which is the result, as we say, of our being shrouded by the “veil of perception.”

Descartes himself claimed to have solved the problem by proving (a priori) the existence and goodness of God, who would not allow us to be deceived about the existence of the external world. But as this solution has generally been rejected as inadequate, the problem of the external world has persisted. There have been many attempts to solve it, including radical proposals such as that of George Berkeley in the eighteenth century, who declared that there is no “external world,” but that all physical reality exists “in the mind.”

Even if we grant the existence of an external world, we must allow that there are many limitations on the ability of sense-perception to discover what it is. It is difficult or impossible for us to see many distant or very small objects. We are subject to all manner of illusions. Our senses may be defective in any number of ways, as with red/green color blindness. It seems that the epistemic position we attain through sense-perception is in need of a good deal of strengthening if we are to make defensible knowledge-claims about the external world.

It is generally held that the strengthening agent is human reason. We use it to infer from coherent patterns in sense-experience to mathematical representation of them and ultimately to natural laws that govern the behavior of the objects in the external world. A skeptical challenge to this kind of use of reason would seem to be a challenge against the whole body of natural science.

We will only note here one very famous challenge to the use of reason as an aid to sense-experience. This challenge was formulated by David Hume in the eighteenth century. Hume examined inductive reasoning, which is inference from a sample of cases to the general population. His conclusion was (in the terms we have been using here) that the use of inductive reasoning contains a hidden circularity, and circular reasoning does not advance the strength of our epistemic position. Hume’s argument has been the subject of much examination, and it is not clear that it has yet been refuted.

At this point, we have seen that there are limitations to the strength of the epistemic positions of even the most competent epistemic subjects. This raises the question of how to respond to these limitations: can a dogmatic position be maintained, or should we give up claims to knowledge? A number of approaches are available.

It is always open to the dogmatist to deny that we have the limitations which form the basis of the skeptic’s objections. “Direct realists” with respect to sense-perception claim that there is no “veil of perception,” and that the mind is directly acquainted with the objects of sense-perception. The skeptic would respond to this move by noting that it would have a problem explaining perceptual error. As Hume pointed out, upon pressing one’s eyeball, there is an image of two objects in place of the one object that is seen under normal conditions (A Treatise of Human Nature, Book 1, Part 4, Paragraph 45).

Another approach is to try to find ways around the limitations we have. We might appeal to an epistemically powerful faculty, such as reason, to provide information that is not accessible to a weaker faculty, such as sense-perception. This approach was taken by Descartes, as noted above, and it is the hallmark of “rationalist” epistemology. The chief problem with rationalism is that while reason may give us a strong epistemic position with respect to an array of abstract objects (such as numbers and universals), it does not seem that objects of sense-perception are among them.

It seems that the most promising use of reason to overcome the limitations of sense-perception is through abductive or explanatory inference. It is sometimes held that inference from the data provided by sense-perception to the existence of physical objects is the best explanation of that data. And if it is the best explanation, that fact strengthens our epistemic position sufficiently to allow knowledge of the existence of those objects.

A dogmatist might appeal to some source of epistemic strength other than sense-perception or reason. Descartes had examined the “teachings of nature,” spontaneous impulses to believe, and found them wanting, since they often conflict with reason (Meditation Six). Thomas Reid, on the other hand, claimed that there are teachings of nature which are “first principles” that cannot be undermined by any argument. One of these principles is, “That those things do really exist which we distinctly perceive by our senses, and are what we perceive them to be.” This principle is supported by the fact that, “all men are by nature led to give implicit faith to the distinct testimony of their senses, long before they are capable of any bias from prejudices of education or of philosophy” (Essays on the Intellectual Powers of Man, Essay Six, Chapter Five).

A second approach is to acknowledge our limitations as epistemic subjects and accordingly to bring our epistemic norms into line with our limited capacities. Adopting fallibilist norms is a step in this direction, but it remains to establish exactly which fallibilist norms should govern our attributions of knowledge.

At this point, we must return to the question of the origin of our epistemic norms. A particularist account, such as that of G. E. Moore, takes our ordinary attributions of knowledge to be correct and calls for epistemic norms to fit them. Methodists, on the other hand, would reject such a methodology and insist that there be grounds for adopting norms other than their yielding a desired outcome of their application.

While nearly everyone does not ordinarily question their knowledge-attributions, many people are impressed by the skeptical appeals to our limitations and are inclined, when thinking about them, to doubt that they have the knowledge they ordinarily think they have. They become temporary skeptics. Those who advance a contextualist account of knowledge attribution have a way of describing what happens when a skeptical hypothesis is considered. The normative standard for knowledge is raised, temporarily, to the point where it is not satisfied. Thus the contextualists can acknowledge the force of skeptical hypotheses while allowing that there is knowledge (according to lower standards) in most contexts of attribution.

Skepticism is generally thought to be more of a problem for internalists than for externalists. Recall that the basic requirement of internalism is that one must be at least potentially aware of what makes one warranted in one’s beliefs. For the internalist, if S cannot determine that his beliefs are warranted, then S lacks knowledge. The skeptic will argue that due to the limitations of human cognitive faculties, it is not possible for anyone to determine whether they are sufficiently warranted. For example, we may be unable to detect whether our cognitive faculties are working properly, which is surely a requirement for warranted belief based on the workings of those faculties.

The externalist, on the other hand, does not require awareness of what warrants one’s beliefs. As long some external condition, such as, for example, the reliability of the belief-forming process, is met, one can have knowledge. The internalist counters that even if the externalist condition is satisfied, one might be left wondering whether one knows or not.


It is possible to apply skeptical considerations to the theory of knowledge itself. Virtually every position that has been described in this introduction is subject to controversy—sometimes to intense controversy—among the students of knowledge. In many cases, the parties seem to have exhausted the arguments for their positions, yet without persuading their opponents. Each new account of knowledge is promoted as more satisfactory than its rivals, but nothing even approaching a consensus has been reached by epistemologists. This holds more generally in philosophy. There simply is no agreement on substantive philosophical issues that looks anything like the general agreement on, say, principles of natural science.

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