2002 Lecture Notes, Lehrer's Theory of Knowledge, second edition

Chapter 4, The Foundation Theory: Fallible Foundations

By G. J. Mattey, Senior Lecturer, UC Davis Philosophy Department


The infallible foundations program was criticized by Lehrer on two chief points:

It is the second point that has been taken most seriously by philosophers, for it has the potential to land us in skepticism about the very existence of a physical world. In response, it has been proposed that there can be justification without a gurantee of truth: this is the doctrine of fallibilism with respect to justification. (A broader form of fallibilism is that anything we accept about the world may be mistaken.) When fallibilism is adopted by a foundations theorist, the result is a fallible foundations theory. We shall turn to fallible foundations theories shortly, but first something more will said about their motivation.

Skepticism about the External World

Consider the question whether we are justified in believing that a physical world exists. As David Hume pointed out, the skepticism generated by philosophical arguments is contrary to our natural inclination to believe that there are physical objects.

[T]he skeptic . . . must assent to the principle concerning the existence of body, tho' he cannot pretend by any arguments of philosophy to maintain its veracity. Nature has not left this to his choice, and has doubtless esteem'd it an affair of too great importance to be trusted to our uncertain reasonings and speculations. We may well ask, What causes induce us to believe in the existence of body?, but 'tis in vain to ask, Whether there be body or not? That is a point, which we must take for granted in all our reasoning. (A Treatise of Human Nature, Book I, Part IV, Section II)
Nonetheless, after considering the causes of our belief in the existence of body and finding them inadequate for the justification of that belief, Hume admitted to being drawn away form his original assumption that bodies exist. "To be ingenuous, I feel myself at present . . . more inclin'd to repose no faith at all in my senses, or rather imagination, than to place in it such an implicit confidence," because "'tis impossible upon any system to defend either our understanding or senses." His solution to these doubts was "carelessness and in-attention," which divert the mind from skeptical arguments.

Reid's Defense of Common-Sense Beliefs

Thomas Reid, a contemporary rival of Hume's, claimed that our beliefs in the external world are justified. "I shall take it for granted that the evidence of sense, when the proper circumstances concur, is good evidence, and a just ground of belief" (Essay on the Intellectual Powers of Man, Essay IV, Chapter XX). This evidence is different from that of reasoning from premises to a conclusion, however.

That the evidence of sense is of a different kind, needs little proof. No man seeks a reason for believing what he sees or feels; and, if he did, it would be difficult to find one. But, though he can give no reason for believing his senses, his belief remains as firm as if it were grounded on demonstration.

Many eminent philosophers, thinking it unreasonable to believe when they could not shew a reason, have laboured to furnish us with reasons for believing our senses; but their reasons are very insufficient, and will not bear examination. Other philosophers have shewn very clearly the fallacy of these reasons, and have, as they imagine, discovered invincible reasons against this belief; but they have never been able either to shake it themselves or to convince others. The statesman continues to plod, the soldier to fight, and the merchant to export and import, without being in the least moved by the demonstations that have been offered of the non-existence of those things about which they are so seriously employed. And a man may as soon by reasoning, pull the moon out of her orbit, as destroy the belief of the objects of sense. (Essay on the Intellectual Powers of Man, Essay IV, Chapter XX)

Here Reid shows himself to have foundationalist tendencies, in the sense that our beliefs about physical objects are not justified by appeal to other beliefs. On the other hand, all he has established at this point is what Hume had already observed, that beliefs about physical objects are very hard to shake off. Hume himself admitted only to losing his faith in the senses at the time that he was deeply immersed in skeptical reflections. But why should Reid think these deeply-held beliefs are based on "good evidence" or "a just ground?" One particularly telling observation is that a philosopher's "knowledge of what really exists, or did exist, comes by another channel [than reason], which is open to those who cannot reason. He is led to it in the dark, and knows not how he came by it" (Essay on the Intellectual Powers of Man, Essay IV, Chapter XX). Philosophers "cannot account for" this knowledge and must humbly accept it is a gift of heaven.

If there is no philosophical account of justification of beliefs about the physical world, how could Reid claim that they are justified at all? The answer is the way in which they support common sense.

Such original and natural judgments [based on sense-experience] are, therefore, a part of that furniture which Nature hath given to the human understanding. They are the inspiration of the Almighty, no less than our notions or simple apprehensions. They serve to direct us in the common affairs of life, where our reasoning faculty would leave us in the dark. They are part of our constitution; and all the discoveries of our reason are grounded upon them. They make up what is called the common sense of mankind; and, what is manifestly contrary to any of those first principles, is what we call absurd. (An Inquiry into the Human Mind, Chapter VII, Section 4)
One might say that judgments from sense-experience they are justified insofar as they justify other beliefs we have, or perhaps because they are the output of a perceptual system designed by God to convey the truth. (Of course, if the latter is what gives these beliefs their justification, the claim that we are designed in this way needs to be justified as well.)

Prima Facie Justification

At any rate, what Lehrer emphasizes in Reid's doctrine is his fallibilism: "our senses, our memory and our reason, are all limited and imperfect--this is the lot of humanity: but they are such as the Author of our being saw to be best fitted for us in our present state" (On the Intellectual Powers of Man, Chapter XXII). Far from concluding that our senses are "fallacious," Reid placed them on the same footing as memory and reason, though they are "undervalued" by philosophers because "the informations of sense are common to the philosopher and to the most illiterate. . . . Nature likewise forces our belief in those informations, and all the attempts of philosophy to weaken it are fruitless and in vain."

Reid pointed out that when we fall into error regarding the objects of sense, we correct our errors "by more accurate attention to the informations we may receive by our senses themselves." So the "original and natural judgments" that are made on the basis of our constitution lose their original justification in the presence of additional information. Contemporary philosophers call this kind of justification "prima facie," a term from law which describes an initially plausible case that could prove to be entirely implausible given further evidence. A belief of common sense, then, is justified "on the face of it."

According to the doctrine of prima facie justification, one is justified in accepting that things are the way they appear, when

But if there is such a reason, one's justification is "defeated." Thus prima facie justification is "defeasible."

For Reid, our beliefs about physical objects are justified by sense-experience, which he took to be a product of the interaction between the senses and physical objects. Twentieth-century philosophers have been somewhat more cautious, however, and have followed more closely the account of perceptual knowledge given by Reid's predecessors such as Descartes, Locke and Hume: that what justifies our beliefs about physical objects is a mental state such as:

For example, what justifies a person in believing that he sees something red is that it looks to him as though there is something red. The mental state of that person is one in which there is an appearance of red. On a non-doxastic theory of justification, just being in this mental state is what gives prima facie justification to the belief that he really sees something red. For a theory that makes the doxastic assumption, that all justification flows only from belief, what confers justification would be a belief about something's appearing red.

Epistemic Principles

To see how each of these approaches can be developed, we will look at principles of justification or epistemic principles endorsed by two contemporary philosophers.

John Pollock, Lehrer's colleague at the University of Arizona, endorses the following epistemic principle in Contemporary Theories of Knowledge (second edition, p. 148):

"S appears red to me" is a defeasible reason for me to believe that S is red.

An earlier advocate of fallible foundations, Roderick Chisholm (Lehrer's teacher) adopted this doxastic epistemic principle in his 1977 book Theory of Knowledge (second edition, Chapter 4):

(C) For any subject S, if S believes, without ground for doubt, that he is perceiving something to be F, then it is evident for S that he perceives something to be F.
(Note that a color is the sort of thing that counts for Chisholm as a "sensible characteristic." Also, to perceive something to be F implies that it really is F.) This principle, like Pollock's, contains the "no defeater clause," which indicates that it is fallibilist. But it is a doxastic principle, in that what provides the justification for the belief that S perceives something to be F is the very fact that S believes that he is perceiving something to be F. Unlike most alleged beliefs about one's mental states, however, this one makes reference to something outside the state itself, what the belief is about. This fact makes it it less clear that the belief should be counted as self-justified. It would seem that one need information about the reliability of beliefs about what one perceives in order for it to be evident to a person that he is perceiving something to be F.

Before moving to Lehrer's account of fallible foundations theories, it should be noted that both Chisholm's and Pollock's principles do not involve any notion of probability. That is, they do not say that a thing's looking a certain way to a person makes it probable that for that person that it is the way it looks. There is simply a direct connection drawn between the evidence and what it justified. If you were to ask an ordinary, non-philosophical, person why she believes that an apple is red, she would naturally respond that it looks red. We would take her to be justified on that basis, so long as she had no reason to think that something was odd about the situation. We shall return to Pollock's and Chisholm's theories shortly.

Fallible Foundations

Lehrer begins his treatment of fallible foundations theories by examining the alleged foundations themselves, confining himself to doxastic theories. He insists that what confers justification must itself be justified, so that a basic belief is self-justified. Thus his criticism of fallible basic beliefs does not even apply to Pollock's epistemic principle, as he notes on p. 68.

Let us begin our examination of Lehrer's criticism with the kind of basic belief used in Chisholm's principle (C): the belief that S is perceiving something to be red. Lehrer objects that such a belief is not basic because it is not self-justified. That is, in order for it to be justified, other "independent" information is required. Specifically, one is not justified unless one has the information which allows one to determine whether his perception really is that of red. One must be able to tell whether the perceptual state one is having really is one which is a perception of red. Lehrer notes that one need not be able to articulate this information, but he insists that one must be in possession of it in a way that backs up the belief that one is having a perception of red.

This kind of objection led Chisholm to argue that there are some states which require no independent information in order for someone to tell whether he is in such a state. These states are "ways of being appeared to," for example, "red-ly." Chisholm noted that such states do not involve any comparisons, but are basic information. When we say that an apple is red, we can be taken as saying that the apple looks the way red things do under certain conditions. But if I were to believe that I am appeared to redl-ly, there is no comparison with anything else involved. Nonetheless, Lehrer argues that for justification one still needs independent information about the kind of state a state of being appeared to red-ly is.

It is interesting to note that Chisholm first proposed (Perceiving: A Philosophical Study, 1957, Chapter 5, Section 4) the "adverbial" approach to foundational beliefs because he thought that they are in fact infallible.

Hence if we do not say, of such statments as 'I am now appeared to in a way which is blue,' when intended noncomparatively, that they are certain, we should say, at least, that they are statements which cannot express any error or mistake. For if our perceiver cannot be said to believe, at the time when he is being 'appeared blue to,' that he is not being 'appeared blue to,' or to believe, at a time when he is not, that he is, then he cannot be said to believe erroneously or mistakenly at any time either that he is or that he is not being thus 'appeared to.' Perhaps we should say, more technically, that the appear statements in question are statements with respect to which it would 'make no sense' to say that they can express any error or mistake.
Even if Chisholm's approach falls to Lehrer's demand for independent information, there may some other description of mentals states that does not. In particular, Pollock once claimed that the basic mental states are those of appearing, non-F-ly for some kind F, but "in that way," which is whatever way they do appear (Knowledge and Justification, Princeton, 1974, p. 76.) By making the state of a kind whose recognition involves nothing but a "mental pointing," Pollock seems to eliminate any dependence on outside information about the type of appearing that is going on. (It should be noted that Pollock was defending the infallibility of beliefs about being appeared to in "that" way.)


Lehrer's claim that independent information is required to justify even the minimal belief that one is appeared to in a certain way is subject to criticism. Someone with externalist leanings could hold that what is required for justification is that the person be able to tell, that is, be competent in identifying this way of being appeard to. Lehrer requires more: that the person have a view about his own competence. It is fundamental to Lehrer's theory of knowledge that to be justified, you must be able to answer the question, "How do you know?" One may be unaware of one's competence. As with the infallible foundations theory, Lehrer thinks that key information that might make a person justified may be "opaque" to that person. If it is, then the person could not tap into that information to explain how he knows, and hence he lacks justification.

Lehrer also appeals to our intuitions in this regard. We are given the case of a person who is competent to sort diamonds from non-diamonds without having the faintest idea how, or even a notion that she is successful at doing it. The diamonds look different from the non-diamonds, but not in such a way that the sorter could tell from the way they look what they are. Lehrer holds that the sorter does not know she has picked out a diamond when she does so. If asked how she knows it is a diamond, she would have nothing to say, because she lacks the information required to state what a diamond is. This example is the epitome of Lehrer's case against externalism in general, as we will see in Chapter 8.

The Case for Coherentism

The criticism of fallible foundations can be put more generally. The alleged foundational beliefs are about particular propositions, e.g. the color of a specific object. What is said to make them justified is the particular circumstances of the subject, so that when I am appeared to red-ly and have no grounds for doubt that I see a red thing, then I am justified in accepting that I see a red thing. Lehrer counters that for one to be justified, certain general information must be available to me. I must have information about my ability to recognize the kind of thing in question. But this general information is not basic. It could only be justified on the basis of particular instances of success in recognition. Are those, then, the basic beliefs for which we have been searching? They could not be, because my recognition that I am successful is justified only if I have the general information that I have the ability to tell whether I have been successful in a given case. It now seems as if we must cycle back and forth between particular and general information, and this cycling is incompatible with a foundations theory.

Lehrer has argued that there is no privileged starting point for justification. The aim of acceptance is to accept all and only what is true. To begin to carry out this objective, one must have some grounds for assessing whether one is going to be successful in a given case. These grounds will be general beliefs about one's own competence to judge in the case at hand. But beliefs about one's competence could only be justified on the basis of what one accepts about particular cases in which one has been successful in accepting what is true. And to judge that one has judged successfully, one must appeal to one's competence to tell that one has. There is a back-and-forth cycling between the particular and the general. Ultimately, the two kinds of acceptances support each other, and complete justification must be a matter of coherence.

Having laid out the general case for Lehrer's rejection of fallible foundations theories, we will return to the thread of the text by examining some alternative ways in which these theories could be developed. Perhaps some of Lehrer's objections could be overcome if the fallible foundations theory were properly tailored.

Semantic Foundationalism

A theory Lehrer takes some pains to refute is what he calls "semantic foundationalism," whose main advocate is none other than Pollock (footnote 9). According to this view, beliefs with a certain kind of content are self-justified as a matter of semantics or meanings. Pollock did advance a view of this kind, though it is quite different from that which Lehrer describes.

According to Lehrer, what makes a belief self-justified, on semantic foundationalism, is that there is some "meaning postulate" which ties together the content of the belief and its being justified. Insofar as meaning postulates are necessarily true, claims of self-justification would have to be necessarily true as well.

Lehrer's objection to this approach is that there is no contradiction in denying that a person with the requisite belief is justified, and there is no violation of any principle of meaning. A skeptic who holds that nobody is justified in believing anything is not inconsistent, nor is he using language in a deviant manner. (We can tell that the latter is the case by the way his use of 'justified' relates systematically to his use of other terms such as 'certain,' 'know,' and 'evident.')

Pollock's theory is not so simply dismissed. For he proposes a radical theory of meaning, according to which the meanings of mental contents are bound to the conditions under which one is justified in making assertions about them. The "epistemological theory of concepts" holds that the role a term plays in reasoning is what gives it the meaning it has. "What makes a concept the concept that it is is the way we can use it in reasoning, and that is described by saying how it enters into various kinds of reasons" (Contemporary Theories of Knowledge, p. 147).Thus if a term like "red" has this role in inference: if something looks red to me (and there is no reason to think that I am deceived), then I am justified in believing that it is red.

Pollock vs. Skepticism

Pollock's view would deal with Lehrer' skeptic in the following way. If someone S is not justified in accepting that x is red under certain conditions, then S is not using the concept red, but some other concept. Suppose a skeptic holds that something looking red to me (without my having any grounds for doubting that it is red) is not sufficient for my being justified in accepting that it is red. The reason the skeptic holds this is because he thinks that to be justified one requires stronger evidence, perhaps a guarantee of truth. Pollock would hold that the skeptic does not, therefore, mean the same thing by 'red' as I mean.

It might seem as if Pollock's response to the skeptic is dogmatic. In fact, Lehrer levels this charge against any theory which endorses prima facie justification. His argument is that anything at all could be claimed as prima facie justified. Suppose I held a principle according to which, when I accept that I am receiving a telepathic message, and I have no grounds for doubting this, I am justified in accepting that I am receiving a telepathic message. If someone pointed out to me grave grounds for doubt, I might reply that I am nonetheless prima facie justified, though admittedly my justification has now been defeated.

Pollock would hardly admit that his choice of cases of prima facie justified beliefs is arbitrary. He has described them as the outcome of patterns of reasoning which are fundamental to us as cognitive agents. Ultimately, Pollock looks for a naturalistic account of these reasoning processes. He thinks that if we were to reflect on how we might build a person, that is, a cognitive agent capable of survival in a relatively hostile environment, we would build in just the type of inference patterns which he takes to constitute the meanings of our concepts.

This brings out a key difference between Lehrer and Pollock. The former thinks that all justification rests ultimately on beliefs (or more precisely, acceptances). The latter thinks that justification rests on the utilization of internalized cognitive processes. Pollock likes to compare justification to riding a bicycle. We are justified when we use internalized rules, which require no thought at all. But he sees the kind of account of justification given by Lehrer as like one where to act we must look things up in an instruction manual. How do I know that I am appeared to red-ly? To find out, I need to "look up" the information I have about how red-ly appearings differ from green-ly appearances and brown-ly appearances, etc., as well as the information I have about my competence to tell the difference.

Chisholm vs. Skepticism

Finally, something should be said about how Chisholm could answer the charge of arbitrariness. How does he arrive at this epistemic principles? Unabashedly, Chisholm admits that what validates his principles is the fact that they justify the very things that we common-sensically take to be justified. If asked whether we really are justified about those things, Chisholm throws up his hands and says that there is no way of telling without using the epistemic principles in question. On the other hand, he asks whether we really want to be skeptics, which is the same question asked by Thomas Reid some two hundred years earlier. Referring to the skepticism he claimed to originate in Descartes and become worse in the philosophy of Malebranche, Locke, Berkeley and Hume, Reid used a striking metaphor.

A traveller of good judgment may mistake his way, and be unawares led into a wrong track; and, while the road is fair before him, he may go on without suspicion and be followed by others; but when it ends in a coal-pit, it requires no great judgment to know that he hath gone wrong, nor perhaps to find out what misled him. (An Inquiry into the Human Mind, Introduction, Section VIII)


Philosophers such as Chisholm and Pollock formulate epistemic principles which lay it down that when one is being appeared to in a certain way (or believes he is appeared to in that way), he is justified to a greater or lesser degree in believing that he does. Other philosophers understand the relation between basic beliefs and other beliefs in terms of probability. It should be noted that the view that high probability is sufficient for knowledge (along with truth, belief, and no dependence on a false statement) is of very recent vintage. Traditionally, epistemologists have held that knowledge requires certainty. But fallible foundations theorists reject that view, and in the process, some of them embrace probability as adequate for knowledge (all else being equal).

Probability and Justification

Lehrer accords probability a key, though not very prominent, role in his account of acceptance. As a fallibilist, he admits that we may be justified in believing what is false. Justification involves a risk of error, and this risk of error Lehrer identifies with probability of error. A minimum condition on justification, then, will be that a belief have a relatively high probability of being true. If I do not think that my belief is highly probable, then I cannot take it that I am succeeding in satisfying my epistemic goal of accepting only what is true.

The use of probability is particularly appealing as a way to explain how one arrives at justification concerning general information or other information that has not been entirely collected (about the future, for example). The specific information that we possess makes probable information which we do not possess. On the other hand, a general belief about my competence, say in identifying red, may help to make probable a particular belief I have, such as that I see something red.

There is a significant initial obstacle to building an account of justification on high probability, however. It is known as the lottery paradox. Let us suppose that 99.9% probability is to be sufficient for justification. (If you think it is too high or too low, pick your own number.) Now let there be a fair lottery with 1000 tickets. All have been sold, and one has been drawn. Given the equal probability that any one of the tickets will win (1 in 1000, or .001), the probability that a given ticket will lose is .999, or 99.9%. On the hypothesis that this is the degree of probability required for knowledge, we can conclude that the proposition that the #1 ticket is a lose is justified. But because the probabilities for each one of the tickets' losing is the same, the proposition that the #2 ticket is a loser is also justified.

If we apply this reasoning to each ticket, we will be justified in accepting of every one of them that they are losers. A simple step takes us to the conclusion that they all are losers. But we know that one of them has been drawn and hence is the winner. So we are justified in accepting that all the tickets are losers and that one is a winner: a paradox.

Some people have tried to disarm the paradox by rejecting the "conjunctive" principle that I called a "simple step." A good reason for suspicion is that each of the individual propositions is said to be justified without taking the justification of the others into account. One starts all over in considering each ticket. But if we keep in mind that we were just now justified in accepting that the #1 ticket is a loser, when we consider the #2 ticket, things are different. The probability that it is a loser is now lower, falling below 99.9%. In that case, it is not justified. The lesson Lehrer draws from the paradox is that high probability of propositions in isolation is not enough. We need to take into account all the other information we have at our disposal, which is characteristic of a coherence theory. But development of such a theory will have to wait until Chapters 5 and 6. In the meantime, we shall examine the possibility of probability as justification in detail.

The Probability Calculus

The heart of probability is a logical system known as the probability calculus. Using it, one may calculate the probability of something complex in terms of something more simple. For example, if the probability of p is .4, then the probability of not-p is .6, i.e., 1 - .4. Similar rules hold for conjunction and disjunction. However, the most basic probabilities are not defined by the calculus. Nor does the calculus itself state what the meaning of probability is. Various interpretations of probability have been worked out in the twentieth century. We follow the tradition in dividing them as follows.

The main distinction is between the understanding of probability as expressing definite facts about the world and as expressing an attitude of an individual subject.

The Logical Interpretation of Probability

Most of us would agree that it is a fact that a fair die has a one-in-six chance of turning up any of its given sides on a given throw. The reason is that there are six possible outcomes, and we assign each outcome an equal probability. We do so independently of any information about actual outcomes. All we need to know is the "logical space" of possibilities: that there are six outcomes. Rudolf Carnap proposed that if we could somehow carve up the logical space of the universe into discrete atomic facts, we could, independently of experience, determine the probabilities of any combination of possible facts. Carnap's ambition project was never fulfilled, it should be added.

The main objection to the a priori determination of probabilities is that the division of logical space can be made in any number of ways, each yielding a different outcome. I could, for example, decide that one basic possibility is the outcome of one on a die roll, and the other basic possibility is any other number being rolled. Since these are the two basic possibilities, I can assign each of them a probability of .5. There is nothing preventing such an assignment. So the problem with the a priori interpretation, in application to justification, is that the arbitrariness of probability assignments conflicts with our goal of getting at the truth.

The Frequency Interpretation of Probability

This deficiency is overcome by the frequency theory, which requires that we look to experience for the probabilities which hold of the world. According to the frequency theory, probability statements are meant to express the relative frequency in which a certain kind of event occurs under certain conditions. For example, it is highly probable that a bond issue will fail if there is an extremely low turnout at the polls.

Lehrer thinks that frequency probabilities do play a role in justification, but he claims that they cannot be used to characterize what makes basic beliefs self-justified. Particular beliefs about appearances, for example, would have a high probability of being true only if they are true most of the time. But for someone to be justified in believing that beliefs of this kind have a high ratio of truth to falsehood, one would have to appeal to general information. And the evidence for the truth of this justification will have to be the fact that our particular beliefs have generally been true, which is what was to be established in the first place. What we accept about the frequency of true belief can indeed aid in justification, but it is not basic, and anything it helps justify is not basic, either.

The Subjective Interpretation of Probability

So perhaps we should regard probability subjectively. That is, the probability of a proposition for a person is the degree to which that person is confident in its truth. The standard account of how to measure this degree of confidence is by the kind of wagers a person would be willing to make. Subjective probability is not plagued with the problem of objectivity. That is, one need not have evidence which supports the probability assessment. I may be confident in my own competence to judge when a color exists in an object, for example, on some grounds other than my past successes in identifying things of that color.

The problem for the subjective account of probability is that it is too liberal. So long as I am very confident in the truth of p, p is highly probable for me, regardless of whether my confidence is based on evidence that I have. So long as there is no direct conflict between p and whatever else I accept, I may hold p as confidently as I like. (Conflict of this sort is called "incoherence," which is reflected in one's willingness to make a bet that one must lose.) And this would mean that I am justified in accepting that p, whether I had good reasons or not.

Despite this weakness in the notion of subjective probability, Lehrer initially adopted it as an element in his coherence theory of justification. In the 1980 book Knowledge, his chief objection was that identifying justification with high probability runs afoul of the lottery paradox. He had hit upon a device ("answering objections," described in Chapter 6) to overcome this paradox, and this required him to adopt a coherence theory of justification. But in our present text, Lehrer also incorporates explanatory elements into his account of justification. So in the next chapter, we will consider both explanation and coherence in their roles in justification.

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