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

Chapter 5, The Explanatory Coherence Theory

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

Avoiding Foundationalism

The rejection of foundationalism leaves open the possibility of skepticism. It may be that if there are no self-justified beliefs, then there are no justified beliefs whatsoever. An argument for this conclusion can be generated easily, based on Aristotle's "logical" motivation for foundationalism.

  1. If there are no self-justified beliefs, then the process of justification is either endless or else loops back on itself in a circle.
  2. An endless or circular process cannot produce justification.
  3. Therefore, if there are no self-justified beliefs, then there is no process that produces justification.
  4. If there is no process that produces justification, then no beliefs are justified.
  5. Therefore, if there are no self-justified beliefs, then there are no justified beliefs.
Lehrer wishes to avoid skepticism, so he tries to counter this argument.

The first attack is a denial of the claim made in step 4. Justification, according to Lehrer, need not be a process at all. We commonly think of justification in terms of a process of "appealing to evidence," as is reflected in Lehrer's linkage of justification with answering the question "How do you know?" To give an answer, one would appeal to evidence. But S can be justified without such an appeal if p, the information at issue, is related to the body of S's beliefs by cohering with it in a suitable way. Lehrer motivates this view by appealing to analogies.

A belief such as this one [that my friend is now in Tucson] may be justified for a person because of some relation of the belief to a system of information to which it belongs, the way it coheres with the system, just as a color in a painting may be beautiful because of some relation of the color to the other components in the painting, or as a piece in a puzzle has place in it because of the way in which it fits with the other pieces. (p. 98)
This is a plausible response, since we typically ascribe knowledge to people who have not gone through any explicit process which we might call "appeal to evidence."

The foundationalist might press this line of objection by demanding that S at least be able to go through the process of justification. It seems that Lehrer is committed to at least this much, given statements like this one in Chapter One, "The person must be justified in a way that would justify him in accepting that he knows, if he considers whether he does" (p. 14). It is plausible to assume that the way S would, on consideration, justify accepting that he knows would be by appealing to evidence.

Lehrer gives one response that is aimed at part of premise 2 of the foundationalist argument. We might be capable of carrying any given step in an infinite process of appealing to evidence, though we could not carry out every step. By analogy, we may be able to add one to given any given number, though we could not add one to every number. (For an extended discussion of this strategy, see Ernest Sosa, "The Raft and the Pyramid: Coherence vs. Foundations in the Theory of Knowledge" Midwest Studies in Philosophy 5, 1980, pp. 3-25. The essay is reprinted in Sosa's Knowledge in Perspective.) Lehrer does not follow up on this line, however.

Instead, he turns to another foundationalist objection, namely that some beliefs seem not able to be justified by appeal to evidence.

For example, a person might justify her belief that she sees an apple by appeal to the evidence that there is an object before her that looks red and apple shaped, and she might justify her belief that the apple before her looks this way by appeal to the evidence that she thinks that there is an object that looks this way; but, eventually, she must reach a point where no further evidence can be elicited. (p. 99)
These beliefs would correspond to what Aristotle called "indemonstrables." (Note that Aristotle's argument for foundationalism was aimed at what we might call justification through demonstration, and in demonstration there is an explicit appeal to evidence.) One response to this is that in practice we would be willing to call off the demand for further justification. If someone told me that she thinks there is an object that looks red and apple-shaped, I would not see any point in asking her to adduce evidence that this is what she thinks. But the issue here is epistemic, not practical: "there is a kind of justification aimed at obtaining truth and avoiding error that requires only those things should be taken for granted that are already justified in terms of those objective" (p. 99). So how can the beliefs about how things appear to a person, which we take for granted, get the justification they need?

To answer this question, Lehrer reverts to his first response to the foundationalist argument: "Even when no evidence is offered to justify a belief, the belief may be justified by the relation of the belief to a person's system of beliefs" (p. 99). The belief system "supports" the beliefs without any appeal being made to it. The example Lehrer uses to illustrate this claim is tricky.

Suppose we grant that someone cannot appeal to evidence to support her belief that something looks red to her. Her belief system implies that the fact that something looks red to her (and that there are no unusual circumstances) explains why she believes that something looks red to her. "People ordinarily believe that something looks red to them because something looks red to them!" (p. 99). This might be enough to justify her belief.

I would also argue that this kind of justification involves at least a potential appeal to evidence. If asked, "How do you know that something looks red to you?" she might reply in this way. "'People ordinarily believe that something looks red to them because something looks red to them,' and moreover I believe that something looks red to me and have no reason to think that anything is out of the ordinary. So the best explanation for why I believe what I do is that something does look red to me. And since this explanation requires that my belief be true, I have good evidence for my belief and am justified in believing it." This looks a great deal like an appeal to evidence.

Yet Lehrer claims that "It might seems strange for a person to appeal to such a consideration as evidence that something looks red to her" (p. 99). We are not told why it might seem strange. I think that the way Lehrer phrases his description of what seems strange may be misleading. To be sure, if someone asked me, "What evidence do you have that something looks red to you?" I might be unable to respond. But is this the right question? It seems that the question should be this, "What evidence do you have that your belief that something looks red to you is a true belief?" Then I could answer as above: the very fact that I believe it, coupled with my further, general, belief about why people believe such things.

Avoiding the Appeal to Evidence

In my view, Lehrer's primary response to the foundationalist should not be to deny that justification requires potential appeal to evidence. We are trying to determine when a person is justified in accepting something, that is, when a person has reason to think that the goal of believing all and only what is true has been met. Since acceptance is essentially tied to evaluation (p. 40), we need to be able to appeal to evidence in order to be able to provide that evaluation.

This point is especially important in view of Lehrer's use of the charge of opacity against his foundationalist opponents (pp. 61-63, 83). Any information which is germaine to providing justification for S must be "revealed and transparent" to S (p. 61). The mere fact that a belief is guaranteed or likely to be true does not suffice for justification. I think this consideration applies to the relation of coherence of a belief with a belief system. The fact of this coherence must be "revealed and transparent" in order for it to be a factor in the person's justification. The coherence is revealed in the present case by appeal to the evidence that people ordinarily believe they do about the way things look because things do look that way.

If I am correct, then Lehrer's only serviceable response to the foundationalist here is in conceding the possibility of a "loop" of justification. In Chapter 1, he had offered coherentism as an alternative to foundationalism which denies that justification requires argumentation. I have argued that it still requires at least potential appeal to evidence, which Lehrer seems to equate with argumentation. I think that the best response to the foundationalist is to recognize that the relation of "mutual support" (p. 16) is compatible with the demand for appeal to evidence in all justification. It may be that p is appealed to in the justification of q and q is appealed to in the justification of p. Lehrer had already made the point in Chapter 4, though not in terms of appeal to evidence.

It is difficult to believe that such general beliefs [about the truth-frequency of beliefs] are not justified by other particular beliefs. Within a foundation theory, these general beliefs cannot be justified by particular beliefs without arguing in a circle. But the particular beliefs cannot be justified by those general beliefs without arguing in a circle, either. This suggests, contrary to the foundation theory, that the justification of both kinds of statements may be reciprocal, that each justifies the other as a result of cohering with a system of beliefs containing particular beliefs about what we experience, as well as general beliefs about our competence to discern truth from error and the frequency of our success in so doing" (p. 93).

So I am suggesting that the coherentist counters the foundationalist's argument by allowing that the justification for a belief can loop back on itself, which is dismissed in premise 2. Lehrer wants to avoid the charge of circular reasoning by claiming that some justification does not require appeal to evidence (though it does require coherence with one's system of beliefs). My view is that his basic approach to knowledge cannot dispense with appeal to evidence. Given Lehrer's embrace of "the virtuous loop of reason" for another purpose in Chapter 6, one wonders why he is so eager to avoid the foundationalist's charge of circular reasoning here. A fuller examination of this issue will have to wait until we get to the next chapter.


Classically, philosophers have turned to coherence as a factor in justifying belief when the belief is to some extent uncertain. We will begin our discussion of coherence with a look at a relation we can call "concurrence," which has been appealed to by a number of philosophers in the past. Our beliefs about objects of sense-perception are at least partly justified by their concurrence with other beliefs, as are beliefs about the unobserved causes of what is observed. The general idea is that we have different sources of information, whose testimony is made more plausible when each source is in agreement with the other. For example, the presentations of the various senses may or may not be harmonious. Or, various symptoms of a certain cause may agree or not agree.

The seventeenth-century philosopher John Locke held that agreement between sense-presentations testifies to the existence of a given external object.

Our senses in many cases bear witness to the truth of each other's report, concerning the existence of sensible things without us. He that sees a fire, may, if he doubt whether it be anything more than a bare fancy, feel it too; and be convinced, by putting his hand in it. (An Essay Concerning Human Understanding, Book IV, Chapter XI, Section 7)
The ancient Academic skeptic Carneades made concurrence a factor in plausible belief, which he thought falls short of the justification required for knowledge.
And just as some doctors do not conclude from one symptom that someone is really feverish, for example a quickened pulse or just a high temperature, but from a combination of symptoms, for example, high temperature, quickened pulse, soreness of touch, a rash, thirst and the like, so the Academic makes the judgment about the truth on the basis of a combination of presentations, and when no one of these [strikes] him as controverted [and so] false, he states that the [impression] he receives is true. (Sextus Empiricus, Against the Mathematicians, Book VII, 179.)

Descartes, also writing in the seventeenth century, put coherence up to a more demanding task: to enable us to distinguish sleeping from waking, something which cannot be done merely on the basis of appearances, as the realistic appearance of vivid dreams shows.

For now I notice that there is a vast difference between the two, in that dreams are never linked by memory with all the other actions of life as waking experiences are. If, while I am awake, anyone were suddenly to appear to me and then disappear immediately, as happens in sleep, so that I could not see where he had come from or where he had gone to, it would not be unreasonable for me to judge that he was a ghost, or a vision created in my brain, rather than a real man. But when I distinctly see where things come from and where and when they come to me, and when I can connect my perceptions of them with the whole rest of my life without a break, then I am quite certain that when I encounter these things I am not asleep but awake. And I ought not to have even the slightest doubt of their reality if, after calling upon all the senses as well as my memory and my intellect in order to check them, I receive no conflicting reports from any of these sources. (Meditations, the Sixth
Here it looks as if Descartes is claiming that concurrence is a necessary condition for justifying beliefs about one's being awake. And given that one must be justified in believing that one is awake to be justified in the belief one has about the presence of a physical object, it seems that all justification for this kind of belief depends on considerations of coherence.

For all these philosophers, concurrence is used to boost the reasonableness for beliefs which already are reasonable to some extent. Locke had advanced several considerations that make it reasonable to believe that a physical object is present, e.g. that one cannot avoid having the perception of the object when the senses are turned toward it. (Section 5). Carneades required as a starting point the apparently true or "plausible" sense-presentation. He advocated the test of agreement for important matters in contexts when we have enough time to apply it. Descartes had said that "nature" teaches him some truths (though our sense-perceptions are largely confused). Roderick Chisholm in the 1960s developed a theory of justification where concurrence provides further justification to beliefs that are already justified to some degree (Theory of Knowledge, Chapter 4.)

Lehrer would regard all of these as foundations account of justification or plausibility, which he rejected in Chapters 3 and 4. His task is to present an account of justification where coherence is what makes all of our justified beliefs justified. According to him, a coherence theory of justification holds that:

S is justified in accepting that p if and only if p coheres with other beliefs belonging to a system C of kind k.

Lehrer states that the development of a coherence theory will have to state what the relation of coherence is (beyond the metaphor "mutual support") and what the right kind of system is. As will be seen, his ultimate account of coherence differs from the kinds of concurrence that have just been illustrated.

Logical Coherence

It was in the nineteenth century that philosophers began to develop more detailed accounts of coherence and turned it to a new use. Hegel, writing at the beginning of the century, proposed a dialectical method of doing philosophy, such that more advanced forms of knowledge absorb elements of the older forms, until knowledge becomes a completely comprehensive whole. In the end, the only "justification" of a belief lies in its relation to the totality. This approach was picked up by some British and American "absolute idealist" philosophers in the late nineteenth and early twentieth centuries. The kind of coherence account they proposed was not based on Hegel's dialectical method, but instead was based on the logical relation of implication. The account of implication they and Lehrer us is one according to which p logically implies q just in case it is not possible for p to be true and q to be false. I call an account of coherence based on the notion of logical implication (or logical possibility), a theory of "logical coherence."

The minimum level of logical coherence is consistency. So for a body of information to be coherent in this minimal sense, it must harbor no contradiction. An individual piece of information p would cohere with a body of information C by failing to contradict anything in C or anything implied by C. Lehrer assumes that consistency is a necessary condition for coherence (p. 104). But consistency is far too weak a relation to suffice for justification. Otherwise, I could be justified in accepting anything not containing a contradiction in itself, so long as it is consistent with my belief system C. I could be justified in believing that there are mice on the moon if this information does not conflict logically with any other information I hold, even if I have no positive evidence for there being moon-mice. (It is a virtue of foundationalisam that every justified belief requires some degree of support, even if it is self-support.)

On the other hand, the relation of coherence becomes extemely strong--too strong--when based on logical implication. There is a good deal of disagreement about the details of this kind of coherence, but we can work with a simple version: p is logically implied by the set of the beliefs in C. On the face of it, such a demand seems almost impossible to meet, at least for information about what is a matter of fact rather than logic. All my beliefs taken together do not logically imply my belief that I am now writing these notes, though they make it very reasonable.

Moreover, as Bertrand Russell pointed out, it is possible to have two systems of equal coherence, that is, where each member of the system is implied by all others, but where the first is the exact opposite of the second. Logical coherentists have responded to this type of criticism by claiming that the system C must contain observation statements, so there are grounds favoring one system over another which is "equally coherent" with it. (See Jonathan Dancy, Introduction to Contemporary Epistemology, pp. 113-116.) We will see below, however, that it is not clear how such a requirement can be implemented.

As Lehrer understands logical coherence, p coheres with C just in case it implies or is implied by every individual member of C (p. 100). This seems to be an impossibly strong requirement. Take a system with three beliefs: that q, that if q then p, and that p. The belief that p is implied by the other two beliefs, but it would not meet Lehrer's condition for coherence because p is not implied by q alone, to take one case.

For proponents of a logical view of coherence, it is the relation of a belief to the body of beliefs taken as a whole that is important. Thus A. C. Ewing proposed this definition:

a set of propositions in which each one stands in such a relation to the rest that it is logically necessary that it should be true if all the rest are true, and such that no set of propositions within the whole set is logically independent of all the propositions in the remainder of the set." (Idealism: A Critical Survey, pp. 229-30)
We can see that in the schematic example of the last paragraph, the belief that p meets the first part of this test. (But notice that neither the belief that q nor the belief that if q then p is logically implied by all the members of the set.)

Lehrer gives us a recipe for generating "decisive" counter-examples against logical coherence as he understands it as a necessary condition for justification. Take any two beliefs that do not imply each other, and hence would not satisfy the conditions Lehrer lays down for coherence, but which (intuitively), we would say are justified. They "may be related in some way: they may be consequences of some more general law of nature, but they are not related to each other" (p. 100). If they are consequences of a more general law of nature, then each of the two is related to the others in the way Ewing requires. For each of the two, if all the other members of the set are true, it is too. And each is a member of a set that includes the general law, so they do not belong to two isolated sets.

Moreover, a logical coherence theorist would probably not allow, as Lehrer does, that beliefs can be justified if they do not meet the coherence condition. For them, justification is more than being relatively reasonable. It is instead the fitting of a belief into a comprehensive account of the world, a metaphysical theory. Like Hegel, the logical coherence theorist is a "metaphysical holist," who claims that the nature of each thing in the universe depends to some extent on the nature of all other things.

The seventeenth century German philosopher Leibniz gives a classic statement of holism, illustrating it with the metaphor of a pebble tossed into a pond: though its rippling effect diminishes as the distance from the point of impact increases, there is still some effect throughout the pond. So no body in the universe is unaffected by anything else, and in fact my present activity does bear some connection to the movements of a distant star in the distant past.

Ewing succinctly lists three conditions that he claims imply the truth of the logical coherence view:

(a) that everything is causally determined; (b) that everything is, directly or indirectly, causally connected with everything else, so that there is no series of events in the universe which is causally dependent of all events outside that series; (c) that the relation of causality involves a relation of logical entailment, so that whatever is causally impossible is also logically impossible relatively to the rest of the system. (Idealism: A Critical Survey, p. 231)
It is not at all clear how these metaphysical doctrines can be of help in a theory of justification of they type we are trying to develop.

In order to know that p, one would have to have a system of beliefs C that pictures a connected causal order of things in a way that p is a logical consequence of that order. Suppose, with Lehrer, that someone can infer an observation statement about an object from "some more general law of nature" (p. 100). This would not suffice to make it justified on the logical coherence view, since this general law of nature would itself have to be implied by the rest of the system. Moreover, as we will see below, specific observation statements do not follow by themselves from general laws of nature. They require information about "boundary conditions," which determine how the law will operate on a given occasion. And this information would also have to fit absolutely tightly with all the other information the person has.

Thus, it looks as if logical coherence is an ideal to which we can only aspire. Anyone adopting logical coherence as an account of justification will have to hold either that few, if any, of our beliefs are justified, or else that they are justified only to a certain degree. (One way out would be to make the system C very simple, but as Lehrer points out later in the chapter, this leads to sterility (pp. 108-109).)

Explanatory Coherence

So it appears that logical coherence is too strong a condition for the kind of justification that individual humans attain in their quest for correct information. In particular, as Jonathan Dancy points out, we would like to have a view of coherence that will account for the fact that "justification can grow." If we understand coherence in terms of explanation, which we may suppose is not so demanding as logical implication, we can hope that a system of beliefs can become increasingly more coherent as "each member of it is better explained by the rest" (An Introduction to Contemporary Epistemology, p. 111). This suggests that the standard for justification rests in a comparison of systems C, so that p is justified better in a system with more explanatory coherence than in one with less.

This kind of view, enunciated by Lehrer's teacher Wilfrid Sellars, is the focus of discussion in Chapter 5. It should be noted from the outset that the motivation for such a theory, to account for the growth of knowledge, is not the same as Lehrer's motivation for a theory of justification, to account for the adequacy of one's evidence at a single time. The idea of explanatory coherence is that one's justification is relatively good because it is supported by belief system C, which is relatively better than other systems. This immediately raises the question of opacity: how could someone answer the question "How do you know?" by appealing to the superiority of his belief system to other systems? Lehrer does limit the comparison systems to ones that the person could understand, but if that person were unaware of there being or not being better explanatory systems, then that information would be opaque and could not be a part of the person's justification. So in general, it looks as if this kind of explanatory coherence is a non-starter for Lehrer. We will consider another kind of explanatory coherence below.

Justifying by Explaining

Traditionally, philosophers have taken a kind of foundationalist approach to explanation. We begin with observable "data" which we take as given and through explanation provide new information about what is not observable: an "explanatory hypothesis." We observe that bread nourishes, but not how it does so. We observe that the heavenly bodies change position relative to our position on earth, but not what brings about this change. In general, explanation provides us with causes of observed phenomena. We are justified in believing that the causes exist, it is held, by virtue of their role as explainers of what we already are justified in believing exists. A classic example cited by Lehrer is Bertrand Russell's claim that it is reasonable to believe that physical objects exist by virtue of taking them as causes of what we directly observe, which is our own psychological states (p. 101). As Lehrer notes, one might make the stronger claim that the explanatory role of physical objects makes belief in their existence justified.

A revealing statement of the asymmetrical relation between what is justified by the observations and what is justified by explaining the observations comes from Descartes.

For I take my reasonings to be so closely interconnected that just as the last are proved by the first, which are their causes, so the first are proved by the last, which are their effects. It must not be supposed that I am here committing the fallacy which logicians call 'arguing in a circle.' For as experience renders most of these effects quite certain, the causes from which I deduce them serve not so much to prove them as to explain them; indeed, quite to the contrary, it is the causes which are proved by the effects. (Discourse on Method, Part Six)
We may rephrase Descartes's description by saying that our belief in an explanatory hypothesis (what Descartes calls a "supposition") is justified by our beliefs about the data of observation, which themselves are justified independently.

The tricky issue is deciding how hypotheses are justified, given that in principle there are potentially many different causes which would explain something that is observed. Descartes, in the part of the Discourse just cited, claimed that he could in fact derive the causes from "primary truths." In that case, the cause is not really proved by the effect, however: it is justified "from above" (so to speak) by beliefs which are independently justified. (In Descartes's case, we derive the primary truths from our knowledge of God.)

Most philosophers have not been so confident as Descartes about possibility of independent justification of explanatory hypotheses. They think that there is no other way to justify belief in causes than through their ability to explain the effects. Epicurus, in his letters to Herodotus and Pythocles, took the possibility of alternative explanations to be a virtue, as it frees one from the fear of the gods brought about by theological explanations of meteorological phenomena. Nearly everyone else, however, has held that some explanations are better than others. If being an explanation is to justify a belief, it should be the best explanation. But as we will see, it is difficult to say what makes one explanation better than another.

We have not yet made an explicit connection between a relatively good explanation and justification. So far, Lehrer has given us little to go on in understanding what justification is. Here is a summary of what we have gleaned so far. S's justification for a belief that p requires that there is a body of evidence E, consisting in what S believes, that supports p. Support can be understood as promoting the goal of accepting all and only what is true. E makes it more than merely reasonable for S to think that the goal is satisifed in the case of p. One way in which this might occur is that E makes it possible to exclude possibilities under which p is false. Does p's role in an optimal explanation conform to this notion of justification?

Lehrer states that "Explanatory relationships can yield justifications" (p. 120), but he thinks that they do not always do so. One reason they need not produce justification is that the goal of explaining why something is the case can diverge from the goal of attaining the truth and avoiding error. "We may aim at truth without aiming at explanation, and we may aim at explanation without aiming at truth" (p. 120). In order to evaluate this claim, we need to know what it is that we are aiming at when we aim at explanation.

When we try to explain something whose existence we take for granted, our aim is to fill a gap in the information we possess. We do not look for explanations unless there is some aspect of a state of affairs that we fail to understand. But what does it mean for someone to understand something? It is difficult to give a simple answer to this question. Roughly, we want to be able to integrate the given data with a more comprehensive view of things, a view which we take ourselves already to understand. This can be done in various ways. Often, we turn to analogies. If I want to understand the behavior of an object with a body like my own which behaves very much like I do, I hypothesize that the body is controlled by a mind like my own. Another way to get integration is to bring the data under a causal law that applies in cases we think we do understand. Of course, often an explanation will require the hypothesis of a new law that deviates greatly from our current understanding.

Because some explanations are better than others, we shall now list some desirable characteristics of explanations. They are desirable because they appear to promote the end of integration with a more comprehensive view of things, in ways that are more or less obvious.

A cursory inspection of this list reveals that these features may have to be weighed against one another, and as Lehrer points out, it may be that rival explanations may turn out to be equally good overall by being stronger on different points.

Granted that the aim of explanation and the aim of justification are defined differently, the question remains whether meeting the aim of explanation is sufficient to satisfy the aim of justification. Lehrer (in Chapter 6) recognizes that one of the aims of justification is promoted by explanation, i.e., generality. "The more informative a statement is, the more it tells us about the world, the greater our gain in accepting it if it is true, and the greater our risk of error" (p. 145). The aim of accepting all of what is true, then, is promoted by the generality of explanation. The most informative statements are the high-level explanatory claims of science. "The reasonableness of accepting such claims is influenced by our interest in accepting claims, which, if true, are important general truths about ourselves and the universe" (p. 145).

I would add that the comparative aspect of an explanation's being the best is directly relevant to the other aspect of acceptance: accepting only what is true. Indeed, when we seek a good explanation, we are especially careful not to draw hasty conclusions. We must take into account alternative hypotheses and try to show how they are excluded. Also, it must be shown how the explanation coheres with the relevant portions of the rest of our view of the world. What I am describing resembles very much the account we have seen so far of justification.

So although the aim of justification and the aim of explanation are different, the way in which the aim of explanation is realized directly promotes the aim of justification. The real difference between the two is that the aim of explanation is more specialized. Specifically, it is the discovery of new information that will allow us to improve our understanding of what we already accept.

One way to see the difference between explanation and acceptance is to note that, for Lehrer, justification is "synchronic." It is a relation holding among the beliefs of S at a particular time t. It involves an evaluation of existing beliefs. Explanation, when viewed as a process with an aim in mind, is "diachronic," spanning a range of time. The beginning point is the recognition that new information is needed to correct a deficiency in the information we already have. The ending point is the absorption of the new information, resulting in a new (and, it is hoped, improved) system of beliefs.

There is a synchronic way to understand explanation. What one believes at a given time may be justified by the explanatory role played by what is believed at that time. In that case, explanation does not fill a gap by providing new information: the information that does the explaining already exists. But it does fill a gap that would exist were one not to have the belief. And it does so in ways that, as has been argued above, are very similar to what Lehrer recognizes as being justification.

Justifying by Being Explained

So far, our focus has been on explanatory hypotheses or purported laws of nature that are more than empirical generalizations, both of which seem to be justified, if at all, by the way they explain. Lehrer widens the field by noting that some beliefs might be justified because they are explained. Consider beliefs I have about physical objects. As already mentioned, these beliefs might be justified because they explain some of my psychological states. But they are, in turn, explained by theories of perception. It seems that being explained increases their justification. "It is those beliefs that both explain and are explained whose justification seems most adequate" (p. 103).

Lehrer conjectures that the combination of explaining and being explained is what recently has moved "philosophers of empiricist leanings [to tend] to construe the fundamental empirical statements as perceptual claims concerning physical objects rather than reports concerning sense data" (p. 103). My own conjecture is that the move away from sense data is due more to the influences of externalism and of recent psychological theory. Indeed, sense data themselves might be construed as explanatory postulates.

It remains to be seen why the fact that p is well-explained contributes to its justification. One thing it can do is provide new information. This is reflected in Lehrer's account of what he sees in a cloud chamber. He observes a streak and conjectures that it is the path of an alpha particle, and after receiving an explanation of how alpha particles cause condensation, he allows that he may "become justified" (p. 103). The explanation gives him evidence about what the streak is. If asked, "How do you know that this is the path of an alpha particle?" he can give an account of how alpha particles cause condensation of the kind he observes. But one might want to say that what supplies the missing justification is simply the addition of new information. The fact that it is explanatory information does not per se account for why he is now justified synchronically.

The cases that fit better with Lehrer's synchronic account of justification are those in which one already has the information which is explained. Does the explanatory role of information that explains the fact that p help justify S in believing that p? To put it in Descartes's provocative language, these would have to be cases where "the cause proves the effect." One has the information that alpha particles produce a certain sort of streak under the current conditions and that this sort of streak is observed. This directly supports the belief that the streak is the path of an alpha particle. It is the generality of explanation which, in conjunction with information about the specific situation (the "boundary conditions"), shows us how to apply unobservable properties to what we observe.

Lehrer gives another example that may seem to involve only observable properties, i.e., the belief that a chair supports him. This explains why he does not fall to the floor given his posture (where we assume he would fall to the floor if unsupported). And the rigidity of the chair, along with other factors, might explain why the chair supports him. But I think that the relation of supporting is not observable. I can observe that the chair is under me, but this is not an observation of its supporting me. It might be that the chair is extremely fragile, and I am being supported by some system of magnets. Thus the claim that the chair is rigid is a kind of theoretical claim, which fits the information that I am not falling into a broader framework of beliefs. The bottom line is that in cases of p's being explained, as in the cases where it explains, the explanation consists in the kind of information that would lead one to think that p is true in the first place.

Theory and Observation

Throughout the preceeding discussion, we have been assuming that there is a distinction between those beliefs which are the justified on the basis of observation, and theoretical beliefs which are justified at least in part by their role as explainers. Philosophers in the last half of the twentieth century have questioned whether there is a clear distinction between theoretical beliefs and observational beliefs. A very clear example of this is the sixteenth-century dispute between Galileo and the Aristotelians about the motion of the earth.

Since the beginning of astronomical speculation, philosophers have tried to account for their observations of the heavens. What is observed is changes over time in the relative positions of heavenly bodies. Consider the position of the sun relative to the Earth. We seem to observe that the sun moves while the Earth remains at rest.

It was recognized early in the development of Greek astronomy that there are alternative ways of explaining what is observed. The situation in the 4th century BCE is described by Aristotle in Chapter 14 of his book On the Heavens.

Let us first decide the question whether the earth moves or is at rest. For, as we said, there are some who make it one of the stars, and others who, setting it at the center, suppose it to be 'rolled' and in motion about its pole as axis. (On the Heavens, Book II, Chpater 14).
Although he ultimately decided in favor of the claim that the earth is at rest, he regarded this as a theoretical claim, not an observational claim. He tried to show that the earth's motion conflicts with various established principles of physics and with observational data. One argument begins with the observational data which show that the parts of the earth move in a straight line toward its center. Now suppose the earth were rotating on its axis. Then the whole motion of the earth would be different from the motion of the parts. The motion of the parts is "natural," and so the motion of the whole earth would be "unnatural." But what is unnatural is not eternal, while "the order of the universe is eternal."

The Aristotelian explanation became dominant during the Middle Ages and was defended by the Roman Catholic Church. The appeal of Aristotle's view was its conformity to Biblical passages stating that the earth moves. Copernicus challenged Aristotle's doctrine, on the grounds that he could give a better explanation of the observations of the motions of the heavenly bodies. He claimed what the ancient Greek theorists recognized, that observation can never determine "real" motion or rest, but only motion or rest relative to a framework. Thus we humans may be at rest relative to the Earth, but the Earth itself may be moving around the sun (with us along for the ride). "The principal arguments by which the natural philosophers attempt to establish the immobility of the earth rest for the most part on appearances; it is particularly such arguments that collapse here, since I treat the earth's immobility as due to an appearance" (The Commentariolus, comment on the assumptions). Galileo supported the Copernican hypothesis in his book Dialogues Concerning the Two Chief World Systems. He presented the Aristotleian position as taking as the base-line observational data the straight-line motion of falling bodies. He has the spokesman for Aristotle, Simplicius, state the following:

He held in his philosophy that sensible experiments were to be preferred above any argument built by human ingenuity, and he said that those who would contradict the evidence of any sense deserved to be punished by loss of that sense. Now who is there so blind as not to see that earthy and watery parts, as heavy things, move naturally downward--that is to say toward the center of the universe, assigned by nature herself as the end and terminus of straight motion? Dialogues, The First Day
The obvious answer here is that all one sees is apparent straight-line motions. Galileo advanced an ingenious argument to show that the appearance of straight-down falling would be the same if the earth were moving.

A related case is that of the relative positions of the heavenly bodies. Historically, these were the base-line data that astronomers like Copernicus and Galileo thought they had to explain. These can be established very roughly by the naked eye, but precise observations require the use of instruments. In order to interpret the data produced by the instruments, we need some kind of theory.

Wilfrid Sellars made the point explicitly. There is no clear line between what is theoretical and what is observational. Thus we should prefer scientific systems which bring their general laws ("nomologicals") and particular information into the greatest degree of harmony.

Instead of justifying nomologicals by an appeal to observation statements the predicates of which would have conceptual meaning independently of any commitment to laws, the problem is rather that of deciding which conceptual meaning our observation vocabulary is to have, our aim being so to manipulate the three basic components of a world picture: (a) observed objects and events, (b) unobserved objects and events, and (c) nomological connections, so as to achieve a world picture with a maximum of 'explanatory coherence.' In this reshuffle, no item is sacred. On the other hand, it is obviously reasonable to preserve the achievement status of as many observation claims as possible, for the more we preserve, the more the world picture we select is 'based on observational evidence.' ("Some Reflections on Language Games," in Science, Perception and Reality, p. 256)
Sellars's vision is clearly aimed at the practice of science by the scientific community. We would like our science to achieve a "maximum" of explanatory coherence, to give us the "best" explanation among as many competing explanations as possible. The reason the explanatory relation is one of coherence, rather than the simple model of cause and effect we worked with in the previous sections, is that explanation is holistic, to the point that we must be prepared to abandon some of our current "observational" beliefs if a better explanation dispenses with them.

The Best of All Explanations and Justification

Lehrer formulates the explanatory coherence theory in terms of the explanatory values of different systems of beliefs C.

S is justified in accepting that p if and only if the belief of S that p is consistent with that system C of beliefs having a maximum of explanatory coherence among those systems of beliefs understood by S, and the belief that p either explains something relative to C that is not explained better by anything that contradicts p or the belief that p is explained by something relative to C and nothing which contradicts it is explained better relative to C. (p. 105)
We may be spared the details of this analysis, because it is doomed from the start. This kind of explanatory coherence is clearly ill-suited to the analysis of justification for ordinary beliefs, for in our everyday explanations we do not have global alternatives before us. As mentioned above, what counts as the "best" of all explanations may be opaque to a person in a given case. Lehrer thinks that relativizing C to systems the person can understand takes care of the opacity objection (p. 104, though see p. 116 where in another context he applies the opacity objection in much the same way as has been done here). But even if S were aware of all the systems he could understand (a dubious assumption at best), there is no reason to think that S can tell which of them is the best system of explanation. We often have a very difficult time telling when one simple explanation is better than another!

Lehrer himself levels a number of criticisms at this proposal. They can be divided into three types:

These will be discussed in turn.

What is Explanation?

We have listed a number of features of a good explanation without ever having really said what explanation is. It is tempting to try to give a rigorous definition in terms of logical relations, reminiscent of the logical account of coherence. The "covering law" account of explanation holds that an explanation consists of a general law, a set of boundary conditions, and a deduction of what is to be explained from the two.

For example, suppose there are very few mice in the field near my house, while the area near my friend's house is overrun with mice. An explanation might be that there is an owl that lives in my barn, while there are no owls living near my neighbors. On the covering law view, there would be a statistical law about the eating habits of owls which, when combined with the boundary condition that there is an owl in one vicinity but not the other, yields the result that the number of mice in the first will be much less than that in the second.

So one might think that it is enough for an explanation to be able to specify how the given data are consequences of some general pattern or law and some boundary conditions. However, the example taken from Bromberger is intended to show that fitting into a pattern is not enough. In this example, an owl is atop a flag pole four feet high, and a mouse is three feet from the base of the pole. The general pattern is the Pythagorean theorem, according to which it can be concluded that the mouse is five feet from the owl. But the boundary conditions and the Pythagorean theorem do not together explain the distance from the mouse to the owl, because owls eat mice. To explain the distance, one needs to show why the pattern of predatory behavior is not in effect in this case.

Lehrer takes this to indicate that a second condition for explanation is needed. An explanation must give a satisfying account of why a given state of affairs exists. But it is no easy matter to state what is to count as a good answer to the "why" question. It seems as though a good answer is one which gives the individual knowledge. But if this is correct, then we cannot use the concept of explanation to give an account of justification, for we have counted justification as a condition of knowledge. To invoke knowledge as a condition of justification would be to go in a circle.

One suggestion for overcoming this problem for giving a non-circular account of justification would be to appeal to the holistic character of explanation. It would seem that the covering-law account of justification unduly isolates one feature of the situation. It abstracts the distance between two objects from their nature, treating them as mere geometrical quantities. This has proved to be a powerful tool for providing simple explanations. But it fails to explain the current situation because there are factors there which remain to be explained. So we get, at best, a partial explanation based on the use of purely mathematical reasoning. We could say that the distance is explained but not why those two animals are so close to each other.

What is the Best Explanation?

As noted above, a number of different factors are relevant to how good an explanation is, so it is difficult to state when any given explanation is "better" than another (let alone when one explanatory system is better than another). Take simplicity as an example. It is hard to define precisely what it is; and whatever it is, it takes many forms. One can make great gains in simplicity by eliminating observational information. Galileo himself introduced the practice of "idealization," in which many observational details (which might be resistant to explanation) are left out in order to get simple explanatory equations. Explanatory coherence is also promoted when the explanatory laws are very general, but this coherence may be purchased at the price of comprehensiveness. In the history of science, there are cases in which a theory of sweeping generality fails to explain a few observations and eventually gives way to an even more general theory. (Newtonian physics could not explain the orbit of Mercury, but Einsteinian physics could.)


The problem of gaining simplicity by reducing the data-set suggests that it is more than relative explanatory coherence which makes one explanation better than another. As the passage from Sellars suggests, another factor is the conservation of the observation statements we presently accept. This is a principle of conservatism, and it is the basis of Harman's explicit linking of explanatory cohrence with justification.

It is important to note at the outset a crucial difference between Harman's program and Lehrer's. According to Lehrer, being justified is a state of a person at a time. This is one way to understand the locution 'S is justified in accepting that p.' There is another way to understand it, however. If we take accepting to be an activity, then we can look at justification dynamically: to be justified is to have good reasons to "take the plunge" and accept new information. The activity of accepting results in what Harman calls a "change in view." What is especially important is that the admission of new information may force a person to reject old information that was previously accepted. This is why what justifies us in accepting some new information is that the new total system of information is better than the old total system.

What makes a change in view a change for the better? First, as has already been noted, existing information should be conserved as far as possible. Second, the new information should fill gaps in the body of old information. A good example of this is the admission of general information, which ties together the particular information we have. We make inductive generalizations from a limited body of evidence to generalities which go far beyond them. We are justified in doing so because they increase the explanatory coherence of our body of information. Lehrer himself, in Chapter 6, emphasizes the importance of generality in justification.

Lehrer objects to Harman's account of justification in part because of its conservatism, which he takes to be an impediment to bold leaps in what one accepts, "a roadblock to inquiry" (119). This criticism does not seem quite fair, given what Harman actually states:

We seek to minimize change. We attempt to make the least change in our antecedent view that will maximize explanatory coherence. Thought, p. 159.
Sometimes the least change that will maximize explanatory coherence will have to be a massive change, as with the conversion from Aristotelian to Galilean science. As the late Harvard historian Thomas Kuhn noted in The Structure of Scientific Revolutions, bodies of information invariably contain anomalies which grow less and less tolerable, until a revolution occurs which sweeps away both the anomalies and the information in which they are embedded. Nothing in Harman's description of our attempt to minimize change precludes this.

There are some other defects of the explanatory coherence theory. Sometimes the best explanatory coherence will be found in a system that is, with regard to p, relatively weak--too weak to count as justification, as in many criminal cases. Lehrer concludes that "beliefs must cohere in some comparatively strong way with other beliefs within a system for such coherence, however it is explicated, to yield justification" (p. 117).

As with the version of the logical account of coherence, Lehrer raises the possibility that equally coherent systems can yield conflicting results. It would be arbitrary to claim that there is only one system of maximal explanatory coherence. We might try to understand justification as relative to a system of beliefs C. Instead of saying that S is justified in accepting that p, we would say that S is justified-in-C in accepting that p. Then it would not matter how many conflicting systems of maximal explanatory coherence there are, since each would produce a system in which p is justified. The problem with this view is that it leaves us in the dark as to which of these relativized justifications is the one which is a necessary condition of knowledge.

Is Explanation a Necessary Condition for Justification?

The final objection to the explanatory coherence theory does not depend on the sweeping analysis of explanatory coherence itself. Lehrer tries to drive a wedge between explanation and justification, claiming that explanation is not a necessary condition for justification. There are some cases in which what justifies us explains nothing. The Pythagorean theorem may justify my belief that there is an owl five feet from a mouse, since the owl sits on a flagpole four feet high and the mouse is three feet from its base. But it does not explain why the mouse is five feet from the owl, since owls eat mice. There is no explanatory coherence here, but there is justification.

The present use of this case, which was originally proposed as a counter-example to a logical analysis of explanation, is not convincing. Given that owls eat mice, I should be suspicious of the information that there is an owl five feet from a mouse. The predator/prey relation gives me reason to doubt that the situation is as it appears to be. Perhaps there is only a wooden owl atop the flagpole or a stuffed mouse three feet from its base. These doubts must be overcome before I can be said to be justified: even Lehrer's own account of justification in Chapter 6 demands it.

Perhaps Lehrer's example of the tribe of non-explainers takes care of this objection. In this case, there is an isolated group of individuals who refuse to explain anything and do not even accept mathematical laws except as inductive generalizations. They might be said to be justified in what they accept on the basis of observation, induction and deduction from the laws and generalities. Thus they might be justified in the situation involving the owl and the mouse.

This objection does not seem to get Lehrer very far. It is not clear why the fact that these people eschew explanation means that they are not obliged, in order to have a justified belief, to face up to the fact that owls eat mice. Moreover, it is said that they use the Pythagorean theorem, which they arrive at by observation. This must mean that it is an inductive generalization, which goes beyond the observed facts; otherwise, they could not appeal to their other observations to support their belief that the owl in the present case is five feet from the mouse. But an inductive generalization is more than a mere calculating device: its generality allows us to understand cases which were not involved in the initial generalization. It closes gaps in our body of information and thereby serves as an explanation.

One could always object that not all gap-closing is explanatory. To give an explanation is to answer the question "why?" Appeal to the Pythagorean theorem does not answer the "why" question, though it does supply us with new information about the distance of the owl from the mouse. Perhaps the best response on behalf of the explanatory coherence theorist is to claim that such a construal of explanation is too narrow. As Harman puts it,

Although there appear to be cases in which there are relations of coherence that support inference that are not explanatory, this appearance may rest on a failure to remember that there are explanations that are not causal, as in mathematical explanations or Newton's explanation of Kepler's law.
If Harman is right, perhaps the Lehrer's dispute with the explanatory coherence theory is to a large extent verbal. It may be that the most salient feature of explanation is that it subsumes the particular under the general. Also, since we are talking about coherence with the whole body of one's beliefs, the line between what is explanatory and what is not must be quite blurry.

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