Version 2, November 29, 2005
Norms in Contemporary Epistemology
It is generally agreed that the concept (or concepts) of knowledge involve in some way norms or standards. (See Pollock and Cruz, Contemporary Theories of Knowledge, Second Edition, p. 123 for some sources.) We have seen how ancient and modern epistemologists have tried to account for norms relevant to knowledge. In contemporary philosophy, the treatment of epistemic norms has become much more sophisticated. Some of the main developments will be discussed here. It has already been noted that epistemic norms resemble ethical norms. Some epistemologists (most notably internalists, like Pollock) hold that the norms have to do with "epistemic responsibility," in a way that is analogous to norms governing moral responsibility. One might say, for example, that a belief is warranted insofar as it is epistemically permissible to hold the belief, given some set of standards for permissible belief.
Other epistemologists (most notably externalists, like Plantinga) think that such a "deontological" approach to norms has no place in epistemology, and that norms must be understood in a different way. They are interested in norms such as "proper functioning" (Plantinga), or "epistemic virtue" (Sosa), or "reliability" (Goldman). These external norms are largely irrelevant to whether it is permissible to hold a belief.
It might be useful here to try to find a common element in the two approaches. It seems that they would agree that norms governing knowledge have something to do with the relation between belief and truth. One might describe a belief as epistemic permissible to hold when it is conducive to a disinterested pursuit of the truth. And one might understand the satisfaction of external norms such as reliability as being conducive to attaining the truth itself. (Here we will restrict our discussion of norms connecting belief and truth to those norms which are built into a "warrant" condition of knowledge. We will not discuss conditions that might attach to knowledge directly, such as Nozick's tracking condition.)
One way of understanding the divide between the internalism and externalism is as over whether epistemic norms should be understood in terms of the actual relation between belief and truth, as the externalists would have it, or in terms of what appears internally to the subject to be the relation between belief and truth. It seems that only the latter kind of norm can be the basis of ascribing "responsibility" or irresponsibility" to a subject.
The focus of the discussion will be on claims that fulfilment of a standard or norm N is a necessary or sufficient condition for warrant. Since it may not be the case that all warranted beliefs are warranted in the same way, we will generally restrict the application of the norms in question to beliefs whose content is propositions of a certain kind. With this in mind, we can give a schema for the connection of norms and warrant.
For propositions p of kind K, if S's commitment to the truth of p is warranted, then S's commitment to the truth of p satisfies standard N.Conversely, satisfaction of a set of standards N1. . . Nn (which might consist of a single standard) is often thought to be a sufficient condition for warrant.
For propositions p of kind K, if S's commitment to the truth of p satisfies standards N1. . . Nn, then S's commitment to the truth of p is warranted.As was pointed out in the introductory module, norms can be classified generally as belonging to one of two kinds. Some norms govern the warrant of belief that p without reference to any other propositions, while others enunciate the degree of "support" that p gets from other propositions. We will consider each in turn.
Norms for Foundational Beliefs
Foundationalism is largely emphasized by internalists, and this for two reasons. First, the externalist has no real need to distinguish between kinds of beliefs, since warrant for any belief is covered by the same condition, be it "proper function," "intellectual virtue," or "reliability." Second, internalists, in emphasizing connections between belief and truth that are only apparent, would like at least to base the apparent connection on a close real connection between warranted foundational beliefs and truth.
The connection between the foundational belief and the truth might be infallible or fallible. In some cases, it appears that foundational beliefs cannot be false. But even in those cases where there is a possibility of falsehood, it is held that this possibility is mitigated in some way.
There is a small class of beliefs, including the Cartesian "I exist when thinking that I exist," that seem immune from error because of the relation between the proposition believed and the believing of the proposition. This reflects the two-fold character of belief. A belief can be regarded as a kind of mental state, which might be called the act of believing. (Such a state may be a present state, in which case it belief is "occurrent," or it may be a dispositional state.) The act of believing is directed at a content (or "intentional content"), what the belief is "about," which is expressed propositionally.
Some beliefs are self-referential, in the sense that the content of the belief involves the act of believing that very content. For example, there is my belief that I exist, and my belief that I believe something. In both cases, the act of believing makes the content true. It would seem that such beliefs are warranted in the sense that there is no way for the content of the belief to represent what is not the case.
Most beliefs about one's own beliefs do not have this self-referential character. The content of the belief is about something other than the act of believing or what it presupposes. In that case, the connection between the belief and the truth may be fallible, and at any rate is to be sought elsewhere.
The most common kind of beliefs that seem to be tightly connected to the truth is belief about one's present mental state. The reason given by many epistemologists for the connection is that we have some kind of "direct access" to our present (or occurrent) states of mind, an access that can be contrasted with our indirect access to states of the past or states of the world outside our minds. There is nothing that, so to speak, "stands between" our believing self and the state of that self which is the object of the belief.
If the belief about one's mental state is the result of this self-observation or introspection, it seems to meet a strong standard of connection to the truth, which might be sufficient for warrant.
For some p which describe a present mental state of S, if S believes that p and S's belief is based on direct access to the mental state described by p, then S's commitment to the truth of p is warranted.
One might object to this condition on the grounds that there is no direct access to one's occurrent mental states. As this is an issue in the philosophy of mind, we will only note it here.
A further criticism is that direct access to one's mental state is not by itself sufficient for warrant. The criticism has its origin in Kant, was picked up by Sellars, and was developed in more detail by Keith Lehrer and Laurence BonJour, though BonJour has since repudiated it, as will be seen below.
The kind of proposition p at work here is a description of the mental state, and as such it has conceptual content. If I am warranted in describing my mental state as one of thinking about Boston, then I need to have a reason to think that the content of my mental state is accurately described as being directed toward Boston and not, say New York or the moon. This requires the use of some general information about Boston—information that cannot be "read off" from my belief itself.
The same kind of criticism applies to beliefs about perceptual states. If I believe that I am imagining something red, I need to rely on information about what red things look like in order for my belief to be warranted. As John Pollock points out, the only way such reliance can be avoided is by reducing p to an indexical proposition expressed by a sentence such as "This is my mental state," accompanied by a kind of mental pointing. But such a proposition does not seem very promising as a foundation for warrant for beliefs with conceptual content.
BonJour has recently developed a line of defense against this kind of criticism. Consider first a meta-belief such as my belief that I presently believe that Boston is the capital of Massachusetts. According to BonJour, we have a "built-in" or "constitutive" awareness of the content of the belief just by having the belief. This awareness is infallible: there is no way that one can have, so to speak, a "mis-awareness" of what it is that one is believing.
BonJour concludes that a meta-belief that describes the content of a belief is warranted because of this built-in awareness, which puts one "in an ideal position to judge whether or not this description is true" (BonJour and Sosa, Epistemic Justification, p. 64). This is not to say that such a belief is infallible. One can have false meta-beliefs due to inattention, etc. But our attentive meta-beliefs are closely connected to the truth due to the infallibility of our constitutive awareness.
For any p which describes a present belief B of S, if S believes that p and S's belief is based on a constitutive awareness the content of B, then S's commitment to the truth of p is warranted.
This result for beliefs about beliefs is extended to beliefs about perceptual states. The parallel claim is that we have an infallible constitutive awareness of what it is we are experiencing at a given time. (This is awareness does not extend to the external objects which might be represented in our sensory experience.) Because of this awareness, we are in an ideal position to judge truly about what we are experiencing.
For any p which describes a present experiential state E of S, if S believes that p and S's belief is based on a constitutive awareness of E, then S's commitment to the truth of p is warranted.We shall not discuss BonJour's proposal further, except to note a potential difficulty. The description contained in p must contain concepts if it is to be propositional. For the constitutive awareness of an experience by itself to warrant a belief about the content of that experience, it would seem that it must be in some way awareness of conceptual content, rather than just of the pure "look and feel" of the experience.
We will end our discussion of norms for foundational beliefs at this point, though we are far from having exhausted the issues surrounding them.
Norms for Non-Foundational Beliefs
If we understand epistemic norms as involving in some way a connection between belief and truth, then the norms for beliefs that are not foundational should be concerned with way in which the truth of some beliefs is connected to the truth of others. This is a matter of "logic," in its broadest sense.
The strongest connection between the truth of propositions is that of deductive validity. If conclusion c follows deductively from premises p1, p2, . . . pn, then given the truth of the premises, the truth of c is assured. For this reason, we might formulate a principle of warrant in one of two wayas. The first is based wholly on the deductive relation between premises and conclusion, and so would be adequate for most externalists. The second requires that the premises and conclusion be connected by inference. which is what an internalist might require.
For any c and any p1, p2, . . ., pn, if S's commitment to the truth of p1, p2, . . ., pn is warranted, and c follows deductively from p1, p2, . . ., pn, then S's commitment to the truth of c is warranted.
For any c and any p1, p2, . . ., pn, if S's commitment to the truth of p1, p2, . . ., pn is warranted, and S has validly inferred c from p1, p2, . . ., pn using rules of deductive logic, then S's commitment to the truth of c is warranted.Either version of this kind of transmission-rule for warrant is very limited in its scope. The price of deductive validity is the lack of any information in the conclusion that is not already in the premises. For this reason, most contemporary epistemologists look for weaker transmission-rules for warrant.
A schematic necessary condition linking probability and warrant might be this:
If S's commitment to the truth of p is warranted, then the truth of p is probable for S.A corresponding sufficient condition would be:
If the truth of p is probable for S, then S's commitment to the truth of p is warranted.Requiring probability as a necessary condition for warrant is relatively uncontroversial, at least for internalists. Here we will focus on whether probability can serve as a sufficient condition for warrant.
Perhaps some propositions are probable in themselves, but we will focus here on probability as it functions in transmission-rules, so that p is made probable by the evidence one has. There are many important issues that arise in this connection, but before turning to them, we would do well to consider what probability is in the first place.
It is generally agreed that ascriptions of probability should conform to a set of mathematically expressed rules known as the calculus of probability (or probability calculus). These rules have been given many formulations, and we will give just one. Probability values, ranging from 0 to 1, are treated as the values of functions whose arguments are propositions. If p and q are assigned probabilities, then so are all of their logical (Boolean) combinations formed with 'not,' 'and' and 'or.' A further condition is that where p and q have probability values, so does the conditional probability of q given p, or pr(q / p).
We can illustrate the use of the calculus through an example involving throws of a die. Assume that the result of any given throw is that one and only one side will come up. We will assume as well that on any given throw, pr(1-up) = pr(2-up) = pr(3-up) = pr(4-up) = pr(5-up) = pr(6-up) = 1/6. We might have assumed other values if we thought the die were "loaded."
Thus, pr(1-up and 2-up) = 0, and pr(1-up or 2-up or 3-up or 4-up or 5-up or 6-up) = 1. Further, pr(not-1-up) = 1 - pr(1-up) = 1 - 1/6 = 5/6. Since pr(1-up and 2-up) = 0, pr(1-up or 2-up) = 1/6 + 1/6 = 1/3.
Now let us calculate the probability that the die will come up 1 on each of two consecutive throws. We already know that pr(1-up-throw-one) = 1/6. To calculate pr(1-up-throw-one and 1-up-throw-two, we need to know the value of pr(1-up-throw-two / 1-up-throw-one). We can assume that the two throws are independent: the first result has no effect on the second. In that case, pr((1-up-throw-two / 1-up-throw-one) = pr(1-up-throw-two). Thus, pr(1-up-throw-one and 1-up-throw-two) = pr(1-up-throw-one) × pr(1-up-throw-two) = 1/6 × 1/6 = 1/12.
Interpretations of the Calculus of Probability
The calculus of probability is nothing more than a device for the calculation of the probabilities of more complex propositions on the basis to probabilities assigned to simpler propositions. It says nothing about what probability is. There are three main accounts of the meaning of the calculus, each with different consequences for the use of probabilities as epistemic norms.
Probability as Degree of Confirmation
Rudolf Carnap's interpretation of probability is directly relevant to its use as an epistemic norm. On Carnap's view, pr(h / e) indicates the degree to which the truth of a hypothesis h is confirmed or supported by the empirical evidence e. On this view, warrant can be tied to the degree of confirmation.
For propositions p of kind K, if p is highly confirmed by the evidence possessed by S, then S's commitment to the truth of p is warranted.
The immediate question that arises on this view is how to determine pr(h / e). Carnap believed that the relation is purely "logical," in the sense that it is strictly a function of the ratio of possibilities in which h holds to the possibilities in which e holds.
It is generally agreed that this proposal falls prey to a fatal objection. (For an opposing view, click here.) The problem lies in the probabilities of the non-compound propositions. Suppose there is an objective fact that there is an array of possible configurations of the universe. How are they to be described? For example, we could just as well say that one kind of possibility is that a throw of a die will come 1-up and the other that it come not-1-up as to say that there are the usual six possibilities.
Probability as Degree of Commitment
One way to overcome the problem of assigning initial probabilities is to take them to express the degree of commitment or belief on the part of an individual. Understood in this way, probabilities are subjective, and may be different for different people. On this view, the only constraint on initial probability assignments is that they be consistent in a certain limited sense known as probabilistic "coherence." (Roughly, an incoherent assignment would allow a bet that must be lost.)
On this kind of account, probability is measured in terms of what kinds of bets a person would make on the truth of p. The willingness to make such bets indicates the degree of confidence that the person has that p is true. Warrant arises when the probability of a hypothesis h is high given the probabilities assigned to evidence e.
For propositions p of kind K, if p is highly probable subjectively given the subjective probabilities for S of evidence relevant to p, then S's commitment to the truth of p is warranted.
An obvious objection to this kind of condition is that it is too weak . The constraint on the subjective probability of the evidence blocks only a kind of incoherence, and S may use the most outlandish coherent initial probabilities as "evidence" that to support almost any hypothesis.
The standard defense against this objection is that with the addition of new evidence, the initial probability assignments have less and less of an effect on the probability of the hypothesis. This is a consequence of the "Bayesian" approach to probability, an approach that has numerous adherents.
Although high subjective probability might be plausible as a necessary condition for warrant, it is questionable whether it could serve as a sufficient condition. This is due to a puzzle known as the "lottery paradox."
Suppose there is a "fair" lottery, in which one ticket has been drawn from a pool of 1,000. The presumption of fairness is that for each ticket, the probability that that ticket has been drawn is one in one thousand. Let 't1' indicate that ticket number 1 has been drawn, and so on for each of the other tickets. Then pr(t1) = .001, and the same holds through t1000. If follows from the probability calculus that pr(not-t1)=.999, and this will hold for all ti.
Now suppose that a probability of .999 is sufficient for warrant. In that case, the belief that not-t1 is a warranted belief. And so is the belief that not-t2, etc. If we accept a further principle, that if one is warranted in believing all the conjuncts of a conjunction, one is warranted in believing the conjunction itself, there is a problem. Since not all the tickets are losers, pr(not-t1 and not-t2 and . . . and not-t1000) = 0, and so one is not warranted in believing the conjunction despite being justified in believing all the conjuncts. Note that it does not depend on the specific numbers used here. It works no matter how many tickets are entered in the lottery, and consequently no matter how high pr(t1) is.
Various suggestions have been made as to how to evade the paradox. One could, for example, throw out the principle that warranted belief in the conjuncts of a conjunction implies a warranted belief in the conjunction. Lehrer takes the lesson to be that high probability is sufficient for warrant. In the lottery case, the various results of the draw are not independent. The assumption that one of the tickets is a loser diminishes the probability that another is. For example, pr(not-t1 / not-t2) = 998/999, which is less than 999/1000. The information that not-t2 is negatively relevant to the information that not-t1.
The problem for warrant, as Lehrer sees it, is that there is no way to rule out the negatively relevant information merely on the basis of probabilities. Specifically, not-t1 is no more probable than the negatively relevant not-t2. The idea that a warranted belief must be more plausible (in this case, more probable) than all negatively relevant information is the core of Lehrer's theory of warrant.Probability as Relative Frequency
The main rival to the subjective interpretation of probability understands it in a much different way. On the "frequency" interpretation, probability is a measure of proportions in a given population. For example, according to the Centers for Disease Control, 20% of all deaths in the United States in 1990 were attributable to smoking. So, the probability of a death in 1990 being caused by smoking is 1/5 on this interpretation.
We want to be able to extend our claims about probabilities to the future. Under the frequency interpretation, this requires that the ratio constituting the probability expresses the convergence toward a limit of the ratio of observed cases to the population. For example, if we say that the probability of a coin's coming up heads is 1/2, we mean that the frequency of heads coming up compared to the number of tosses converges to a limit of 1/2 in an infinite series of tosses.
The frequency interpretation is subject to a very serious limitation, one which has important consequences for its use in understanding warrant. According to it, the very meaning of probability is that of a mathematical ratio of things of certain kinds (deaths attributable to smoking to total deaths). It has no meaning for individual events. So, it makes no sense to say that the probability of the next coin-toss coming up heads is 1/2.
For internalists, the limitation blocks a straightforward account of warrant in terms of probability, since such an account would make reference to the probability of p. For externalists, however, the frequency interpretation of probability is quite useful, as probability can be used to explain reliability. We might put it this way.
For propositions p of kind K, if S's commitment to the truth of p is warranted, then the probability of true beliefs generated by the process that produced the belief that p is high.
The third kind of transmissive condition that might be tied to warrant is explanatory inference or abduction. Most commonly, this is understood in terms of inference to the best explanation. A hypothesis h which best explains the truth of the set of all warranted beliefs relevant to the truth of h is itself warranted. (We would want to rule out warrant for a hypothesis that explained the truth of only some relevant beliefs but left other the truth of other relevant beliefs unexplained.)
For any h and any relevant e1, e2, . . ., en, if S's commitment to the truth of e1, e2, . . ., en is warranted, and h is the best explanation of the truth of e1, e2, . . ., en, then S's commitment to the truth of h is warranted.
There are at least two prominent uses of explanation as warrant in the literature of epistemology. One is to claim warrant for beliefs about the existence of the physical world. It is held by many that we are warranted in believing that there are physical objects beyond our mental states because the hypothesis that they exist best explains the vivacity and coherence of those states. The second appeal to explanation as providing warrant concerns beliefs about theoretical objects, such as curved four-dimensional space-time or quarks. Most people take it that at least scientists who understand their explanatory roles are warranted in believing that such objects exist.
It is not easy to give an account of what makes for the best explanation. For example, a relatively more simple explanation is generally regarded as better than one which is more complex, all else being equal. It should be noted, though, that there are many ways of understanding simplicity. Relative comprehensiveness is another desideratum, as is the probability of the explanatory hypothesis has independently of its explanatory role. A further factor is the coherence of the hypothesis with the rest of what one believes. How to balance these several factors against one another is a very difficult problem.
A further question concerns why being the best explanation should confer warrant. If we understand warrant to involve a connection between belief and truth, why should we think that the fact that a hypothesis explains best has anything to do with the truth of the matter? Historically, myriad explanations which were the best (or were taken to be the best) available at their time have been rejected. What reason have we to believe that our current explanations are any better?
Coherence accounts of warrant might take one of two quite different forms. The first, championed by Lehrer, takes coherence to be a relation between S's belief that p and the other things that S believes.
If p coheres with S's body of beliefs, then S's commitment to the truth of p is warranted.The second form of coherentism, once advocated by BonJour, understands warrant in terms of the coherence of the body of beliefs itself.
If p is a member of the body of S's beliefs D and D is coherent, then S's commitment to the truth of p is warranted.Here is how BonJour described coherence at the time he was a coherentist.
Intuitively, coherence is a matter of how well a body of beliefs "hangs together": how well its component beliefs fit together, agree or dovetail with each other, so as to produce an organized, tightly structured system of beliefs, rather than either a helter-skelter collection or a set of conflicting subsystems. It is reasonably clear that "hanging together" depends on various sorts of inferential, evidential, and explanatory relations which obtain among the various members of a system of beliefs, and especially on the more holistic and systematic of these. (The Structure of Empirical Knowledge, p. 93)Having already had a glimpse of Lehrer's approach in the last module, we shall make a few comments about BonJour's. It should be noted that the objection that a coherent system may be isolated from reality applies just as well to both formulations of a coherence condition for warrant. Two bodies of belief might be equally coherent, with one warranting the belief that p and one warranting the belief that not-p.
An advantage of BonJour's approach over Lehrer's is that it requires that the belief system on which warrant is based to meet a standard, i.e., the standard of coherence. For Lehrer, warrant is based on whatever system of rational acceptance a person happens to have at a time, no matter how tightly tied together are its components.
A major problem for BonJour's type of approach lies in giving anything close to a precise specification of the many relations which constitute coherence. A number of fairly simple, straightforward attempts have been made, but they all seem to be unsatisfactory. The kind of coherence BonJour sketches is a very messy affair.
A further objection is that the formulation of the coherence condition on warrant seems unacceptable to an internalist, who would demand that to be warranted, one must have some kind of access to the coherence of one's beliefs. So an alternative formulation is needed, perhaps something like this:
If p is a member of S's body of beliefs D, and D is coherent, and S is committed to the truth of p because of the membership of p in coherent D, then S's commitment to the truth of p is warranted.There are two problems here. The first is how S would be able to determine that his body of beliefs is coherent, especially given the complexity of coherence. The second is how S would be able to tell, at a given time, what all his beliefs are. The inability to answer questions of this sort (without becoming a foundationalist) is what led BonJour to abandon the coherence theory. Since Lehrer's account of coherence does not require that one be able to determine the coherence of the system as such, but only to answer objections, it is not subject to these criticisms.
A problem common to most of the epistemic norms we have discussed to this point is that they seem too weak in one way or another to confer warrant. Roderick Chisholm used a particularist strategy to overcome this kind of problem. He began with the assumption that we are warranted in beliefs we have, specifically beliefs about ordinary objects of perception. He then worked backward from that assumption to elucidate norms which would be sufficient for that warrant.
In the various editions of Theory of Knowledge, Chisholm refined a set of "epistemic principles" which confer warrant to various degrees on a scale from "some presumption in its favor" to "certain." A typical example of such a principle is this:
(B) For any subject S, if S believes, without ground for doubt, that he is perceiving something to be F, then it is beyond reasonable doubt for S that he perceives something to be F. (Theory of Knowledge, second edition, p. 76).This principle, and others like it, are, so to speak, "customized" to fit our intuitions about what is warranted, and to what degree it is warranted, but they are not motivated independently.
It may be that this is the best we can do, particularly given the problem of the criterion. There may simply be no non-circular way in which standards can be justified. Nelson Goodman made this argument for the case of induction. He held that our norms for induction must ultimately be read off from how we make inductive inferences ("The New Riddle of Induction").
John Pollock has laid down some very elaborate epistemic norms grounded in artificial intelligence. He has argued that the norms that govern our knowledge are psychological facts about ourselves as human beings. On Pollock's theory, "epistemic norms are 'psychologically real' features of human cognition. They represent contingent features of the human cognitive architecture" (Contemporary Theories of Knowledge, second edition, p. 171).
This completes our brief survey of the relation between epistemic norms and warrant. Epistemologists have labored mightily to give clear accounts of the norms that are ordinarily invoked in attributions of warrant. It appears that the clearer the account, the more easily it is rejected as insufficient to play for its intended role.
Perhaps the reason is that we attribute warrant in many different, specialized, ways. Different norms are appropriate for different modes of attribution. When we try to make them necessary or sufficient conditions for a more generalized notion of warrant, we find that they are inadequate.
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