Justified False Beliefs and Truth as a Redundant Condition

By: STEVE TENSMEYER

Despite the common intuition that something is very wrong with the Gettier problems, after forty years they still seem to be intractable. The responses to these paradoxes of knowledge range from complaints against their logical structure to conclusions that knowledge simply cannot be analyzed. Most philosophers, however, take a position somewhere in between these two extremes; their responses advocate changing the traditional Justified True Belief model of knowledge to something that “de-Gettierizes” knowledge. This almost always means either adding some fourth condition or clarifying or changing the definition of justification. In this essay I will consider different possible solutions to the Gettier problems. After establishing the validity of these problems by defending Gettier against an objection to the logical structure of his counterexamples, I will then look at several attempts to change the justified true belief model to avoid the Gettier problems. I will then show that when these proposed solutions fail, as many of them do, it is because of a common defect. Finally, I will suggest that Nozick’s proposition analysis of knowledge is an elegant and insightful solution to this basic problem, and defend it against an objection from Kripke.

There are really only a few general strategies that can be used to resolve the Gettier problems. First, one could concede the point and claim that Gettier beliefs are knowledge; Smith does indeed know that the man who will get the job has ten coins in his pocket, and Smith does know that either Jones owns a Ford or Brown is in Brest-Litovsk. Second, one could argue that knowledge is a basic concept that cannot be analyzed. Third, one could argue against Gettier’s principle that “for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q” (Gettier 121). Fourth, one could argue that justification has some necessary conditions that preclude these types of beliefs. Fifth and finally, one could argue that there is some necessary condition for knowledge in addition to justified true belief that precludes these types of beliefs.

I. Arguments against the Validity of the Counterexamples

The first strategy, arguing that Gettier beliefs are knowledge, is a cure clearly worse than the disease. A concept of knowledge that allowed such cases would be strongly counterintuitive. The second strategy, arguing that knowledge is a basic concept that cannot be analyzed, certainly has its merits, but it is mostly beyond the scope of this paper and I can do little more than give a broad objection it: it simply feels wrong. There are many basic concepts, but for the most part they are self-evidently basic; we feel no compulsion to try to analyze them. Knowledge intuitively seems like something for which there are fairly strict, logical conditions, and if it were a basic concept it would be unique in not being obviously so.

The third strategy, arguing that being justified in believing a proposition does not necessarily make one justified in believing all propositions entailed by that proposition, shows more promise. In “In Defense of Justified True Belief,” Irving Thalberg argues against the transitivity of justification using the analogy of betting. For instance, in the case in which Smith believes the proposition “the man who will get the job has ten coins in his pocket,” Thalberg argues that though Smith may be justified in believing the propositions “Jones has ten coins in his pocket” and “Jones will get the job,” he nevertheless may not be justified in believing even the conjunction of these two propositions, let alone the general proposition containing the denoting phrase “the man.” To explain why this is so, Thalberg considers the conditions for betting on each proposition. Even if Smith were willing to vote independently on the proposition “Jones will get the job” and the proposition “Jones has ten coins in his pocket,” he may still be unwilling to bet on the conjunction of these two (Thalberg 798). Conjoining propositions increases one’s possibilities for error, as a falsehood in any one of the conjuncts renders the entire conjunction false. This reasoning presupposes that the justification of a proposition is simply one’s reliable judgment of the probability that the proposition is true. If this is the case, then the justification of a conjunction will only be as strong as the probability that the entire conjunction is true, which is obtained by multiplying together the probabilities of all of the conjuncts. A belief is justified if the probability that it is true is above a certain cutoff, which may vary according to circumstance. Therefore, while two propositions composing a conjunction may be justified, the conjunction itself may not be.

Of course, this argument relies on the assumption that justification is a matter of probability and that it admits of degrees in the way that Thalberg believes it does. But even if this assumption is granted, the argument still has problems; Thalberg’s point about the intransitivity of justification in conjunctions may be valid, but his argument against the Gettier problem arising from disjunction is seriously flawed. Thalberg believes that Smith’s compound belief that either Jones owns a Ford or Brown is in Brest-Litovsk is invalid for basically the same reasons that the compound statement is invalid: since justification is based on probability, a proposition may be less justified than its premises. In this case again, Thalberg states that adding a disjunct to the proposition “Jones owns a Ford” alters the odds that it is true. However, Thalberg does not seem to appreciate how different this case is: here, rather than making the compound proposition less probable, it makes it more probable. If justification is indeed a matter of degree and is based on accurately judged probability, then the proposition “either Jones owns a Ford or Brown is in Brest-Litovsk” is more justified than the proposition that entails it. Extending the betting analogy, Thalberg states “no bookmaker would permit Smith to gamble on (the disjunction) under the same conditions as he bets on (the original proposition). . . Smith might be justified in accepting (the disjunction) whenever he is justified in accepting (the original proposition), but we might not be justified in allowing him to shift from (the original proposition to the disjunction)” (Thalberg 798). But why should Smith care about what we are justified in allowing him to do? This must be an entirely different kind of justification that Thalberg is talking about; whatever this justification is, it shares no connection with the kind of justification we are concerned other than name. The kind of justification that matters here is Smith’s justification in believing this series of propositions. In fact, the reason that we are not “justified in allowing him to shift” is that it is more probable that it is true; far from making Smith less justified in believing the proposition, this is rather precisely what makes him more justified. Therefore, the Gettier paradox is still present; by Thalberg’s admission, Smith is justified in believing a proposition which is true, but in circumstances that do not intuitively seem to constitute knowledge.

II. Truth as a Redundant Condition

As Gettier points out, his counterexamples rely on two principles: first, it is possible to have justified false beliefs; and second (as discussed above), justification is transitive from a proposition to any propositions entailed by that proposition. We have just seen the failure of an argument against the second of these principles. However, this strategy of challenging whether Smith’s beliefs are justified is certainly the minority. Most philosophers concede Gettier’s point and attempt to either strengthen justification or add some other condition that avoids such problems. But unless justification is strengthened to the point that justified false belief is impossible, Gettier problems will always arise. If both justified false belief and unjustified true belief are possible, one can always make a Gettier problem from them by putting one of each together in a disjunction.

This same general principle applies to models adding some other condition to justified true belief. However many conditions are added, if it is possible that all of these conditions (except truth) can be fulfilled and the belief still be false, then a Gettier problem can always be made by forming a disjunction by adding a belief that fulfills the truth condition but not some other condition or conditions. In any analysis of knowledge, truth must be a redundant condition. If the other conditions do not already guarantee truth, a disjunctive Gettier problem can always be made. This means that, despite what many philosophers have assumed, the analysis of knowledge is not a matter of what conditions to attach to truth and belief to get knowledge; truth must be a necessary consequence of the other conditions. Therefore, there is no such thing as “knowledge minus truth”, or beliefs that qualify as knowledge in every condition except that their propositional content is not true (I will henceforth refer to these beliefs as “condition-fulfilling false beliefs”).

Based on this criterion that truth must be a redundant condition, it seems that any analysis that merely strengthens the justification condition will end up being very counterintuitive. Justification that entails truth seems too strong, but if it does not entail truth, an analysis that only contains the conditions of justified true belief will always be subject to Gettier problems. If justification is taken to be normative; that is, if an unjustified proposition is one that we ought not to believe and a justified proposition is one that we may or should believe, then clearly truth cannot be a necessary condition for it. Certainly there are sometimes propositions which we have every reason to believe, which we do not violate any epistemic duty by believing, and even which we would be violating some duty by not believing, but which are nevertheless false.

III. The Basic Fourth Condition and Defense of Nozick

It seems then that if we hope to analyze knowledge in a way that conforms to our intuitions, we must add some fourth condition to justification, belief, and truth; or more precisely, we must add some condition to justification and belief that necessarily entails truth. Many further conditions have been suggested. Some of these allow for condition-fulfilling false beliefs and therefore fail. Others explicitly forbid justified false beliefs, and still others do not commit themselves either way, but can be interpreted as forbidding such beliefs. For example, consider Lehrer and Paxson’s theory of knowledge as undefeated justified true belief. According to this theory, a belief is knowledge if it is justified and true and if there is no other true proposition that the subject justifiably believes to be false and which, if known, would render belief in the original proposition unjustified (Lehrer and Paxson 227). Though Lehrer and Paxson do not say so explicitly, this clearly disallows any condition-fulfilling false beliefs, because in such cases there will always be a defeater: namely, the true proposition “this belief is false.”

There are several other possibilities given for conditions added to justified true belief that will avoid Gettier problems. Goldman’s causal theory, Plantinga’s theory of proper function, the many variations on the theory of “no false lemmas,” and all other theories proposing adding conditions to justified true belief all avoid the Gettier problems to the extent that they succeed in connecting the subject’s belief necessarily to the truth of the proposition. The condition must be such that condition-fulfilling false beliefs are impossible, and therefore such that the proposition’s being false is sufficient to preclude belief in it. Robert Nozick recognized this most basic element of any condition added to knowledge and formalized it as “if p weren’t true S wouldn’t believe that p” (Nozick 211).

This condition, I believe, captures the essence of the Gettier problems and provides an elegant way to avoid them. However, it is not without its critics. Kripke proposes as a counterexample a variation on the traditional “Barn County” thought experiment. In the original thought experiment, Matthew is traveling through Barn County, in which, unbeknownst to Matthew, there is only one barn but thousands of barn façades. Matthew sees the one real barn and forms the belief “I see a barn,” though it is by sheer luck that Matthew happened to see the one real barn instead of one of the thousands of facades. The justified true belief account would consider this knowledge. Nozick’s account deals with this easily. Even if Matthew had seen a façade, rendering the belief “I see a barn” false, Matthew would still have believed it. Therefore, Nozick’s added condition is not fulfilled, and Matthew’s belief is not knowledge.

Kripke’s counterexample adjusts Barn County so that only the one real barn is painted red, and all others are left unpainted by law. Matthew sees this barn and forms the belief “I see a red barn.” This, Kripke claims, counts as knowledge under Nozick’s definition, because if this were false and Matthew did not see a red barn, but rather saw an unpainted façade, he would not have believed the proposition. But if this is knowledge, then Matthew knows that he sees a red barn, and from that can deduce that he sees a barn, which is what we rejected in the first place (Luper-Foy 265).

This objection, however, is flawed. Kripke states that when Matthew believes the proposition “I see a red barn,” this qualifies as knowledge under Nozick’s definition because if Matthew hadn’t seen a red barn, he would not have believed that he saw a red barn. But Kripke seems to have formalized this sentence incorrectly. He is treating Nozick’s condition as though it were “there is some state of affairs such that p is not true and Matthew does not believe p.” One might as well say that Matthew’s original assertion, “I see a barn,” qualifies as knowledge because there exists some possible state of affairs, say, if Matthew had been blind, such that if this state obtained, Matthew’s proposition “I see a barn” would have false and he would not have not believed it. But Nozick’s condition is more stringent; it is that every time and under whatever circumstances p is false, S will not believe p. And in Kripke’s counterexample there are clearly cases in which it is false that Matthew does not see a red barn and yet believes that he does; for example, in the next county over where all façades are red and all real barns are unpainted.

IV. Conclusion

In this essay, I have defended both of Gettier’s foundational principles: the transitivity of justification and the existence of justified false beliefs. By delving further into the reasons why objections to the second principle fail, and concluded that the central issue was that in any analysis of knowledge, truth must be a redundant condition. With this core insight in mind, Nozick’s theory of knowledge, which does not have truth as an explicit condition, seems to be the simplest and best solution to the Gettier problems. The implications of Nozick’s theory are yet to be fully developed, but I believe they have the potential to both challenge and hone many of our intuitions about what knowledge is, and particularly to give us greater understanding of the role of truth.

Works Cited

Gettier, Edmund. “Is Justified True Belief Knowledge?” Analysis 23.6 (1963): 121-23. Print.

Lehrer, Keith, and Thomas Paxson. “Knowledge: Undefeated Justified True Belief.” The Journal of Philosophy 66.8 (1969): 225-37. Print.

Luper-Foy, Steven. The Possibility of Knowledge: Nozick and his Critics. Totowa, NJ: Rowman and Littlefield, 1987. Print.

Nozick, Robert. Philosophical Explanations. Cambridge, MA: Robert Nozick, 1981. Print.

Thalberg, Irving. “In Defense of Justified True Belief.” The Journal of Philosophy 66.2 (1969): 794-803. Print.

Steve Tensmeyer (’11) is a Philosophy and International Relations Major at Bringham Young University

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