Friday, May 3, 2013

Lehrer, Paxson and the Insufficiency of Knowledge as “Undefeated Justified True Belief”


In their essay, “Knowledge: Undefeated Justified True Belief,” Keith Lehrer and Thomas D. Paxson undertake a revision of the traditional analysis of knowledge as justified true belief, by adding a defeasibility condition. It is their intent to strengthen the traditional analysis through this fourth clause as to avoid Gettier cases. Additionally, Lehrer and Paxson offer their analysis of the conditions of knowledge as an improvement over Roderick Chisholm’s analysis who imports a defeasibility condition from ethics. It is their complaint that Chisholm’s analysis is too strong. It allows misleading defeaters to override would be cases of knowledge. Consequently, they also undertake a revision of Chisholm’s defeasibility clause that avoids these errors. Yet, it is my contention that Lehrer’s and Paxson’s revision of Chisholm’s defeasibility conditions create a characterization of knowledge which is too weak.

In characterizing knowledge as “undefeated justified true belief”, Lehrer and Paxson intend a specific type of knowledge. They are careful to demarcate basic knowledge from nonbasic knowledge. In brevity they characterize basic knowledge as: “S has basic knowledge that h if and only if (i) h is true, (ii) S believes that h, (iii) S is completely justified in believing that h, and (iv) the satisfaction of condition (iii) does not depend on any evidence p justifying S in believing that h” (Lehrer and Paxson, 255) As such, basic knowledge is non-mediate knowledge. Lehrer and Paxson are both agnostic about the existence of this type of knowledge[1] although they indicate that if such knowledge exists, it is not defeasible and as such cannot be properly characterized as “undefeated justified true belief.” So, their revision of the traditional analysis of knowledge is solely aimed at nonbasic belief.

Initially, they look at a preliminary definition of nonbasic knowledge that is essentially co-extensive with the traditional definition of the same. Specifically, they define non-basic belief as, “(i) h is true, (ii) S believes that h, and (iii*) p  completely justifies S in believing that h” ( 226-27). They are quick to point out the insufficiency of this definition as it does not block Gettier cases. In indicating a direction towards which a solution may be found, they point to Roderick Chisholm’s suggestion that justifications are defeasible (Chisholm, 48).  Taking their que from Chisholm they propose the following analysis of nonbasic knowledge: “S has nonbasic knowledge that h if and only if (i) h is true, (ii) S believes that h, and (iii) there is some statement p that completely justifies S in believing that h and no other statement defeats this justification” (Lehrer and Paxson, 227).

This characterization of nonbasic knowledge requires an additional definition however, viz. a definition of “defeats”. Lehrer and Paxson “adopting a suggestion of Chisholm’s” attempt the following: “when p completely justifies S in believing that h this justification is defeated by q if and only if (i) q is true, and (ii) the conjunction of p and q does not completely justify S in believing that h.” As persuasive as this definition may be, Lehrer and Paxson are emphatic that it is far too strong. Specifically, they claim that Chisholm’s suggestion allows misleading defeaters (i.e. defeaters which are themselves defeated) to override cases of would be knowledge. To demonstrate this point, Lehrer and Paxson present the “Tom Grabit” thought experiment. In this experiment it is suggested that a person S, sees a man—a man whom he takes to be Tom Grabit—walk into a library and remove a book. S is completely justified in his belief since he knows John personally and saw the individual in the library that he has characterized as Tom Grabit, in optimal epistemic conditions. Yet, suppose that unknown to S, Tom Grabit’s mother, Mrs. Grabit, has claimed that John was thousands of miles away on the day in question. Instead, it was Tom’s identical and maniacal twin, John Grabit. Further suppose that Mrs. Grabit is a pathological liar, and that her supposed son, John, is nothing more than an aberration of her sickened mind. John does not exist. Owing to the fact that the true statement q, “Mrs. Grabit has claimed that . . .” when conjoined with p does not completely justified S in believing that h, and further owing to the fact that Chisholm’s characterization of “defeats” does not contain a clause to block misleading defeaters, it follows that on Chisholm’s account, S does not have knowledge. Clearly, this definition of “defeats” is far too stringent. A revision is needed.

In searching for a plausible revision of Chisholm’s proposal, Lehrer and Paxson look at another thought experiment, one in which justification deserves to be overridden. Specifically, they look at a Gettier case wherein a professor is completely justified in believing that a student, Mr. Nogot, owns a Ford and on this basis forms the inference that someone in my class owns a Ford. As it turns out Mr. Nogot does not own a Ford, but Mr. Havit does. So, the professor is completely justified in holding a true belief, viz., that someone in his class owns a Ford. However, that justification is overridden by the defeater that Mr. Nogot does not own a Ford, Mr. Havit does.

In looking at this additional thought experiment, Lehrer and Paxson note the differences between the two thought experiments given. Specifically, they claim that in the case of Tom Grabit, the defeater ought not count against my original justification whereas in the case of Mr. Nogot, the defeater ought to count against my original justification (229). Formulating this insight into an amended clause for the definition of “defeats” is awkward. For, as Lehrer and Paxson point out,

Why should one true statement but not the other be allowed to defeat my justification? The answer is that in one case my justification depends on my being completely justified in believing that Tom removed the book does not depend on my being completely justified in believing it to be false that Mrs. Grabit said Tom was not in the library and so forth. But my justification for believing that someone in my class owns a Ford does depend on my being completely justified in believing it to be false that Mr. Nogot does not own a Ford. Thus, a defeating statement must be one which, though true, is such that the subject is completely justified in believing it to be false. (229)

In other words, complete justification in the case of misleading defeaters does not depend upon believing the misleading defeater to be false. In the case wherein a person’s justification is overridden, in order for them to be completely justified in believing a true statement h, they must be completely justified in believing a true defeater to be false. If they did not, their original justification, in regards to believing proposition h to be true, would not be complete. Lehrer and Paxson are playing upon the intuition that defeaters are completely unexpected facts. The fact that Mr. Havit owns a Ford, whereas Mr. Nogot does not, is unexpected and as such cannot factor into the requirement for complete justification.

Their suggested amendment to Chisholms proposal is as follows: “when p completely justifies S in believing that h, this justification is defeated by q if and only if (i) q is true, (ii) S is completely justified in believing q to be false, and (iii) the conjunction of p and q does not completely justify S in believing that h” (230). This amendment, however, contains a certain weakness; a weakness which I will outline in its most basic of structures. Lehrer and Paxson ask us to consider a case in which S has nonbasic knowledge of h. Additionally, in this thought experiment, “there is some true statement which is completely irrelevant to this knowledge and which [S] happen[s] to be completely justified in believing to be false” (230). Conjoin this irrelevant proposition, call it r, which S is completely justified in believing to be false, with q, which S is not completely justified in believing to be false, and you get the result that S is completely justified in believing the entire conjunction, call it c, to be false—for S is justified in believing the entire conjunction to be false if S is completely justified in believing any of its members to be false. The conjunction c when conjoined with p will, according to Lehrer’s and Paxson’s definition of “defeats”, override S’s justification for h on the basis of p; for p when conjoined with the conjunction c will not fully justify S in believing that h.

To remedy this problem an additional clause must be amended to the already cumbersome definition of “defeats”:

if p completely justifies S in believing that h, then this justification is defeated by q if and only if (i) q is true, (ii) the conjunction of p and q does not completely justify S in believing that h, (iii) S is completely justified in believing q to be false, and (iv) if c is a logical consequence of q such that the conjunction of c and p does not completely justify S in believing that h, then S is completely justified in believing c to be false. (231)

With this amendment, irrelevant propositions which S is completely justified in believing to be false, are ruled out. Conjunction c can only count against S’s justification for h if c is a “logical consequence” of a proposed defeater q—i.e. relevant to q. Furthermore, if c is a logical consequence, and if the conjunction of c and p overrides S’s justification, then S is completely justified in believing c to be false. In restricting their analysis in this manner, Lehrer and Paxson are confident that their definition of “defeats” is complete.

However, it is clear that this cumbersome definition of “defeats” is too weak. It allows in certain cases as knowledge, even when they ought not be considered as such. Taking a cue from Lehrer and Paxson, suppose that S is completely justified in believing that Tom Grabit took a book from the library. Further suppose that there is some true proposition, call it q, which S is not completely justified in believing. For example, “Mrs. Grabit claims that Tom was thousands of miles away and that it was Tom’s identical and maniacal twin John Grabit who took the book.” Additionally, suppose that there is some true proposition, call it r, which is added to q creating a disjunction, call it c, that S is completely justified in believing to be false: “Tom was actually thousands of miles away on the day in question and a secret government agent by the name of Ethan Hunt had access to a mask which was a perfect replica of Tom’s face and Hunt had access to a voice modulator that made his voice sound exactly like Tom’s.” Importantly, each member of the disjunction c, i.e. ‘q or r’, when conjoined with p does not completely justify S in believing that h. Furthermore, since S is only completely justified in believing any true disjunction to be false, when S is completely justified in believing each of its members to be false, it follows that S is not completely justified in believing that the conjunction of the disjunction c and the proposition p to be false. The result? The disjunction in question is ruled a misleading defeater by Lehrer’s and Paxson’s definition of defeats and as such it cannot count against S’s justification. S is said to have knowledge. Yet, this result is clearly incorrect. The true proposition c, dealing with government agent Ethan Hunt, should override S’s justification for h.[2]

Remedying the weakness in the conditions supplied by Lehrer and Paxson will not be easy. What is required is an amended condition which adjudicates between disjunctive statements which are bonafide defeaters and those which are misleading. On first blush, the most attractive solution is the following: If c is a logical consequence of q such that the conjunction of c and p does not completely justify S in believing that h, then S is completely justified in believing c to be false only if S is completely justified in believing each of the members of c in being false. Yet, it is clearly the case that this proposed condition is ad hoc. As such it is an unacceptable amendment to the already cumbersome list of conditions of defeasibility.

An alternative route, which may provide promise, appeals to the desirable notion of simplicity. Specifically, Lehrer and Paxson could claim that complex statements (i.e. conjunctions, disjunctions, conditionals, etc.) must, if possible, be simplified via additional logical inferences which would decompose the statements before a conjunction is formed with p. In cases of complex conjunction, reduction would be produced simplification. In the current case of disjunction, simplification could be performed via disjunctive syllogism. Specifically, since S is completely justified in believing r (i.e. the proposition concerning agent Ethan Hunt) to be false, r can be used to infer q. With the disjunction decomposed down to q, a misleading defeater, r will override S’s justification. Stated more succinctly this condition is as follows: If c is a logical consequence of q such that the conjunction of c and p does not completely justify S in believing that h, then S is completely justified in believing c to be false, only if c (a complex statement) cannot bear further simplification via additional logical inferences which would decompose the statement.

While this approach is not susceptible to the charge of ad hoc—it does, after all, work well for conjunctions, conditionals and could, with additional language indicating that c be a logical consequence of q, replace Lehrer’s and Paxson’s current fourth condition—it still faces a number of problems. It is not clear than any statement, c, could survive in order to be conjoined with p. In the case of a conjunction, it is always the case that a conjunction can be simplified further. With a disjunction, if S is completely justified in believing any or all of the parts to be false, then the statement can be decomposed. In the end, the only statements which can survive are probably misleading defeaters. As such this proposed condition effectively blocks any complex statement from surviving except for disjunctions whose parts are all misleading defeaters.

This may not strike the reader as problematic until it is born in mind that some complex statements cannot be torn apart without loss to their content. For example, consider a slightly modified statement q: “Mrs. Grabit claimed that John Grabit, Tom’s twin brother, actually took the book and a week later it was determined that Mrs. Grabit has been suffering from schizophrenia and has completely imagined the former son who is non-existent.” Clearly, this statement is complex and can be broken apart via simplification. However, when broken apart, and individually conjoined to p, vital information is lost. For example, the statement, “a week later it was determined that Mrs. Grabit”, while in isolation, is not appropriately indexed to a particular event. The same goes for the statement “has completely imagined the former son who is non-existent son.” Without the larger context, the possibility remains that John Grabit is not an imagined son—some other former son being the imagined son—and that the statement was made after the onset of Mrs. Grabit’s schizophrenia. Clearly, certain complex statement, while susceptible to simplification, cannot bear decomposition without irrevocable loss to content. So, requiring of all complex statements that they bear further simplification via available logical inferences annihilates content from certain statements and as a result is inappropriate.  Lehrer and Paxson could attempt a modification to this current proposed condition which would attempt to save it from this type of difficulty. Specifically, they could identify complex statements that require unity for preservation of content and provide a language within the clause which eliminates them from the requirement of simplification. However, it is clear that any such attempt would be susceptible to the charge of ad hoc. Consequently, the current proposed condition must be scrapped.

Finally, at this point, it may seem appealing to simply amend a condition which effectively blocks all complex statements. Aside from being ad hoc, this approach would not even be desirable. There are plenty of imaginable statements which, like the modified statement q just given, require various conjunctions and disjunctions. Disbarring them out of hand could lead to the undesirable effect that S is ruled as having knowledge because a complex, bonafide defeater can’t get through. Clearly, this approach would be a step backwards and as such is not advisable.

Conclusion

In the end, it is clear that Lehrer’s and Paxson’s analysis of knowledge as “undefeated justified true belief” is insufficient. Furthermore, remedying the defects of their analysis is not easy. The unpredictable nature of defeaters affords to possibility of providing a highly complex logical inference which would show Lehrer’s and Paxson’s analysis to be either too strong or too weak. Additionally, it seems apparent from the foregoing analysis, that clauses attempting to remedy these problems will, in the end, be guilty of being ad hoc. So, it appears that Lehrer and Paxson will have tremendous difficulty in supporting this type of analysis and, in the opinion of this author, it seems apparent that this line of thought (i.e. characterizing nonbasic knowledge as “undefeated justified true belief”) will prove unfruitful in identifying the individually necessary and jointly sufficient conditions of nonbasic knowledge.

Works Cited

Chisholm, Roderick M. “The Ethics of Requirement.” American Philosophical Quarterly. Vol. 1, No. 2. April 1964. Web. July 2012. pp. 147-53.

Lehrer, Keith and Thomas Paxson, Jr. “Knowledge: Undefeated Justified True Belief.” The Journal of Philosophy. Vol. 66, No. 8. April 1969. Web. July 2012. pp. 225-237.





[1] In giving an analysis of basic knowledge—the existence of which they are agnostic towards—Lehrer and Paxson want to insure that “such proposals are not excluded by [their] analysis” (226).
[2] It is important to note, that this type of counter example, has also been offered by Marshall Swain, although in abstract form. See Marshall Swain, American Philosophical Quarterly, Vol. 11, No.1 (Jan., 1974), pp. 18-19.

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