Hauptli's Lecture Supplement on Lehrer & Paxson’s “Knowledge: Undefeated JTB”[1] [1969]

     Copyright © 2013 Bruce W. Hauptli

1. Introduction:

Lehrer and Paxson offer a version of a “defeasibility” analysis of knowledge.  According to Bruce Hunter,

the warrant a proposition p has for us on the basis of evidence e is defeasible when expanded evidence could decrease p’s warrant.  For example, ‘The next crow I see will be black’ is less warranted when, despite evidence e that observed crows were black, we are told on unusually reliable authority that there are many albino birds nearby, and have no evidence this present testimony is an exception.  Our actual warrant depends on our total evidence.  In stock cases, we don’t ‘lose’ e, but its import is undercut when it and the rest of our original total evidence is combined with additional evidence e'.[2] 

It may be helpful to distinguish here between additional facts or evidence which we are unaware of, and the same facts or evidence when we become aware of it.  In the former case, we can call the additional factors “defeaters,” while in the latter case, they should be called “overriders”—once we now have added the information to our evidence base, our original evidence is “overridden” by the new additions.  As Ralph Baergen says (changing the order in his treatment of these),

an overrider is some fact that when added to S’s justification, eliminates that justification; that is, the new expanded body of information no longer supports the target belief.  A defeater is a potential overrider; that is, a defeater is a fact such that, if S knew about it, it would act as an overrider.  Now, here’s how defeaters and overriders fit into this account of knowledge: A defeater will prevent a JTB...from counting as knowledge (but won’t prevent it from being a JTB), but an overrider prevents a belief from being a JTB (because it prevents it from being justified).[3] 

Lehrer and Paxson will offer an analysis of knowledge which appeals to this notion of defeasibility to avoid “Gettier” counter-examples (to avoid cases of lucky or accidental truth).  As Jack Crumley notes, however, a difficulty they encounter is with the possibility of misleading defeaters:

imagine that you attend a wedding of two close friends and that the ceremony is performed by a priest well known to you and the others at the ceremony.  The wedding is conducted and concluded without a hitch.  On the basis of this evidence, you come to believe that the couple is married.  Clearly, your belief is justified; you have every reason to think that you know your friends are married.  But let us suppose that unbeknownst to you and the others present, including the priest, the bishop has gone crazy.  Among other things, the bishop falsely denounces the priest as a fraud.  Now, there is a true proposition: The bishop has denounced the priest as a fraud.  Were you aware of this proposition, you would not be justified in believing your friends to be married, because fraudulent priests cannot marry anyone....Despite the apparent defeater, we are still tempted to say that you know. 

  The crazy bishop can illustrate that a distinction must be drawn between genuine and misleading defeaters.  Misleading defeaters are defeaters that can themselves be defeated; that is, still further evidence can be obtained that would “restore” the original justification.[4] 

Before we try to understand this problem, however, we should turn to Lehrer and Paxson's essay. 

2. Basic Knowledge:

Our authors begin by distinguishing basic knowledge from nonbasic knowledge.  The former, of course, is to provide the basis for the latter.  According to them:

31 if a man knows that a statement is true even though there is no other statement that justifies his belief, then his knowledge is basic.  Basic knowledge is completely justified true belief. 

Most of our knowledge claims will be nonbasic in character—they will depend on other beliefs and statements:

on the other hand, if a man knows that a statement is true because there is some other statement that justifies his belief, then his knowledge is nonbasic.  Nonbasic knowledge requires something in addition to completely justified true belief; for, though a statement completely justifies a man in his belief, there may be some true statement that defeats his justification. 

Clearly, for Lehrer and Paxson, basic belief is not defeasible, while nonbasic belief is defeasible:

nonbasic knowledge is undefeated justified true belief. 

They offer the following analysis of basic knowledge:

...S has basic knowledge that h iff (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. 

What examples do they give us of such knowledge claims?  Well, it turns out that they don’t provide any which they are willing to countenance.  Indeed, they say they are “agnostic” as to whether or not there are cases of basic knowledge.  Their analysis allows for the “possibility.”  Moreover, one may ask why they use ‘h’ rather than ‘p’ here—I believe that they conceive of it as standing for a “hypothesis” (rather than a “proposition”). 

We should also note, in passing, that they require “complete” justification here, and we might wonder what this is, whether it is attainable, whether it is too strong a requirement, and whether or not it will leave us with the sort of skepticism which Lehrer advanced in his “Why Not Scepticism?”[5] 

32 They do mention Unger’s example of the crystal-ball-gazing gypsy who is always right, but has no evidence to this effect and, generally [but not this time] believes s/he is wrong about his/her beliefs.  They also briefly mention that many philosophers have held that certain memory and perceptual beliefs fit this category. 

It is important for us to note, here, that if there are such cases of knowledge, then the notion of “complete justification” will not be appropriately conceived in terms of “reasons, evidence, or justifications which the agent explicitly has.” 

3. Nonbasic Knowledge:

32-33 They discuss “Gettier counterexamples” to traditional JTB analysis of knowledge:

-33 Brian Skyrms’ pyromaniac and the sure-fire matches example (the matches are wet but there is also a burst of Q-radiation which ignites the match). 

--As I have noted, the problem raised by such cases is that of “lucky” (or “accidental”) truths.  The belief is believed, it is true, and the believer has evidence (which prevents his belief being a “lucky guess”), but the evidence isn’t appropriately related to the truth and to the believing, and so the truth’s truth is “lucky” (or accidental) on the evidence at hand. 

Following a suggestion of Chisholm’s, Lehrer and Paxson offer a “defeasibility analysis,” because they contend that justifications are defeasible:

in the examples referred to above, there is some true statement that would defeat any justification of S for believing that h. 

-S has nonbasic knowledge that h iff (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. 

They note that this leaves us in need of a “definition” of ‘defeats’!  I would note that it there seems a tension here within the “third condition:” p is to be both defeasible and supposed to “completely justify” S in believing that h!  Lehrer and Paxson propose the following “initial” definition of ‘defeats’:

-...when p completely justifies S in believing that h, this justification is defeated by q iff (i) q is true, and (ii) the conjunction of p and q does not completely justify S in believing that h. 

33-34 This is too restrictive a definition, however—it doesn’t take account of the possibility of misleading defeaters!  Consider the Tom Grabit example:

-Tom is a student, the professor sees him steal a book from the library.  Tom’s mother says it was his evil twin brother John. 

--The mother’s statement defeats the professor’s knowledge claim. 

-34 Suppose that the mother is a pathological liar.  “The fact that Mrs. Grabit said what she did should not be allowed to defeat any justification I have for believing that Tom Grabit removed the book, because I neither entertained any beliefs concerning Mrs. Grabit nor would I have been justified in doing so.  More specifically, my justification does not depend on being completely justified in believing that Mrs. Grabit did not say the things in question.” 

According to Lehrer and Paxson, we need to define ‘defeat’ in a way which allows us to avoid misleading defeaters (as in the “Grabit” example) while capturing the sort of defeaters we encounter in the “Nogot/Havit” case (discussed in detail on p. 140):

-34-35 In the case of Tom Grabit, the true statement that Mrs. Grabit said Tom was not in the library and so forth, should not be allowed to defeat my justification for believing that Tom removed the book, whereas in the case of Mr. Nogot, the true statement that Mr. Nogot does not own a Ford, should defeat my justification for believing that someone in my class owns a Ford.  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 the true statement to be false while in the other it does not....a defeating statement must be one which, though true, is such that the subject is completely justified in believing it to be false. 

     Thus, we get their “first” revised definition of defeasibility:

35 ...when p completely justifies S in believing that h, this justification is defeated by q iff (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.

-There is a “technical problem” with this definition however: the fact that q may not be relevant to p (for example if I wrongly believe that I was born is Miami while I am thinking about the Grabit case).  Where we are dealing with a complex situation wherein there are consequences of a fact some of which might be irrelevant and some of which might be relevant and defeaters we need to come up with a better definition. 

     Thus we get to their Final Revised Definition of Defeasibility:

...if p completely justifies S in believing that h, then this justification is defeated by q iff (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. 

Here, Lehrer and Paxson contend, we have an adequate analysis of nonbasic knowledge, and when it is coupled with the definition of basic knowledge, we have a full analysis of [propositional] knowledge. 

4. Comparison with Other Analyses:

36-40 They go on to discuss how their analysis differs from, and is better than, those of Brian Skyrms, Roderick Chisholm, and Peter Unger (in his pre-skeptical incarnation).  I am not going to discuss this material and will not hold you responsible for the discussion, but the additional examples discussed enrich one's set of intuition-challenging examples in the Gettier discussion.  

41 They end the discussion with the claim that:

...on any satisfactory theory of justification, some knowledge must be undefeated completely justified true belief, and the rest is basic.  

5. Difficulties for Defeasibility Analyses:

As noted above, one of the fundamental problems encountered by such analyses will be that of the existence of “misleading defeaters.” 

     Another problem with the sort of analysis offered by Lehrer and Paxson is stated by Baergen as follows:

a further difficulty is found in the claim that to count as knowledge a belief must be “completely (or fully) justified.”  What are we to make of this?  Justification, it will be remembered, admits of degree, and not just any degree of justification will satisfy the justification of the JTB requirements for knowledge.  A rather high degree of justification is needed, but the question is, How high?  Saying that justification must be full or complete suggests that it must be justification to the highest possible degree.  This is awkward, for there is reason to believe that we rarely—if ever—attain this sort of justification; certainly, we do not attain it in every case that we want to count as knowledge.  But if the threshold for justification is set lower than this, we need to be told how this [level] is to be determined.[6] 

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File revised on 10/08/2013.