Supplement to Hauptli's Lectures on Gettier's "Is JTB Knowledge?"

     Copyright (c) 2002 Bruce W. Hauptli

1. Introduction--Analysis and Propositional Knowledge:

Having briefly examined the skeptical challenge to knowledge, we naturally come to wonder what knowledge is (what separates it from "mere" belief.  The traditional analysis1  is that knowledge is justified true belief [JTB].  Plato offered this claim first,2 and it was a staple of the Western philosophical tradition until 1963.

     It is important for us to note in passing that the analysis of knowledge to be discussed here, the problems with this analysis, and almost all of the ensuing articles and discussions are all discussions of "propositional knowledge"--that is, knowledge that p.3   As I have noted, there are other senses of knowledge which are not covered by such analyses.  Moreover, one might well question whether anyone can provide a single correct "analysis" of "knowledge"--one might claim that there is no single unified concept of knowledge.  In his "Plato's Euthyphro, Peter Geach maintains that a particular "style of mistaken philosophical thinking:"

...may well be called the Socratic fallacy, for its locus classicus is the Socratic dialogues.  Its influence has, I think, been greater than that of the theory of Forms; certainly people can fall into it independently of any theory of Forms.  I have myself heard a philosopher refuse to allow that a proper name is a word in a sentence unless a "rigorous definition" of `word' could be produced; again, if someone remarks that machines are certainly not even alive, still less able to think and reason, he may be challenged to define `alive'.  Both these controversial moves are clear examples of the Socratic fallacy; and neither originates from any belief in Forms.
       Let us be clear that this is a fallacy, and nothing better.  It has stimulated philosophical enquiry, but still it is a fallacy.  We know heaps of things without being able to define the terms in which we express our knowledge.  Formal definitions are only one way of elucidating terms; a set of examples may in a given case be more useful than a formal definition.4

While there may be senses of `knowledge' which are not covered by the sorts of analyses we will be discussing, and while we must keep an open mind to the possibility that the search for a single analysis may be the result of an overly simplistic assumption, the pursuit of such an analysis has engendered much epistemological understanding, and we now turn to this topic.

2. The Traditional Analysis of Knowledge:

142  JTB thesis: S knows that P iff:5

          (i)   P is true,
          (ii)  S believes that P, and,
          (iii) P is true.

Chisholm's version: S accepts P and has adequate evidence for P; and Ayer's: S is sure that P is true and S has the right to be sure that P is true.

3. Gettier's First Case for the Rejection of the Traditional Analysis:

According to Gettier, traditional analyses are incorrect because they do not actually state sufficient conditions for knowledge.6  To show this he will rely upon two points:

     " is possible for a person to be justified in believing a proposition that is in fact false"

          and when this is coupled with

what is called "the transmissibility principle:7  "...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", counterexamples to the traditional analysis ensue.

The principle works like this:

-Example: P="Socrates is an Athenian," Q="Socrates is a Greek," S is justified in believing P, P entails Q, S deduces Q from P and accepts Q as a result of P, and, thus (on the transmissibility principle), S is justified in believing Q.

Gettier puts these two points together to engender counter-examples to the traditional JTB analysis.  Here we should note that an analysis of a concept is said to be too strong when it excludes cases which clearly fall under the concept--for example, an analysis of "triangularity" which held that "triangles are closed three-sided figures all of whose sides are of equal length" would be too strong as it excludes isosceles and scalene triangles!  An analysis is said to be too weak when it includes cases which clearly do not fall under the concept--for example, an analysis of "triangularity" which held that "triangles are figures" would be too weak as it includes squares under the concept.

Gettier's Case I:

     Smith and Jones are candidates for a job, and Smith has strong evidence for:

          (d)  Jones is the man who will get the job, and Jones has ten coins in his pocket.

His evidence might be that the president of the company assured him that Jones would get the job, and he himself has counted the coins in Jones' pocket.

 Now, (d) implies (e):

          (e)  The man who will get the job has ten coins in his pocket.

Suppose that Smith recognizes the entailment, and that he believes (e) on the basis of this.   It seems clear (by the above principle) that Smith is clearly justified in believing that (e) is true!

143 Imagine, however, that Smith does not realize it, but he is getting the job, moreover, while he is unaware of the fact, he [also] has ten coins in his pocket!

Gettier maintains that this example is one where proposition (e) is true, Smith believes it, and Smith's belief is justified (even though (d)--through which he inferred (e)--is false).  But, Gettier contends, Smith does not know (e).

Thus, he is saying, the traditional JTB analysis is inadequate (it is too weak, and does not state sufficient conditions for propositional knowledge).

4. Lucky Guesses, and Lucky (or Accidental) Truths:

Philosophers disagree over how to describe the "problem" which Gettier uncovers.  In his An Introduction to Contemporary Epistemology, Matthias Steup distinguishes between a lucky guess (my naming the winning team of the super bowl [given the woeful state of my ignorance in the area of professional football]--cases where given S's evidence, the truth of p is not a likely outcome), and a lucky truth (my getting a job at FIU in 1976 [when there were hundreds of candidates, many more qualified]--cases where in relation to the relevant facts, p's truth was not a likely outcome).  As Steup notes

justification is what prevents a true belief from being a lucky guess, but not from being a lucky truth.
  ...What the Gettier problem shows us is that in order for a true belief to qualify as knowledge, it must satisfy two conditions; it must not be a lucky guess (that is, it must be justified), and it must not be a lucky truth.  A true belief that isn't a lucky guess--like Smith's belief...may still be a lucky truth, and thus fall short of being knowledge.  Hence in order to solve the Gettier problem, epistemologists have to figure out what kind of condition can prevent a true belief from being a lucky truth.8
-In his "Epistemic Luck and the Purely Epistemic," however, Richard Foley maintains that: lucky truths may not be all bad in epistemology: "we can criticize the person's intellectual character, or his cognitive equipment, without criticizing everything which is a product of that character or equipment.  A belief can be rational even though what prompts the believer to choose his belief or what cognitive equipment causes him to have the belief regularly produces epistemic howlers.  In such cases, we should admit...that the believer has been epistemically lucky."9

     Other epistemologists seek to characterize the Gettier problem by speaking of "accidental truths."  For example, Ralph Baergen says what goes wrong in the Gettier cases is:

the target belief is true, but the way in which it is true isn't what the subject has in mind.  One has the feeling that these beliefs are only accidentally true, and this seems to be what prevents us from regarding these beliefs as knowledge.  The weakness of the JTB theory, then, seems to be that it doesn't rule out the possibility that the target belief could be true only accidentally.10

Whether we think the problem is inference through false beliefs, lucky truths, or accidental truths, clearly something is amiss with the traditional analysis.  To cinch his case, Gettier provides a second case:

Gettier's Case II:

143  Smith has strong evidence for believing that:

          (f) Jones owns a ford.

His evidence might be that Jones has for all of Smith's past acquaintance owned Fords, he has ridden in Jones' Fords, he has just been offered a ride in Jones' Ford, etc.  Now (f) clearly implies each of the following:
(g) Either Jones owns a Ford, or Brown (another of Smith's many friends) is in Boston.

(h) Either Jones owns a Ford, or Brown is in Barcelona.

(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.

Suppose Smith recognizes the implications, and he believes (g), (h), and (i) on the basis of this recognition.  His beliefs are, by the above principle justified (even though he doesn't know where in the world Brown is).

Suppose, further, that Jones doesn't now own a Ford, but that Brown is in Barcelona.

Does Smith know that (h)?  He believes it, his belief is justified, and it is true!  Again, Gettier says, we have a case of JTB which isn't a ase of knowledge.  This means that the fulfillment of the JTB condition is not sufficient for knowledge.  Again, epistemologists contend, we have a case of an accidental truth.

(end of essay)

5. Modified Gettier Counter-Examples:

Both of Gettier's examples involve reasoning through false beliefs.11  As John Pollock points out, however (building on an example from Alvin Goldman), this is not a central requirement for "Gettier cases:"

suppose you are driving through the countryside and see what you take to be a barn.  You see it in good light and from not too great a distance, it looks the way barns look, and so on.  Furthermore, it is a barn.  You then have justified true belief that it is a barn.  But in an attempt to appear more opulent than they are, the people around here have taken to constructing very realistic barn facades that cannot readily be distinguished from the real thing when viewed from the highway.  Under these circumstances we would not agree that you know that what you see is a barn, even though you have justified true belief.  Furthermore, your belief that you see a barn is not in any way inferred from a belief about the absence of barn facades.  Most likely the possibility of barn facades is something that will not even have occurred to you, much less have played a role in your reasoning.
       We can construct an even simpler perceptual example.  Suppose S sees a ball that looks red to him, and on that basis he correctly judges that it is red.  But unbeknownst to S, the ball is illuminated by red lights and would look red to him even if it were not red.  Then S does not know that the ball is red despite his having a justified true belief to that effect....These examples...indicate that justified true belief can fail to be knowledge because of the truth values of propositions that do not play a direct role in the reasoning underlying the belief.12

This version of the problem doesn't "reason through false beliefs," and there are many other versions which raise the problem--indeed, in his, The Analysis of Knowledge Robert Shope has cataloged 98 distinct examples of  "the Gettier problem" as of 1983.13

6. An Over-View of Some of the Responses to Gettier's Counter-Examples:

There are a number of contemporary attempts to devise an "adequate" analysis of knowledge so as to avoid the "Gettier problem."  Each of these endeavors to avoid the possibility of accidental truths (or lucky truths/guesses) counting as knowledge.14

     One approach adds a causal condition maintaining that there must be "an appropriate causal connection" between our belief and that which justifies it.15  Of course, the specification of the "appropriate sort of causal connection" becomes the main job of such an approach.  Goldman maintains that in addition to the obtaining of the "appropriate sort of causal connection," the individual in question must be able to "correctly reconstruct" (mentally), the causal chain.  The idea here is that accidental truths will be ruled out because of this condition.  If a causal connection obtains but the individual has a radically altered conception of it, then the true belief will be deemed an "accidental" one!

     A second approach focuses on the evidence the subject has for the belief by adding a "conclusive reasons condition" to the traditional JTB account of knowledge.16  It maintains that we know only if

...the reasons the subject has for holding the target belief guarantee the truth of the belief.  This rules out the possibility that the theory will label a belief as knowledge if one's reasons for holding the belief don't preclude errors.17

Conclusive reasons, then, are intended to eliminate the possibility of an accidental truth.

     A third sort of account argues that knowledge is undefeated JTB.18  As Ralph Baergen notes,

 in looking back at the Gettier cases, one sees that in each one there is some relevant fact (or facts) about the situation of which the subject is unaware, and the existence of these facts (along with the subject's failure to be aware of them) prevents the target belief from counting as knowledge....Such facts (when they are still undiscovered) are called defeaters; when they are in fact added to one's stock of information they become overriders.
  Suppose S is prima facie justified in believing that P.  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).19

     There is a complex interrelationship between these various accounts but each is aiming at offering an analysis of knowledge--each would offer a characterization which improves upon the traditional account and allows us to better understand what knowledge is by identifying necessary and sufficient conditions for knowing.  John Pollock offers the following rationale for the seeming intractability of the Gettier problem:

to a certain extent, I think that the claim that knowledge requires objective epistemic justification provides a solution to the Gettier problem.  But it might be disqualified as a solution to the Gettier problem on the grounds that the definition of objective justification is vague in one crucial respect. It talks about being justified for some reason, in believing P.  I think that that notion makes pre-theoretic good sense, but to spell out what it involves requires us to construct a complete epistemological theory.  That, I think, is why the Gettier problem has proven so intractable.  The complexities in the analysis of knowing all have to do with filling out this clause.  The important thing to realize, however, is that these complexities have nothing special to do with knowledge per se.  What they pertain to is the structure of epistemic justification and the way in which beliefs come to be justified on the basis of other beliefs and nondoxastic states.  Thus even if it is deemed that we have not yet solved the Gettier problem, we have at least put the blame where it belongs--not on knowledge but on the structure of epistemic justification and the complexity of our epistemic norms.20

In his Pyrrhonian Reflections On Knowledge and Justification, Robert Fogelin maintains that:

...the justification clause in the traditional doctrine that knowledge equals justified true belief is now seen to have two components.  The first concerns the manner in which S came to adopt a belief.  This is the (iiip)21 clause, which demands that he do this in an epistemically responsible manner.  The second concerns a relationship between the proposition believed and the grounds on which it is believed.  This is the (iiig) clause, which demands that these grounds establish the truth of the proposition believed on their basis.22

I claim that in every version of the Gettier problems we will find this same situation: S will be justified in his belief, having come to it in a responsible manner; that is, his performance will satisfy the (iiip) clause of the amended biconditional.  At the same time, his grounds will not establish the truth of what he believes, so the (iiig) clause will not be satisfied.23

Fogelin contends that knowledge is "...justified true belief, justifiably arrived at."24

     Finally, in her Evidence and Inquiry, Susan Haack maintains that:

Gettier-type `paradoxes' arise because of a mismatch between the concept of knowledge, which, though vague and shifting, is surely categorical, and the concept of justification, which is essentially gradational.  If so, there may be no intuitively satisfactory analysis of knowledge to be had, no sharp line to be drawn between cases where a subject does, and cases where he doesn't, know, no ideal point of equilibrium which precludes our having knowledge by luck without precluding our having knowledge altogether.  And to me, at any rate, the question: what counts as better or worse evidence for believing something? seems both deeper and more important than the question: supposing that what one believes is true, how good does one's evidence have to be before one can count as knowing?25

     In the remainder of this section of the course, we will examine two responses to what has come to be called "the Gettier Problem" (Goldman's causal theory and a version of the defeasibility  analysis--Lehrer and Paxson's "fallibilistic" theory).  Before we turn to that discussion, however, I want to discuss the use of examples in the above discussion (and in what will ensue).

7. Conceptual Analysis, Intuitions, and "Reflective Equilibrium:"

How is it that Gettier is so certain that we will agree with him--what makes him so sure that we will accept his examples as cases of JTB without knowledge?  Our other authors (Lehrer, Goldman, BonJour, etc.) will make similar appeals to epistemological examples.  Indeed, when we look back at Plato's dialogues we see something very similar.

     How is it, then, that Plato's Socrates' and Gettier's opponents are supposed to recognize the "error" of their views?  As Stanley Cavell points out that:

Socrates gets his antagonists to withdraw their definitions not because they do not know what their words mean, but because they do know what they (their words) mean, and therefore know that Socrates has led them into paradox.26

Socrates and Gettier are to seek a "reflective equilibrium" between their reflective theories and judgments, on the one hand, and our ordinary (or pre-reflective) judgments (or "intuitions"),27 on the other.  Before we continue, then, we should critically consider the appropriateness of employing the technique of seeking such a "reflective equilibrium."  In his Naturalizing the Mind, Fred Dretske maintains that it typical of philosophical thought experiments...[that] one is asked to make judgments about situations that differ profoundly from the familiar regularities of daily life.  Intuitions are generated by, they bubble out of, customary patterns of thought, exactly the patterns of thought that are not applicable in the bizarre circumstances of philosophical thought experiments.  The time to suspend intuitions, the time to not trust snap judgments, is in the midst of a philosophical thought experiment.  That is where they are least likely to be reliable.28

In the case of Lehrer, Gettier, and Goldman (and of others who we will be reading), we must be on our guard as we encounter the philosophical use of examples (and counter-examples) intended to produce reflective equilibrium.  One must guard against adhering too rigidly to one's "pretheoretic intuitions," but one must also guard against adhering too rigidly to one's "theoretical positions."

     A further discussion of Roderick Chisholm's "particularism" helps explain why epistemologists are drawn to seek a "reflective equilibrium."29  As Ralph Baergen notes, Chisholm contends that one can think of epistemologists as faced with this pair of questions:

(1) Which of our beliefs are justified? and (2) What conditions must a belief meet in order to qualify as justified?  If we can work out an answer to one of the questions, the answer to the other should fall into place.  If we knew which of our beliefs where justified, we could examine them for common features and draw out the conditions that justified beliefs must meet; and if we knew the conditions on justified belief, we could apply them to our beliefs to see which are justified.  The methodological question is this: Which of these [questions] should epistemologists address first?  Those who say we should address (1) have been called [by Chisholm] "particularists," and those who give priority to (2) are "methodists."  Which of these questions we take on first will influence what sort of results we end up with.30

Descartes can be seen as an adherent of "methodism"--he contends that some of our beliefs are justified, some not, and we must find (and that he has found) a general method which we can employ to distinguish them.  Chisholm opts for "particularism," and Baergen maintains that:

my preference is to begin with our ordinary judgments about both questions, find the points at which these seem to conflict, and resolve these conflicts by having each side trade away some of its claims.  This approach allows us to avoid having to identify one of the above questions as having precedence over the other.  Also, we needn't begin with the assumption that we know the answer to either question; we need only assume that we have some idea of the answers to both questions, and work from there.  As was pointed out earlier, we do have a concept of justification and we do manage to employ it in a regular manner, so this is not an unreasonable assumption.  Of course, there is a shortcoming involved in this business of trading away parts of our answers to each question to get these to agree.  There are many ways of getting the answers to these two questions to agree.  In deciding which of these resolutions to adopt, one should look for reasonable grounds for departing from our ordinary judgments.31

The case for the utilization of the method of analysis and reflective equilibrium is straightforwardly put forth here by Baergen.

     Of course, there is something suspicious about such a "bootstrapping" activity (after all, one can not, literally speaking, pull oneself up by one's bootstraps).  But we will save that question for later.


1 An  "analysis," in the sense intended here, is meant to provide an answer to a philosophical (Socratic) question like: "What  is it to have knowledge?" or "What is knowledge?"   The skeptical challenge makes some worry that knowledge may be  unattainable, and makes others uncertain as to what could count as knowledge, and generally seems to raise these questions for us.   Back

2 Cf., Plato, Theaetetus, trans. F.M. Cornford, in The Collected Dialogues of Plato, eds. Edith Hamilton and  Huntington  Cairns (Princeton: Princeton U.P., 1961), 200d-201d.  Back

3 Where  `p' stands proxy for any proposition (any assertion or denial).   Not all sentences are propositions (questions and commands, for example, don't make assertions).   Back

4 Peter Geach,  "Plato's Euthyphro," The Monist  v.  50  (1966), pp. 369-382, p. 371.   Back

5 "iff" stands for "if and only if."   Back

6 Note that he is not claiming that this analysis does not  state necessary conditions for knowing!   Back

7 According  to Peter Klein, in his essay  "Scepticism, Contemporary" (in A Companion to Epistemology, eds. Jonathan Dancy and  Ernest Sosa [Oxford: Blackwell, 1992], p. 458-462, p.  459), Gettier may be the first to explicitly appeal to the principle.  The principle is also often called "the closure principle"--it says that "...moving from one proposition to another on the basis of a recognized entailment does not get us outside of the closed area of justified beliefs" (Matthias Steup, An Introduction to Contemporary Epistemology  [Upper Saddle River:  Prentice  Hall, 1996], p. 20 [footnote] 6).   Back

8 Matthias  Steup, An Introduction to Contemporary  Epistemology, (Upper Saddle River: Prentice Hall, 1996), p. 9.  Back

9 Richard Foley,  "Epistemic Luck and the Purely Epistemic," American Philosophical Quarterly  v. 21  (1984),  pp.  113-124, p. 121.   Back

10 Ralph Baergen, Contemporary Epistemology (Fort Worth: Harcourt, 1995), p. 110.   Back

11 In Case I the false belief is (d), while in case II it is (f).   Back

12 John  Pollock, "The Gettier Problem," in On Knowing and the Known, ed. Kenneth G. Lucey (Amherst: Prometheus, 1996), pp.  89-101,   p.  90.   The essay originally appeared in Pollock's Contemporary Theories of Knowledge (Totowa:  Rowman,  1986)  on pp. 183-193.   Back

13 Cf.,  Robert  Shope, The Analysis of Knowledge  (Princeton: Princeton U.P., 1983).   Back

14 For  excellent introductory discussions of the  "responses"  to the  Gettier  problem,  cf., Louis Pojman's  "The Analysis of Knowledge,"  in his edited collection The Theory of Knowledge (Belmont: Wadsworth, 1999),  pp.137-141;  George Pappas and Marshall Swain, "Introduction," in their edited collection Essays on Knowledge and Justification (Ithaca: Cornell U.P., 1978),  pp. 11-40;  Ralph  Baergen, Contemporary Epistemology, op. cit., Chapter 5; and Paul Moser's "Gettier Problem," in A Companion to Epistemology, eds. Jonathan  Dancy and Ernest Sosa, op. cit., pp. 157-159.   Back

15 Cf.,  Alvin Goldman, "A Causal Theory of Knowing," The Journal of Philosophy v. 64  (1967),  pp. 335-372.  Goldman has considerably modified his view, and his more mature view is developed in his Epistemology and Cognition (Cambridge:  Harvard U.P., 1986).   Back

16 Cf.,  Fred Dretske, "Conclusive Reasons," Australasian Journal of  Philosophy  v. 49 (1971), pp. 1-22.  Reprinted in  Essays on Knowledge and Justification, eds. George  Pappas  and  Marshall Swain,  op.  cit., pp. 41-60.  Dretske has come to  abandon  this sort of  approach for one which involves a complex  analysis  of "information"--cf.,  his Knowledge and the Flow of Information (Cambridge: Bradford Books, 1981).   Back

17 Ralph Baergen, Contemporary Epistemology, op. cit., p. 110.   Back

18 Cf.,  Keith  Lehrer and Thomas Paxson,  "Knowledge:  Undefeated Justified  True Belief," The Journal of Philosophy v. 66  (1969), pp.  225-237; and David Annis, "Knowledge and Defeasibility,"  which originally appeared in Philosophical Studies v. 24 (1973), pp. 199-203.  It is reprinted in Essays  on  Knowledge and Justification, eds. George  Pappas  and Marshall Swain, op. cit., pp. 155-159.    Back

19 Ralph Baergen, Contemporary Epistemology, op. cit.,  pp.  119-120.   Back

20 John Pollock, "The Gettier Problem," op. cit., p. 95.   Back

21 Fogelin calls this the "performance" clause, the other is called the "grounds" clause.   Back

22 Robert  Fogelin, Pyrrhonistic Reflections On Knowledge and Justification (N.Y.: Oxford U.P., 1994), p. 20.  Back

23 Ibid., pp. 20-21.   Back

24 Ibid., p. 28.   Back

25 Susan Haack, Evidence and Inquiry: Towards Reconstruction in Epistemology (Oxford: Blackwell, 1993), p. 7.   Back

26 Stanley  Cavell,  "Must We Mean What We Say?", in his Must We Mean What We Say?  A Book of Essays (Cambridge: Cambridge  U.P., 1969), pp. 1-43, p. 39.   Back

27 The sense of `intuition' use here is not that of a  "special faculty of  knowledge,"  but, rather, that of our ordinary, everyday, pre-reflective judgments about whether a concept is  to be  applied to a specific situation--whether, for example, "bean bag chairs" are properly considered to be "chairs."   Back

28 Fred Dretske, Naturalizing The Mind  (Cambridge:  MIT  U.P., 1995), p. 147.   Back

29 Cf., Roderick Chisholm, The Problem  of  the Criterion (Milwaukee:  Marquette  Univ.,  1973), and Theory  of  Knowledge (third edition) (Englewood Cliffs: Prentice Hall, 1989).   Back

30 Ralph Baergen, Contemporary Epistemology, op. cit., p. 23.   Back

31 Ibid.   Back

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