Justified True Belief

There are a couple of passages where Plato seems to define knowledge as “justified true belief.”  So, if you have enough evidence that you have a right to accept a given proposition as true, if you do in fact exercise this right and accept that proposition as true, and if  it so happens that the proposition is true, then Plato might have said that your belief in that proposition is an example of knowledge.

This definition was occasionally challenged in an oblique sort of way in the first 24 centuries after Plato put it forward, but it was still uncontroversial enough that philosophers could use it matter-of-factly as late as the 1950s.  In 1963, Professor Edmund L. Gettier of Wayne State University wrote a very short, indeed tiny, article in which he gave two counterexamples to the definition of knowledge as justified true belief.  Here is example one:

Suppose that Smith and Jones have applied for a certain job. And suppose that Smith has strong evidence for the following conjunctive proposition:

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

Smith’s evidence for (d) might be that the president of the company assured him that Jones would in the end be selected, and that he, Smith, had counted the coins in Jones’s pocket ten minutes ago. Proposition (d) entails:

  1. The man who will get the job has ten coins in his pocket.

Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e) on the grounds of (d), for which he has strong evidence. In this case, Smith is clearly justified in believing that (e) is true.

But imagine, further, that unknown to Smith, he himself, not Jones, will get the job. And, also, unknown to Smith, he himself has ten coins in his pocket. Proposition (e) is then true, though proposition (d), from which Smith inferred (e), is false. In our example, then, all of the following are true: (i) (e) is true, (ii) Smith believes that (e) is true, and (iii) Smith is justified in believing that (e) is true. But it is equally clear that Smith does not know that (e) is true; for (e) is true in virtue of the number of coins in Smith’s pocket, while Smith does not know how many coins are in Smith’s pocket, and bases his belief in (e) on a count of the coins in Jones’s pocket, whom he falsely believes to be the man who will get the job.

Here Smith is justified in believing that “The man who will get the job has ten coins in his pocket,” and it is in fact true that the man who will get the job has ten coins in his pocket.  However, the same evidence which justifies that true belief also justifies Smith’s false belief that Jones will get the job.  In Smith’s mind, these two beliefs are so intertwined that the true proposition is unlikely to figure in any line of reasoning uncoupled from the false one.  Moreover, since Smith does not realize that he himself has ten coins in his pocket, nor presumably that there is any applicant for the job other than Jones who has ten coins in his pocket, there is no reason to suppose that he would regard such a proposition as anything other than a statement that Jones will get the job.  So, true though the proposition may be, and justified as Smith may be in accepting it as true, his belief in it can lead him to nothing but error.

This counterexample is of course highly contrived, as is Professor Gettier’s second counterexample.  That doesn’t matter.  His only goal was to show that there can be justified true beliefs which we would not call knowledge, not that such beliefs are particularly commonplace.  Having given even one counterexample, Professor Gettier showed that justified true belief is not an adequate definition of knowledge.  Needless to say, Plato himself would probably have been thrilled with these counterexamples.  One can easily imagine him starting from them and proceeding to spin out a whole theory of justification, perhaps based on the idea that what we have a right to believe varies depending on the plane of existence to which our belief pertains, or that justification isn’t really justification unless the subject is approaching the topic in the true character of a philosopher, or some such Platonistic thing.

As it happens, Professor Gettier’s article was followed by a great many publications giving “Gettier-style” counterexamples, including many that are far more natural and straightforward than his original two.  Evidently all that needed to be done was to give some counterexamples, and the floodgates of creativity came open.  Professor Gettier himself did not write any of these articles, or indeed any articles at all after his 1963 paper.

Once you’ve read the 1963 paper, you may begin to notice naturally-occurring Gettier-style counterexamples.  The first novel I read after I was introduced to this topic about 20 years ago was Anthony Trollope’s The Eustace Diamonds.  Trollope is not often called a philosophical novelist.  However, a Gettier-style counterexample lies at the heart of this novel.  Lizzie Eustace is the childless widow of Sir Florian Eustace.  Among Sir Florian’s possessions had been a diamond necklace valued at £ 10,000.  Lady Eustace claimed that Sir Florian wanted her to have the necklace, and so insisted on treating it as her own; however, the Eustace family lawyer claimed that it was a family heirloom, entailed to Sir Florian’s blood relations, and so that it should revert to the family in event of his death without issue.   While this dispute was moving towards the courts, a person or persons unknown broke into a safe where Lady Eustace was known to keep the necklace.  The burglary was discovered; the necklace was not there.  Lady Eustace did not tell the police what was in fact true, that she had taken the necklace from the safe before the burglary and still had it in her possession.  The leader of the police investigation is Inspector Gage, a wily and experienced detective who quickly arrives at the conclusion that Lady Eustace has stolen the necklace herself, likely in conjunction with her lover, Lord George de Bruce Carruthers.

In fact, Inspector Gage is mistaken not only about Lady Lizzie’s complicity in the burglary, but also about the nature of her relationship with Lord George and about Lord George’s character.  For all that they seem like lovers, and for all that Lady Eustace would like to become Lord George’s lover, they never quite come together.  And for all that Lord George’s sources of income are shrouded in mystery, he proves in the end to be thoroughly law-abiding.  However, the collection of evidence on which the inspector bases his theory is so impressive that if it did not justify him believing it, one can hardly imagine how anyone could be justified in believing anything.  So those three propositions could be classified as justified false beliefs.  At the nub of them all, however, is a justified true belief: that the necklace is in the possession of Lady Eustace.  Surrounded as it is by these false beliefs, false beliefs which would prevent the inspector from forming a true theory of the case, he cannot be said to know even this.

Cartoonist Zach Weiner devoted a recent installment of his Saturday Morning Breakfast Cereal to laying out some thoughts about Gettier-style counterexamples:


I want to make a few remarks about this strip.  First, it doesn’t seem right to say that Professor Gettier proposed a “philosophical problem.”  To the extent that there is a “Gettier problem,” it is a problem with Plato’s proposed definition of knowledge.  By finding a weakness in that definition, Professor Gettier may have reopened philosophical problems that some had hoped to use the definition to mark as solved, but his article does not in itself suggest any new problems.  To jump directly from Professor Gettier’s challenge to Plato’s definition to a statement that “humans find the order of events to be cute” is to introduce quite an unnecessarily grandiose generalization.

Second, it’s clever that the irate child denounces “the Gettier ‘problem'” with a claim that “Maybe all the ‘problems’ of philosophy are just emergent properties that disappear when you simplify.”   Professor Gettier’s 1963 paper includes just three footnotes.  One refers to the two passages where Plato floats the definition of knowledge as justified true belief (“Plato seems to be considering some such definition at Theaetetus 201, and perhaps accepting one at Meno 98.”)  The other two cite uses of the definition by Roderick Chisholm and Alfred Ayer, two very eminent philosophers working in the Anglo-American tradition of analytic philosophy (“Roderick M. Chisholm, Perceiving: A Philosophical Study (Ithaca, New York: Cornell University Press, 1957), p. 16,” and “A. J. Ayer, The Problem of Knowledge (London: Macmillan, 1956), p. 34.”)  Much of the analytic tradition stems from the suspicion that “all the ‘problems’ of philosophy are just emergent properties that disappear when you simplify,” and Ayer and Chisholm both had interesting things to say about this suspicion.

Third, by what criterion can brain cells be regarded as “small stuff” and consciousness as “big stuff”? I’d say the only person to whom that idea makes sense is one who has heard straightforward explanations of the basics of brain anatomy and woolly explanations of the metaphysics of consciousness.  Everyone who is likely to read this strip either is, or has at some time been, awake.  Consciousness is thus familiar to all of them, an everyday thing, the very smallest of the “small stuff.” Conversely, brain cells are knowable only to people who have access to a microscope or to findings arrived at by use of a microscope.  They are, therefore, a relatively recherche topic, and most definitely “big stuff” to any truly naive subject.  To connect the phenomena of consciousness with brain cells, or with brain anatomy, is not only an even more sophisticated topic, but is at present wildly speculative.

Fourth, it’s clever to have the irate child find that “the small stuff” is no easier to understand than “the big stuff.”  I think Plato would have liked the strip, not for its defense of his definition, but for its illustration of the difficulty of separating “the small stuff” from “the big stuff.”  After all, probability wobbles and the rest of quantum theory are, so far as we are concerned, highly abstract.  We may use various images to make physics intelligible, but the deeper we enter into the subject the more thoroughly mathematical it becomes.  As the final nose-flicking indicates, our experience of “facts” and “brain cells” and “stuff that happens” are also theory-laden, so that it is an empty boast to claim that one regards them as real and the ideas behind them as unreal.

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