Wednesday, September 2, 2009

Gettier Problems

GettierGettier problems or cases are named in honor of the American
philosopher Edmund Gettier, who discovered them in 1963. They function
as challenges to the philosophical tradition of defining knowledge of
a proposition as justified true belief in that proposition. The
problems are actual or possible situations in which someone has a
belief that is both true and well supported by evidence, yet which —
according to almost all epistemologists — fails to be knowledge.
Gettier's original article had a dramatic impact, as epistemologists
began trying to ascertain afresh what knowledge is, with almost all
agreeing that Gettier had refuted the traditional definition of
knowledge. They have made many attempts to repair or replace that
traditional definition of knowledge, resulting in several new
conceptions of knowledge and of justificatory support. In this
respect, Gettier sparked a period of pronounced epistemological energy
and innovation — all with a single two-and-a-half page article. There
is no consensus, however, that any one of the attempts to solve the
Gettier challenge has succeeded in fully defining what it is to have
knowledge of a truth or fact. So, the force of that challenge
continues to be felt in various ways, and to various extents, within
epistemology. Sometimes, the challenge is ignored in frustration at
the existence of so many possibly failed efforts to solve it. Often,
the assumption is made that somehow it can — and will, one of these
days — be solved. Usually, it is agreed to show something about
knowledge, even if not all epistemologists concur as to exactly what
it shows.

1. Introduction

Gettier problems or cases arose as a challenge to our understanding of
the nature of knowledge. Initially, that challenge appeared in an
article by Edmund Gettier, published in 1963. But his article had a
striking impact among epistemologists, so much so that hundreds of
subsequent articles and sections of books have generalized Gettier's
original idea into a more wide-ranging concept of a Gettier case or
problem, where instances of this concept might differ in many ways
from Gettier's own cases. Philosophers swiftly became adept at
thinking of variations on Gettier's own particular cases; and, over
the years, this fecundity has been taken to render his challenge even
more significant. This is especially so, given that there has been no
general agreement on how to solve the challenge posed by Gettier cases
as a group — Gettier's own ones or those that other epistemologists
have observed or imagined. (Note that sometimes this general challenge
is called the Gettier problem.) What, then, is the nature of
knowledge? And can we rigorously define what it is to know? Gettier's
article gave to these questions a precision and urgency that they had
formerly lacked. The questions are still being debated — more or less
fervently at different times — within post-Gettier epistemology.
2. The Justified-True-Belief Analysis of Knowledge

Gettier cases are meant to challenge our understanding of
propositional knowledge. This is knowledge which is described by
phrases of the form "knowledge that p," with "p" being replaced by
some indicative sentence (such as "Kangaroos have no wings"). It is
knowledge of a truth or fact — knowledge of how the world is in
whatever respect is being described by a given occurrence of "p".
Usually, when epistemologists talk simply of knowledge they are
referring to propositional knowledge. It is a kind of knowledge which
we attribute to ourselves routinely and fundamentally.

Hence, it is philosophically important to ask what, more fully, such
knowledge is. If we do not fully understand what it is, will we not
fully understand ourselves either? That is a possibility, as
philosophers have long realized. Those questions are ancient ones; in
his own way, Plato asked them.

And, prior to Gettier's challenge, different epistemologists would
routinely have offered in reply some more or less detailed and precise
version of the following generic three-part analysis of what it is for
a person to have knowledge that p (for any particular "p"):

1. Belief. The person believes that p. This belief might be
more or less confident. And it might — but it need not — be manifested
in the person's speech, such as by her saying that p or by her saying
that she believes that p. All that is needed, strictly speaking, is
for her belief to exist (while possessing at least the two further
properties that are about to be listed).
2. Truth. The person's belief that p needs to be true. If it is
incorrect instead, then — no matter what else is good or useful about
it — it is not knowledge. It would only be something else, something
lesser. Admittedly, even when a belief is mistaken it can feel to the
believer as if it is true. But in that circumstance the feeling would
be mistaken; and so the belief would not be knowledge, no matter how
much it might feel to the believer like knowledge.
3. Justification. The person's belief that p needs to be well
supported, such as by being based upon some good evidence or
reasoning, or perhaps some other kind of rational justification.
Otherwise, the belief, even if it is true, may as well be a lucky
guess. It would be correct without being knowledge. It would only be
something else, something lesser.

Supposedly (on standard pre-Gettier epistemology), each of those three
conditions needs to be satisfied, if there is to be knowledge; and,
equally, if all are satisfied together, the result is an instance of
knowledge. In other words, the analysis presents what it regards as
being three individually necessary, and jointly sufficient, kinds of
condition for having an instance of knowledge that p.

The analysis is generally called the justified-true-belief form of
analysis of knowledge (or, for short, JTB). For instance, your knowing
that you are a person would be your believing (as you do) that you are
one, along with this belief's being true (as it is) and its resting
(as it does) upon much good evidence. That evidence will probably
include such matters as your having been told that you are a person,
your having reflected upon what it is to be a person, your seeing
relevant similarities between yourself and other persons, and so on.

It is important to bear in mind that JTB, as presented here, is a
generic analysis. It is intended to describe a general structuring
which can absorb or generate comparatively specific analyses that
might be suggested, either of all knowledge at once or of particular
kinds of knowledge. It provides a basic outline — a form — of a
theory. In practice, epistemologists would suggest further details,
while respecting that general form. So, even when particular analyses
suggested by particular philosophers at first glance seem different to
JTB, these analyses can simply be more specific instances or versions
of that more general form of theory.

Probably the most common way for this to occur involves the specific
analyses incorporating, in turn, further analyses of some or all of
belief, truth, and justification. For example, some of the later
sections in this article may be interpreted as discussing attempts to
understand justification more precisely, along with how it functions
as part of knowledge. In general, the goal of such attempts can be
that of ascertaining aspects of knowledge's microstructure, thereby
rendering the general theory JTB as precise and full as it needs to be
in order genuinely to constitute an understanding of particular
instances of knowing and of not knowing. Steps in that direction by
various epistemologists have tended to be more detailed and
complicated after Gettier's 1963 challenge than had previously been
the case. Roderick Chisholm (1966/1977/1989) was an influential
exemplar of the post-1963 tendency; A. J. Ayer (1956) famously
exemplified the pre-1963 approach.
3. Gettier's Original Challenge

Gettier's article described two possible situations. This section
presents his Case I. (It is perhaps the more widely discussed of the
two. The second will be mentioned in the next section.) Subsequent
sections will use this Case I of Gettier's as a focal point for
analysis.

The case's protagonist is Smith. He and Jones have applied for a
particular job. But Smith has been told by the company president that
Jones will win the job. Smith combines that testimony with his
observational evidence of there being ten coins in Jones's pocket. (He
had counted them himself — an odd but imaginable circumstance.) And he
proceeds to infer that whoever will get the job has ten coins in their
pocket. (As the present article proceeds, we will refer to this belief
several times more. For convenience, therefore, let us call it belief
b.) Notice that Smith is not thereby guessing. On the contrary; his
belief b enjoys a reasonable amount of justificatory support. There is
the company president's testimony; there is Smith's observation of the
coins in Jones's pocket; and there is Smith's proceeding to infer
belief b carefully and sensibly from that other evidence. Belief b is
thereby at least fairly well justified — supported by evidence which
is good in a reasonably normal way. As it happens, too, belief b is
true — although not in the way in which Smith was expecting it to be
true. For it is Smith who will get the job, and Smith himself has ten
coins in his pocket. These two facts combine to make his belief b
true. Nevertheless, neither of those facts is something that, on its
own, was known by Smith. Is his belief b therefore not knowledge? In
other words, does Smith fail to know that the person who will get the
job has ten coins in his pocket? Surely so (thought Gettier).

That is Gettier's Case I, as it was interpreted by him, and as it has
subsequently been regarded by almost all other epistemologists. The
immediately pertinent aspects of it are standardly claimed to be as
follows. It contains a belief which is true and justified — but which
is not knowledge. And if that is an accurate reading of the case, then
JTB is false. Case I would show that it is possible for a belief to be
true and justified without being knowledge. Case I would have
established that the combination of truth, belief, and justification
does not entail the presence of knowledge. In that sense, a belief's
being true and justified would not be sufficient for its being
knowledge.

But if JTB is false as it stands, with what should it be replaced?
(Gettier himself made no suggestions about this.) Its failing to
describe a jointly sufficient condition of knowing does not entail
that the three conditions it does describe are not individually
necessary to knowing. And if each of truth, belief, and justification
is needed, then what aspect of knowledge is still missing? What
feature of Case I prevents Smith's belief b from being knowledge? What
is the smallest imaginable alteration to the case that would allow
belief b to become knowledge? Would we need to add some wholly new
kind of element to the situation? Or is JTB false only because it is
too general — too unspecific? For instance, are only some kinds of
justification both needed and enough, if a true belief is to become
knowledge? Must we describe more specifically how justification ever
makes a true belief knowledge? Is Smith's belief b justified in the
wrong way, if it is to be knowledge?
4. Some other Gettier Cases

Having posed those questions, though, we should realize that they are
merely representative of a more general epistemological line of
inquiry. The epistemological challenge is not just to discover the
minimal repair that we could make to Gettier's Case I, say, so that
knowledge would then be present. Rather, it is to find a failing — a
reason for a lack of knowledge — that is common to all Gettier cases
that have been, or could be, thought of (that is, all actual or
possible cases relevantly like Gettier's own ones). Only thus will we
be understanding knowledge in general — all instances of knowledge,
everyone's knowledge. And this is our goal when responding to Gettier
cases.

Sections 7 through 11 will present some attempted diagnoses of such
cases. In order to evaluate them, therefore, it would be advantageous
to have some sense of the apparent potential range of the concept of a
Gettier case. I will mention four notable cases.

The lucky disjunction (Gettier's second case: 1963). Again, Smith is
the protagonist. This time, he possesses good evidence in favor of the
proposition that Jones owns a Ford. Smith also has a friend, Brown.
Where is Brown to be found at the moment? Smith does not know.
Nonetheless, on the basis of his accepting that Jones owns a Ford, he
infers — and accepts — each of these three disjunctive propositions:

* Either Jones owns a Ford, or Brown is in Boston.
* Either Jones owns a Ford, or Brown is in Barcelona.
* Either Jones owns a Ford, or Brown is in Brest-Litovsk.

No insight into Jones's location guides Smith in any of this
reasoning. He realizes that he has good evidence for the first
disjunct (regarding Jones) in each of those three disjunctions, and he
sees this evidence as thereby supporting each disjunction as a whole.
Seemingly, he is right about that. (These are inclusive disjunctions,
not exclusive. That is, each can, if need be, accommodate the truth of
both of its disjuncts. Each is true if even one — let alone both — of
its disjuncts is true.) Moreover, in fact one of the three
disjunctions is true (albeit in a way that would surprise Smith if he
were to be told of how it is true). The second disjunction is true
because, as good luck would have it, Brown is in Barcelona — even
though, as bad luck would have it, Jones does not own a Ford. (As it
happened, the evidence for his doing so, although good, was
misleading.) Accordingly, Smith's belief that either Jones owns a Ford
or Brown is in Barcelona is true. And there is good evidence
supporting — justifying — it. But is it knowledge?

The sheep in the field (Chisholm 1966/1977/1989). Imagine that you are
standing outside a field. You see, within it, what looks exactly like
a sheep. What belief instantly occurs to you? Among the many that
could have done so, it happens to be the belief that there is a sheep
in the field. And in fact you are right, because there is a sheep
behind the hill in the middle of the field. You cannot see that sheep,
though, and you have no direct evidence of its existence. Moreover,
what you are seeing is a dog, disguised as a sheep. Hence, you have a
well justified true belief that there is a sheep in the field. But is
that belief knowledge?

The pyromaniac (Skyrms 1967). A pyromaniac reaches eagerly for his box
of Sure-Fire matches. He has excellent evidence of the past
reliability of such matches, as well as of the present conditions —
the clear air and dry matches — being as they should be, if his aim of
lighting one of the matches is to be satisfied. He thus has good
justification for believing, of the particular match he proceeds to
pluck from the box, that it will light. This is what occurs, too: the
match does light. However, what the pyromaniac did not realize is that
there were impurities in this specific match, and that it would not
have lit if not for the sudden (and rare) jolt of Q-radiation it
receives exactly when he is striking it. His belief is therefore true
and well justified. But is it knowledge?

The fake barns (Goldman 1976). Henry is driving in the countryside,
looking at objects in fields. He sees what looks exactly like a barn.
Accordingly, he thinks that he is seeing a barn. Now, that is indeed
what he is doing. But what he does not realize is that the
neighborhood contains many fake barns — mere barn facades that look
like real barns when viewed from the road. And if he had been looking
at one of them, he would have been deceived into believing that he was
seeing a barn. Luckily, he was not doing this. Consequently, his
belief is justified and true. But is it knowledge?

In none of those cases (or relevantly similar ones), say almost all
epistemologists, is the belief in question knowledge. (Note that some
epistemologists do not regard the fake barns case as being a genuine
Gettier case. There is a touch of vagueness in the concept of a
Gettier case.)
5. The Basic Structure of Gettier Cases

Although the multitude of actual and possible Gettier cases differ in
their details, some characteristics unite them. For a start, each
Gettier case contains a belief which is true and well justified
without — according to epistemologists as a whole — being knowledge.
The following two generic features also help to constitute Gettier
cases:

1. Fallibility. The justification that is present within each
case is fallible. Although it provides good support for the truth of
the belief in question, that support is not perfect, strictly
speaking. This means that the justification leaves open at least the
possibility of the belief's being false. The justification indicates
strongly that the belief is true — without proving conclusively that
it is.
2. Luck. What is most distinctive of Gettier cases is the luck
they contain. Within any Gettier case, in fact the well-but-fallibly
justified belief in question is true. Nevertheless, there is
significant luck in how the belief manages to combine being true with
being justified. Some abnormal or odd circumstance is present in the
case, a circumstance which makes the existence of that justified and
true belief quite fortuitous.

Here is how those two features, (1) and (2), are instantiated in
Gettier's Case I. Smith's evidence for his belief b was good but
fallible. This left open the possibility of belief b being mistaken,
even given that supporting evidence. As it happened, that possibility
was not realized: Smith's belief b was actually true. Yet this was due
to the intervention of some good luck. Belief b could easily have been
false; it was made true only by circumstances which were hidden from
Smith. That is, belief b was in fact made true by circumstances
(namely, Smith's getting the job and there being ten coins in his
pocket) other than those which Smith's evidence noticed and which his
evidence indicated as being a good enough reason for holding b to be
true. What Smith thought were the circumstances (concerning Jones)
making his belief b true were nothing of the sort. Luckily, though,
some facts of which he had no inkling were making his belief true.

Similar remarks pertain to the sheep-in-the-field case. Within it,
your sensory evidence is good. You rely on your senses, taking for
granted — as one normally would — that the situation is normal. Then,
by standard reasoning, you gain a true belief (that there is a sheep
in the field) on the basis of that fallible-but-good evidence.
Nonetheless, wherever there is fallibility there is a chance of being
mistaken — of gaining a belief which is false. And that is exactly
what would have occurred in this case (given that you are actually
looking at a disguised dog) — if not, luckily, for the presence behind
the hill of the hidden real sheep. Only luckily, therefore, is your
belief both justified and true. And because of that luck (say
epistemologists in general), the belief fails to be knowledge.
6. The Generality of Gettier Cases

JTB says that any actual or possible case of knowledge that p is an
actual or possible instance of some kind of well justified true belief
that p — and that any actual or possible instance of some kind of well
justified true belief that p is an actual or possible instance of
knowledge that p. Hence, JTB is false if there is even one actual or
possible Gettier situation (in which some justified true belief fails
to be knowledge). Accordingly, since 1963 epistemologists have tried —
again and again and again — to revise or repair or replace JTB in
response to Gettier cases. The main aim has been to modify JTB so as
to gain a 'Gettier-proof' definition of knowledge.

How extensive would such repairs need to be? After all, even if some
justified true beliefs arise within Gettier situations, not all do so.
In practise, such situations are rare, with few of our actual
justified true beliefs ever being "Gettiered." Has Gettier therefore
shown only that not all justified true beliefs are knowledge?
Correlatively, might JTB be almost correct as it is — in the sense of
being accurate about almost all actual or possible cases of knowledge?

On the face of it, Gettier cases do indeed show only that not all
actual or possible justified true beliefs are knowledge — rather than
that a belief's being justified and true is never enough for its being
knowledge. Nevertheless, epistemologists generally report the impact
of Gettier cases in the latter way, describing them as showing that
being justified and true is never enough to make a belief knowledge.
Why do epistemologists interpret the Gettier challenge in that
stronger way?

The reason is that they wish — by way of some universally applicable
definition or formula or analysis — to understand knowledge in all of
its actual or possible instances and manifestations, not only in some
of them. Hence, epistemologists strive to understand how to avoid ever
being in a Gettier situation (from which knowledge will be absent,
regardless of whether such situations are uncommon). But that goal is,
equally, the aim of understanding what it is about most situations
that constitutes their not being Gettier situations. If we do not know
what, exactly, makes a situation a Gettier case and what changes to it
would suffice for its no longer being a Gettier case, then we do not
know how, exactly, to describe the boundary between Gettier cases and
other situations.

We call various situations in which we form beliefs "everyday" or
"ordinary," for example. In particular, therefore, we might wonder
whether all "normally" justified true beliefs are still instances of
knowledge (even if in Gettier situations the justified true beliefs
are not knowledge). Yet even that tempting idea is not as
straightforward as we might have assumed. For do we know what it is,
exactly, that makes a situation ordinary? Specifically, what are the
details of ordinary situations that allow them not to be Gettier
situations — and hence that allow them to contain knowledge? To the
extent that we do not understand what it takes for a situation not to
be a Gettier situation, we do not understand what it takes for a
situation to be a normal one (thereby being able to contain
knowledge). Understanding Gettier situations would be part of
understanding non-Gettier situations — including ordinary situations.
Until we adequately understand Gettier situations, we do not
adequately understand ordinary situations — because we would not
adequately understand the difference between these two kinds of
situation.
7. Attempted Solutions: Infallibility

To the extent that we understand what makes something a Gettier case,
we understand what would suffice for that situation not to be a
Gettier case. Section 5 outlined two key components — fallibility and
luck — of Gettier situations. In this section and the next, we will
consider whether removing one of those two components — the removal of
which will suffice for a situation's no longer being a Gettier case —
would solve Gettier's epistemological challenge. That is, we will be
asking whether we may come to understand the nature of knowledge by
recognizing its being incompatible with the presence of at least one
of those two components (fallibility and luck).

There is a prima facie case, at any rate, for regarding justificatory
fallibility with concern in this setting. So, let us examine the
Infallibility Proposal for solving Gettier's challenge. There have
long been philosophers who doubt (independently of encountering
Gettier cases) that allowing fallible justification is all that it
would take to convert a true belief into knowledge. ("If you know that
p, there must have been no possibility of your being mistaken about
p," they might say.) The classic philosophical expression of that sort
of doubt was by René Descartes, most famously in his Meditations on
First Philosophy (1641). Contemporary epistemologists who have voiced
similar doubts include Keith Lehrer (1971) and Peter Unger (1971). In
the opinion of epistemologists who embrace the Infallibility Proposal,
we can eliminate Gettier cases as challenges to our understanding of
knowledge, simply by refusing to allow that one's having fallible
justification for a belief that p could ever adequately satisfy JTB's
justification condition. Stronger justification than that is required
within knowledge (they will claim); infallibilist justificatory
support is needed. (They might even say that there is no justification
present at all, let alone an insufficient amount of it, given the
fallibility within the cases.)

Thus, for instance, an infallibilist about knowledge might claim that
because (in Case I) Smith's justification provided only fallible
support for his belief b, this justification was always leaving open
the possibility of that belief being mistaken — and that this is why
the belief is not knowledge. The infallibilist might also say
something similar — as follows — about the sheep-in-the-field case.
Because you were relying on your fallible senses in the first place,
you were bound not to gain knowledge of there being a sheep in the
field. ("It could never be real knowledge, given the inherent
possibility of error in using one's senses.") And the infallibilist
will regard the fake-barns case in the same way, claiming that the
potential for mistake (that is, the existence of fallibility) was
particularly real, due to the existence of the fake barns. And that is
why (infers the infallibilist) there is a lack of knowledge within the
case — as indeed there would be within any situation where fallible
justification is being used.

So, that is the Infallibility Proposal. The standard epistemological
objection to it is that it fails to do justice to the reality of our
lives, seemingly as knowers of many aspects of the surrounding world.
In our apparently "ordinary" situations, moving from one moment to
another, we take ourselves to have much knowledge. Yet we rarely, if
ever, possess infallible justificatory support for a belief. And we
accept this about ourselves, realizing that we are not wholly —
conclusively — reliable. We accept that if we are knowers, then, we
are at least not infallible knowers. But the Infallibility Proposal —
when combined with that acceptance of our general fallibility — would
imply that we are not knowers at all. It would thereby ground a
skepticism about our ever having knowledge.

Accordingly, most epistemologists would regard the Infallibility
Proposal as being a drastic and mistaken reaction to Gettier's
challenge in particular. In response to Gettier, most seek to
understand how we do have at least some knowledge — where such
knowledge will either always or almost always be presumed to involve
some fallibility. The majority of epistemologists still work towards
what they hope will be a non-skeptical conception of knowledge; and
attaining this outcome could well need to include their solving the
Gettier challenge without adopting the Infallibility Proposal.
8. Attempted Solutions: Eliminating Luck

The other feature of Gettier cases that was highlighted in section 5
is the lucky way in which such a case's protagonist has a belief which
is both justified and true. Is it this luck that needs to be
eliminated if the situation is to become one in which the belief in
question is knowledge? In general, must any instance of knowledge
include no accidentalness in how its combination of truth, belief, and
justification is effected? The Eliminate Luck Proposal claims so.

Almost all epistemologists, when analyzing Gettier cases, reach for
some version of this idea, at least in their initial or intuitive
explanations of why knowledge is absent from the cases. Unger (1968)
is one who has also sought to make this a fuller and more considered
part of an explanation for the lack of knowledge. He says that a
belief is not knowledge if it is true only courtesy of some relevant
accident. That description is meant to allow for some flexibility.
Even so, further care will still be needed if the Eliminate Luck
Proposal is to provide real insight and understanding. After all, if
we seek to eliminate all luck whatsoever from the production of the
justified true belief (if knowledge is thereby to be present), then we
are again endorsing a version of infallibilism (as described in
section 7). If no luck is involved in the justificatory situation, the
justification renders the belief's truth wholly predictable or
inescapable; in which case, the belief is being infallibly justified.
And this would be a requirement which (as section 7 explained) few
epistemologists will find illuminating, certainly not as a response to
Gettier cases.

What many epistemologists therefore say, instead, is that the problem
within Gettier cases is the presence of too much luck. Some luck is to
be allowed; otherwise, we would again have reached for the
Infallibility Proposal. But too large a degree of luck is not to be
allowed. This is why we often find epistemologists describing Gettier
cases as containing too much chance or flukiness for knowledge to be
present.

Nevertheless, how helpful is that kind of description by those
epistemologists? How much luck is too much? That is a conceptually
vital question. Yet there has been no general agreement among
epistemologists as to what degree of luck precludes knowledge. There
has not even been much attempt to determine that degree. (It is no
coincidence, similarly, that epistemologists in general are also yet
to determine how strong — if it is allowed to be something short of
infallibility — the justificatory support needs to be within any case
of knowledge.) A specter of irremediable vagueness thus haunts the
Eliminate Luck Proposal.

Perhaps understandably, therefore, the more detailed epistemological
analyses of knowledge have focused less on delineating dangerous
degrees of luck than on characterizing substantive kinds of luck that
are held to drive away knowledge. Are there ways in which Gettier
situations are structured, say, which amount to the presence of a kind
of luck which precludes the presence of knowledge (even when there is
a justified true belief)? Most attempts to solve Gettier's challenge
instantiate this form of thinking. In sections 9 through 11, we will
encounter a few of the main suggestions that have been made.
9. Attempted Solutions: Eliminating False Evidence

A lot of epistemologists have been attracted to the idea that the
failing within Gettier cases is the person's including something false
in her evidence. This would be a problem for her, because she is
relying upon that evidence in her attempt to gain knowledge, and
because knowledge is itself always true. To the extent that falsity is
guiding the person's thinking in forming the belief that p, she will
be lucky to derive a belief that p which is true. And (as section 8
indicated) there are epistemologists who think that a lucky derivation
of a true belief is not a way to know that truth. Let us therefore
consider the No False Evidence Proposal.

In Gettier's Case I, for example, Smith includes in his evidence the
false belief that Jones will get the job. If Smith had lacked that
evidence (and if nothing else were to change within the case),
presumably he would not have inferred belief b. He would probably have
had no belief at all as to who would get the job (because he would
have had no evidence at all on the matter). If so, he would thereby
not have had a justified and true belief b which failed to be
knowledge. Should JTB therefore be modified so as to say that no
belief is knowledge if the person's justificatory support for it
includes something false? JTB would then tell us that one's knowing
that p is one's having a justified true belief which is well supported
by evidence, none of which is false.

That is the No False Evidence Proposal. But epistemologists have
noticed a few possible problems with it.

First, as Richard Feldman (1974) saw, there seem to be some Gettier
cases in which no false evidence is used. Imagine that (contrary to
Gettier's own version of Case I) Smith does not believe, falsely,
"Jones will get the job." Imagine instead that he believes, "The
company president told me that Jones will get the job." (He could have
continued to form the first belief. But suppose that, as it happens,
he does not form it.) This alternative belief would be true. It would
also provide belief b with as much justification as the false belief
provided. So, if all else is held constant within the case (with
belief b still being formed), again Smith has a true belief which is
well-although-fallibly justified, yet which might well not be
knowledge.

Second, it will be difficult for the No False Evidence Proposal not to
imply an unwelcome skepticism. Quite possibly, there is always some
false evidence being relied upon, at least implicitly, as we form
beliefs. Is there nothing false at all — not even a single falsity —
in your thinking, as you move through the world, enlarging your stock
of beliefs in various ways (not all of which ways are completely
reliable and clearly under your control)? If there is even some
falsity among the beliefs you use, but if you do not wholly remove it
or if you do not isolate it from the other beliefs you are using, then
— on the No False Evidence Proposal — there is a danger of its
preventing those other beliefs from ever being knowledge. This is a
worry to be taken seriously, if a belief's being knowledge is to
depend upon the total absence of falsity from one's thinking in
support of that belief.

Unsurprisingly, therefore, some epistemologists, such as Lehrer
(1965), have proposed a further modification of JTB — a less demanding
one. They have suggested that what is needed for knowing that p is an
absence only of significant and ineliminable (non-isolable) falsehoods
from one's evidence for p's being true. Here is what that means.
First, false beliefs which you are — but need not have been — using as
evidence for p are eliminable from your evidence for p. And, second,
false beliefs whose absence would seriously weaken your evidence for p
are significant within your evidence for p. Accordingly, the No False
Evidence Proposal now becomes the No False Core Evidence Proposal. The
latter proposal says that if the only falsehoods in your evidence for
p are ones which you could discard, and ones whose absence would not
seriously weaken your evidence for p, then (with all else being equal)
your justification is adequate for giving you knowledge that p. The
accompanying application of that proposal to Gettier cases would claim
that because, within each such case, some falsehood plays an important
role in the protagonist's evidence, her justified true belief based on
that evidence fails to be knowledge. On the modified proposal, this
would be the reason for the lack of that knowledge.

One fundamental problem confronting that proposal is obviously its
potential vagueness. To what extent, precisely, need you be able to
eliminate the false evidence in question if knowledge that p is to be
present? How easy, exactly, must this be for you? And just how
weakened, exactly, may your evidence for p become — courtesy of the
elimination of false elements within it — before it is too weak to be
part of making your belief that p knowledge? Such questions still
await answers from epistemologists.
10. Attempted Solutions: Eliminating Defeat

Section 9 explored the suggestion that the failing within any Gettier
case is a matter of what is included within a given person's evidence:
specifically, some core falsehood is accepted within her evidence. A
converse idea has also received epistemological attention — the
thought that the failing within any Gettier case is a matter of what
is not included in the person's evidence: specifically, some notable
truth or fact is absent from her evidence. This proposal would not
simply be that the evidence overlooks at least one fact or truth. Like
the unmodified No False Evidence Proposal (with which section 9
began), that would be far too demanding, undoubtedly leading to
skepticism. Because there are always some facts or truths not noticed
by anyone's evidence for a particular belief, there would be no
knowledge either. No one's evidence for p would ever be good enough to
satisfy the justification requirement that is generally held to be
necessary to a belief that p's being knowledge.

Epistemologists therefore restrict the proposal, turning it into what
is often called a defeasibility analysis of knowledge. It can also be
termed the No Defeat Proposal. The thought behind it is that JTB
should be modified so as to say that what is needed in knowing that p
is an absence from the inquirer's context of any defeaters of her
evidence for p. And what is a defeater? A particular fact or truth t
defeats a body of justification j (as support for a belief that p) if
adding t to j, thereby producing a new body of justification j*, would
seriously weaken the justificatory support being provided for that
belief that p — so much so that j* does not provide strong enough
support to make even the true belief that p knowledge. This means that
t is relevant to justifying p (because otherwise adding it to j would
produce neither a weakened nor a strengthened j*) as support for p —
but damagingly so. In effect, insofar as one wishes to have beliefs
which are knowledge, one should only have beliefs which are supported
by evidence that is not overlooking any facts or truths which — if
left overlooked — function as defeaters of whatever support is being
provided by that evidence for those beliefs.

In Case I, for instance, we might think that the reason why Smith's
belief b fails to be knowledge is that his evidence includes no
awareness of the facts that he will get the job himself and that his
own pocket contains ten coins. Thus, imagine a variation on Gettier's
case, in which Smith's evidence does include a recognition of these
facts about himself. Then either (i) he would have conflicting
evidence (by having this evidence supporting his, plus the original
evidence supporting Jones's, being about to get the job), or (ii) he
would not have conflicting evidence (if his original evidence about
Jones had been discarded, leaving him with only the evidence about
himself). But in either of those circumstances Smith would be
justified in having belief b — concerning "the person," whoever it
would be, who will get the job. Moreover, in that circumstance he
would not obviously be in a Gettier situation — with his belief b
still failing to be knowledge. For, on either (i) or (ii), there would
be no defeaters of his evidence — no facts which are being overlooked
by his evidence, and which would seriously weaken his evidence if he
were not overlooking them.

Unfortunately, however, this proposal — like the No False Core
Evidence Proposal in section 9 — faces a fundamental problem of
vagueness. As we have seen, defeaters defeat by weakening
justification: as more and stronger defeaters are being overlooked by
a particular body of evidence, that evidence is correlatively
weakened. (This is so, even when the defeaters clash directly with
one's belief that p. And it is so, regardless of the believer's not
realizing that the evidence is thereby weakened.) How weak, exactly,
can the justification for a belief that p become before it is too weak
to sustain the belief's being knowledge that p? This question — which,
in one form or another, arises for all proposals which allow
knowledge's justificatory component to be satisfied by fallible
justificatory support — is yet to be answered by epistemologists as a
group. In the particular instance of the No Defeat Proposal, it is the
question, raised by epistemologists such as William Lycan (1977) and
Lehrer and Paxson (1969), of how much — and which aspects — of one's
environment need to be noticed by one's evidence, if that evidence is
to be justification that makes one's belief that p knowledge. There
can be much complexity in one's environment, with it not always being
clear where to draw the line between aspects of the environment which
do — and those which do not — need to be noticed by one's evidence.
How strict should we be in what we expect of people in this respect?
11. Attempted Solutions: Eliminating Inappropriate Causality

It has also been suggested that the failing within Gettier situations
is one of causality, with the justified true belief being caused —
generated, brought about — in too odd or abnormal a way for it to be
knowledge. This Appropriate Causality Proposal — initially advocated
by Alvin Goldman (1967) — will ask us to consider, by way of contrast,
any case of observational knowledge. Seemingly, a necessary part of
such knowledge's being produced is a stable and normal causal
pattern's generating the belief in question. You use your eyes in a
standard way, for example. A belief might then form in a standard way,
reporting what you observed. That belief will be justified in a
standard way, too, partly by that use of your eyes. And it will be
true in a standard way, reporting how the world actually is in a
specific respect. All of this reflects the causal stability of normal
visually-based belief-forming processes. In particular, we realize
that the object of the knowledge — that perceived aspect of the world
which most immediately makes the belief true — is playing an
appropriate role in bringing the belief into existence.

Within Gettier's Case I, however, that pattern of normality is absent.
The aspects of the world which make Smith's belief b true are the
facts of his getting the job and of there being ten coins in his own
pocket. But these do not help to cause the existence of belief b.
(That belief is caused by Smith's awareness of other facts — his
conversation with the company president and his observation of the
contents of Jones's pocket.) Should JTB be modified accordingly, so as
to tell us that a justified true belief is knowledge only if those
aspects of the world which make it true are appropriately involved in
causing it to exist?

Epistemologists have noticed problems with that Appropriate Causality
Proposal, though.

First, some objects of knowledge might be aspects of the world which
are unable ever to have causal influences. In knowing that 2 + 2 = 4
(this being a prima facie instance of what epistemologists term a
priori knowledge), you know a truth — perhaps a fact — about numbers.
And do they have causal effects? Most epistemologists do not believe
so. (Maybe instances of numerals, such as marks on paper being
interpreted on particular occasions in specific minds, can have causal
effects. Yet — it is usually said — such numerals are merely
representations of numbers. They are not the actual numbers.)
Consequently, it is quite possible that the scope of the Appropriate
Causality Proposal is more restricted than is epistemologically
desirable. The proposal would apply only to empirical or a posteriori
knowledge, knowledge of the observable world — which is to say that it
might not apply to all of the knowledge that is actually or possibly
available to people. And (as section 6 explained) epistemologists seek
to understand all actual or possible knowledge, not just some of it.

Second, to what extent will the Appropriate Causality Proposal help us
to understand even empirical knowledge? The problem is that
epistemologists have not agreed on any formula for exactly how (if
there is to be knowledge that p) the fact that p is to contribute to
bringing about the existence of the justified true belief that p.
Inevitably (and especially when reasoning is involved), there will be
indirectness in the causal process resulting in the formation of the
belief that p. But how much indirectness is too much? That is, are
there degrees of indirectness that are incompatible with there being
knowledge that p? And if so, how are we to specify those critical
degrees?

For example, suppose that (in an altered Case I of which we might
conceive) Smith's being about to be offered the job is actually part
of the causal explanation of why the company president told him that
Jones would get the job. The president, with his mischievous sense of
humor, wished to mislead Smith. And suppose that Smith's having ten
coins in his pocket made a jingling noise, subtly putting him in mind
of coins in pockets, subsequently leading him to discover how many
coins were in Jones's pocket. Given all of this, the facts which make
belief b true (namely, those ones concerning Smith's getting the job
and concerning the presence of the ten coins in his pocket) will
actually have been involved in the causal process that brings belief b
into existence. Would the Appropriate Causality Proposal thereby be
satisfied — so that (in this altered Case I) belief b would now be
knowledge? Or should we continue regarding the situation as being a
Gettier case, a situation in which (as in the original Case I) the
belief b fails to be knowledge? If we say that the situation remains a
Gettier case, we need to explain why this new causal ancestry for
belief b would still be too inappropriate to allow belief b to be
knowledge.

Most epistemologists will regard the altered case as a Gettier case.
But in that event they continue to owe us an analysis of what makes a
given causal history inappropriate. Often, they talk of deviant causal
chains. And that is an evocative phrase. But how clear is it? Once
more, we will wonder about vagueness. In particular, we will ask, how
deviant can a causal chain (one that results in some belief-formation)
become before it is too deviant to be able to be bringing knowledge
into existence? As we also found in sections 9 and 10, a conceptually
deep problem of vagueness thus remains to be solved.
12. Attempted Dissolutions: Competing Intuitions

Sections 9 through 11 described some of the main proposals that
epistemologists have made for solving the Gettier challenge directly.
Those proposals accept the usual interpretation of each Gettier case
as containing a justified true belief which fails to be knowledge.
Each proposal then attempts to modify JTB, the traditional
epistemological suggestion for what it is to know that p. What is
sought by those proposals, therefore, is an analysis of knowledge
which accords with the usual interpretation of Gettier cases. That
analysis would be intended to cohere with the claim that knowledge is
not present within Gettier cases. And why is it so important to cohere
with the latter claim? The standard answer offered by epistemologists
points to what they believe is their strong intuition that, within any
Gettier case, knowledge is absent. Almost all epistemologists claim to
have this intuition about Gettier cases. They treat this intuition
with much respect. (It seems that most do so as part of a more general
methodology, one which involves the respectful use of intuitions
within many areas of philosophy. Frank Jackson [1998] is a prominent
proponent of that methodology's ability to aid our philosophical
understanding of key concepts.)

Nonetheless, a few epistemological voices dissent from that approach
(as this section and the next will indicate). These seek to dissolve
the Gettier challenge. Instead of accepting the standard
interpretation of Gettier cases, and instead of trying to find a
direct solution to the challenge that the cases are thereby taken to
ground, a dissolution of the cases denies that they ground any such
challenge in the first place. And one way of developing such a
dissolution is to deny or weaken the usual intuition by which almost
all epistemologists claim to be guided in interpreting Gettier cases.

One such attempt has involved a few epistemologists — Jonathan
Weinberg, Shaun Nichols, and Stephen Stich (2001) — conducting
empirical research which (they argue) casts doubt upon the evidential
force of the usual epistemological intuition about the cases. When
epistemologists claim to have a strong intuition that knowledge is
missing from Gettier cases, they take themselves to be representative
of people in general (specifically, in how they use the word
"knowledge" and its cognates such as "know," knower," and the like).
That intuition is therefore taken to reflect how "we" — people in
general — conceive of knowledge. It is thereby assumed to be an
accurate indicator of pertinent details of the concept of knowledge —
which is to say, "our" concept of knowledge. Yet what is it that gives
epistemologists such confidence in their being representative of how
people in general use the word "knowledge"? Mostly, epistemologists
test this view of themselves upon their students and upon other
epistemologists. The empirical research by Weinberg, Nichols, and
Stich asked a wider variety of people — including ones from outside of
university or college settings — about Gettier cases. And that
research has reported encountering a wider variety of reactions to the
cases. When people who lack much, or even any, prior epistemological
awareness are presented with descriptions of Gettier cases, will they
unhesitatingly say (as epistemologists do) that the justified true
beliefs within those cases fail to be knowledge? The empirical
evidence gathered so far suggests some intriguing disparities in this
regard — including ones that might reflect varying ethnic ancestries
or backgrounds. In particular, respondents of east Asian or Indian
sub-continental descent were found to be more open than were European
Americans (of "Western" descent) to classifying Gettier cases as
situations in which knowledge is present. A similar disparity seemed
to be correlated with respondents' socio-economic status.

Those data are preliminary. (And other epistemologists have not sought
to replicate those surveys.) Nonetheless, the data are suggestive. At
the very least, they constitute some empirical evidence that does not
simply accord with epistemologists' usual interpretation of Gettier
cases. Hence, a real possibility has been raised that epistemologists,
in how they interpret Gettier cases, are not so accurately
representative of people in general. Their shared, supposedly
intuitive, interpretation of the cases might be due to something
distinctive in how they, as a group, think about knowledge, rather
than being merely how people as a whole regard knowledge. In other
words, perhaps the apparent intuition about knowledge (as it pertains
to Gettier situations) that epistemologists share with each other is
not universally shared. Maybe it is at least not shared with as many
other people as epistemologists assume is the case. And if so, then
the epistemologists' intuition might not merit the significance they
have accorded it when seeking a solution to the Gettier challenge.
(Indeed, that challenge itself might not be as distinctively
significant as epistemologists have assumed it to be. This possibility
arises once we recognize that the prevalence of that usual putative
intuition among epistemologists has been important to their deeming,
in the first place, that Gettier cases constitute a decisive challenge
to our understanding of what it is to know that p.)

Epistemologists might reply that people who think that knowledge is
present within Gettier cases are not evaluating the cases properly —
that is, as the cases should be interpreted. The question thus emerges
of whether epistemologists' intuitions are particularly trustworthy on
this topic. Are they more likely to be accurate (than are other
people's intuitions) in what they say about knowledge — in assessing
its presence in, or its absence from, specific situations? Presumably,
most epistemologists will think so, claiming that when other people do
not concur that in Gettier cases there is a lack of knowledge, those
competing reactions reflect a lack of understanding of the cases — a
lack of understanding which could well be rectified by sustained
epistemological reflection.

Potentially, that disagreement has methodological implications about
the nature and point of epistemological inquiry. For we should wonder
whether those epistemologists, insofar as their confidence in their
interpretation of Gettier cases rests upon their more sustained
reflection about such matters, are really giving voice to intuitions
as such about Gettier cases when claiming to be doing so. Or are they
instead applying some comparatively reflective theories of knowledge?
The latter alternative need not make their analyses mistaken, of
course. But it would make more likely the possibility that the
analyses of knowledge which epistemologists develop in order to
understand Gettier cases are not based upon a directly intuitive
reading of the cases. This might weaken the strength and independence
of the epistemologists' evidential support for those analyses of
knowledge.

For example, maybe the usual epistemological interpretation of Gettier
cases is manifesting a commitment to a comparatively technical and
demanding concept of knowledge, one that only reflective philosophers
would use and understand. Even if the application of that concept
feels intuitive to them, this could be due to the kind of technical
training that they have experienced. It might not be a coincidence,
either, that epistemologists tend to present Gettier cases by asking
the audience, "So, is this justified true belief within the case
really knowledge?" — thereby suggesting, through this use of emphasis,
that there is an increased importance in making the correct assessment
of the situation. The audience might well feel a correlative caution
about saying that knowledge is present. They could feel obliged to
take care not to accord knowledge if there is anything odd — as,
clearly, there is — about the situation being discussed. When that
kind of caution and care are felt to be required, then — as
contextualist philosophers such as David Lewis (1996) have argued is
appropriate — we are more likely to deny that knowledge is present.

Hence, if epistemologists continue to insist that the nature of
knowledge is such as to satisfy one of their analyses (where this
includes knowledge's being such that it is absent from Gettier cases),
then there is a correlative possibility that they are talking about
something — knowledge — that is too difficult for many, if any,
inquirers ever to attain. How should people — as potential or actual
inquirers — react to that possibility? Mark Kaplan (1985) has argued
that insofar as knowledge must conform to the demands of Gettier cases
(and to the usual epistemological interpretation of them), knowledge
is not something about which we should care greatly as inquirers. And
the fault would be knowledge's, not ours. Kaplan advocates our seeking
something less demanding and more realistically attainable than
knowledge is if it needs to cohere with the usual interpretation of
Gettier cases. (An alternative thought which Kaplan's argument might
prompt us to investigate is that of whether knowledge itself could be
something less demanding — even while still being at least somewhat
worth seeking. Section 13 will discuss that idea.)

Those pivotal issues are currently unresolved. In the meantime, their
presence confirms that, by thinking about Gettier cases, we may
naturally raise some substantial questions about epistemological
methodology — about the methods via which we should be trying to
understand knowledge. Those questions include the following ones. What
evidence should epistemologists consult as they strive to learn the
nature of knowledge? Should they be perusing intuitions? If so, whose?
Their own? How should competing intuitions be assessed? And how
strongly should favored intuitions be relied upon anyway? Are they to
be decisive? Are they at least powerful? Or are they no more than a
starting-point for further debate — a provider, not an adjudicator, of
relevant ideas?
13. Attempted Dissolutions: Knowing Luckily

Section 12 posed the question of whether supposedly intuitive
assessments of Gettier situations support the usual interpretation of
the cases as strongly — or even as intuitively — as epistemologists
generally believe is the case. How best might that question be
answered? Sections 5 and 8 explained that when epistemologists seek to
support that usual interpretation in a way that is meant to remain
intuitive, they typically begin by pointing to the luck that is
present within the cases. That luck is standardly thought to be a
powerful — yet still intuitive — reason why the justified true beliefs
inside Gettier cases fail to be knowledge.

Nevertheless, a contrary interpretation of the luck's role has also
been proposed, by Stephen Hetherington (1998; 2001). It means to
reinstate the sufficiency of JTB, thereby dissolving Gettier's
challenge. That contrary interpretation could be called the Knowing
Luckily Proposal. And it analyses Gettier's Case I along the following
lines.

This alternative interpretation concedes (in accord with the usual
interpretation) that, in forming his belief b, Smith is lucky to be
gaining a belief which is true. More fully: He is lucky to do so,
given the evidence by which he is being guided in forming that belief,
and given the surrounding facts of his situation. In that sense (we
might say), Smith came close to definitely lacking knowledge. (For in
that sense he came close to forming a false belief; and a belief which
is false is definitely not knowledge.) But to come close to definitely
lacking knowledge need not be to lack knowledge. It might merely be to
almost lack knowledge. So (as we might also say), it could be to know,
albeit luckily so. Smith would have knowledge, in virtue of having a
justified true belief. (We would thus continue to regard JTB as being
true.) However, because Smith would only luckily have that justified
true belief, he would only luckily have that knowledge.

Most epistemologists will object that this sounds like too puzzling a
way to talk about knowing. Their reaction is natural. Even this
Knowing Luckily Proposal would probably concede that there is very
little (if any) knowledge which is lucky in so marked or dramatic a
way. And because there is so little (if any) such knowledge, our
everyday lives leave us quite unused to thinking of some knowledge as
being present within ourselves or others quite so luckily: we would
actually encounter little (if any) such knowledge. To the extent that
the kind of luck involved in such cases reflects the statistical
unlikelihood of such circumstances occurring, therefore, we should
expect at least most knowledge not to be present in that lucky way.
(Otherwise, this would be the normal way for knowledge to be present.
It would not in fact be an unusual way. Hence, strictly speaking, the
knowledge would not be present only luckily.)

But even if the Knowing Luckily Proposal agrees that, inevitably, at
least most knowledge will be present in comparatively normal ways, the
proposal will deny that this entails the impossibility of there ever
being at least some knowledge which is present more luckily.
Ordinarily, when good evidence for a belief that p accompanies the
belief's being true (as it does in Case I), this combination of good
evidence and true belief occurs (unlike in Case I) without any notable
luck being needed. Ordinary knowledge is thereby constituted, with
that absence of notable luck being part of what makes instances of
ordinary knowledge ordinary in our eyes. What is ordinary to us will
not strike us as being present only luckily. Again, though, is it
therefore impossible for knowledge ever to be constituted luckily? The
Knowing Luckily Proposal claims that such knowledge is possible even
if uncommon. The proposal will grant that there would be a difference
between knowing that p in a comparatively ordinary way and knowing
that p in a comparatively lucky way. Knowing comparatively luckily
that p would be (i) knowing that p (where this might remain one's
having a justified true belief that p), even while also (ii) running,
or having run, a greater risk of not having that knowledge that p. In
that sense, it would be to know that p less securely or stably or
dependably, more fleetingly or unpredictably.

There are many forms that the lack of stability — the luck involved in
the knowledge's being present — could take. Sometimes it might include
the knowledge's having one of the failings found within Gettier cases.
The knowledge — the justified true belief — would be present in a
correspondingly lucky way. One interpretive possibility — from
Hetherington (2001) — is that of describing this knowledge that p as
being of a comparatively poor quality as knowledge that p. Normally,
knowledge that p is of a higher quality than this — being less
obviously flawed, by being less luckily present. The question
persists, though: Must all knowledge that p be, in effect, normal
knowledge that p — being of a normal quality as knowledge that p? Or
could we sometimes — even if rarely — know that p in a comparatively
poor and undesirable way? The Knowing Luckily Proposal allows that
this is possible — that this is a conceivable form for some knowledge
to take.

That proposal is yet to be widely accepted among epistemologists.
Their main objection to it has been what they have felt to be the
oddity of talking of knowledge in that way. Accordingly, the
epistemological resistance to the proposal partly reflects the
standard adherence to the dominant ("intuitive") interpretation of
Gettier cases. Yet this section and the previous one have asked
whether epistemologists should be wedded to that interpretation of
Gettier cases. So, this section leaves us with the following question:
Is it conceptually coherent to regard the justified true beliefs
within Gettier cases as instances of knowledge which are luckily
produced or present? And how are we to answer that question anyway?
With intuitions? Whose? Once again, we encounter section 12's
questions about the proper methodology for making epistemological
progress on this issue.
14. Gettier Cases and Analytic Epistemology

Since the initial philosophical description in 1963 of Gettier cases,
the project of responding to them (so as to understand what it is to
know that p) has often been central to the practice of analytic
epistemology. Partly this recurrent centrality has been due to
epistemologists' taking the opportunity to think in detail about the
nature of justification — about what justification is like in itself,
and about how it is constitutively related to knowledge. But partly,
too, that recurrent centrality reflects the way in which,
epistemologists have often assumed, responding adequately to Gettier
cases requires the use of a paradigm example of a method that has long
been central to analytic philosophy. That method involves the
considered manipulation and modification of definitional models or
theories, in reaction to clear counterexamples to those models or
theories.

Thus (we saw in section 2), JTB purported to provide a definitional
analysis of what it is to know that p. JTB aimed to describe, at least
in general terms, the separable-yet-combinable components of such
knowledge. Then Gettier cases emerged, functioning as apparently
successful counterexamples to one aspect — the sufficiency — of JTB's
generic analysis. That interpretation of the cases' impact rested upon
epistemologists' claims to have reflective-yet-intuitive insight into
the absence of knowledge from those actual or possible Gettier
circumstances. These claims of intuitive insight were treated by
epistemologists as decisive data, somewhat akin to favored
observations. The claims were to be respected accordingly; and, it was
assumed, any modification of the theory encapsulated in JTB would need
to be evaluated for how well it accommodated them. So, the
entrenchment of the Gettier challenge at the core of analytic
epistemology hinged upon epistemologists' confident assumptions that
(i) JTB failed to accommodate the data provided by those intuitions —
and that (ii) any analytical modification of JTB would need (and would
be able) to be assessed for whether it accommodated such intuitions.
That was the analytical method which epistemologists proceeded to
apply, vigorously and repeatedly.

Nevertheless, the history of post-1963 analytic epistemology has also
contained repeated expressions of frustration at the seemingly
insoluble difficulties that have accompanied the many attempts to
respond to Gettier's disarmingly simple paper. Precisely how should
the theory JTB be revised, in accord with the relevant data? Exactly
which data are relevant anyway? We have seen in the foregoing sections
that there is much room for dispute and uncertainty about all of this.
For example, we have found a persistent problem of vagueness
confronting various attempts to revise JTB. This might have us
wondering whether a complete analytical definition of knowledge that p
is even possible.

That is especially so, given that vagueness itself is a phenomenon,
the proper understanding of which is yet to be agreed upon by
philosophers. There is much contemporary discussion of what it even is
(see Keefe and Smith 1996). On one suggested interpretation, vagueness
is a matter of people in general not knowing where to draw a precise
and clearly accurate line between instances of X and instances of
non-X (for some supposedly vague phenomenon of being X, such as being
bald or being tall). On that interpretation of vagueness, such a
dividing line would exist; we would just be ignorant of its location.
To many philosophers, that idea sounds regrettably odd when the vague
phenomenon in question is baldness, say. ("You claim that there is an
exact dividing line, in terms of the number of hairs on a person's
head, between being bald and not being bald? I find that claim
extremely hard to believe.") But should philosophers react with such
incredulity when the phenomenon in question is that of knowing, and
when the possibility of vagueness is being prompted by discussions of
the Gettier problem? For most epistemologists remain convinced that
their standard reaction to Gettier cases reflects, in part, the
existence of a definite difference between knowing and not knowing.
But where, exactly, is that dividing line to be found? As we have
observed, the usual epistemological answers to this question seek to
locate and to understand the dividing line in terms of degrees and
kinds of justification or something similar. Accordingly, the threats
of vagueness we have noticed in some earlier sections of this article
might be a problem for many epistemologists. Possibly, those forms of
vagueness afflict epistemologists' knowing that a difference between
knowledge and non-knowledge is revealed by Gettier cases.
Epistemologists continue regarding the cases in that way. Are they
right to do so? Do they have that supposed knowledge of what Gettier
cases show about knowledge?

The Gettier challenge has therefore become a test case for
analytically inclined philosophers. The following questions have
become progressively more pressing with each failed attempt to
convince epistemologists as a group that, in a given article or talk
or book, the correct analysis of knowledge has finally been reached.
Will an adequate understanding of knowledge ever emerge from an
analytical balancing of various theories of knowledge against relevant
data such as intuitions? Must any theory of the nature of knowledge be
answerable to intuitions prompted by Gettier cases in particular? And
must epistemologists' intuitions about the cases be supplemented by
other people's intuitions, too? What kind of theory of knowledge is at
stake? What general form should the theory take? And what degree of
precision should it have? If we are seeking an understanding of
knowledge, must this be a logically or conceptually exhaustive
understanding? (The methodological model of
theory-being-tested-against-data suggests a scientific parallel. Yet
need scientific understanding always be logically or conceptually
exhaustive if it is to be real understanding?)

The issues involved are complex and subtle. No analysis has received
general assent from epistemologists, and the methodological questions
remain puzzling. Debate therefore continues. There is uncertainty as
to whether Gettier cases — and thereby knowledge — can ever be fully
understood. There is also uncertainty as to whether the Gettier
challenge can be dissolved. Have we fully understood the challenge
itself? What exactly is Gettier's legacy? As epistemologists continue
to ponder these questions, it is not wholly clear where their efforts
will lead us. Conceptual possibilities still abound.
15. References and Further Reading

Ayer, A. J. (1956). The Problem of Knowledge (London: Macmillan), ch.
1. Presents a well-regarded pre-Gettier JTB analysis of knowledge.

Chisholm, R. M. (1966/1977/1989). Theory of Knowledge (any of the
three editions). (Englewood Cliffs, NJ: Prentice Hall). Includes the
sheep-in-the-field Gettier case, along with attempts to repair JTB.

Descartes, R. (1911 [1641]). The Philosophical Works of Descartes,
Vol. I, (eds. and trans.) E. S. Haldane and G. R. T. Ross. (Cambridge:
Cambridge University Press). Contains the Meditations, which develops
and applies Descartes's conception of knowledge as needing to be
infallible.

Feldman, R. (1974). "An Alleged Defect in Gettier Counterexamples."
Australasian Journal of Philosophy 52: 68-9. Reprinted in Moser
(1986). Presents a Gettier case in which, it is claimed, no false
evidence is used by the believer.

Gettier, E. L. (1963). "Is Justified True Belief Knowledge?" Analysis
23: 121-3. Reprinted in Roth and Galis (1970) and Moser (1986).

Goldman, A. I. (1967). "A Causal Theory of Knowing." Journal of
Philosophy 64: 357-72. Reprinted, with revisions, in Roth and Galis
(1970). The initial presentation of a No Inappropriate Causality
Proposal.

Goldman, A. I.. (1976). "Discrimination and Perceptual Knowledge."
Journal of Philosophy 73: 771-91. Reprinted in Pappas and Swain
(1978). Includes the fake-barns Gettier case.

Hetherington, S. (1996). Knowledge Puzzles: An Introduction to
Epistemology (Boulder, Colo.: Westview Press). Includes an
introduction to the justified-true-belief analysis of knowledge, and
to several responses to Gettier's challenge.

Hetherington, S. (1998). "Actually Knowing." Philosophical Quarterly
48: 453-69. Includes a version of the Knowing Luckily Proposal.

Hetherington, S. (2001). Good Knowledge, Bad Knowledge: On Two Dogmas
of Epistemology (Oxford: Oxford University Press). Extends the Knowing
Luckily Proposal, by explaining the idea of having qualitatively
better or worse knowledge that p.

Jackson, F. (1998). From Metaphysics to Ethics: A Defence of
Conceptual Analysis (Oxford: Oxford University Press). Includes
discussion of Gettier cases and the role of intuitions and conceptual
analysis.

Kaplan, M. (1985). "It's Not What You Know That Counts." Journal of
Philosophy 82: 350-63. Argues that, given Gettier cases, knowledge is
not what inquirers should seek.

Keefe, R. and Smith, P. (eds.) (1996). Vagueness: A Reader (Cambridge,
Mass.: The MIT Press). Contains both historical and contemporary
analyses of the nature and significance of vagueness in general.

Kirkham, R. L. (1984). "Does the Gettier Problem Rest on a Mistake?"
Mind 93: 501-13. Argues that the usual interpretation of Gettier cases
depends upon applying an extremely demanding conception of knowledge
to the described situations, a conception with skeptical implications.

Lehrer, K. (1965). "Knowledge, Truth and Evidence." Analysis 25:
168-75. Reprinted in Roth and Galis (1970). Presents a No Core False
Evidence Proposal.

Lehrer, K. (1971). "Why Not Scepticism?" The Philosophical Forum 2:
283-98. Reprinted in Pappas and Swain (1978). Outlines a skepticism
based on an Infallibility Proposal about knowledge.

Lehrer, K., and Paxson, T. D. (1969). "Knowledge: Undefeated Justified
True Belief." Journal of Philosophy 66: 225-37. Reprinted in Pappas
and Swain (1978). Presents a No Defeat Proposal.

Lewis, D. (1996). "Elusive Knowledge." Australasian Journal of
Philosophy 74: 549-67. Includes a much-discussed response to Gettier
cases which pays attention to nuances in how people discuss knowledge.

Lycan, W. G. (1977). "Evidence One Does not Possess." Australasian
Journal of Philosophy 55: 114-26. Discusses potential complications in
a No Defeat Proposal.

Lycan, W. G. (2006). "On the Gettier Problem Problem." In Epistemology
Futures, (ed.) S. Hetherington. (Oxford: Oxford University Press). A
recent overview of the history of attempted solutions to the Gettier
problem.

Moser, P. K. (ed.) (1986). Empirical Knowledge: Readings in
Contemporary Epistemology (Totowa, NJ: Rowman & Littlefield). Contains
some influential papers on Gettier cases.

Pappas, G. S., and Swain, M. (eds.) (1978). Essays on Knowledge and
Justification (Ithaca, NY: Cornell University Press). A key anthology,
mainly on the Gettier problem.

Plato. Meno 97a-98b. For what epistemologists generally regard as
being an early version of JTB.

Plato. Theatetus 200d-210c. For seminal philosophical discussion of
some possible instances of JTB.

Roth, M. D., and Galis, L. (eds.) (1970). Knowing: Essays in the
Analysis of Knowledge (New York: Random House). Includes some
noteworthy papers on Gettier's challenge.

Shope, R. K. (1983). The Analysis of Knowing: A Decade of Research
(Princeton: Princeton University Press). Presents many Gettier cases;
discusses several proposed analyses of them.

Skyrms, B. (1967). "The Explication of 'X Knows that p'." Journal of
Philosophy 64: 373-89. Reprinted in Roth and Galis (1970). Includes
the pyromaniac Gettier case.

Unger, P. (1968). "An Analysis of Factual Knowledge." Journal of
Philosophy 65: 157-70. Reprinted in Roth and Galis (1970). Presents an
Eliminate Luck Proposal.

Unger, P. (1971). "A Defense of Skepticism." The Philosophical Review
30: 198-218. Reprinted in Pappas and Swain (1978). Defends and applies
an Infallibility Proposal about knowledge.

Weinberg, J., Nichols, S., and Stich, S. (2001). "Normativity and
Epistemic Intuitions." Philosophical Topics 29: 429-60. Includes
empirical data on competing ('intuitive') reactions to Gettier cases.

Williamson, T. (2000). Knowledge and Its Limits (Oxford: Oxford
University Press), Intro., ch. 1. Includes arguments against
responding to Gettier cases with an analysis of knowledge.

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