**Various attempts
have been made in recent years to state necessary and sufficient
conditions for someone's knowing a given proposition. The attempts have
often been such that they can be stated in a form similar to the
following:**^{1}

**a. S knows that P
IFF [if and only if] P is true, S believes that P, and S is justified in
believing that P. **

**For example,
Chisholm has held that the following gives the necessary and sufficient
conditions for knowledge:**^{2}

**b. S knows that P
IFF S accepts P, S has adequate evidence for P, and P is true. **

**Ayer has stated
the necessary and sufficient conditions for knowledge as follows:**^{3}

**c. S knows that P
IFF P is true, S is sure that P is true, and S has the right to be sure
that P is true.**

** I shall argue
that (a) is false in that the conditions stated therein do not
constitute a sufficient condition for the truth of the proposition that
S knows that P. The same argument will show that (b) and (c) fail if
'has adequate evidence for' or 'has the right to be sure that' is
substituted for 'is justified in believing that' throughout. **

**
I shall begin by
noting two points. First, in that sense of 'justified' in which S's
being justified in believing P is a necessary condition of S's knowing
that P, it is possible for a person to be justified in believing a
proposition that is in fact false Secondly, for any proposition P, 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. Keeping these two points in mind, I shall now present two
cases in which the conditions stated in (a) are true for some
proposition, though it is at the same time false that the person in
question knows that proposition. **

# Case I

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

**d. 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: **

**e. 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.

# Case II** **

**
Let us suppose that
Smith has strong evidence for the following proposition: **

**f. Jones owns a
Ford. **

**
Smith's evidence might be that Jones has at all times in the past within
Smith's memory owned a car, and always a Ford, and that Jones has just
offered Smith a ride while driving a Ford. Let us imagine, now, that
Smith has another friend, Brown, of whose whereabouts he is totally
ignorant. Smith selects three place names quite at random and constructs
the following three propositions: **

**g. Either Jones
owns a Ford, or Brown 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. **

**
Each of these propositions is entailed by (f). Imagine that Smith
realizes the entailment of each of these propositions he has constructed
by (f), and proceeds to accept (g), (h), and (i) on the basis of (f).
Smith has correctly inferred (g), (h), and (i) from a proposition for
which be has strong evidence. Smith is therefore completely justified in
believing each of these three propositions, Smith, of course, has no
idea where Brown is. **

**But imagine now
that two further conditions hold. First Jones does ***not* own a
Ford, but is at present driving a rented car. And secondly, by the
sheerest coincidence, and entirely unknown to Smith, the place mentioned
in proposition (h) happens really to be the place where Brown is. If
these two conditions hold, then Smith does *not* know that (h) is
true, even though (*i*) (h) is true, (*ii*) Smith does believe
that (h) is true, and (*iii*) Smith is justified in believing that
(h) is true.

**These two
examples show that definition (a) does not state a ***sufficient*
condition for someone's knowing a given proposition. The same cases,
with appropriate changes, will suffice to show that neither definition
(b) nor definition (c) do *[sic] *so either.

**
Notes**

**
1. Plato seems to be
considering some such definition at ***Theaetetus* 201, and perhaps
accepting one at *Meno* 98.

**
2.
Roderick M. Chisholm, ***Perceiving: A Philosophical Study*
(Ithaca, New York: Cornell University Press, 1957), p. 16.

**
3. A. J. Ayer, ***The
Problem of Knowledge* (London: Macmillan, 1956), p. 34.

**
Posted December 6, 2005**