### TL;DR
**What is knowledge?**
The question of "what consti...
Edmund L. Gettier III was an American philosopher and Professor Eme...
Here is one kind of example:
> "Imagine that we are seeking wate...
Another example of a Gettier Problem:
Pluto was a planet
For ...
Here is a brief video explanation of Gettier's first counter exampl...
ANALYSIS
23.6
JUNE
1963
IS
JUSTIFIED TRUE BELIEF KNOWLEDGE?
v
ARIOUS 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
fo1lowing:l
(a) S knows that
P
IFF
(i)
P
is true,
(ii)
S
believes that
l',
and
(iii)
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
(i)
S
accepts P,
(ii) S has adequate evidence for P,
and
(iii)
P
is true.
Ayer has stated the necessary and sufficient conditions for knowledge as
follows
:3
(c)
S
knows that
P
IFF
(i) P is true,
(ii) S is sure that
P
is true, and
(iii) 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
sttficietzt
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 sub-
stituted 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
Plato seems to be considering some such definition at
Th~aefetz~.
201, and perhaps
accepting one at
Meno
98.
2
Roderick
M.
Chisholm,
P?rceivin,o:
a
l'hilosop~~ical
Sfdy,
Cornell University Press (Ithaca,
New
York,
1957),
p. 16.
A.
J.
Ayer,
The Pr~blem of Knowledge,
Macmillan (London, 1956),
p.
34.
121
ANALYSIS
23.6
JUNE
1963
IS JUSTIFIED
TRUE
BELIEF
KNOWLEDGE?
By
EDMUND
L.
GETTIER
V
ARIOUS 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
(i)
P
is
true,
(ii) S believes that P, and
(iii) 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
(i)
S accepts P,
(ii) S has adequate evidence for P,
and
(iii) P
is
true.
Ayer has stated the necessary and sufficient conditions for knowledge
as
follows:
3
(c)
S knows that P
iFF
(i)
P
is
true,
(ii) S
is
sure that P
is
true, and
(iii) 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
stlfficient
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
sub-
stituted
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
1 Plato seems to be considering some such definition at
Tbeaetetus
201,
and perhaps
accepting one at
Meno 98.
2 Roderick M. Chi5holm,
PBrceiving:
a
Philosopbical
Study, Cornell University Press (Ithaca,
New
York, 1957), p. 16.
3 A.
J.
Ayer,
Tbo
Prob/em
of
Knowledge,
Macmillan (London, 1956), p. 34.
121
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
11:
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;
122
ANALYSIS
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;
123
CIRCULARITY
AND
INDUCTION
(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 he 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 szflcient
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 so either.
Wqne State Universit_r
CIRCULARITY AND INDUCTION
ECENTLY1
I
suggested why an argument proposed by Max
'.
R
Black, which attempts to support an inductive rule by citing
its past success, suffers from circularity. The inductive rule under
discussion is this
:
R
:
To argue from Most instances
of
As examined z/n&r a wide variety
of
conditions have been
B
to (probably) The next
A
to be encoznteredwi/I
be
B.
The argument in favour of the rule is as follows:
(a)
:
In most instances of the use of R in arguments with true prernisses
examined in a wide variety of conditions, R has been successful.
Hence (probabb)
:
In the next instance to be encountered of use of
R
in an argument
with a true premiss,
R
will be successful.
"
The
Circularity
of
a
Self-Suppotting Inductive
Argument
",
ANALYSIS,
22.6(June
1%2).
CIRCULARITY
AND
INDUCTION
123
(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
correcdy inferred (g), (h), and
(i) from a proposition for which he 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 so either.
wayne
State
University
CIRCULARITY AND INDUCTION
By
PETER
ACHINSTEIN
1.
DECENTL
yl
I suggested why an argument proposed by
Max
.n. Black, which attempts
to
support an inductive rule by citing
its past success,
suffers
from circularity. The inductive rule under
discussion
is
this:
R:
To
argue from
Most
instances
of
As
examined
under
a
11Iide
variety
of
conditions
have
been
B
to
(probably)
The
next A
to
be
encountered
11Iil/
be
B.
The argument in favour
of
the rule
is
as
follows:
(a):
In most instances
of
the use
ofR
in arguments with true premisses
examined in a wide variety
of
conditions, R has been successful.
Hence
(probablY):
In the next instance to be encountered
of
use
of
R in an argument
with a true premiss, R will be successful.
1 "
The
Circularity
of
II
Self-Supporting Inductive Argument
"0
ANALYSIS, 22.6 (June 1962).
Edmund L. Gettier III was an American philosopher and Professor Emeritus at the University of Massachusetts Amherst. Gettier obtained his B.A. from Johns Hopkins University in 1949 and earned his PhD in philosophy from Cornell University in 1961 with a dissertation on “Bertrand Russell’s Theories of Belief”.
He is best known for this paper, which remains one of the most famous in recent philosophical history.
Learn more here: [Edmund Gettier](https://en.wikipedia.org/wiki/Edmund_Gettier)
Here is a brief video explanation of Gettier's first counter example:
[](https://youtu.be/5wCVhhzmSlU?t=160)
Another example of a Gettier Problem:
Pluto was a planet
For years we believed that there were 9 planets in the solar system and that Pluto was the 9th planet. Nowadays we no longer consider Pluto a planet but we know of the Planet Nine - hypothetical planet in the outer region of the Solar System.
Using the JTB framework we have that:
- We believed that there were 9 planets
- It was true
- We were justified in believing it because of observations
We were in a sense wrong because we believed that Pluto was planet number 9 and it turns out it wasn't.
Here is one kind of example:
> "Imagine that we are seeking water on a hot day. We suddenly see water, or so we think. In fact, we are not seeing water but a mirage, but when we reach the spot, we are lucky and find water right there under a rock. Can we say that we had genuine knowledge of water? The answer seems to be negative, for we were just lucky. (quoted from Dreyfus 1997: 292)"
Source: [The Analysis of Knowledge - 3. The Gettier Problem](https://plato.stanford.edu/entries/knowledge-analysis/#GettProb)
### TL;DR
**What is knowledge?**
The question of "what constitutes knowledge?" is as old as philosophy itself. Since Plato the universally accepted theory was that justified, true belief is necessary and sufficient for knowledge - **Justified True Belief (JTB).** The JTB framework for knowledge can be described as follows:
A subject S knows that a proposition P is true if and only if:
- P is true, and
- S believes that P is true, and
- S is justified in believing that P is true
In this short and insightful paper E. Gettier sets out to challenge the dominant theory of knowledge by providing 2 simple cases famously known as the "Gettier Problems".
Gettier problems are possible situations in which someone has a belief that is both true and well supported by evidence, yet fails to be knowledge.
This paper had a dramatic impact, as epistemologists began questioning what knowledge is, with almost all agreeing that Gettier had refuted the traditional definition of knowledge.
Further reading:
- [The Analysis of Knowledge](https://plato.stanford.edu/entries/knowledge-analysis/#KnowJustTrueBeli)
- [Gettier Problems](https://iep.utm.edu/gettier/)