Reduction and Elimination in Philosophy and the Sciences

Exorcizing Gettier
Claudio F. Costa, Natal, Brazil
50
Knowledge is not simply justified true belief,
but it is justified true belief, justifiably arrived at.
Robert J. Fogelin
Gettier’s problem 1 seems to be a daunting treat to our
belief in the rationality of the human knowledge. In what
follows I intend to show with some formal precision the
natural way out of the trap.
Using the symbol a to a person, K to knowledge, B
to the belief, E to a reasonable justifying evidence (justification),
and p to the proposition, we might symbolize the
tripartite definition of knowledge as follows:
(i) (ii) (iii)
(Df.1) aKp = p & aBp & aEBp
According to this definition, a knows that p (aKp) means
the same as the conjunction of these three conditions,
namely (i) that p is true, (ii) that a believes that p is true,
and (iii) that a has a reasonable justification for her belief
in the truth of p. As it is well-known, Gettier’s problem
arises from the discovery of counterexamples to this definition,
namely, from cases where the person a fails to attain
knowledge though satisfying these three conditions.
To remember Gettier’s counterexamples, consider
the following 2 . Suppose that professor Stone said to Mary
yesterday that he would come to the university this night to
give a lecture. Since Mary knows that Stone is a highly
responsible person, she can claim that she knows that he
came to the university this night. However, unknown to
her, one of Stone’s sons suffered an accident and he
needed to drop the lecture. However, it is true that he
came to the university, since he was momentarily in his
room to take some documents. Mary’s claim to know that
Stone came to the University this night seems to satisfy
the conditions to the traditional definition: it is a true belief
and the justification presented by her is reasonable
enough. Nevertheless, its truth is only accidentally
achieved and nobody would say that Mary really knows
that Stone was at the university tonight.
As it was sometimes noted, there is a
straightforward and effective way to answer the problem,
which seems to be nearly buried under the considerable
amount of alternative answers explored in the literature 3 . It
consists simply in the request that a sound epistemic
justification must belong to what we are able to accept as
making the proposition p true 4 . So, Mary’s justification for
1 E. L. Gettier: “Is Justified Belief Knowledge?” Analysis 23, 6, 1963, 121-23.
2 I take this example (with slight changes) from D. J. O’Connor and Brian Carr,
Introduction to the Theory of Knowledge (The Harverster Press: Brighton
1982).
3 Similar considerations can be found in D. J. O’Connor and B. Carr, Introduction
to the Theory of Knowledge, p. 82. The origin of this view seems to be due
to Robert F. Almeder, particularly in the paper “Truth and Evidence”, The
Philosophical Quarterly 24, 1974, 365-68. The most original and compelling
defense of a similar view can be found in Robert Fogelin’s book, Pyrrhonian
Reflections on Knowledge and Justification (Oxford University Press: Oxford
1994), chapter 1.
4 This requirement was stated by D. J. O’Connor and by Brian Carr, who also
say that “the reason why the proposition is true must not be independent on
the facts asserted in the proposition constituting the grounds for the belief”,
claiming for elaboration (Introduction to the Theory of Knowledge, p. 81).
Robert Fogelin stated the same point more concisely his definition of knowledge:
“S knows that P iff S justifiably came to believe that P on grounds that
establish the truth of P” (Pyrrhonian Reflections on Knowledge and Justification,
p. 28)
her belief that professor Stone came to the University this
night, based on the evidence given by his statement that
he would give a lecture, might be reasonable, but is
epistemically unsound, since this information is no part of
what we – as the epistemic evaluators of Mary’s
knowledge claim – are prepared to accept as making true
the belief that Stone came to the university this night.
Reasonability is not enough. A justification must also be
epistemically sound, by making itself acceptable to the
epistemic evaluators of a knowledge claimer a as making a
proposition p true 5 . In the case of the gettierian
counterexamples, these epistemic evaluators have always
some information that overrides the epistemic soundness
of the reasonable justification given by the knowledge
claimer. 6
My aim here is to improve the tripartite definition of
knowledge by stating more formaly this intuitive solution.
This can be done by making explicit the internal link
between the condition of justification and the condition of
truth. In order to do it, we shall review the formulation of
the conditions (i) and (iii) of (Df.1).
We begin with the condition of truth. As it appears in
the traditional definition, it is surely a simplification. For it
seems like the truth-value of the proposition when it is
contemplated by God. Since God doesn’t need to verify
anything in order to know the truth, he does not need to
consider whether any truth-condition is satisfied. So, for
him “p” or “p is true” is enough. However, if we intend to
make justice to the condition of the truth of p as it is known
by us (that is, by the knowledge-evaluators of knowledgeclaimers),
we need to consider whether the truthconditions
were satisfied. Now, how to do it? We need first
to see that, when an evidence E for the ascent of p is
found, it must be seen by us as sufficient to make the
proposition p true. The meaning of ‘sufficient’ here can be
made precise as follows:
An evidence E is sufficient for the assent of p as
true iff E makes p either (i) necessarily true (when p
is a non-empirical, deductively grounded truth) or (ii)
probable in a very high level (for the cases of empirical,
inductively grounded truths) 7 .
We can introduce the symbol ‘~>’ (to be read as “is sufficient
to”) in order to express this conditional. Thus, given
the evidence E for the ascent of p, this means that E ~> p,
in other words, that for us either E makes p necessarily
true or very probably true.
With this in mind we can introduce the symbol E* to
designate the set of all justifying evidences that we
consider individually sufficient for the truth or falsity of p in
the already specified sense. To give an example: suppose
5 My distinction between a reasonable justification and an epistemically sound
justification is equivalent to the distinction between a personal justification
(epistemically responsible) and a justification given on the basis of adequate
grounds. See Michael Williams, Problems of Knowledge: a Critical Introduction
to Philosophy (Oxford University Press: Oxford 2001) pp. 22-23.
6 The words ‘we’ and ‘us’ point usually to the knowledge-evaluators, with their
usually wider informational set. However, this does not precludes the possibility
that the knowledge-evaluator is the knowledge-claimer herself, by making a
self-evaluation of her own past knowledge claims.
7 I am not considering Kripkian cases like that of necessary a posteriori beliefs
derived from E (they are also controversial).