Reduction and Elimination in Philosophy and the Sciences

that I am sure that it is true that Stone came to the
university tonight because of E1: “I saw him parking
outside”, and/or because of E2: “he called me on phone,
saying that he was coming here”. Since I take these
evidences as true, and I see each of them as sufficient to
make me accept the truth of the proposition p, I can say
that E1 ~> p, that E2 ~> p, and that E* = {E1, E2}. An
important characteristic of E* is that, under the assumption
that we are rational evaluators, either all its members are
sufficient to make p true or they are all sufficient to make p
false, otherwise they would cancel one another 8 . With
these concepts we can redefine the condition of truth by
making explicit the role of the evidential truth-conditions to
our acceptance of p as true. Here is the formulation for the
condition of truth:
(i’) (E* & (E* ~> p))
This is the same as saying that p is true, since given
our acceptance of E* as true (that is, the truth of at least
one evidence E such that E ~> p), our acceptance of the
truth of p follows (by modus ponens or inductively). The
difference is that now the satisfied evidential truthconditions
can be made explicit as the members of the set
E*. I claim that this is what we, fallible truth-searchers,
ultimately mean with the condition (i).
The second improvemente concerns the
reformulation of the condition of justification in the
definition of knowledge, linking this justification with the set
of evidences that make the proposition p true. What we
need to do is only to require, additionally, that the
evidential justification E given by a might be seen by us as
belonging to our accepted *E, namely, to the set of
evidences that we (as the evaluators of knowledge-claims)
are prepared to accept as the satisfied truth-conditions
which are individually sufficient to make p true (cases in
which E* ~> p). Here is our reformulation of the third
condition:
(iii’) aEBp & (E ∈ E*)
The condition (iii’) says that, additionally to the condition
that a has a reasonable evidence justifying the truth of p, it
is required that this evidence, for being sound, must be
able to be accepted by us as belonging to the set of evidences
that we are prepared to accept as individually making
p true.
8 For example: evidences for the roundness of the earth are E1 (photos from
the all) and E2 (the circumnavigation of the globe). Each one is a member of
E*, sufficient for the truth the proposition p saying that the earth is round. But if
~E2 were an element of E*, E1 would loose its force and would not be a
sufficient condition, do not belonging to E* anymore.
Exorcizing Gettier — Claudio F. Costa
With this in mind we are prepared to reformulate the
tripartite definition of knowledge in a way that makes
explicit the internal relation between the condition of
justification (iii) and the condition of truth (i). Here it goes:
(i’) (ii) (iii’)
(Df.2) aKp = (E* & (E* ~> p)) & aBp & (aEBp &(E ∈ E*))
Dropping the condition (ii) as redundant, since it is repeated
in the first conjunct of (iii), we get the following
version:
(i’) (iii’)
(Df.3) aKp = (E* & (E* ~> p)) & (aEBp &(E ∈ E*))
What these definitions tells us is that the justifying evidence
E given by a must belong to the set of evidences (of
fulfilled truth-conditions) that might be hold by us (the
knowledge-evaluators) as individually sufficient to make p
true. If the evidence E given by a belongs to E*, and E* is
so that its individual members lead to the necessary or at
least highly probable truth of the proposition p, so that E*
~> p, than E is epistemically sound, for it assures us the
truth of p either as necessary or as practically certain.
Now, consider again our gettierian counterexample.
Mary’s evidence E (“Stone said to me he would give a
lecture today”) would not be accepted by us (since we are
better informed, and also know about the accident with his
son etc.) as belonging to our E*, even if we know that
Stone was (by different reasons) at the university this
night. So we conclude that, according with our definition of
knowledge, she really does not know. And this result can
be generalized in order to exorcize any conceivable
gettierian counterexample. Since in no counterexample of
Gettier kind the justifying evidence E belongs to the set E*,
none of these counterexamples satisfies the proposed
reformulation of the tripartite definition of knowledge.
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