Reduction and Elimination in Philosophy and the Sciences
Reduction and Elimination in Philosophy and the Sciences
Reduction and Elimination in Philosophy and the Sciences
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that I am sure that it is true that Stone came to <strong>the</strong><br />
university tonight because of E1: “I saw him park<strong>in</strong>g<br />
outside”, <strong>and</strong>/or because of E2: “he called me on phone,<br />
say<strong>in</strong>g that he was com<strong>in</strong>g here”. S<strong>in</strong>ce I take <strong>the</strong>se<br />
evidences as true, <strong>and</strong> I see each of <strong>the</strong>m as sufficient to<br />
make me accept <strong>the</strong> truth of <strong>the</strong> proposition p, I can say<br />
that E1 ~> p, that E2 ~> p, <strong>and</strong> that E* = {E1, E2}. An<br />
important characteristic of E* is that, under <strong>the</strong> assumption<br />
that we are rational evaluators, ei<strong>the</strong>r all its members are<br />
sufficient to make p true or <strong>the</strong>y are all sufficient to make p<br />
false, o<strong>the</strong>rwise <strong>the</strong>y would cancel one ano<strong>the</strong>r 8 . With<br />
<strong>the</strong>se concepts we can redef<strong>in</strong>e <strong>the</strong> condition of truth by<br />
mak<strong>in</strong>g explicit <strong>the</strong> role of <strong>the</strong> evidential truth-conditions to<br />
our acceptance of p as true. Here is <strong>the</strong> formulation for <strong>the</strong><br />
condition of truth:<br />
(i’) (E* & (E* ~> p))<br />
This is <strong>the</strong> same as say<strong>in</strong>g that p is true, s<strong>in</strong>ce given<br />
our acceptance of E* as true (that is, <strong>the</strong> truth of at least<br />
one evidence E such that E ~> p), our acceptance of <strong>the</strong><br />
truth of p follows (by modus ponens or <strong>in</strong>ductively). The<br />
difference is that now <strong>the</strong> satisfied evidential truthconditions<br />
can be made explicit as <strong>the</strong> members of <strong>the</strong> set<br />
E*. I claim that this is what we, fallible truth-searchers,<br />
ultimately mean with <strong>the</strong> condition (i).<br />
The second improvemente concerns <strong>the</strong><br />
reformulation of <strong>the</strong> condition of justification <strong>in</strong> <strong>the</strong><br />
def<strong>in</strong>ition of knowledge, l<strong>in</strong>k<strong>in</strong>g this justification with <strong>the</strong> set<br />
of evidences that make <strong>the</strong> proposition p true. What we<br />
need to do is only to require, additionally, that <strong>the</strong><br />
evidential justification E given by a might be seen by us as<br />
belong<strong>in</strong>g to our accepted *E, namely, to <strong>the</strong> set of<br />
evidences that we (as <strong>the</strong> evaluators of knowledge-claims)<br />
are prepared to accept as <strong>the</strong> satisfied truth-conditions<br />
which are <strong>in</strong>dividually sufficient to make p true (cases <strong>in</strong><br />
which E* ~> p). Here is our reformulation of <strong>the</strong> third<br />
condition:<br />
(iii’) aEBp & (E ∈ E*)<br />
The condition (iii’) says that, additionally to <strong>the</strong> condition<br />
that a has a reasonable evidence justify<strong>in</strong>g <strong>the</strong> truth of p, it<br />
is required that this evidence, for be<strong>in</strong>g sound, must be<br />
able to be accepted by us as belong<strong>in</strong>g to <strong>the</strong> set of evidences<br />
that we are prepared to accept as <strong>in</strong>dividually mak<strong>in</strong>g<br />
p true.<br />
8 For example: evidences for <strong>the</strong> roundness of <strong>the</strong> earth are E1 (photos from<br />
<strong>the</strong> all) <strong>and</strong> E2 (<strong>the</strong> circumnavigation of <strong>the</strong> globe). Each one is a member of<br />
E*, sufficient for <strong>the</strong> truth <strong>the</strong> proposition p say<strong>in</strong>g that <strong>the</strong> earth is round. But if<br />
~E2 were an element of E*, E1 would loose its force <strong>and</strong> would not be a<br />
sufficient condition, do not belong<strong>in</strong>g to E* anymore.<br />
Exorciz<strong>in</strong>g Gettier — Claudio F. Costa<br />
With this <strong>in</strong> m<strong>in</strong>d we are prepared to reformulate <strong>the</strong><br />
tripartite def<strong>in</strong>ition of knowledge <strong>in</strong> a way that makes<br />
explicit <strong>the</strong> <strong>in</strong>ternal relation between <strong>the</strong> condition of<br />
justification (iii) <strong>and</strong> <strong>the</strong> condition of truth (i). Here it goes:<br />
(i’) (ii) (iii’)<br />
(Df.2) aKp = (E* & (E* ~> p)) & aBp & (aEBp &(E ∈ E*))<br />
Dropp<strong>in</strong>g <strong>the</strong> condition (ii) as redundant, s<strong>in</strong>ce it is repeated<br />
<strong>in</strong> <strong>the</strong> first conjunct of (iii), we get <strong>the</strong> follow<strong>in</strong>g<br />
version:<br />
(i’) (iii’)<br />
(Df.3) aKp = (E* & (E* ~> p)) & (aEBp &(E ∈ E*))<br />
What <strong>the</strong>se def<strong>in</strong>itions tells us is that <strong>the</strong> justify<strong>in</strong>g evidence<br />
E given by a must belong to <strong>the</strong> set of evidences (of<br />
fulfilled truth-conditions) that might be hold by us (<strong>the</strong><br />
knowledge-evaluators) as <strong>in</strong>dividually sufficient to make p<br />
true. If <strong>the</strong> evidence E given by a belongs to E*, <strong>and</strong> E* is<br />
so that its <strong>in</strong>dividual members lead to <strong>the</strong> necessary or at<br />
least highly probable truth of <strong>the</strong> proposition p, so that E*<br />
~> p, than E is epistemically sound, for it assures us <strong>the</strong><br />
truth of p ei<strong>the</strong>r as necessary or as practically certa<strong>in</strong>.<br />
Now, consider aga<strong>in</strong> our gettierian counterexample.<br />
Mary’s evidence E (“Stone said to me he would give a<br />
lecture today”) would not be accepted by us (s<strong>in</strong>ce we are<br />
better <strong>in</strong>formed, <strong>and</strong> also know about <strong>the</strong> accident with his<br />
son etc.) as belong<strong>in</strong>g to our E*, even if we know that<br />
Stone was (by different reasons) at <strong>the</strong> university this<br />
night. So we conclude that, accord<strong>in</strong>g with our def<strong>in</strong>ition of<br />
knowledge, she really does not know. And this result can<br />
be generalized <strong>in</strong> order to exorcize any conceivable<br />
gettierian counterexample. S<strong>in</strong>ce <strong>in</strong> no counterexample of<br />
Gettier k<strong>in</strong>d <strong>the</strong> justify<strong>in</strong>g evidence E belongs to <strong>the</strong> set E*,<br />
none of <strong>the</strong>se counterexamples satisfies <strong>the</strong> proposed<br />
reformulation of <strong>the</strong> tripartite def<strong>in</strong>ition of knowledge.<br />
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