[lit-ideas] Re: Gettieriana
- From: "" <dmarc-noreply@xxxxxxxxxxxxx> (Redacted sender "Jlsperanza@xxxxxxx" for DMARC)
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Fri, 13 Mar 2015 12:10:04 -0400
In a message dated 3/13/2015 6:21:20 A.M. Eastern Daylight Time,
donalmcevoyuk@xxxxxxxxxxx writes in "Re: Some Gettier examples":
Donal
Logician to the stars
The implication (or implicature) of 'to the stars' seems to be that McEvoy
suggests that a formalisation of the Gettier alleged counterexamples is
the way to go.
Here is its natural formalization:
"Smith is justified in believing that p"
can be formalized as
“for some t, t:P”
"Smith deduces Q from P"
can be rephrased as:
“there is a deduction of P !Q (available to Smith)”;
"Smith is justified in believing Q" — “t:Q for some t.”
Such a rule holds for the so-called Logic of Proofs, as well as for all
other Justification Logic systems.
After all, epistemic logic is a branch of modal logic, and it is
interesting that if Gettier never published on this, he taught on this -- a
simplified semantics for modal logic. Hintikka speaks of two modalities
relevant
here: epistemic modality, and doxastic modality -- there are others.
The rule above is a combination of
The Internalization Rule:
if ` F, ` s:F for some s
and
The Application Axiom:
s:(P !Q)!(t:P !(s·t):Q).
Indeed, suppose t:P and there is a deduction of P !Q. By the
Internalization Rule, s:(P !Q) for
some s.
From the Application Axiom, by Modus Ponens twice, we get (s·t):Q.
But Gettier already KNEW that?
-- and I'm hoping he even supplied a more simplified version for it!
Cheers,
Speranza
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