[lit-ideas] Re: Gettieriana
- From: Omar Kusturica <omarkusto@xxxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Fri, 13 Mar 2015 18:25:34 +0100
Perhaps we can try something like this:
"First we take a vague or ambiguous statement. Then we imagine a context in
which it is believed to be true but it comes out false in the sense in
which it was ostensibly intended in that imaginary context. Next, we
imagine another context which has nothing whatsoever to do with what was
ostensibly intended but in which the same statement can be read as true.
For effect, we add one or two improbable turns to the story."
I think that would be the general recipee for producing examples of
"justified true belief that is not knowledge," although variations can be
tried.
O.K.
On Fri, Mar 13, 2015 at 5:10 PM, Redacted sender Jlsperanza@xxxxxxx for
DMARC <dmarc-noreply@xxxxxxxxxxxxx> wrote:
> 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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