Announcements and Such
•
One Song —
Pink Floyd
•
“Pigs (Three Different Ones)” from
Animals
•
Final Exam will be:
Wednesday, May 16, 5–8pm @ 141 MCCONE
•
Possible Questions to be posted tomorrow
•
•
I will not have OH’s Thursday
or
next week, but
I’ll be on email.
And, I’ll have OH May 14, 1–5pm
•
James will have a Review Session on Monday, May
14th at 4pm in 220 Wheeler
•
Today:
•
Next Time:
Skepticism V (Contextualism)
•
Tuesday
: Inclass Review Session (Vanessa)
•
Consider the following selfreferential statement:
•
(
p
) Sentence
p
is not known to be true.
•
Oddly, we can
prove
that
p
is true, as follows:
•
(1) If
p
is false, then
p
is true.
•
(2) If (1), then
p
is true.
•
Therefore, (3)
p
is true.
•
To see (1), reason as follows.
Assume
p
is false.
Nothing false can be known to be true.
Therefore,
p
is not known to be true. Hence,
p
.
•
(2) is a theorem of logic.
Basically, (2) is
equivalent to: either
p
is true or
p
is true.
•
(3) follows from (1) and (2) by
modus
ponens
.
•
So, we’ve just
proven
p
(
selfevidently
)!
Skepticism IV
The Paradox of the Knower I
•
Here’s another plausible principle:
•
(*) If you can
prove
p
(
selfevidently
), then you
know
that
p
is true (
a priori
).
•
Therefore, by (*), we
know
that
p is true
(
a priori
).
•
Hence,
p
is
known to be true.
•
But,
p
says of itself that it is
not
known to be
true!
This is
The Paradox of the Knower
.
•
NOTE: (*)
is a subtle instance of closure
:
If
K
ℷ
and
K
(
ℷ
⇒
p
), then
Kp
.
•
Here’s a related paradox:
•
(G) God does not know that G is true.
•
We
can
prove
(unparadoxically!) that God does
not know that G is true!
But,
He
can’t
!
Skepticism IV
The Paradox of the Knower II
•
When I say things like the following (and I do):
•
Goldbach’s conjecture
might
be true.
•
I do
not
mean to imply that Goldbach’s
conjecture is
metaphysically
possible.
•
After all, I know that mathematical conjectures
are
non

contingent
.
So, if I were to assert
that
, I
might as well say the following instead:
•
Goldbach’s conjecture
must
be true.
•
But, I do
not
want to assert
that
, since it is a long
standing open question in mathematics.
•
Thus, the kind of possibility involved in the first
claim is
not
metaphysical
possibility.
•
Then, what is it?
It’s
epistemic
possibility.
Skepticism IV
Epistemic
vs
Metaphysical Possibility I
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Roughly,
epistemic
possibility is something like:
•
p
is epistemically possible for
S
if
p
is
consistent with everything
S
knows.
•
Slogan: “For all
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 Spring '07
 FITELSON
 Epistemology, Closure, Closure Revisited II

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