lecture_26_2x2

lecture_26_2x2 - Announcements and Such One Song - Pink...

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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 : In-class Review Session (Vanessa) Consider the following self-referential 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 ( self-evidently )! Skepticism IV The Paradox of the Knower I Here’s another plausible principle: (*) If you can prove p ( self-evidently ), 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 and K ( 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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lecture_26_2x2 - Announcements and Such One Song - Pink...

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