lecture_24_2x2 - Announcements and Such Three Songs(by...

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Announcements and Such Three Songs (by request) — Ratatat [ Classics ] “Loud Pipes” “Nostrand” “Spanish Armada” Final Exam will be: Wednesday, May 16, 5–8pm @ 141 MCCONE Possible Questions to be posted on May 1 Today: Skepticism II Finishing-up inductive skepticism from last time Paradoxes of confirmation (inductive support) Fallibility and general skepticism Nelson Goodman posed a “new riddle of induction”, which aims to show that there can be no purely formal conception of inductive support It is sometimes claimed that the premise of the following argument inductively supports its conclusion — and in a purely formal sense: All observed A ’s have been B ’s. Therefore, the next A observed will be B . Example: All observed emeralds have been green. Therefore, the next emerald observed will be green. Goodman purports to show that, whatever support the premise of such an argument might provide for its conclusion, it cannot be purely formal . Skepticism I Skepticism About Induction VII Goodman defines a predicate “Grue” as follows: x is Grue = x is green iff x has been observed Now, consider the following argument: All observed emeralds have been Grue. Therefore, the next emerald observed will be Grue. Since this argument is of the “good form”, its premise inductively supports its conclusion. But, this seems odd. Assuming that emeralds don’t change color over time, and that there are some unobserved emeralds, this is equivalent to: All observed emeralds have been green. Therefore, the next emerald observed won’t be green. This seems to show that IL is not purely formal . Skepticism I Skepticism About Induction VIII In other words, the assumption that there is a purely formal notion of inductive support seems to have led (the details are subtle) to a case in which: E inductively supports p, and E inductively supports ~ p Where, E and p are defined using “Grue”, as above. Goodman concludes ( via reductio ad absurdum ”) that there is no purely formal notion of inductive support. This is better than Popper’s argument. But, this also conflates (to some extent) logic and epistemology . Even if it turned out that this was a situation in which formal inductive support relations were “absurd”, what would that show? Analogy: if B is logically inconsistent , then B deductively supports p and ~ p ! So what ? Skepticism I Skepticism About Induction IX
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I think there are better arguments against “purely formal” explications of inductive support. Carnap proposed a purely formal analogical inference principle to the effect that: The more properties two objects share, the more probable it is that they share a novel property.
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