Combining Texts

All the ideas for 'Necessary Existents', '11: Book of Kings 1' and 'Bayesianism'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / n. Pi
He made a molten sea, which was ten cubits across, and thirty cubits round the edge [Anon (Kings)]
     Full Idea: And he made a molten sea, ten cubits from the one brim to the other; it was round all about, and his height was five cubits: and a line of cubits did compass it round about.
     From: Anon (Kings) (11: Book of Kings 1 [c.550 BCE], 7:23)
     A reaction: In the sixth century BCE, this appears to give 3 as the value of Pi, though perhaps it shouldn't be taken too literally!
14. Science / C. Induction / 6. Bayes's Theorem
Probability of H, given evidence E, is prob(H) x prob(E given H) / prob(E) [Horwich]
     Full Idea: Bayesianism says ideally rational people should have degrees of belief (not all-or-nothing beliefs), corresponding with probability theory. Probability of H, given evidence E, is prob(H) X prob(E given H) / prob(E).
     From: Paul Horwich (Bayesianism [1992], p.41)
Bayes' theorem explains why very surprising predictions have a higher value as evidence [Horwich]
     Full Idea: Bayesianism can explain the fact that in science surprising predictions have greater evidential value, as the equation produces a higher degree of confirmation.
     From: Paul Horwich (Bayesianism [1992], p.42)
19. Language / D. Propositions / 3. Concrete Propositions
Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]
     Full Idea: A proposition about an item exists only if that item exists... how could something be the proposition that that dog is barking in circumstances in which that dog does not exist?
     From: Timothy Williamson (Necessary Existents [2002], p.240), quoted by Trenton Merricks - Propositions
     A reaction: This is a view of propositions I can't make sense of. If I'm under an illusion that there is a dog barking nearby, when there isn't one, can I not say 'that dog is barking'? If I haven't expressed a proposition, what have I done?