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Homework assignment 8.docx

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Department
Philosophy
Course Code
PHL246H1
Professor
Franz Huber

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Homework assignment 8: Suppose your background assumptions B are such that your degree of belief that an arbitrary object a is not white is lower than your degree of belief that a is a swan – say, because there are more things that are not white than there are swans: Pr(a is not white|B) < Pr(a is a swan|B). Suppose further that, given your background assumptions B, your degree of belief that all swans are white is independent of a not being white as well as of a being a swan: Pr(a is not white|all swans are white, and B) = Pr(a is not white|B) Pr(a is swan|all swans are white, and B) = Pr(a is a swan white|B) Show that these three assumptions imply that conditioning on the information that a is a white swan increases your degree of belief in the swan-hypothesis. That is, show that the following holds: Pr(all swans are white|a is a white swan, and B) > Pr(all swans are white|B) (2 points) We toss a coin twice. There are four possible outcomes: HH, HT, TH, and TT. You consider two hypotheses. Hypothesis fair says that the coin is fair, i.e. that the chance of heads equals the chance of tails and that the two coin tosses are “independent and identically distributed.” Hypothesis 2:1bias says that the coin is biased and that heads is twice as probable as tails and that the two coin tosses are “independent and identically distributed.” You obey the Principal Principle and
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