Lec 5 Skepticism and Deductive Closure

# Lec 5 Skepticism and Deductive Closure - Lec#5 Skepticism...

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Knowledge Closure •Closure of Knowledge under Entailment: If S knows that p, and if p entails q, then S knows that q. •Closure of Knowledge under Known Entailment (C1): If I know one proposition, and I know that this proposition entails a second proposition, then I know the second proposition as well. Or •If S knows that p, and if S knows that p entails q, then S knows that q. Or •(1) S knows that p •(2) S knows that p entails q •(3) Therefore, S knows that q Entailment •One statement entails another when the second is a logically necessary consequence of the first, as Alvin lives in Los Angeles entails Alvin lives in California. •Note that the relationship of entailment, unlike that of paraphrase, is one-way: it is not the case that Alvin lives in California entails Alvin lives in Los Angeles. •To say that one or more statements entail some conclusion is equivalent to saying that the conclusion follows validly from those statements. •More precisely, „P entails Q‟ is equal by definition to „Q is validly deducible from P‟. Examples of Knowledge Closure 1)I know that the animal is a zebra. 2)I know that the animal is a zebra entails the animal is not a cleverly disguised mule 3)Therefore, I know that the animal is not a cleverly disguised mule. 1)I know that my car is now parked in Lot 7. 2)I know that my car is parked in Lot 7 entails my car hasn’t been stolen and driven away from where it was parked 3)Therefore, I know that my car has not been stolen and driven away from where it was parked. 1)I know that I won‟t have enough money to go on a safari this year. 2)If I know that I won‟t have enough money to go on a safari this year, then I know that I will not win a major prize in a lottery this year. 3)Therefore, I know that I will not win a major prize in a lottery this year. 1)I know that I will be living in Vienna for part of this winter. 2)I don‟t know that I will not suffer a fatal heart attack in the next week. 3)I don‟t know that I will be living in Vienna for part of this winter 1)I know that Obama is now the US President. 2)I don‟t know that Obama hasn‟t been assassinated in the last few minutes.

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## This note was uploaded on 04/05/2012 for the course ECON 25 taught by Professor Shirey during the Spring '11 term at UC Irvine.

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Lec 5 Skepticism and Deductive Closure - Lec#5 Skepticism...

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