Exam 3

Exam 3 - Deductive Arguments Intended to guarantee the truth of the conclusion Ex(1 All Decembers are cold(2 its December(C its cold Inductive

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Deductive Arguments Intended to guarantee the truth of the conclusion Ex. (1) All Decembers are cold (2) it’s December (C) it’s cold Inductive Arguments Intended to show that the conclusion is probable given the premises Can insert ‘probably’ in the conclusion (do not regard it as part of the conclusion) It is not deductively valid Ex. (1) Most Decembers are cold (2) It’s December. (C) (Probably) it’s cold. Supply the Implicit Generalization (1) Karen went out into the cold without a sweater (C) Karen will get sick (2) Everyone who goes out in the cold without a sweater gets sick – will give a valid argument (2) Most people who go out in the cold without a sweater get sick – will give an inductively forceful argument Probability Express probability on a numerical scale between 0 and 1, expressed either as a decimal or as a fraction Proportions o Indicated by quantifiers o Ex. ‘most’ and ‘7/8 of’ Frequencies o How often something has occurred Degree of Rational Expectation o How much one is entitled to believe given the evidence Conditional Probability The conditional probability of q given p is how probable q is assuming that p is true Ex. The conditional probability that it’s sunny given that it’s June is how probable it is that it’s sunny assuming that it actually is June Inductive Forcefulness (first pass) An inductively forceful argument is one where the conclusion is probable given the premises An inductively forceful argument is one that is (1) not deductively valid but (2) where the conditional probability of the conclusion given the premises is greater than .5 but less than 1
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Example (1) Most bears are dangerous (2) Smokey is a bear (C) Probably, Smokey is dangerous Points about Probability Conditional probability is often stated implicitly ( we do not always express probabilities as conditional probabilities ) Probably comes in degrees ( different propositions may have various degrees of probability ) o Inductive forcefulness comes in degrees Propositions are still either true or false o Arguments are still either valid or invalid “Probably” carries a conversational implicature of “very likely” – it is also somewhat vague Degree of rational expectation is distinct from degree of actual expectation Inductive forcefulness depends on the structure of the arguments The degree of inductive force of an argument is independent of the truth-values of the premises Generalizations again “Some” is compatible with “all” for the purposes of this class o ‘Some’, whereby ‘some A are B’ does not rule out that all A are B o ‘Some A are B’ means ‘Some, perhaps all, A are B’ When using ‘some’ in our argument-reconstructions, we will take it to mean ‘at least one’ o If only one A is B, then it will be true that some A are B When supplying missing generalization, it is often more charitable to supply soft
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This note was uploaded on 04/05/2012 for the course PHI 2100 taught by Professor Mikepatterson during the Spring '12 term at FSU.

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Exam 3 - Deductive Arguments Intended to guarantee the truth of the conclusion Ex(1 All Decembers are cold(2 its December(C its cold Inductive

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