LPL 2.5 lecture

# LPL 2.5 lecture - Consider the following invalid argument...

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Nonconsequence Not only can we prove that an argument is valid (that is that its conclusion is a logical consequence of its premises), but we can also prove that an argument is invalid (that its conclusion is not a logical consequence of its premises). Demonstrating logical consequence requires that we give either an informal proof on paper or a formal proof in Fitch showing that from a given set of premises we can derive the desired conclusion. Demonstrating logical nonconsequence requires that we give a counterexample to the given argument. This can be done either informally or formally. The informal method for demonstrating nonconsequence is to describe in English a situation in which all the premises of an argument are true while the conclusion remains false. These sorts of proofs will mirror our informal proofs of logical consequence.
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Unformatted text preview: Consider the following invalid argument: All actors who win academy awards are famous. Harrison Ford has never won an academy award. Harrison Ford is not famous How might we demonstrate informally that the conclusion of this argument is not a consequence of the given premises? The formal method for demonstrating logical nonconsequence is to build a counterexample world, using Tarski’s World, in which the premises of the argument are true while the conclusion is false. Consider this invalid argument expressed in the block’s language of Tarski’s World. How might we build a formal counterexample? Adjoins(a, b) SameCol(b, c) FrontOf(c, b) FrontOf(c, a) Another demonstration of nonconsequence: Exercise 2.21...
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