Logic04

# Logic04 - Introduction to Logic Lecture 4 Brian Weatherson,...

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Introduction to Logic Lecture 4 Brian Weatherson, Department of Philosophy September 14, 2009 Logic 201 (Section 5) Lecture 4 1

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Representing Arguments We’ll write arguments in the following format, with premises above a horizontal line, and the conclusion below the line. Anyone who wins an academy award is famous Meryl Streep won an academy award Meryl Streep is famous Logic 201 (Section 5) Lecture 4 2
Two Deﬁnitions of Validity 1 An argument is valid if it’s true that: if the premises are true, the conclusion must be true. 2 An argument is valid if it is impossible for the premises to be true and the conclusion false. These deﬁnitions are equivalent, so you can use either depending on which is more convenient. We’ll say that a valid argument with true premises is sound . An argument that is either invalid, or has false premises, is unsound . Logic 201 (Section 5) Lecture 4 3

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Evaluating Arguments with Tarski’s World Logic 201 (Section 5) Lecture 4 4
Validity An argument is valid if, when the premises are true, the conclusion must be true. That is, there is no world where the premises are true and the conclusion false. If we can build a world where the premises are true and the conclusion false, then we have shown the argument is invalid. The next slide shows a demonstration in Tarski’s World that this argument is invalid. Cube ( a ) Larger ( a , b ) Cube ( b ) Logic 201 (Section 5) Lecture 4 5

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Invalidity Because there is a world where the premises are true and the conclusion false, the argument is invalid . Logic 201 (Section 5) Lecture 4 6
Proofs Logic 201 (Section 5) Lecture 4 7

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What are Proofs A proof that an argument is valid is: 1 A sequence of statements; 2 The ﬁrst statements are the premises of the argument; 3 The last statement is the conclusion of the argument; 4 Each statement follows directly from earlier statements; 5 And we say exactly how each statement follows from earlier statements. We’ll qualify point 4 a little later in the course, but for now that’s the idea. Logic 201 (Section 5) Lecture 4 8
What are Proofs Some proofs are written in English, and some in FOL, and some in other languages. Some proofs are written in paragraphs, and some are written in a version of the way we have been setting out arguments. The next two slides have two versions, both in English, of proofs of the validity of the following argument. Socrates is a man All men are mortal No mortal lives forever Everyone who will eventually die sometimes worries about it Socrates sometimes worries about dying Logic 201 (Section 5) Lecture 4 9

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What are Proofs Here is the proof they give in the textbook of that argument. Suppose we want to show that Socrates sometimes worries about
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## This note was uploaded on 02/01/2012 for the course 730 201 taught by Professor Jonwinterbottom during the Fall '11 term at Rutgers.

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Logic04 - Introduction to Logic Lecture 4 Brian Weatherson,...

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