Logic03

# Logic03 - Introduction to Logic Lecture 3 Brian Weatherson...

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Introduction to Logic Lecture 3 Brian Weatherson, Department of Philosophy September 9, 2009 Logic 201 (Section 5) Lecture 3 1 / 56

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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 3 2 / 56
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 3 3 / 56

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Names Names always pick out individuals. Names are lower case. Usually they will be a single letter, like ‘ a ’, but sometimes they will be longer, like ‘ obama ’. Not all objects have names. Some objects have more than one name. Every name is used just once. Every name picks out something or other. Logic 201 (Section 5) Lecture 3 4 / 56
Predicates and Atomic Sentences Names are used to pick out individuals. Predicates are used to say something about them. We’ll write predicates as full words, with Capital Letters. An atomic sentence in FOL consists of a predicate followed by as many names as the predicate demands. So a full sentence might look like Smokes ( barack ) . Logic 201 (Section 5) Lecture 3 5 / 56

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Predicates and Individuals Each predicate requires a certain number of individuals to make a sentence. We can put no more, and no less, than this number. The number changes for diﬀerent predicates. Smokes and Happy require 1 individual. Taller and Married require 2 individuals. Between requires 3 individuals. The number of individuals that the predicate requires is called the arity of the predicate. Logic 201 (Section 5) Lecture 3 6 / 56
Blocks Language and Tarski’s World Logic 201 (Section 5) Lecture 3 7 / 56

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Tarski’s World The ﬁrst piece of software we’ll be using is called Tarski’s World . It has two components. A ‘world’ - the chessboard like picture at the top Some sentences which are to be evaluated in that world Logic 201 (Section 5) Lecture 3 8 / 56
Tarski’s World The language we’ll use in this program has a restricted range of names and predicates. The names are just the lower case letters,

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Logic03 - Introduction to Logic Lecture 3 Brian Weatherson...

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