Lesson_Six_and_Test - LESSON 6 Truth-functional Logic, Part...

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Section 11: Arguments with Compound Sentences, Barker, pp. 64-71. ***Read the section, then the following additional comments. Don’t forget everything you learned in the last section; we will come back to many of those insights. But right now you need to make a pretty serious about-face into a totally different direction: truth-functional logic. The big point of difference is this: Letters stand for complete sentences. Whereas in categorical logic a sentence such as All dogs wag their tails becomes our familiar combination of two terms, All D are W, under this regimen we want to translate it with a single letter, e.g. W Thus, to repeat, in this section letters stand for sentences. This form of logic is called “truth- functional” logic. Of particular focus is whether sentences (or “propositions”) are true or false, depending on their occurrence in an argument. Remember: A sound argument has true premises and valid logic and its conclusion must be true. Thus the goal of this form of logic is to find ways of testing the truth of conclusions by way of testing the validity of arguments. More on that as we move along. We will look at statements such as, John has a ball. Jane has a bat. But nobody I know past the age of three talks only in such simple sentences. We combine sentences, join thoughts, oppose thoughts, express conditions for a thought to be true or not true, and frequently negate thoughts. Thus, for our logic to be any good we need to be able to bring simple sentences together in such a way as to represent the various combinations. John does not have a ball. Either John has a ball, or Jane has a bat. John has a ball, and Jane has a bat. If John has a ball, then Jane has a bat. 1 LESSON 6 Truth-functional Logic, Part 1
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John has a ball if and only if Jane has a bat. These five sentences represent the five basic logical combinations of truth-functional logic. 1. The first one is negation . Following Barker’s simplified symbolism, we shall indicate a negation with a negative sign, “-.” (In other books, you will see it as a squiggle, “ ” .) -O John does not have a ball. Please keep in mind that this is not a “minus” sign in the mathematical sense. You are not subtracting anything. It is a shorthand way of saying “not.” The meaning of the negation is that everything directly following it is denied—the “opposite” is true. If it precedes a simple proposition (single letter), then that sentence as a whole is negated. If it comes before a combination of letters in parentheses, then the entire parenthetical statement is denied. 2. The second combination is a disjunction , represented by a “v.” O v A Either John has a ball, or Jane has a bat. The meaning of a disjunction is that one of the two statements must be true.
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Lesson_Six_and_Test - LESSON 6 Truth-functional Logic, Part...

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