Examples 6.1

# Examples 6.1 - Notes 6.1 So we should have gotten the point...

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Notes 6.1 So we should have gotten the point now that the validity of a deductive argument depends entirely on the form of an argument. But language, of course, can obscure the form of argument—and this is why we’ve been analyzing more normal language stuff into logically useful statements (like categorical propositions). Now, we’re moving on to look at symbolic logic, where, you guessed it, we’re only dealing with symbols and operators (connectives) , instead of just using terms as the focal point of analysis. So, here’s a look at some simple statements: Fast foods tend to be unhealthy James Joyce wrote Ulysses . Parakeets are colorful birds. The monk seal is threatened with extinction. Any upper-case letter you like (typically, you’d pick a letter which will help remind you what proposition you’re symbolizing) will represent these whole propositions. Like, say, F for the first, J for the second, P for the third, and M for the fourth. Now, you can also have compound statements with at least one simple statement as a component. Here are some: It is not the case that Al-Qaeda is a humanitarian organization. Dianne Reeves sings jazz, and Christina Aguilera sings pop. Either people get serious about conservation or energy prices will skyrocket. If the world’s nations spurn international law, then future wars are guaranteed. The Broncos will win if and only if they run the ball. Let’s bring in some letters to symbolize the content of these propositions: It is not the case that A. D and C. Either P or E. If W then F. B if and only if R. Here, then, comes the idea of the operator (or connective) . When you say ‘ it is not the case that ’ or ‘ and ’, or ‘ or ’, or ‘ if . . . then . . .’, or ‘ if and only if ’, we can introduce these operators to symbolize these relations. Operator Name Logical Function Used to translate ~ tilde negation not, it is not the case that · dot conjunction and, also, moreover, but v wedge disjunction or, unless horseshoe implication if . . . then . . .; only if triple bar equivalence if and only if

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So, let’s further symbolize the above propositions: It is not the case that A ~A D and C. D · C Either P or E P v E If W then F. W F B if and only if R. B ≡ R The statement ~A is called a negation. The second statement D · C is called a conjunctive statement (or just a conjunction ). The third statement P v E is called a disjunctive statement (or just a disjunction ). Also, in conjunctive statements the
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Examples 6.1 - Notes 6.1 So we should have gotten the point...

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