Logic12 - Introduction to Logic Lecture 12 Brian...

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Unformatted text preview: Introduction to Logic Lecture 12 Brian Weatherson, Department of Philosophy October 12, 2009 Logic 201 (Section 5) Lecture 12 1 / 23 Conditionals Logic 201 (Section 5) Lecture 12 2 / 23 Conditionals The second last connective we are going to introduce in part 1 is . Whenever A is a sentence, and B is a sentence, then A B is a sentence. There are a number of ways we can read A B : If A , then B . B if A . Provided A , B . Logic 201 (Section 5) Lecture 12 3 / 23 Conditionals It is important to distinguish A B and B A . The first says that A suffices for the truth of B . The second says that B suffices for the truth of A . These can come apart. Logic 201 (Section 5) Lecture 12 4 / 23 Direction of Conditionals Imagine that to get a particular job, you need three things: 1 Good grades; 2 A good application; and 3 A good interview Then this is true: If you get the job, then youll have good grades. But this might be false, since you might have a lousy interview: If you have good grades, then youll get the job. Logic 201 (Section 5) Lecture 12 5 / 23 Direction of Conditionals Or consider a different case. Failing Freddie has failed every test and assignment in his class all semester. In fact, hes got a 0 on everything hes done, which wasnt much. There is just one test to go, and it only counts for 10% of the course grade. Freddie goes to his instructor and asks, Yes or No: If I fail the test, will I fail the course? The instructor should say Yes, since if Freddie fails the test, he will fail the course. This isnt to say that Freddie will pass the course if he passes the test, in fact hell fail no matter what. Nor is it to say that if Freddie fails the course, hell have failed the test. This is a case where A B is true although B A is false. Logic 201 (Section 5) Lecture 12 6 / 23 Parts of Conditionals In a conditional sentence A B , we have names for the two parts. A is called the antecedent of the conditional. B is called the consequent of the conditional. In English, the antecedent need not always come first. Some sentences are of the form B if A . The antecedent in that case is the clause that starts with if . Logic 201 (Section 5) Lecture 12 7 / 23 Only If We interpret a sentence of the form A only if B as: A B We can see this if we look at the job example again. This sentence is true: Youll get the job only if you have good grades. Since thats true, it should be equivalent to the true conditional 1, not the false conditional 2. 1 If you get the job, youll have good grades. 2 If you have good grades, youll get the job. Logic 201 (Section 5) Lecture 12 8 / 23 Unless We interpret a sentence of the form Unless A , B as: A B ....
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Logic12 - Introduction to Logic Lecture 12 Brian...

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