LESSON #18

Reducing the Number of Terms

Reading assignment: 5.4 (pp. 282-284)

Click here to skip the following discussion and go straight to the assignments.

In this lesson you will be working with obversion, conversion and contraposition. You might want to review section 4.4 (pp. 215-222) and lesson #13.

The point of the exercise is to eliminate term compliments in propositions that are part of a would-be standard form categorical syllogism until you have exactly three terms, each used twice.

Do the problems as Hurley instructs in the text, with one minor difference--draw an arrow between the "before" argument and the "after" (reduced) argument for each line you have changed, and above the arrow write the operation you have performed. If you need to perform more than one operation on the same line, either write both operations above the same line (but don't get confused) or else write out an intermediate step.

Different people will do these different ways. You may end up with non-S where someone else chose to aim for S. That's OK, as long as both instances of each term are the same (both simple or both negated)

These problems take creativity and practice. As you do them you will get used to the different things you can do with your different operations. But I'll try to offer some hints:

First, look carefully at your "before" syllogism, and decide what needs to be done to it. It should have letters standing for terms. I'm assuming it at least has the conclusion listed last. the order of the premises doesn't matter, for now.

Then, get out your "tools":

· contraposition gives term compliments to both terms. Use this when you want both S and P terms in a proposition changed. (But only on A or O statements, of course)

· Conversion plus obversion, when done in that order, give the term compliment to the original S term. (allowed if you start with an E or I statement)

· Obversion gives you the term compliment of the P term only, if that's what you want.

· Obversion plus Contraposition in that order, changes the S term of the original proposition, if you start with an A or O.

Once you have finished your operations, and have three identical terms, each used twice, Check to make sure that the major and minor premises are still in the correct order. If you performed conversion or obversion on the conclusion, you might have to switch their order as a final step to put the syllogism into standard form, even if they were in the correct order to begin with.

REMEMBER:

The Major premise is the premise which contains the predicate term from the conclusion.

The Minor premise contains the subject term from the conclusion.

Logic Coach Assignment: 5.4 1-7

Assignment:

Rewrite the following arguments using the letters you're given to represent the terms, (put the conclusion last, and keep in mind you will have term compliments) and use obversion, conversion and contraposition to put them into standard form. Then use one of the three methods for checking validity that you have learned in this chapter to determine whether they are valid or invalid. (50 points each)

1. No women without brains are mathematicians, so some sensitive people are not women with brains, since some people who are not mathematicians are not insensitive people. (W, M, S)

2. All illiterate people are unsuccessful people, so some literate people are not highschool dropouts, since some highschool graduates are successful people.

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