Mr. Nance,

I have a question about enthymemes. When the conclusion is assumed, how do we know which is the major premise and which is the minor premise? I fear there is a simple explanation that I may have missed but when I compare your example in Introductory Logic on page 221 with Exercise 31 #5, I can’t correlate how you knew which was the major premise and which was the minor premise, and therefore, how to write the assumed conclusion in proper form.

In each case in the textbook in which the enthymeme left the conclusion assumed, the premises were both A statements, with the middle term as the subject of one and the predicate of the other. This sets itself up for an AAA-1, which gives the universal (and thus the strongest) valid conclusion. This form would establish which premises was major and which was minor.

If the premises were other types of statements, the analysis would be more difficult. For example, let’s analyze this enthymeme from P.J. O’Rourke:

“Everybody wants to save the world but nobody wants to help mom with the dishes.”

I cannot tell at first which term is major and which is minor, so let’s start by putting the premises into categorical form:

All people are people who want to save the world.
No people are people who want to help with the dishes.

The conclusion must be negative, since there is a negative premise, and it must use the terms that appear only once. If it were an E statement, it would be “No people who want to help Mom with the dishes are people who want to save the world” (or its converse). In this form, the syllogism would be an illicit major. Consequently, the conclusion must be an O statement, with the undistributed term being the term undistributed in the premise. This makes the conclusion “Some people who want to save the world are not people who want to help with the dishes,” giving this complete syllogism (note that this forces us to change the order):

No people are people who want to help with the dishes.
All people are people who want to save the world.
Therefore, some people who want to save the world are not people who want to help with the dishes.

We see that the rules of formal logic led us to this very reasonable conclusion, a conclusion that P. J. O’Rourke intended but was leaving assumed.

So when faced with an enthymeme with the conclusion left assumed, chose a conclusion that is a conclusion of a valid syllogism, and that makes sense in the context of the argument. This will help you determine which premise is major and which minor.

Blessings!