# Exam Question – Logic

June 13, 2007 pm30 11:05 pm

I asked the following on my final exam. I like this question quite a bit:

Convert each statement into a standard form categorical proposition. Identify the conclusion. Identify the major and minor premise. Move the statements, if necessary, to form a standard form categorical syllogism. Identify the mood and the figure. Is this catgorical syllogism valid? If not, explain what rule is being violated.

The Bushs aren’t Democrats, so the Bushs aren’t big spenders since big spenders are Democrats.

What do you think?

2 Comments
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Good question! I haven’t studied logic, other than what I pick up playing recreational puzzles and a bit of geometry, so I don’t know what several of those words mean (mood? figure? huh?). But the statement is an interesting challenge to unravel, because one has to use the contrapositive form of one part to make a syllogism. And it also has a nice contrast between “valid” and “true” to trip up an unwary student.

I did it like this:

(1) “The Bushs aren’t Democrats…” = “If a person is a member of the Bush family, then he (or she) is not a Democrat.”

Equivalent statement (contrapositive): “If a person is a Democrat, then he is not a member of the Bush family.”

(2) “…so the Bushs aren’t big spenders…” = “If a person is a member of the Bush family, then he is not a big spender.”

Contrapositive: “If a person is a big spender, then he is not a member of the Bush family.”

The “so” is the same as “therefore” and marks this as the conclusion of the syllogism.

(3) “…since big spenders are Democrats.” = “If a person is a big spender, then he is a Democrat.”

Contrapositive: “If a person is not a Democrat, then he is not a big spender.”

Finished syllogism:

If a person is a member of the Bush family, then he (or she) is not a Democrat.

If a person is not a Democrat, then he is not a big spender.

Therefore, if a person is a member of the Bush family, then he is not a big spender.

Valid, but not true.

Bravo. We use some other tools to analyze these. I guess the biggest difference is that we quantify each statement:

No Bushes are Democrats

All big Spenders are Democrats

No Bushes are big Spenders

The mood is No/All/No (we abbreviate EAE)

The figure describes where the “Democrats” are (in the predicate of both premises, we call that Figure 2. There are 4 possible)

And then the students refer to a quality called “distribution.”

“No” distributes both subject and predicate (gives us definite information about both). “All” distributes only the subject (All men are beasts tells us about men, not about beasts).

Finally, the kids check a few rules. 2 negative premises are illegal. A neg conclusion demands a negative premise, and vv. The term that does not appear in the conclusion must be “distributed” at least once. And if a term is distributed in the conclusion, it must be distributed in the proper premise as well.

Since the given syllogism violates none of these rules, it is valid. Though as you point out, the conclusion is false. (and since the syllogism is valid, a false conclusion implies at least one false premise).

Little changes could change the result. If the end said “since Democrats are big Spenders” then it would not be valid.