Logic: Syllogism

Question

A bat is an instrument in baseball;

Some bats are cave dwellers;

So, all cave dwellers are instruments in baseball.

A. valid

B. illicit major term

C. illicit minor term

D. fallacy of four terms

E. misplaced middle term

F. undistributed middle term

Answer 1

Ha! This is a great example of a train wreck argument (and one not unlike many in the culture today).

First, we see that the term "bat" is being used with two meanings. It is, effectively, two terms rather than one. You can probably see that this means that we have four terms, instead of the three required for simple categorical arguments.

The second problem we have is that there is a particular premise, but a universal conclusion. One of the basic rules of categorical validation is that, if we have a particular premise, the conclusion must also be particular. That specific error isn't mentioned in the options, but that is the other serious problem (even if the issue with the bat-term got resolved).

Distribution: The general rules are (1) any term distributed in the conclusion must be distributed in the premises, and (2) the middle term (bat) must be distributed at least once. Bat is distributed in the first premise. Cave dwellers is distributed in the conclusion, but not in the premise. Cave dwellers is the minor term (it comes from the minor premise--the one providing the subject to the conclusion), so this is an illicit minor term.

In any event, there are about 29 different things wrong with this argument. Those are a few. :)