# Syllogism challenge

Some time ago on this blog, I challenged my readers to translate this syllogism from Quintilian into standard categorical form, and to determine its validity:

“Virtue is the only thing that is good, for that alone is good which no one can put to a bad use: but no one can make a bad use of virtue.”

Let’s see what we can do. The word “for” is a premise indicator, so the conclusion is the first statement. Re-arranging into standard order, we get:

That alone is good which no one can put to a bad use.
No one can make a bad use of virtue.
∴ Virtue is the only thing that is good.

The first statement means, “Only things which no one can put to a bad use are good.” Recalling that Only S is P means All P is S (e.g. Only women are mothers means All mothers are women), this statement becomes “All good things are things which no one can put to bad use.”

The second statement is properly translated “All virtue is a thing which no one can out to bad use.” The conclusion means “Only virtue is a good thing” which is properly translated “All good things are virtue.”

The complete, categorical-form syllogism is thus:

All virtue is a thing which no one can out to bad use.
All good things are things which no one can put to bad use.
∴ All good things are virtue.

Interestingly, this AAA-2 is invalid, with an undistributed middle term. That means we should be able to write a counterexample to the original argument to display its invalidity. Here is one possible counterexample:

All rocks are things which no one can kill.
All immortal beings are things which no one can kill.
∴ All immortal beings are rocks.

Put into the form of the original, we get this counterexample, showing the invalidity of the original argument:

“Rocks are the only things that are immortal, for that alone is immortal which no one can kill: but no one can kill a rock.”