Mr. Nance,

Regarding question no. 10 on page 252: What is the reason for its invalidity? Does the pure hypothetical syllogism also use the five rules of validity? The argument is:

If he is the Antichrist, then he opposes God’s people.
If he is the Beast, then he opposes Gods people.
Therefore, if he is the Antichrist, then he is the Beast.

Is the Beast major term? And is the Antichrist the minor term? How do we make it into valid categorical syllogism?

Hypothetical syllogisms can be studied and understood apart from categorical syllogisms. We do not need to translate them into categorical syllogisms in order to determine their validity.

Keep in mind that validity is a function of form of the argument, not the truth of the premises or conclusion. The form of the hypothetical syllogism for #10 on page 252 is:

If p then q
If r then q
∴ If p then r

This is an invalid form, which can be shown by this counterexample:

If a creature is a dog then it has four legs.
If a creature is a cat then it has four legs.
Therefore, if a creature is a dog then it is a cat.

The form of the argument is clearly invalid.

If you want to, you could translate the argument in question into this categorical form syllogism:

All the Beast is an opposer of God’s people.
All the Antichrist is an opposer of God’s people.
∴ All the Antichrist is the Beast.

This is invalid, being an Undistributed Middle. There is no necessary overlap between the two classes of opposers.

Blessings!