orical Form?_

To oppose Hypothetical Syllogisms to Categorical is misleading, unless
we take note of the precise difference between them. It is only in
the form of the Major Premiss that they differ: Minor Premiss and
Conclusion are categorical in both. And the meaning of a Hypothetical
Major Premiss (unless it is a mere arbitrary convention between two
disputants, to the effect that the Consequent will be admitted if the
Antecedent is proved, or that the Antecedent will be relinquished
if the Consequent is disproved), can always be put in the form of a
general proposition, from which, with the Minor Premiss as applying
proposition, a conclusion identical with the original can be drawn in
regular Categorical form.

Thus:--

If the harbour is frozen, the ships cannot come in.
The harbour is frozen.
[.'.] The ships cannot come in.

This is a Hypothetical Syllogism, _Modus Ponens_. Express the
Hypothetical Major in the form of the general proposition which it
implies, and you reach a conclusion (in _Barbara_) which is only
grammatically different from the original.

All frozen harbours exclude ships.
The harbour is frozen.
[.'.] It excludes ships.

Again, take an example of the _Modus Tollens_--

If rain has fallen, the streets are wet.
The streets are not wet.
[.'.] Rain has not fallen.

This is reducible, by formulating the underlying proposition, to
_Camestres_ or _Baroko_ of the Second Figure.

All streets rained upon are wet.
The streets are not wet.
[.'.] They are not streets rained upon.

Hypothetical Syllogisms are thus reducible, by merely grammatical
change[2], or by the statement of self-evident implications, to the
Categorical form. And, similarly, any Categorical Syllogism may be
reduced to the Hypothetical form. Thus:--

All men are mortal.
Socrates is a man.
[.'.] Socrates is mortal.

This argument is not different, except in the expression of the Major
and the Conclusion, from the following:--

If Socrates is a man, death will overtake him.
Socrates is a man.
[.'.] Death will overtake him.

The advantage of the Hypothetical form in argument is that it is
simpler. It was much used in Mediaeval Disputation, and is still more
popular than the Categorical Syllogism. Perhaps the prominence
given to Hypothetical Syllogisms as syllogisms in Post-Renaissance
text-books is due to the