contain all that is worth knowing. The propounder of the
dilemma covertly assumes this. It is in the facility that it affords
for what is technically known as _Petitio Principii_ that the Dilemma
is a useful instrument for the Sophist. We shall illustrate it further
under that head.

What is known as the _Destructive_ Dilemma is of a somewhat different
form. It proceeds upon the denial of the Consequent as involving the
denial of the Antecedent. In the Major you obtain the admission that
if a certain thing holds, it must be followed by one or other of
two consequences. You then prove by way of Minor that neither of the
alternatives is true. The conclusion is that the antecedent is false.

We had an example of this in discussing whether the inference in the
Hypothetical Syllogism is Immediate. Our argument was in this form:--

If the inference is immediate, it must be drawn either from
the Major alone or from the Minor alone. But it cannot be
drawn from the Major alone, neither can it be drawn from the
Minor alone. Therefore, it is not immediate.

In this form of Dilemma, which is often serviceable for clearness
of exposition, we must as in the other make sure of the truth of the
Major: we must take care that the alternatives are really the only two
open. Otherwise the imposing form of the argument is a convenient mask
for sophistry. Zeno's famous dilemma, directed to prove that motion is
impossible, covers a _petitio principii_.

If a body moves, it must move either where it is or where it
is not. But a body cannot move where it is: neither can it
move where it is not. Conclusion, it cannot move at all,
_i.e._, Motion is impossible.

The conclusion is irresistible if we admit the Major, because the
Major covertly assumes the point to be proved. In truth, _if_ a body
moves, it moves neither where it is nor where it is not, but from
where it is to where it is not. Motion consists in change of place:
the Major assumes that the place is unchanged, that is, that there is
no motion.

[Footnote 1: For the history of Hypothetical Syllogism see
Mansel's _Aldrich_, Appendix I.]

[Footnote 2: It may be argued that the change is not merely
grammatical, and that the implication of a general proposition
in a hypothetical and _vice versa_ is a strictly logical
concern. At any rate such an implication exists, whether it is
the function of the Grammarian or the Logic