conditional). Similarly, we might write: _Proof of Joe Smith's not being
a prophet is a proof of his being an impostor_.

This turning of Conditionals into Categoricals is called a Change of
Relation; and the process may be reversed: _All the wise are virtuous_
may be written, _If any man is wise he is virtuous_; or, again, _Either
a man is not-wise or he is virtuous_. But the categorical form is
usually the simplest.

If, then, as substitutes for the corresponding conditionals,
categoricals are formally adequate, though sometimes inelegant, it may
be urged that Logic has nothing to do with elegance; or that, at any
rate, the chief elegance of science is economy, and that therefore, for
scientific purposes, whatever we may write further about conditionals
must be an ugly excrescence. The scientific purpose of Logic is to
assign the conditions of proof. Can we, then, in the conditional form
prove anything that cannot be proved in the categorical? Or does a
conditional require to be itself proved by any method not applicable to
the Categorical? If not, why go on with the discussion of Conditionals?
For all laws of Nature, however stated, are essentially categorical. 'If
a straight line falls on another straight line, the adjacent angles are
together equal to two right angles'; 'If a body is unsupported, it
falls'; 'If population increases, rents tend to rise': here 'if' means
'whenever' or 'all cases in which'; for to raise a doubt whether a
straight line is ever conceived to fall upon another, whether bodies are
ever unsupported, or population ever increases, is a superfluity of
scepticism; and plainly the hypothetical form has nothing to do with the
proof of such propositions, nor with inference from them.

Still, the disjunctive form is necessary in setting out the relation of