itions reciprocally from each other. This formal proof is not
often attempted, except under the pressure of controversy; but, from
mistaking mutual coherency for truth, propositions, which cannot be
proved except from each other, are often _admitted_, when expressed in
different language, without other proof. Frequently a proposition is
presented in abstract terms as a proof of the same in concrete, as, in
Moliere's parody, 'L'opium endormit parcequ'il a une vertu soporifique.'
So, some qualities of a thing selected arbitrarily are termed its nature
or essence, and then reasoned from as though not able to be counteracted
by any of the rest. 'Question-begging appellatives,' particularly, are
cases of Petitio Principii, e.g. the styling any reform an _innovation_,
which it really is, only that _innovation_ conveys, besides its
dictionary meaning, a covert sense of something extreme. Thus, in
Cicero's De Finibus, 'Cupiditas,' which usually implies vice, is used to
express certain desires the moral character of which is the point in
question. Again, the infinite divisibility of matter was assumed by the
argument which was used to prove it, viz. that the least portion of
matter must have both an upper and an under surface (which, as every
other Fallacy of Confusion, when cleared up, appears as a fallacy of a
different sort, under shelter of which, as indeed in ratiocinative
fallacies generally, the mere verbal juggle at first escapes detection).
Such, again, was Euler's argument, that _minus_ multiplied by _minus_
gives _plus_, _because_ it could not give the same as _minus_ multiplied
by _plus_, which gives _minus_. So, some ethical writers begin by
assuming, that certain general sentiments are the _natural_ sentiments
of mankind, and thence argue that any which differ are morbid and
_unnatural_. Thus, lastly, Hobbes and Rousseau rested the existence of
government and law on a supposed social compact, and not on men's
perception of the interests of society, which, however, could be the
only ground for their abiding by such compact if a fact.

3. In Ignoratio Elenchi, or, the Fallacy of Irrelevant Conclusion, the
error lies not either in mistaking the import of the premisses, or in
forgetting what they are, but in mistaking what is the conclusion to be
proved. Sometimes, a particular is substituted for the universal as the
proposition needing proof, and sometimes, a proposition with different
terms. Under this fallacy come th