
On Sophistical Refutations
the expression' means in this doctrine 'not to be directed against the
thought'. For if not all are directed against either expression or
thought, there will be certain other arguments directed neither
against the expression nor against the thought, whereas they say
that all must be one or the other, and divide them all as directed
either against the expression or against the thought, while others
(they say) there are none. But in point of fact those that depend on
mere expression are only a branch of those syllogisms that depend on a
multiplicity of meanings. For the absurd statement has actually been
made that the description 'dependent on mere expression' describes all
the arguments that depend on language: whereas some of these are
fallacies not because the answerer adopts a particular attitude
towards them, but because the argument itself involves the asking of a
question such as bears more than one meaning.
It is, too, altogether absurd to discuss Refutation without first
discussing Proof: for a refutation is a proof, so that one ought to
discuss proof as well before describing false refutation: for a
refutation of that kind is a merely apparent proof of the
contradictory of a thesis. Accordingly, the reason of the falsity will
be either in the proof or in the contradiction (for mention of the
'contradiction' must be added), while sometimes it is in both, if
the refutation be merely apparent. In the argument that speaking of
the silent is possible it lies in the contradiction, not in the proof;
in the argument that one can give what one does not possess, it lies
in both; in the proof that Homer's poem is a figure through its
being a cycle it lies in the proof. An argument that does not fail
in either respect is a true proof.
But, to return to the point whence our argument digressed, are
mathematical reasonings directed against the thought, or not? And if
any one thinks 'triangle' to be a word with many meanings, and granted
it in some different sense from the figure which was proved to contain
two right angles, has the questioner here directed his argument
