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of proving the contradictory universally and in the same respect and
relation and manner； the fallacy may be dependent on some limit of
extent or on one or other of these qualifications： moreover； there
is the assumption of the original point to be proved； in violation
of the clause 'without reckoning in the original point'。 Thus we
should have the number of considerations on which the fallacious
proofs depend： for they could not depend on more； but all will
depend on the points aforesaid。
A sophistical refutation is a refutation not absolutely but
relatively to some one： and so is a proof； in the same way。 For unless
that which depends upon ambiguity assumes that the ambiguous term
has a single meaning； and that which depends on like verbal forms
assumes that substance is the only category； and the rest in the
same way； there will be neither refutations nor proofs； either
absolutely or relatively to the answerer： whereas if they do assume
these things； they will stand； relatively to the answerer； but
absolutely they will not stand： for they have not secured a
statement that does have a single meaning； but only one that appears
to have； and that only from this particular man。
9
The number of considerations on which depend the refutations of
those who are refuted； we ought not to try to grasp without a
knowledge of everything that is。 This； however； is not the province of
any special study： for possibly the sciences are infinite in number；
so that obviously demonstrations may be infinite too。 Now
refutations may be true as well as false： for whenever it is
possible to demonstrate something； it is also possible to refute the
man who maintains the contradictory of the truth； e。g。 if a man has
stated that the diagonal is commensurate with the side of the
square； one might refute him by demonstrating that it is
incommensurate。 Accordingly； to exhaust all possible refutations we
shall have to have scientific knowledge of everything： for some
refutations depend upon the principles that rule in geometry and the
conclusions that follow from these； others upon those that rule in
medicine； and others upon those of the other sciences。 For the
matter of that； the false refutations likewise belong to the number of
the infinite： for according to every art there is false proof； e。g。
according to geometry there is false geometrical proof； and
according to medicine there is false medical proof。 By 'according to
the art'； I mean 'according to the principles of it'。 Clearly； then；
it is not of all refutations； but only of those that depend upon
dialectic that we need to grasp the common…place rules： for these
stand in a common relation to every art and faculty。 And as regards
the refutation that is according to one or other of the particular
sciences it is the task of that particular scientist to examine
whether it is merely apparent without being real； and； if it be
real； what is the reason for it： whereas it is the business of
dialecticians so to examine the refutation that proceeds from the
common first principles that fall under no particular special study。
For if we grasp the startingpoints of the accepted proofs on any
subject whatever we grasp those of the refutations current on that
subject。 For a refutation is the proof of the contradictory of a given
thesis； so that either one or two proofs of the contradictory
constitute a refutation。 We grasp； then； the number of
considerations on which all such depend： if； however； we grasp this；
we also grasp their solutions as well； for the objections to these are
the solutions of them。 We also grasp the number of considerations on
which those refutations depend； that are merely apparent…apparent； I
mean； not to everybody； but to people of a certain stamp； for it is an
indefinite task if one is to inquire how many are the considerations
that make them apparent to the man in the street。 Accordingly it is
clear that the dialectician's business is to be able to grasp on how
many considerations depends the formation； through the common first
principles； of a refutation that is either real or apparent； i。e。
either dialectical or apparently dialectical； or suitable for an
examination。
10
It is no true distinction between arguments which some people draw
when they say that some arguments are directed against the expression；
and others against the thought expressed： for it is absurd to
suppose that some arguments are directed against the expression and
others against the thought； and that they are not the same。 For what
is failure to direct an argument against the thought except what
occurs whenever a man does not in using the expression think it to
be used in his question in the same sense in which the person
questioned granted it？ And this is the same thing as to direct the
argument against the expression。 On the other hand； it is directed
against the thought whenever a man uses the expression in the same
sense which the answerer had in mind when he granted it。 If now any
（i。e。 both the questioner and the person questioned）； in dealing
with an expression with more than one meaning； were to suppose it to
have one meaning…as e。g。 it may be that 'Being' and 'One' have many
meanings； and yet both the answerer answers and the questioner puts
his question supposing it to be one； and the argument is to the effect
that 'All things are one'…will this discussion be directed any more
against the expression than against the thought of the person
questioned？ If； on the other hand； one of them supposes the expression
to have many meanings； it is clear that such a discussion will not
be directed against the thought。 Such being the meanings of the
phrases in question； they clearly cannot describe two separate classes
of argument。 For； in the first place； it is possible for any such
argument as bears more than one meaning to be directed against the
expression and against the thought； and next it is possible for any
argument whatsoever； for the fact of being directed against the
thought consists not in the nature of the argument； but in the special
attitude of the answerer towards the points he concedes。 Next； all
of them may be directed to the expression。 For 'to be directed against
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
against the thought of the former or not？
Moreover； if the expression bears many senses； while the answerer
does not understand or suppose it to have them； surely the
questioner here has directed his argument against his thought！ Or
how else