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Aristotle, Topica and De sophisticis elenchis, trans. WA. Pickard-Cambridge (Oxford: Clarendon Press, 1928). 

====== Aristotle: Sophistical Refutations ======

===== SECTION 1 =====


==== Part 1 ====
 

Let us now discuss sophistic refutations, i.e. what appear to be
refutations but are really fallacies instead. We will begin in the
natural order with the first. 

That some reasonings are genuine, while others seem to be so but are
not, is evident. This happens with arguments, as also elsewhere, through
a certain likeness between the genuine and the sham. For physically
some people are in a vigorous condition, while others merely seem
to be so by blowing and rigging themselves out as the tribesmen do
their victims for sacrifice; and some people are beautiful thanks
to their beauty, while others seem to be so, by dint of embellishing
themselves. So it is, too, with inanimate things; for of these, too,
some are really silver and others gold, while others are not and merely
seem to be such to our sense; e.g. things made of litharge and tin
seem to be of silver, while those made of yellow metal look golden.
In the same way both reasoning and refutation are sometimes genuine,
sometimes not, though inexperience may make them appear so: for inexperienced
people obtain only, as it were, a distant view of these things. For
reasoning rests on certain statements such that they involve necessarily
the assertion of something other than what has been stated, through
what has been stated: refutation is reasoning involving the contradictory
of the given conclusion. Now some of them do not really achieve this,
though they seem to do so for a number of reasons; and of these the
most prolific and usual domain is the argument that turns upon names
only. It is impossible in a discussion to bring in the actual things
discussed: we use their names as symbols instead of them; and therefore
we suppose that what follows in the names, follows in the things as
well, just as people who calculate suppose in regard to their counters.
But the two cases (names and things) are not alike. For names are
finite and so is the sum-total of formulae, while things are infinite
in number. Inevitably, then, the same formulae, and a single name,
have a number of meanings. Accordingly just as, in counting, those
who are not clever in manipulating their counters are taken in by
the experts, in the same way in arguments too those who are not well
acquainted with the force of names misreason both in their own discussions
and when they listen to others. For this reason, then, and for others
to be mentioned later, there exists both reasoning and refutation
that is apparent but not real. Now for some people it is better worth
while to seem to be wise, than to be wise without seeming to be (for
the art of the sophist is the semblance of wisdom without the reality,
and the sophist is one who makes money from an apparent but unreal
wisdom); for them, then, it is clearly essential also to seem to accomplish
the task of a wise man rather than to accomplish it without seeming
to do so. To reduce it to a single point of contrast it is the business
of one who knows a thing, himself to avoid fallacies in the subjects
which he knows and to be able to show up the man who makes them; and
of these accomplishments the one depends on the faculty to render
an answer, and the other upon the securing of one. Those, then, who
would be sophists are bound to study the class of arguments aforesaid:
for it is worth their while: for a faculty of this kind will make
a man seem to be wise, and this is the purpose they happen to have
in view. 

Clearly, then, there exists a class of arguments of this kind, and
it is at this kind of ability that those aim whom we call sophists.
Let us now go on to discuss how many kinds there are of sophistical
arguments, and how many in number are the elements of which this faculty
is composed, and how many branches there happen to be of this inquiry,
and the other factors that contribute to this art. 

==== Part 2 ====


Of arguments in dialogue form there are four classes: 
Didactic, Dialectical, Examination-arguments, and Contentious arguments.
Didactic arguments are those that reason from the principles appropriate
to each subject and not from the opinions held by the answerer (for
the learner should take things on trust): dialectical arguments are
those that reason from premisses generally accepted, to the contradictory
of a given thesis: examination-arguments are those that reason from
premisses which are accepted by the answerer and which any one who
pretends to possess knowledge of the subject is bound to know-in what
manner, has been defined in another treatise: contentious arguments
are those that reason or appear to reason to a conclusion from premisses
that appear to be generally accepted but are not so. The subject,
then, of demonstrative arguments has been discussed in the Analytics,
while that of dialectic arguments and examination-arguments has been
discussed elsewhere: let us now proceed to speak of the arguments
used in competitions and contests. 

==== Part 3 ====


First we must grasp the number of aims entertained by those who argue
as competitors and rivals to the death. These are five in number,
refutation, fallacy, paradox, solecism, and fifthly to reduce the
opponent in the discussion to babbling-i.e. to constrain him to repeat
himself a number of times: or it is to produce the appearance of each
of these things without the reality. For they choose if possible plainly
to refute the other party, or as the second best to show that he is
committing some fallacy, or as a third best to lead him into paradox,
or fourthly to reduce him to solecism, i.e. to make the answerer,
in consequence of the argument, to use an ungrammatical expression;
or, as a last resort, to make him repeat himself. 

==== Part 4 ====


There are two styles of refutation: for some depend on the language
used, while some are independent of language. Those ways of producing
the false appearance of an argument which depend on language are six
in number: they are ambiguity, amphiboly, combination, division of
words, accent, form of expression. Of this we may assure ourselves
both by induction, and by syllogistic proof based on this-and it may
be on other assumptions as well-that this is the number of ways in
which we might fall to mean the same thing by the same names or expressions.
Arguments such as the following depend upon ambiguity. 'Those learn
who know: for it is those who know their letters who learn the letters
dictated to them'. For to 'learn' is ambiguous; it signifies both
'to understand' by the use of knowledge, and also 'to acquire knowledge'.
Again, 'Evils are good: for what needs to be is good, and evils must
needs be'. For 'what needs to be' has a double meaning: it means what
is inevitable, as often is the case with evils, too (for evil of some
kind is inevitable), while on the other hand we say of good things
as well that they 'need to be'. Moreover, 'The same man is both seated
and standing and he is both sick and in health: for it is he who stood
up who is standing, and he who is recovering who is in health: but
it is the seated man who stood up, and the sick man who was recovering'.
For 'The sick man does so and so', or 'has so and so done to him'
is not single in meaning: sometimes it means 'the man who is sick
or is seated now', sometimes 'the man who was sick formerly'. Of course,
the man who was recovering was the sick man, who really was sick at
the time: but the man who is in health is not sick at the same time:
he is 'the sick man' in the sense not that he is sick now, but that
he was sick formerly. Examples such as the following depend upon amphiboly:
'I wish that you the enemy may capture'. Also the thesis, 'There must
be knowledge of what one knows': for it is possible by this phrase
to mean that knowledge belongs to both the knower and the known. Also,
'There must be sight of what one sees: one sees the pillar: ergo the
pillar has sight'. Also, 'What you profess to-be, that you profess
to-be: you profess a stone to-be: ergo you profess-to-be a stone'.
Also, 'Speaking of the silent is possible': for 'speaking of the silent'
also has a double meaning: it may mean that the speaker is silent
or that the things of which he speaks are so. There are three varieties
of these ambiguities and amphibolies: (1) When either the expression
or the name has strictly more than one meaning, e.g. aetos and the
'dog'; (2) when by custom we use them so; (3) when words that have
a simple sense taken alone have more than one meaning in combination;
e.g. 'knowing letters'. For each word, both 'knowing' and 'letters',
possibly has a single meaning: but both together have more than one-either
that the letters themselves have knowledge or that someone else has
it of them. 

Amphiboly and ambiguity, then, depend on these modes of speech. Upon
the combination of words there depend instances such as the following:
'A man can walk while sitting, and can write while not writing'. For
the meaning is not the same if one divides the words and if one combines
them in saying that 'it is possible to walk-while-sitting' and write
while not writing]. The same applies to the latter phrase, too, if
one combines the words 'to write-while-not-writing': for then it means
that he has the power to write and not to write at once; whereas if
one does not combine them, it means that when he is not writing he
has the power to write. Also, 'He now if he has learnt his letters'.
Moreover, there is the saying that 'One single thing if you can carry
a crowd you can carry too'. 

Upon division depend the propositions that 5 is 2 and 3, and odd,
and that the greater is equal: for it is that amount and more besides.
For the same phrase would not be thought always to have the same meaning
when divided and when combined, e.g. 'I made thee a slave once a free
man', and 'God-like Achilles left fifty a hundred men'. 

An argument depending upon accent it is not easy to construct in unwritten
discussion; in written discussions and in poetry it is easier. Thus
(e.g.) some people emend Homer against those who criticize as unnatural
his expression to men ou kataputhetai ombro. For they solve the difficulty
by a change of accent, pronouncing the ou with an acuter accent. Also,
in the passage about Agamemnon's dream, they say that Zeus did not
himself say 'We grant him the fulfilment of his prayer', but that
he bade the dream grant it. Instances such as these, then, turn upon
the accentuation. 

Others come about owing to the form of expression used, when what
is really different is expressed in the same form, e.g. a masculine
thing by a feminine termination, or a feminine thing by a masculine,
or a neuter by either a masculine or a feminine; or, again, when a
quality is expressed by a termination proper to quantity or vice versa,
or what is active by a passive word, or a state by an active word,
and so forth with the other divisions previously' laid down. For it
is possible to use an expression to denote what does not belong to
the class of actions at all as though it did so belong. Thus (e.g.)
'flourishing' is a word which in the form of its expression is like
'cutting' or 'building': yet the one denotes a certain quality-i.e.
a certain condition-while the other denotes a certain action. In the
same manner also in the other instances. 

Refutations, then, that depend upon language are drawn from these
common-place rules. Of fallacies, on the other hand, that are independent
of language there are seven kinds: 

(1) that which depends upon Accident: \\
(2) the use of an expression absolutely or not absolutely but with\\
some qualification of respect or place, or time, or relation:\\

(3) that which depends upon ignorance of what 'refutation' is:\\
\\
(4) that which depends upon the consequent: \\
(5) that which depends upon assuming the original conclusion:\\
\\
(6) stating as cause what is not the cause: \\
(7) the making of more than one question into one. \\

==== Part 5 ====


Fallacies, then, that depend on Accident occur whenever any attribute
is claimed to belong in like manner to a thing and to its accident.
For since the same thing has many accidents there is no necessity
that all the same attributes should belong to all of a thing's predicates
and to their subject as well. Thus (e.g.), 'If Coriscus be different
from "man", he is different from himself: for he is a man': or 'If
he be different from Socrates, and Socrates be a man, then', they
say, 'he has admitted that Coriscus is different from a man, because
it so happens (accidit) that the person from whom he said that he
(Coriscus) is different is a man'. 

Those that depend on whether an expression is used absolutely or in
a certain respect and not strictly, occur whenever an expression used
in a particular sense is taken as though it were used absolutely,
e.g. in the argument 'If what is not is the object of an opinion,
then what is not is': for it is not the same thing 'to be x' and 'to
be' absolutely. Or again, 'What is, is not, if it is not a particular
kind of being, e.g. if it is not a man.' For it is not the same thing
'not to be x' and 'not to be' at all: it looks as if it were, because
of the closeness of the expression, i.e. because 'to be x' is but
little different from 'to be', and 'not to be x' from 'not to be'.
Likewise also with any argument that turns upon the point whether
an expression is used in a certain respect or used absolutely. Thus
e.g. 'Suppose an Indian to be black all over, but white in respect
of his teeth; then he is both white and not white.' Or if both characters
belong in a particular respect, then, they say, 'contrary attributes
belong at the same time'. This kind of thing is in some cases easily
seen by any one, e.g. suppose a man were to secure the statement that
the Ethiopian is black, and were then to ask whether he is white in
respect of his teeth; and then, if he be white in that respect, were
to suppose at the conclusion of his questions that therefore he had
proved dialectically that he was both white and not white. But in
some cases it often passes undetected, viz. in all cases where, whenever
a statement is made of something in a certain respect, it would be
generally thought that the absolute statement follows as well; and
also in all cases where it is not easy to see which of the attributes
ought to be rendered strictly. A situation of this kind arises, where
both the opposite attributes belong alike: for then there is general
support for the view that one must agree absolutely to the assertion
of both, or of neither: e.g. if a thing is half white and half black,
is it white or black? 

Other fallacies occur because the terms 'proof' or 'refutation' have
not been defined, and because something is left out in their definition.
For to refute is to contradict one and the same attribute-not merely
the name, but the reality-and a name that is not merely synonymous
but the same name-and to confute it from the propositions granted,
necessarily, without including in the reckoning the original point
to be proved, in the same respect and relation and manner and time
in which it was asserted. A 'false assertion' about anything has to
be defined in the same way. Some people, however, omit some one of
the said conditions and give a merely apparent refutation, showing
(e.g.) that the same thing is both double and not double: for two
is double of one, but not double of three. Or, it may be, they show
that it is both double and not double of the same thing, but not that
it is so in the same respect: for it is double in length but not double
in breadth. Or, it may be, they show it to be both double and not
double of the same thing and in the same respect and manner, but not
that it is so at the same time: and therefore their refutation is
merely apparent. One might, with some violence, bring this fallacy
into the group of fallacies dependent on language as well.

Those that depend on the assumption of the original point to be proved,
occur in the same way, and in as many ways, as it is possible to beg
the original point; they appear to refute because men lack the power
to keep their eyes at once upon what is the same and what is different.

The refutation which depends upon the consequent arises because people
suppose that the relation of consequence is convertible. For whenever,
suppose A is, B necessarily is, they then suppose also that if B is,
A necessarily is. This is also the source of the deceptions that attend
opinions based on sense-perception. For people often suppose bile
to be honey because honey is attended by a yellow colour: also, since
after rain the ground is wet in consequence, we suppose that if the
ground is wet, it has been raining; whereas that does not necessarily
follow. In rhetoric proofs from signs are based on consequences. For
when rhetoricians wish to show that a man is an adulterer, they take
hold of some consequence of an adulterous life, viz. that the man
is smartly dressed, or that he is observed to wander about at night.
There are, however, many people of whom these things are true, while
the charge in question is untrue. It happens like this also in real
reasoning; e.g. Melissus' argument, that the universe is eternal,
assumes that the universe has not come to be (for from what is not
nothing could possibly come to be) and that what has come to be has
done so from a first beginning. If, therefore, the universe has not
come to be, it has no first beginning, and is therefore eternal. But
this does not necessarily follow: for even if what has come to be
always has a first beginning, it does not also follow that what has
a first beginning has come to be; any more than it follows that if
a man in a fever be hot, a man who is hot must be in a fever.

The refutation which depends upon treating as cause what is not a
cause, occurs whenever what is not a cause is inserted in the argument,
as though the refutation depended upon it. This kind of thing happens
in arguments that reason ad impossible: for in these we are bound
to demolish one of the premisses. If, then, the false cause be reckoned
in among the questions that are necessary to establish the resulting
impossibility, it will often be thought that the refutation depends
upon it, e.g. in the proof that the 'soul' and 'life' are not the
same: for if coming-to-be be contrary to perishing, then a particular
form of perishing will have a particular form of coming-to-be as its
contrary: now death is a particular form of perishing and is contrary
to life: life, therefore, is a coming to-be, and to live is to come-to-be.
But this is impossible: accordingly, the 'soul' and 'life' are not
the same. Now this is not proved: for the impossibility results all
the same, even if one does not say that life is the same as the soul,
but merely says that life is contrary to death, which is a form of
perishing, and that perishing has 'coming-to-be' as its contrary.
Arguments of that kind, then, though not inconclusive absolutely,
are inconclusive in relation to the proposed conclusion. Also even
the questioners themselves often fail quite as much to see a point
of that kind. 

Such, then, are the arguments that depend upon the consequent and
upon false cause. Those that depend upon the making of two questions
into one occur whenever the plurality is undetected and a single answer
is returned as if to a single question. Now, in some cases, it is
easy to see that there is more than one, and that an answer is not
to be given, e.g. 'Does the earth consist of sea, or the sky?' But
in some cases it is less easy, and then people treat the question
as one, and either confess their defeat by failing to answer the question,
or are exposed to an apparent refutation. Thus 'Is A and is B a man?'
'Yes.' 'Then if any one hits A and B, he will strike a man' (singular),'not
men' (plural). Or again, where part is good and part bad, 'is the
whole good or bad?' For whichever he says, it is possible that he
might be thought to expose himself to an apparent refutation or to
make an apparently false statement: for to say that something is good
which is not good, or not good which is good, is to make a false statement.
Sometimes, however, additional premisses may actually give rise to
a genuine refutation; e.g. suppose a man were to grant that the descriptions
'white' and 'naked' and 'blind' apply to one thing and to a number
of things in a like sense. For if 'blind' describes a thing that cannot
see though nature designed it to see, it will also describe things
that cannot see though nature designed them to do so. Whenever, then,
one thing can see while another cannot, they will either both be able
to see or else both be blind; which is impossible. 

==== Part 6 ====


The right way, then, is either to divide apparent proofs and refutations
as above, or else to refer them all to ignorance of what 'refutation'
is, and make that our starting-point: for it is possible to analyse
all the aforesaid modes of fallacy into breaches of the definition
of a refutation. In the first place, we may see if they are inconclusive:
for the conclusion ought to result from the premisses laid down, so
as to compel us necessarily to state it and not merely to seem to
compel us. Next we should also take the definition bit by bit, and
try the fallacy thereby. For of the fallacies that consist in language,
some depend upon a double meaning, e.g. ambiguity of words and of
phrases, and the fallacy of like verbal forms (for we habitually speak
of everything as though it were a particular substance)-while fallacies
of combination and division and accent arise because the phrase in
question or the term as altered is not the same as was intended. Even
this, however, should be the same, just as the thing signified should
be as well, if a refutation or proof is to be effected; e.g. if the
point concerns a doublet, then you should draw the conclusion of a
'doublet', not of a 'cloak'. For the former conclusion also would
be true, but it has not been proved; we need a further question to
show that 'doublet' means the same thing, in order to satisfy any
one who asks why you think your point proved. 

Fallacies that depend on Accident are clear cases of ignoratio elenchi
when once 'proof' has been defined. For the same definition ought
to hold good of 'refutation' too, except that a mention of 'the contradictory'
is here added: for a refutation is a proof of the contradictory. If,
then, there is no proof as regards an accident of anything, there
is no refutation. For supposing, when A and B are, C must necessarily
be, and C is white, there is no necessity for it to be white on account
of the syllogism. So, if the triangle has its angles equal to two
right-angles, and it happens to be a figure, or the simplest element
or starting point, it is not because it is a figure or a starting
point or simplest element that it has this character. For the demonstration
proves the point about it not qua figure or qua simplest element,
but qua triangle. Likewise also in other cases. If, then, refutation
is a proof, an argument which argued per accidens could not be a refutation.
It is, however, just in this that the experts and men of science generally
suffer refutation at the hand of the unscientific: for the latter
meet the scientists with reasonings constituted per accidens; and
the scientists for lack of the power to draw distinctions either say
'Yes' to their questions, or else people suppose them to have said
'Yes', although they have not. 

Those that depend upon whether something is said in a certain respect
only or said absolutely, are clear cases of ignoratio elenchi because
the affirmation and the denial are not concerned with the same point.
For of 'white in a certain respect' the negation is 'not white in
a certain respect', while of 'white absolutely' it is 'not white,
absolutely'. If, then, a man treats the admission that a thing is
'white in a certain respect' as though it were said to be white absolutely,
he does not effect a refutation, but merely appears to do so owing
to ignorance of what refutation is. 

The clearest cases of all, however, are those that were previously
described' as depending upon the definition of a 'refutation': and
this is also why they were called by that name. For the appearance
of a refutation is produced because of the omission in the definition,
and if we divide fallacies in the above manner, we ought to set 'Defective
definition' as a common mark upon them all. 

Those that depend upon the assumption of the original point and upon
stating as the cause what is not the cause, are clearly shown to be
cases of ignoratio elenchi through the definition thereof. For the
conclusion ought to come about 'because these things are so', and
this does not happen where the premisses are not causes of it: and
again it should come about without taking into account the original
point, and this is not the case with those arguments which depend
upon begging the original point. 

Those that depend upon the assumption of the original point and upon
stating as the cause what is not the cause, are clearly shown to be
cases of ignoratio elenchi through the definition thereof. For the
conclusion ought to come about 'because these things are so', and
this does not happen where the premisses are not causes of it: and
again it should come about without taking into account the original
point, and this is not the case with those arguments which depend
upon begging the original point. 

Those that depend upon the consequent are a branch of Accident: for
the consequent is an accident, only it differs from the accident in
this, that you may secure an admission of the accident in the case
of one thing only (e.g. the identity of a yellow thing and honey and
of a white thing and swan), whereas the consequent always involves
more than one thing: for we claim that things that are the same as
one and the same thing are also the same as one another, and this
is the ground of a refutation dependent on the consequent. It is,
however, not always true, e.g. suppose that and B are the same as
C per accidens; for both 'snow' and the 'swan' are the same as something
white'. Or again, as in Melissus' argument, a man assumes that to
'have been generated' and to 'have a beginning' are the same thing,
or to 'become equal' and to 'assume the same magnitude'. For because
what has been generated has a beginning, he claims also that what
has a beginning has been generated, and argues as though both what
has been generated and what is finite were the same because each has
a beginning. Likewise also in the case of things that are made equal
he assumes that if things that assume one and the same magnitude become
equal, then also things that become equal assume one magnitude: i.e.
he assumes the consequent. Inasmuch, then, as a refutation depending
on accident consists in ignorance of what a refutation is, clearly
so also does a refutation depending on the consequent. We shall have
further to examine this in another way as well. 

Those fallacies that depend upon the making of several questions into
one consist in our failure to dissect the definition of 'proposition'.
For a proposition is a single statement about a single thing. For
the same definition applies to 'one single thing only' and to the
'thing', simply, e.g. to 'man' and to 'one single man only' and likewise
also in other cases. If, then, a 'single proposition' be one which
claims a single thing of a single thing, a 'proposition', simply,
will also be the putting of a question of that kind. Now since a proof
starts from propositions and refutation is a proof, refutation, too,
will start from propositions. If, then, a proposition is a single
statement about a single thing, it is obvious that this fallacy too
consists in ignorance of what a refutation is: for in it what is not
a proposition appears to be one. If, then, the answerer has returned
an answer as though to a single question, there will be a refutation;
while if he has returned one not really but apparently, there will
be an apparent refutation of his thesis. All the types of fallacy,
then, fall under ignorance of what a refutation is, some of them because
the contradiction, which is the distinctive mark of a refutation,
is merely apparent, and the rest failing to conform to the definition
of a proof. 

==== Part 7 ====


The deception comes about in the case of arguments that depend on
ambiguity of words and of phrases because we are unable to divide
the ambiguous term (for some terms it is not easy to divide, e.g.
'unity', 'being', and 'sameness'), while in those that depend on combination
and division, it is because we suppose that it makes no difference
whether the phrase be combined or divided, as is indeed the case with
most phrases. Likewise also with those that depend on accent: for
the lowering or raising of the voice upon a phrase is thought not
to alter its meaning-with any phrase, or not with many. With those
that depend on the of expression it is because of the likeness of
expression. For it is hard to distinguish what kind of things are
signified by the same and what by different kinds of expression: for
a man who can do this is practically next door to the understanding
of the truth. A special reason why a man is liable to be hurried into
assent to the fallacy is that we suppose every predicate of everything
to be an individual thing, and we understand it as being one with
the thing: and we therefore treat it as a substance: for it is to
that which is one with a thing or substance, as also to substance
itself, that 'individually' and 'being' are deemed to belong in the
fullest sense. For this reason, too, this type of fallacy is to be
ranked among those that depend on language; in the first place, because
the deception is effected the more readily when we are inquiring into
a problem in company with others than when we do so by ourselves (for
an inquiry with another person is carried on by means of speech, whereas
an inquiry by oneself is carried on quite as much by means of the
object itself); secondly a man is liable to be deceived, even when
inquiring by himself, when he takes speech as the basis of his inquiry:
moreover the deception arises out of the likeness (of two different
things), and the likeness arises out of the language. With those fallacies
that depend upon Accident, deception comes about because we cannot
distinguish the sameness and otherness of terms, i.e. their unity
and multiplicity, or what kinds of predicate have all the same accidents
as their subject. Likewise also with those that depend on the Consequent:
for the consequent is a branch of Accident. Moreover, in many cases
appearances point to this-and the claim is made that if is inseparable
from B, so also is B from With those that depend upon an imperfection
in the definition of a refutation, and with those that depend upon
the difference between a qualified and an absolute statement, the
deception consists in the smallness of the difference involved; for
we treat the limitation to the particular thing or respect or manner
or time as adding nothing to the meaning, and so grant the statement
universally. Likewise also in the case of those that assume the original
point, and those of false cause, and all that treat a number of questions
as one: for in all of them the deception lies in the smallness of
the difference: for our failure to be quite exact in our definition
of 'premiss' and of 'proof' is due to the aforesaid reason.

==== Part 8 ====


Since we know on how many points apparent syllogisms depend, we know
also on how many sophistical syllogisms and refutations may depend.
By a sophistical refutation and syllogism I mean not only a syllogism
or refutation which appears to be valid but is not, but also one which,
though it is valid, only appears to be appropriate to the thing in
question. These are those which fail to refute and prove people to
be ignorant according to the nature of the thing in question, which
was the function of the art of examination. Now the art of examining
is a branch of dialectic: and this may prove a false conclusion because
of the ignorance of the answerer. Sophistic refutations on the other
hand, even though they prove the contradictory of his thesis, do not
make clear whether he is ignorant: for sophists entangle the scientist
as well with these arguments. 

That we know them by the same line of inquiry is clear: for the same
considerations which make it appear to an audience that the points
required for the proof were asked in the questions and that the conclusion
was proved, would make the answerer think so as well, so that false
proof will occur through all or some of these means: for what a man
has not been asked but thinks he has granted, he would also grant
if he were asked. Of course, in some cases the moment we add the missing
question, we also show up its falsity, e.g. in fallacies that depend
on language and on solecism. If then, fallacious proofs of the contradictory
of a thesis depend on their appearing to refute, it is clear that
the considerations on which both proofs of false conclusions and an
apparent refutation depend must be the same in number. Now an apparent
refutation depends upon the elements involved in a genuine one: for
the failure of one or other of these must make the refutation merely
apparent, e.g. that which depends on the failure of the conclusion
to follow from the argument (the argument ad impossible) and that
which treats two questions as one and so depends upon a flaw in the
premiss, and that which depends on the substitution of an accident
for an essential attribute, and-a branch of the last-that which depends
upon the consequent: more over, the conclusion may follow not in fact
but only verbally: then, instead 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. 

==== Part 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. 

==== Part 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 ought
he to put his question except by suggesting a distinction-suppose
one's question to be speaking of the silent possible or not?'-as follows,
'Is the answer "No" in one sense, but "Yes" in another?' If, then,
any one were to answer that it was not possible in any sense and the
other were to argue that it was, has not his argument been directed
against the thought of the answerer? Yet his argument is supposed
to be one of those that depend on the expression. There is not, then,
any definite kind of arguments that is directed against the thought.
Some arguments are, indeed, directed against the expression: but these
are not all even apparent refutations, let alone all refutations.
For there are also apparent refutations which do not depend upon language,
e.g. those that depend upon accident, and others. 

If, however, any one claims that one should actually draw the distinction,
and say, 'By "speaking of the silent" I mean, in one sense this and
in the other sense that', surely to claim this is in the first place
absurd (for sometimes the questioner does not see the ambiguity of
his question, and he cannot possibly draw a distinction which he does
not think to be there): in the second place, what else but this will
didactic argument be? For it will make manifest the state of the case
to one who has never considered, and does not know or suppose that
there is any other meaning but one. For what is there to prevent the
same thing also happening to us in cases where there is no double
meaning? 'Are the units in four equal to the twos? Observe that the
twos are contained in four in one sense in this way, in another sense
in that'. Also, 'Is the knowledge of contraries one or not? Observe
that some contraries are known, while others are unknown'. Thus the
man who makes this claim seems to be unaware of the difference between
didactic and dialectical argument, and of the fact that while he who
argues didactically should not ask questions but make things clear
himself, the other should merely ask questions. 

----------------------------------------------------------------------

===== SECTION 2 =====


==== Part 11 ====
 

Moreover, to claim a 'Yes' or 'No' answer is the business not of
a man who is showing something, but of one who is holding an examination.
For the art of examining is a branch of dialectic and has in view
not the man who has knowledge, but the ignorant pretender. He, then,
is a dialectician who regards the common principles with their application
to the particular matter in hand, while he who only appears to do
this is a sophist. Now for contentious and sophistical reasoning:
(1) one such is a merely apparent reasoning, on subjects on which
dialectical reasoning is the proper method of examination, even though
its conclusion be true: for it misleads us in regard to the cause:
also (2) there are those misreasonings which do not conform to the
line of inquiry proper to the particular subject, but are generally
thought to conform to the art in question. For false diagrams of geometrical
figures are not contentious (for the resulting fallacies conform to
the subject of the art)-any more than is any false diagram that may
be offered in proof of a truth-e.g. Hippocrates' figure or the squaring
of the circle by means of the lunules. But Bryson's method of squaring
the circle, even if the circle is thereby squared, is still sophistical
because it does not conform to the subject in hand. So, then, any
merely apparent reasoning about these things is a contentious argument,
and any reasoning that merely appears to conform to the subject in
hand, even though it be genuine reasoning, is a contentious argument:
for it is merely apparent in its conformity to the subject-matter,
so that it is deceptive and plays foul. For just as a foul in a race
is a definite type of fault, and is a kind of foul fighting, so the
art of contentious reasoning is foul fighting in disputation: for
in the former case those who are resolved to win at all costs snatch
at everything, and so in the latter case do contentious reasoners.
Those, then, who do this in order to win the mere victory are generally
considered to be contentious and quarrelsome persons, while those
who do it to win a reputation with a view to making money are sophistical.
For the art of sophistry is, as we said,' a kind of art of money-making
from a merely apparent wisdom, and this is why they aim at a merely
apparent demonstration: and quarrelsome persons and sophists both
employ the same arguments, but not with the same motives: and the
same argument will be sophistical and contentious, but not in the
same respect; rather, it will be contentious in so far as its aim
is an apparent victory, while in so far as its aim is an apparent
wisdom, it will be sophistical: for the art of sophistry is a certain
appearance of wisdom without the reality. The contentious argument
stands in somewhat the same relation to the dialectical as the drawer
of false diagrams to the geometrician; for it beguiles by misreasoning
from the same principles as dialectic uses, just as the drawer of
a false diagram beguiles the geometrician. But whereas the latter
is not a contentious reasoner, because he bases his false diagram
on the principles and conclusions that fall under the art of geometry,
the argument which is subordinate to the principles of dialectic will
yet clearly be contentious as regards other subjects. Thus, e.g. though
the squaring of the circle by means of the lunules is not contentious,
Bryson's solution is contentious: and the former argument cannot be
adapted to any subject except geometry, because it proceeds from principles
that are peculiar to geometry, whereas the latter can be adapted as
an argument against all the number of people who do not know what
is or is not possible in each particular context: for it will apply
to them all. Or there is the method whereby Antiphon squared the circle.
Or again, an argument which denied that it was better to take a walk
after dinner, because of Zeno's argument, would not be a proper argument
for a doctor, because Zeno's argument is of general application. If,
then, the relation of the contentious argument to the dialectical
were exactly like that of the drawer of false diagrams to the geometrician,
a contentious argument upon the aforesaid subjects could not have
existed. But, as it is, the dialectical argument is not concerned
with any definite kind of being, nor does it show anything, nor is
it even an argument such as we find in the general philosophy of being.
For all beings are not contained in any one kind, nor, if they were,
could they possibly fall under the same principles. Accordingly, no
art that is a method of showing the nature of anything proceeds by
asking questions: for it does not permit a man to grant whichever
he likes of the two alternatives in the question: for they will not
both of them yield a proof. Dialectic, on the other hand, does proceed
by questioning, whereas if it were concerned to show things, it would
have refrained from putting questions, even if not about everything,
at least about the first principles and the special principles that
apply to the particular subject in hand. For suppose the answerer
not to grant these, it would then no longer have had any grounds from
which to argue any longer against the objection. Dialectic is at the
same time a mode of examination as well. For neither is the art of
examination an accomplishment of the same kind as geometry, but one
which a man may possess, even though he has not knowledge. For it
is possible even for one without knowledge to hold an examination
of one who is without knowledge, if also the latter grants him points
taken not from thing that he knows or from the special principles
of the subject under discussion but from all that range of consequences
attaching to the subject which a man may indeed know without knowing
the theory of the subject, but which if he do not know, he is bound
to be ignorant of the theory. So then clearly the art of examining
does not consist in knowledge of any definite subject. For this reason,
too, it deals with everything: for every 'theory' of anything employs
also certain common principles. Hence everybody, including even amateurs,
makes use in a way of dialectic and the practice of examining: for
all undertake to some extent a rough trial of those who profess to
know things. What serves them here is the general principles: for
they know these of themselves just as well as the scientist, even
if in what they say they seem to the latter to go wildly astray from
them. All, then, are engaged in refutation; for they take a hand as
amateurs in the same task with which dialectic is concerned professionally;
and he is a dialectician who examines by the help of a theory of reasoning.
Now there are many identical principles which are true of everything,
though they are not such as to constitute a particular nature, i.e.
a particular kind of being, but are like negative terms, while other
principles are not of this kind but are special to particular subjects;
accordingly it is possible from these general principles to hold an
examination on everything, and that there should be a definite art
of so doing, and, moreover, an art which is not of the same kind as
those which demonstrate. This is why the contentious reasoner does
not stand in the same condition in all respects as the drawer of a
false diagram: for the contentious reasoner will not be given to misreasoning
from any definite class of principles, but will deal with every class.

These, then, are the types of sophistical refutations: and that it
belongs to the dialectician to study these, and to be able to effect
them, is not difficult to see: for the investigation of premisses
comprises the whole of this study. 

==== Part 12 ====


So much, then, for apparent refutations. As for showing that the answerer
is committing some fallacy, and drawing his argument into paradox-for
this was the second item of the sophist's programme-in the first place,
then, this is best brought about by a certain manner of questioning
and through the question. For to put the question without framing
it with reference to any definite subject is a good bait for these
purposes: for people are more inclined to make mistakes when they
talk at large, and they talk at large when they have no definite subject
before them. Also the putting of several questions, even though the
position against which one is arguing be quite definite, and the claim
that he shall say only what he thinks, create abundant opportunity
for drawing him into paradox or fallacy, and also, whether to any
of these questions he replies 'Yes' or replies 'No', of leading him
on to statements against which one is well off for a line of attack.
Nowadays, however, men are less able to play foul by these means than
they were formerly: for people rejoin with the question, 'What has
that to do with the original subject?' It is, too, an elementary rule
for eliciting some fallacy or paradox that one should never put a
controversial question straight away, but say that one puts it from
the wish for information: for the process of inquiry thus invited
gives room for an attack. 

A rule specially appropriate for showing up a fallacy is the sophistic
rule, that one should draw the answerer on to the kind of statements
against which one is well supplied with arguments: this can be done
both properly and improperly, as was said before.' Again, to draw
a paradoxical statement, look and see to what school of philosophers
the person arguing with you belongs, and then question him as to some
point wherein their doctrine is paradoxical to most people: for with
every school there is some point of that kind. It is an elementary
rule in these matters to have a collection of the special 'theses'
of the various schools among your propositions. The solution recommended
as appropriate here, too, is to point out that the paradox does not
come about because of the argument: whereas this is what his opponent
always really wants. 

Moreover, argue from men's wishes and their professed opinions. For
people do not wish the same things as they say they wish: they say
what will look best, whereas they wish what appears to be to their
interest: e.g. they say that a man ought to die nobly rather than
to live in pleasure, and to live in honest poverty rather than in
dishonourable riches; but they wish the opposite. Accordingly, a man
who speaks according to his wishes must be led into stating the professed
opinions of people, while he who speaks according to these must be
led into admitting those that people keep hidden away: for in either
case they are bound to introduce a paradox; for they will speak contrary
either to men's professed or to their hidden opinions. 

The widest range of common-place argument for leading men into paradoxical
statement is that which depends on the standards of Nature and of
the Law: it is so that both Callicles is drawn as arguing in the Gorgias,
and that all the men of old supposed the result to come about: for
nature (they said) and law are opposites, and justice is a fine thing
by a legal standard, but not by that of nature. Accordingly, they
said, the man whose statement agrees with the standard of nature you
should meet by the standard of the law, but the man who agrees with
the law by leading him to the facts of nature: for in both ways paradoxical
statements may be committed. In their view the standard of nature
was the truth, while that of the law was the opinion held by the majority.
So that it is clear that they, too, used to try either to refute the
answerer or to make him make paradoxical statements, just as the men
of to-day do as well. 

Some questions are such that in both forms the answer is paradoxical;
e.g. 'Ought one to obey the wise or one's father?' and 'Ought one
to do what is expedient or what is just?' and 'Is it preferable to
suffer injustice or to do an injury?' You should lead people, then,
into views opposite to the majority and to the philosophers; if any
one speaks as do the expert reasoners, lead him into opposition to
the majority, while if he speaks as do the majority, then into opposition
to the reasoners. For some say that of necessity the happy man is
just, whereas it is paradoxical to the many that a king should be
happy. To lead a man into paradoxes of this sort is the same as to
lead him into the opposition of the standards of nature and law: for
the law represents the opinion of the majority, whereas philosophers
speak according to the standard of nature and the truth.

==== Part 13 ====


Paradoxes, then, you should seek to elicit by means of these common-place
rules. Now as for making any one babble, we have already said what
we mean by 'to babble'. This is the object in view in all arguments
of the following kind: If it is all the same to state a term and to
state its definition, the 'double' and 'double of half' are the same:
if then 'double' be the 'double of half', it will be the 'double of
half of half'. And if, instead of 'double', 'double of half' be again
put, then the same expression will be repeated three times, 'double
of half of half of half'. Also 'desire is of the pleasant, isn't it?'
desire is conation for the pleasant: accordingly, 'desire' is 'conation
for the pleasant for the pleasant'. 

All arguments of this kind occur in dealing (1) with any relative
terms which not only have relative genera, but are also themselves
relative, and are rendered in relation to one and the same thing,
as e.g. conation is conation for something, and desire is desire of
something, and double is double of something, i.e. double of half:
also in dealing (2) with any terms which, though they be not relative
terms at all, yet have their substance, viz. the things of which they
are the states or affections or what not, indicated as well in their
definition, they being predicated of these things. Thus e.g. 'odd'
is a 'number containing a middle': but there is an 'odd number': therefore
there is a 'number-containing-a-middle number'. Also, if snubness
be a concavity of the nose, and there be a snub nose, there is therefore
a 'concave-nose nose'. 

People sometimes appear to produce this result, without really producing
it, because they do not add the question whether the expression 'double',
just by itself, has any meaning or no, and if so, whether it has the
same meaning, or a different one; but they draw their conclusion straight
away. Still it seems, inasmuch as the word is the same, to have the
same meaning as well. 

==== Part 14 ====


We have said before what kind of thing 'solecism' is.' It is possible
both to commit it, and to seem to do so without doing so, and to do
so without seeming to do so. Suppose, as Protagoras used to say that
menis ('wrath') and pelex ('helmet') are masculine: according to him
a man who calls wrath a 'destructress' (oulomenen) commits a solecism,
though he does not seem to do so to other people, where he who calls
it a 'destructor' (oulomenon) commits no solecism though he seems
to do so. It is clear, then, that any one could produce this effect
by art as well: and for this reason many arguments seem to lead to
solecism which do not really do so, as happens in the case of refutations.

Almost all apparent solecisms depend upon the word 'this' (tode),
and upon occasions when the inflection denotes neither a masculine
nor a feminine object but a neuter. For 'he' (outos) signifies a masculine,
and 'she' (aute) feminine; but 'this' (touto), though meant to signify
a neuter, often also signifies one or other of the former: e.g. 'What
is this?' 'It is Calliope'; 'it is a log'; 'it is Coriscus'. Now in
the masculine and feminine the inflections are all different, whereas
in the neuter some are and some are not. Often, then, when 'this'
(touto) has been granted, people reason as if 'him' (touton) had been
said: and likewise also they substitute one inflection for another.
The fallacy comes about because 'this' (touto) is a common form of
several inflections: for 'this' signifies sometimes 'he' (outos) and
sometimes 'him' (touton). It should signify them alternately; when
combined with 'is' (esti) it should be 'he', while with 'being' it
should be 'him': e.g. 'Coriscus (Kopiskos) is', but 'being Coriscus'
(Kopiskon). It happens in the same way in the case of feminine nouns
as well, and in the case of the so-called 'chattels' that have feminine
or masculine designations. For only those names which end in o and
n, have the designation proper to a chattel, e.g. xulon ('log'), schoinion
('rope'); those which do not end so have that of a masculine or feminine
object, though some of them we apply to chattels: e.g. askos ('wineskin')
is a masculine noun, and kline ('bed') a feminine. For this reason
in cases of this kind as well there will be a difference of the same
sort between a construction with 'is' (esti) or with 'being' (to einai).
Also, Solecism resembles in a certain way those refutations which
are said to depend on the like expression of unlike things. For, just
as there we come upon a material solecism, so here we come upon a
verbal: for 'man' is both a 'matter' for expression and also a 'word':
and so is white'. 

It is clear, then, that for solecisms we must try to construct our
argument out of the aforesaid inflections. 

These, then, are the types of contentious arguments, and the subdivisions
of those types, and the methods for conducting them aforesaid. But
it makes no little difference if the materials for putting the question
be arranged in a certain manner with a view to concealment, as in
the case of dialectics. Following then upon what we have said, this
must be discussed first. 

==== Part 15 ====


With a view then to refutation, one resource is length-for it is difficult
to keep several things in view at once; and to secure length the elementary
rules that have been stated before' should be employed. One resource,
on the other hand, is speed; for when people are left behind they
look ahead less. Moreover, there is anger and contentiousness, for
when agitated everybody is less able to take care of himself. Elementary
rules for producing anger are to make a show of the wish to play foul,
and to be altogether shameless. Moreover, there is the putting of
one's questions alternately, whether one has more than one argument
leading to the same conclusion, or whether one has arguments to show
both that something is so, and that it is not so: for the result is
that he has to be on his guard at the same time either against more
than one line, or against contrary lines, of argument. In general,
all the methods described before of producing concealment are useful
also for purposes of contentious argument: for the object of concealment
is to avoid detection, and the object of this is to deceive.

To counter those who refuse to grant whatever they suppose to help
one's argument, one should put the question negatively, as though
desirous of the opposite answer, or at any rate as though one put
the question without prejudice; for when it is obscure what answer
one wants to secure, people are less refractory. Also when, in dealing
with particulars, a man grants the individual case, when the induction
is done you should often not put the universal as a question, but
take it for granted and use it: for sometimes people themselves suppose
that they have granted it, and also appear to the audience to have
done so, for they remember the induction and assume that the questions
could not have been put for nothing. In cases where there is no term
to indicate the universal, still you should avail yourself of the
resemblance of the particulars to suit your purpose; for resemblance
often escapes detection. Also, with a view to obtaining your premiss,
you ought to put it in your question side by side with its contrary.
E.g. if it were necessary to secure the admission that 'A man should
obey his father in everything', ask 'Should a man obey his parents
in everything, or disobey them in everything?'; and to secure that
'A number multiplied by a large number is a large number', ask 'Should
one agree that it is a large number or a small one?' For then, if
compelled to choose, one will be more inclined to think it a large
one: for the placing of their contraries close beside them makes things
look big to men, both relatively and absolutely, and worse and better.

A strong appearance of having been refuted is often produced by the
most highly sophistical of all the unfair tricks of questioners, when
without proving anything, instead of putting their final proposition
as a question, they state it as a conclusion, as though they had proved
that 'Therefore so-and-so is not true' 

It is also a sophistical trick, when a paradox has been laid down,
first to propose at the start some view that is generally accepted,
and then claim that the answerer shall answer what he thinks about
it, and to put one's question on matters of that kind in the form
'Do you think that...?' For then, if the question be taken as one
of the premisses of one's argument, either a refutation or a paradox
is bound to result; if he grants the view, a refutation; if he refuses
to grant it or even to admit it as the received opinion, a paradox;
if he refuses to grant it, but admits that it is the received opinion,
something very like a refutation, results. 

Moreover, just as in rhetorical discourses, so also in those aimed
at refutation, you should examine the discrepancies of the answerer's
position either with his own statements, or with those of persons
whom he admits to say and do aright, moreover with those of people
who are generally supposed to bear that kind of character, or who
are like them, or with those of the majority or of all men. Also just
as answerers, too, often, when they are in process of being confuted,
draw a distinction, if their confutation is just about to take place,
so questioners also should resort to this from time to time to counter
objectors, pointing out, supposing that against one sense of the words
the objection holds, but not against the other, that they have taken
it in the latter sense, as e.g. Cleophon does in the Mandrobulus.
They should also break off their argument and cut down their other
lines of attack, while in answering, if a man perceives this being
done beforehand, he should put in his objection and have his say first.
One should also lead attacks sometimes against positions other than
the one stated, on the understood condition that one cannot find lines
of attack against the view laid down, as Lycophron did when ordered
to deliver a eulogy upon the lyre. To counter those who demand 'Against
what are you directing your effort?', since one is generally thought
bound to state the charge made, while, on the other hand, some ways
of stating it make the defence too easy, you should state as your
aim only the general result that always happens in refutations, namely
the contradiction of his thesis -viz. that your effort is to deny
what he has affirmed, or to affirm what he denied: don't say that
you are trying to show that the knowledge of contraries is, or is
not, the same. One must not ask one's conclusion in the form of a
premiss, while some conclusions should not even be put as questions
at all; one should take and use it as granted. 

==== Part 16 ====


We have now therefore dealt with the sources of questions, and the
methods of questioning in contentious disputations: next we have to
speak of answering, and of how solutions should be made, and of what
requires them, and of what use is served by arguments of this kind.

The use of them, then, is, for philosophy, twofold. For in the first
place, since for the most part they depend upon the expression, they
put us in a better condition for seeing in how many senses any term
is used, and what kind of resemblances and what kind of differences
occur between things and between their names. In the second place
they are useful for one's own personal researches; for the man who
is easily committed to a fallacy by some one else, and does not perceive
it, is likely to incur this fate of himself also on many occasions.
Thirdly and lastly, they further contribute to one's reputation, viz.
the reputation of being well trained in everything, and not inexperienced
in anything: for that a party to arguments should find fault with
them, if he cannot definitely point out their weakness, creates a
suspicion, making it seem as though it were not the truth of the matter
but merely inexperience that put him out of temper. 

Answerers may clearly see how to meet arguments of this kind, if our
previous account was right of the sources whence fallacies came, and
also our distinctions adequate of the forms of dishonesty in putting
questions. But it is not the same thing take an argument in one's
hand and then to see and solve its faults, as it is to be able to
meet it quickly while being subjected to questions: for what we know,
we often do not know in a different context. Moreover, just as in
other things speed is enhanced by training, so it is with arguments
too, so that supposing we are unpractised, even though a point be
clear to us, we are often too late for the right moment. Sometimes
too it happens as with diagrams; for there we can sometimes analyse
the figure, but not construct it again: so too in refutations, though
we know the thing on which the connexion of the argument depends,
we still are at a loss to split the argument apart. 

==== Part 17 ====


First then, just as we say that we ought sometimes to choose to prove
something in the general estimation rather than in truth, so also
we have sometimes to solve arguments rather in the general estimation
than according to the truth. For it is a general rule in fighting
contentious persons, to treat them not as refuting, but as merely
appearing to refute: for we say that they don't really prove their
case, so that our object in correcting them must be to dispel the
appearance of it. For if refutation be an unambiguous contradiction
arrived at from certain views, there could be no need to draw distinctions
against amphiboly and ambiguity: they do not effect a proof. The only
motive for drawing further distinctions is that the conclusion reached
looks like a refutation. What, then, we have to beware of, is not
being refuted, but seeming to be, because of course the asking of
amphibolies and of questions that turn upon ambiguity, and all the
other tricks of that kind, conceal even a genuine refutation, and
make it uncertain who is refuted and who is not. For since one has
the right at the end, when the conclusion is drawn, to say that the
only denial made of One's statement is ambiguous, no matter how precisely
he may have addressed his argument to the very same point as oneself,
it is not clear whether one has been refuted: for it is not clear
whether at the moment one is speaking the truth. If, on the other
hand, one had drawn a distinction, and questioned him on the ambiguous
term or the amphiboly, the refutation would not have been a matter
of uncertainty. Also what is incidentally the object of contentious
arguers, though less so nowadays than formerly, would have been fulfilled,
namely that the person questioned should answer either 'Yes' or 'No':
whereas nowadays the improper forms in which questioners put their
questions compel the party questioned to add something to his answer
in correction of the faultiness of the proposition as put: for certainly,
if the questioner distinguishes his meaning adequately, the answerer
is bound to reply either 'Yes' or 'No'. 

If any one is going to suppose that an argument which turns upon ambiguity
is a refutation, it will be impossible for an answerer to escape being
refuted in a sense: for in the case of visible objects one is bound
of necessity to deny the term one has asserted, and to assert what
one has denied. For the remedy which some people have for this is
quite unavailing. They say, not that Coriscus is both musical and
unmusical, but that this Coriscus is musical and this Coriscus unmusical.
But this will not do, for to say 'this Coriscus is unmusical', or
'musical', and to say 'this Coriscus' is so, is to use the same expression:
and this he is both affirming and denying at once. 'But perhaps they
do not mean the same.' Well, nor did the simple name in the former
case: so where is the difference? If, however, he is to ascribe to
the one person the simple title 'Coriscus', while to the other he
is to add the prefix 'one' or 'this', he commits an absurdity: for
the latter is no more applicable to the one than to the other: for
to whichever he adds it, it makes no difference. 

All the same, since if a man does not distinguish the senses of an
amphiboly, it is not clear whether he has been confuted or has not
been confuted, and since in arguments the right to distinguish them
is granted, it is evident that to grant the question simply without
drawing any distinction is a mistake, so that, even if not the man
himself, at any rate his argument looks as though it had been refuted.
It often happens, however, that, though they see the amphiboly, people
hesitate to draw such distinctions, because of the dense crowd of
persons who propose questions of the kind, in order that they may
not be thought to be obstructionists at every turn: then, though they
would never have supposed that that was the point on which the argument
turned, they often find themselves faced by a paradox. Accordingly,
since the right of drawing the distinction is granted, one should
not hesitate, as has been said before. 

If people never made two questions into one question, the fallacy
that turns upon ambiguity and amphiboly would not have existed either,
but either genuine refutation or none. For what is the difference
between asking 'Are Callias and Themistocles musical?' and what one
might have asked if they, being different, had had one name? For if
the term applied means more than one thing, he has asked more than
one question. If then it be not right to demand simply to be given
a single answer to two questions, it is evident that it is not proper
to give a simple answer to any ambiguous question, not even if the
predicate be true of all the subjects, as some claim that one should.
For this is exactly as though he had asked 'Are Coriscus and Callias
at home or not at home?', supposing them to be both in or both out:
for in both cases there is a number of propositions: for though the
simple answer be true, that does not make the question one. For it
is possible for it to be true to answer even countless different questions
when put to one, all together with either a 'Yes' or a 'No': but still
one should not answer them with a single answer: for that is the death
of discussion. Rather, the case is like as though different things
has actually had the same name applied to them. If then, one should
not give a single answer to two questions, it is evident that we should
not say simply 'Yes' or 'No' in the case of ambiguous terms either:
for the remark is simply a remark, not an answer at all, although
among disputants such remarks are loosely deemed to be answers, because
they do not see what the consequence is. 

As we said, then, inasmuch as certain refutations are generally taken
for such, though not such really, in the same way also certain solutions
will be generally taken for solutions, though not really such. Now
these, we say, must sometimes be advanced rather than the true solutions
in contentious reasonings and in the encounter with ambiguity. The
proper answer in saying what one thinks is to say 'Granted'; for in
that way the likelihood of being refuted on a side issue is minimized.
If, on the other hand, one is compelled to say something paradoxical,
one should then be most careful to add that 'it seems' so: for in
that way one avoids the impression of being either refuted or paradoxical.
Since it is clear what is meant by 'begging the original question',
and people think that they must at all costs overthrow the premisses
that lie near the conclusion, and plead in excuse for refusing to
grant him some of them that he is begging the original question, so
whenever any one claims from us a point such as is bound to follow
as a consequence from our thesis, but is false or paradoxical, we
must plead the same: for the necessary consequences are generally
held to be a part of the thesis itself. Moreover, whenever the universal
has been secured not under a definite name, but by a comparison of
instances, one should say that the questioner assumes it not in the
sense in which it was granted nor in which he proposed it in the premiss:
for this too is a point upon which a refutation often depends.

If one is debarred from these defences one must pass to the argument
that the conclusion has not been properly shown, approaching it in
the light of the aforesaid distinction between the different kinds
of fallacy. 

In the case, then, of names that are used literally one is bound to
answer either simply or by drawing a distinction: the tacit understandings
implied in our statements, e.g. in answer to questions that are not
put clearly but elliptically-it is upon this that the consequent refutation
depends. For example, 'Is what belongs to Athenians the property of
Athenians?' Yes. 'And so it is likewise in other cases. But observe;
man belongs to the animal kingdom, doesn't he?' Yes. 'Then man is
the property of the animal kingdom.' But this is a fallacy: for we
say that man 'belongs to' the animal kingdom because he is an animal,
just as we say that Lysander 'belongs to' the Spartans, because he
is a Spartan. It is evident, then, that where the premiss put forward
is not clear, one must not grant it simply. 

Whenever of two things it is generally thought that if the one is
true the other is true of necessity, whereas, if the other is true,
the first is not true of necessity, one should, if asked which of
them is true, grant the smaller one: for the larger the number of
premisses, the harder it is to draw a conclusion from them. If, again,
the sophist tries to secure that has a contrary while B has not, suppose
what he says is true, you should say that each has a contrary, only
for the one there is no established name. 

Since, again, in regard to some of the views they express, most people
would say that any one who did not admit them was telling a falsehood,
while they would not say this in regard to some, e.g. to any matters
whereon opinion is divided (for most people have no distinct view
whether the soul of animals is destructible or immortal), accordingly
(1) it is uncertain in which of two senses the premiss proposed is
usually meant-whether as maxims are (for people call by the name of
'maxims' both true opinions and general assertions) or like the doctrine
'the diagonal of a square is incommensurate with its side': and moreover
(2) whenever opinions are divided as to the truth, we then have subjects
of which it is very easy to change the terminology undetected. For
because of the uncertainty in which of the two senses the premiss
contains the truth, one will not be thought to be playing any trick,
while because of the division of opinion, one will not be thought
to be telling a falsehood. Change the terminology therefore, for the
change will make the position irrefutable. 

Moreover, whenever one foresees any question coming, one should put
in one's objection and have one's say beforehand: for by doing so
one is likely to embarrass the questioner most effectually.

==== Part 18 ====


Inasmuch as a proper solution is an exposure of false reasoning, showing
on what kind of question the falsity depends, and whereas 'false reasoning'
has a double meaning-for it is used either if a false conclusion has
been proved, or if there is only an apparent proof and no real one-there
must be both the kind of solution just described,' and also the correction
of a merely apparent proof, so as to show upon which of the questions
the appearance depends. Thus it comes about that one solves arguments
that are properly reasoned by demolishing them, whereas one solves
merely apparent arguments by drawing distinctions. Again, inasmuch
as of arguments that are properly reasoned some have a true and others
a false conclusion, those that are false in respect of their conclusion
it is possible to solve in two ways; for it is possible both by demolishing
one of the premisses asked, and by showing that the conclusion is
not the real state of the case: those, on the other hand, that are
false in respect of the premisses can be solved only by a demolition
of one of them; for the conclusion is true. So that those who wish
to solve an argument should in the first place look and see if it
is properly reasoned, or is unreasoned; and next, whether the conclusion
be true or false, in order that we may effect the solution either
by drawing some distinction or by demolishing something, and demolishing
it either in this way or in that, as was laid down before. There is
a very great deal of difference between solving an argument when being
subjected to questions and when not: for to foresee traps is difficult,
whereas to see them at one's leisure is easier. 

==== Part 19 ====


Of the refutations, then, that depend upon ambiguity and amphiboly
some contain some question with more than one meaning, while others
contain a conclusion bearing a number of senses: e.g. in the proof
that 'speaking of the silent' is possible, the conclusion has a double
meaning, while in the proof that 'he who knows does not understand
what he knows' one of the questions contains an amphiboly. Also the
double-edged saying is true in one context but not in another: it
means something that is and something that is not. 

Whenever, then, the many senses lie in the conclusion no refutation
takes place unless the sophist secures as well the contradiction of
the conclusion he means to prove; e.g. in the proof that 'seeing of
the blind' is possible: for without the contradiction there was no
refutation. Whenever, on the other hand, the many senses lie in the
questions, there is no necessity to begin by denying the double-edged
premiss: for this was not the goal of the argument but only its support.
At the start, then, one should reply with regard to an ambiguity,
whether of a term or of a phrase, in this manner, that 'in one sense
it is so, and in another not so', as e.g. that 'speaking of the silent'
is in one sense possible but in another not possible: also that in
one sense 'one should do what must needs be done', but not in another:
for 'what must needs be' bears a number of senses. If, however, the
ambiguity escapes one, one should correct it at the end by making
an addition to the question: 'Is speaking of the silent possible?'
'No, but to speak of while he is silent is possible.' Also, in cases
which contain the ambiguity in their premisses, one should reply in
like manner: 'Do people-then not understand what they know? "Yes,
but not those who know it in the manner described': for it is not
the same thing to say that 'those who know cannot understand what
they know', and to say that 'those who know something in this particular
manner cannot do so'. In general, too, even though he draws his conclusion
in a quite unambiguous manner, one should contend that what he has
negated is not the fact which one has asserted but only its name;
and that therefore there is no refutation. 

==== Part 20 ====


It is evident also how one should solve those refutations that depend
upon the division and combination of words: for if the expression
means something different when divided and when combined, as soon
as one's opponent draws his conclusion one should take the expression
in the contrary way. All such expressions as the following depend
upon the combination or division of the words: 'Was X being beaten
with that with which you saw him being beaten?' and 'Did you see him
being beaten with that with which he was being beaten?' This fallacy
has also in it an element of amphiboly in the questions, but it really
depends upon combination. For the meaning that depends upon the division
of the words is not really a double meaning (for the expression when
divided is not the same), unless also the word that is pronounced,
according to its breathing, as eros and eros is a case of double meaning.
(In writing, indeed, a word is the same whenever it is written of
the same letters and in the same manner- and even there people nowadays
put marks at the side to show the pronunciation- but the spoken words
are not the same.) Accordingly an expression that depends upon division
is not an ambiguous one. It is evident also that not all refutations
depend upon ambiguity as some people say they do. 

The answerer, then, must divide the expression: for 'I-saw-a-man-being-beaten
with my eyes' is not the same as to say 'I saw a man being-beaten-with-my-eyes'.
Also there is the argument of Euthydemus proving 'Then you know now
in Sicily that there are triremes in Piraeus': and again, 'Can a good
man who is a cobbler be bad?' 'No.' 'But a good man may be a bad cobbler:
therefore a good cobbler will be bad.' Again, 'Things the knowledge
of which is good, are good things to learn, aren't they?' 'Yes.' 'The
knowledge, however, of evil is good: therefore evil is a good thing
to know.' 'Yes. But, you see, evil is both evil and a thing-to-learn,
so that evil is an evil-thing-to-learn, although the knowledge of
evils is good.' Again, 'Is it true to say in the present moment that
you are born?' 'Yes.' 'Then you are born in the present moment.' 'No;
the expression as divided has a different meaning: for it is true
to say-in-the-present-moment that "you are born", but not "You are
born-in-the-present-moment".' Again, 'Could you do what you can, and
as you can?' 'Yes.' 'But when not harping, you have the power to harp:
and therefore you could harp when not harping.' 'No: he has not the
power to harp-while-not-harping; merely, when he is not doing it,
he has the power to do it.' Some people solve this last refutation
in another way as well. For, they say, if he has granted that he can
do anything in the way he can, still it does not follow that he can
harp when not harping: for it has not been granted that he will do
anything in every way in which he can; and it is not the same thing'
to do a thing in the way he can' and 'to do it in every way in which
he can'. But evidently they do not solve it properly: for of arguments
that depend upon the same point the solution is the same, whereas
this will not fit all cases of the kind nor yet all ways of putting
the questions: it is valid against the questioner, but not against
his argument. 

----------------------------------------------------------------------

===== SECTION 3 =====


==== Part 21 ====
 

Accentuation gives rise to no fallacious arguments, either as written
or as spoken, except perhaps some few that might be made up; e.g.
the following argument. 'Is ou katalueis a house?' 'Yes.' 'Is then
ou katalueis the negation of katalueis?' 'Yes.' 'But you said that
ou katalueis is a house: therefore the house is a negation.' How one
should solve this, is clear: for the word does not mean the same when
spoken with an acuter and when spoken with a graver accent.

==== Part 22 ====


It is clear also how one must meet those fallacies that depend on
the identical expressions of things that are not identical, seeing
that we are in possession of the kinds of predications. For the one
man, say, has granted, when asked, that a term denoting a substance
does not belong as an attribute, while the other has shown that some
attribute belongs which is in the Category of Relation or of Quantity,
but is usually thought to denote a substance because of its expression;
e.g. in the following argument: 'Is it possible to be doing and to
have done the same thing at the same time?' 'No.' 'But, you see, it
is surely possible to be seeing and to have seen the same thing at
the same time, and in the same aspect.' Again, 'Is any mode of passivity
a mode of activity?' 'No.' 'Then "he is cut", "he is burnt", "he is
struck by some sensible object" are alike in expression and all denote
some form of passivity, while again "to say", "to run", "to see" are
like one like one another in expression: but, you see, "to see" is
surely a form of being struck by a sensible object; therefore it is
at the same time a form of passivity and of activity.' Suppose, however,
that in that case any one, after granting that it is not possible
to do and to have done the same thing in the same time, were to say
that it is possible to see and to have seen it, still he has not yet
been refuted, suppose him to say that 'to see' is not a form of 'doing'
(activity) but of 'passivity': for this question is required as well,
though he is supposed by the listener to have already granted it,
when he granted that 'to cut' is a form of present, and 'to have cut'
a form of past, activity, and so on with the other things that have
a like expression. For the listener adds the rest by himself, thinking
the meaning to be alike: whereas really the meaning is not alike,
though it appears to be so because of the expression. The same thing
happens here as happens in cases of ambiguity: for in dealing with
ambiguous expressions the tyro in argument supposes the sophist to
have negated the fact which he (the tyro) affirmed, and not merely
the name: whereas there still wants the question whether in using
the ambiguous term he had a single meaning in view: for if he grants
that that was so, the refutation will be effected. 

Like the above are also the following arguments. It is asked if a
man has lost what he once had and afterwards has not: for a man will
no longer have ten dice even though he has only lost one die. No:
rather it is that he has lost what he had before and has not now;
but there is no necessity for him to have lost as much or as many
things as he has not now. So then, he asks the questions as to what
he has, and draws the conclusion as to the whole number that he has:
for ten is a number. If then he had asked to begin with, whether a
man no longer having the number of things he once had has lost the
whole number, no one would have granted it, but would have said 'Either
the whole number or one of them'. Also there is the argument that
'a man may give what he has not got': for he has not got only one
die. No: rather it is that he has given not what he had not got, but
in a manner in which he had not got it, viz. just the one. For the
word 'only' does not signify a particular substance or quality or
number, but a manner relation, e.g. that it is not coupled with any
other. It is therefore just as if he had asked 'Could a man give what
he has not got?' and, on being given the answer 'No', were to ask
if a man could give a thing quickly when he had not got it quickly,
and, on this being granted, were to conclude that 'a man could give
what he had not got'. It is quite evident that he has not proved his
point: for to 'give quickly' is not to give a thing, but to give in
a certain manner; and a man could certainly give a thing in a manner
in which he has not got it, e.g. he might have got it with pleasure
and give it with pain. 

Like these are also all arguments of the following kind: 'Could a
man strike a blow with a hand which he has not got, or see with an
eye which he has not got?' For he has not got only one eye. Some people
solve this case, where a man has more than one eye, or more than one
of anything else, by saying also that he has only one. Others also
solve it as they solve the refutation of the view that 'what a man
has, he has received': for A gave only one vote; and certainly B,
they say, has only one vote from A. Others, again, proceed by demolishing
straight away the proposition asked, and admitting that it is quite
possible to have what one has not received; e.g. to have received
sweet wine, but then, owing to its going bad in the course of receipt,
to have it sour. But, as was said also above,' all these persons direct
their solutions against the man, not against his argument. For if
this were a genuine solution, then, suppose any one to grant the opposite,
he could find no solution, just as happens in other cases; e.g. suppose
the true solution to be 'So-and-so is partly true and partly not',
then, if the answerer grants the expression without any qualification,
the sophist's conclusion follows. If, on the other hand, the conclusion
does not follow, then that could not be the true solution: and what
we say in regard to the foregoing examples is that, even if all the
sophist's premisses be granted, still no proof is effected.

Moreover, the following too belong to this group of arguments. 'If
something be in writing did some one write it?' 'Yes.' 'But it is
now in writing that you are seated-a false statement, though it was
true at the time when it was written: therefore the statement that
was written is at the same time false and true.' But this is fallacious,
for the falsity or truth of a statement or opinion indicates not a
substance but a quality: for the same account applies to the case
of an opinion as well. Again, 'Is what a learner learns what he learns?'
'Yes.' 'But suppose some one learns "slow" quick'. Then his (the sophist's)
words denote not what the learner learns but how he learns it. Also,
'Does a man tread upon what he walks through? 'Yes.' 'But X walks
through a whole day.' No, rather the words denote not what he walks
through, but when he walks; just as when any one uses the words 'to
drink the cup' he denotes not what he drinks, but the vessel out of
which he drinks. Also, 'Is it either by learning or by discovery that
a man knows what he knows?' 'Yes.' 'But suppose that of a pair of
things he has discovered one and learned the other, the pair is not
known to him by either method.' No: 'what' he knows, means' every
single thing' he knows, individually; but this does not mean 'all
the things' he knows, collectively. Again, there is the proof that
there is a 'third man' distinct from Man and from individual men.
But that is a fallacy, for 'Man', and indeed every general predicate,
denotes not an individual substance, but a particular quality, or
the being related to something in a particular manner, or something
of that sort. Likewise also in the case of 'Coriscus' and 'Coriscus
the musician' there is the problem, Are they the same or different?'
For the one denotes an individual substance and the other a quality,
so that it cannot be isolated; though it is not the isolation which
creates the 'third man', but the admission that it is an individual
substance. For 'Man' cannot be an individual substance, as Callias
is. Nor is the case improved one whit even if one were to call the
clement he has isolated not an individual substance but a quality:
for there will still be the one beside the many, just as 'Man' was.
It is evident then that one must not grant that what is a common predicate
applying to a class universally is an individual substance, but must
say that denotes either a quality, or a relation, or a quantity, or
something of that kind. 

==== Part 23 ====


It is a general rule in dealing with arguments that depend on language
that the solution always follows the opposite of the point on which
the argument turns: e.g. if the argument depends upon combination,
then the solution consists in division; if upon division, then in
combination. Again, if it depends on an acute accent, the solution
is a grave accent; if on a grave accent, it is an acute. If it depends
on ambiguity, one can solve it by using the opposite term; e.g. if
you find yourself calling something inanimate, despite your previous
denial that it was so, show in what sense it is alive: if, on the
other hand, one has declared it to be inanimate and the sophist has
proved it to be animate, say how it is inanimate. Likewise also in
a case of amphiboly. If the argument depends on likeness of expression,
the opposite will be the solution. 'Could a man give what he has not
got? 'No, not what he has not got; but he could give it in a way in
which he has not got it, e.g. one die by itself.' Does a man know
either by learning or by discovery each thing that he knows, singly?
but not the things that he knows, collectively.' Also a man treads,
perhaps, on any thing he walks through, but not on the time he walks
through. Likewise also in the case of the other examples.

==== Part 24 ====


In dealing with arguments that depend on Accident, one and the same
solution meets all cases. For since it is indeterminate when an attribute
should be ascribed to a thing, in cases where it belongs to the accident
of the thing, and since in some cases it is generally agreed and people
admit that it belongs, while in others they deny that it need belong,
we should therefore, as soon as the conclusion has been drawn, say
in answer to them all alike, that there is no need for such an attribute
to belong. One must, however, be prepared to adduce an example of
the kind of attribute meant. All arguments such as the following depend
upon Accident. 'Do you know what I am going to ask you? you know the
man who is approaching', or 'the man in the mask'? 'Is the statue
your work of art?' or 'Is the dog your father?' 'Is the product of
a small number with a small number a small number?' For it is evident
in all these cases that there is no necessity for the attribute which
is true of the thing's accident to be true of the thing as well. For
only to things that are indistinguishable and one in essence is it
generally agreed that all the same attributes belong; whereas in the
case of a good thing, to be good is not the same as to be going to
be the subject of a question; nor in the case of a man approaching,
or wearing a mask, is 'to be approaching' the same thing as 'to be
Coriscus', so that suppose I know Coriscus, but do not know the man
who is approaching, it still isn't the case that I both know and do
not know the same man; nor, again, if this is mine and is also a work
of art, is it therefore my work of art, but my property or thing or
something else. (The solution is after the same manner in the other
cases as well.) 

Some solve these refutations by demolishing the original proposition
asked: for they say that it is possible to know and not to know the
same thing, only not in the same respect: accordingly, when they don't
know the man who is coming towards them, but do know Corsicus, they
assert that they do know and don't know the same object, but not in
the same respect. Yet, as we have already remarked, the correction
of arguments that depend upon the same point ought to be the same,
whereas this one will not stand if one adopts the same principle in
regard not to knowing something, but to being, or to being is a in
a certain state, e.g. suppose that X is father, and is also yours:
for if in some cases this is true and it is possible to know and not
to know the same thing, yet with that case the solution stated has
nothing to do. Certainly there is nothing to prevent the same argument
from having a number of flaws; but it is not the exposition of any
and every fault that constitutes a solution: for it is possible for
a man to show that a false conclusion has been proved, but not to
show on what it depends, e.g. in the case of Zeno's argument to prove
that motion is impossible. So that even if any one were to try to
establish that this doctrine is an impossible one, he still is mistaken,
and even if he proved his case ten thousand times over, still this
is no solution of Zeno's argument: for the solution was all along
an exposition of false reasoning, showing on what its falsity depends.
If then he has not proved his case, or is trying to establish even
a true proposition, or a false one, in a false manner, to point this
out is a true solution. Possibly, indeed, the present suggestion may
very well apply in some cases: but in these cases, at any rate, not
even this would be generally agreed: for he knows both that Coriscus
is Coriscus and that the approaching figure is approaching. To know
and not to know the same thing is generally thought to be possible,
when e.g. one knows that X is white, but does not realize that he
is musical: for in that way he does know and not know the same thing,
though not in the same respect. But as to the approaching figure and
Coriscus he knows both that it is approaching and that he is Coriscus.

A like mistake to that of those whom we have mentioned is that of
those who solve the proof that every number is a small number: for
if, when the conclusion is not proved, they pass this over and say
that a conclusion has been proved and is true, on the ground that
every number is both great and small, they make a mistake.

Some people also use the principle of ambiguity to solve the aforesaid
reasonings, e.g. the proof that 'X is your father', or 'son', or 'slave'.
Yet it is evident that if the appearance a proof depends upon a plurality
of meanings, the term, or the expression in question, ought to bear
a number of literal senses, whereas no one speaks of A as being 'B's
child' in the literal sense, if B is the child's master, but the combination
depends upon Accident. 'Is A yours?' 'Yes.' 'And is A a child?' 'Yes.'
'Then the child A is yours,' because he happens to be both yours and
a child; but he is not 'your child'. 

There is also the proof that 'something "of evils" is good'; for wisdom
is a 'knowledge "of evils"'. But the expression that this is 'of so
and-so' (='so-and-so's') has not a number of meanings: it means that
it is 'so-and-so's property'. We may suppose of course, on the other
hand, that it has a number of meanings-for we also say that man is
'of the animals', though not their property; and also that any term
related to 'evils' in a way expressed by a genitive case is on that
account a so-and-so 'of evils', though it is not one of the evils-but
in that case the apparently different meanings seem to depend on whether
the term is used relatively or absolutely. 'Yet it is conceivably
possible to find a real ambiguity in the phrase "Something of evils
is good".' Perhaps, but not with regard to the phrase in question.
It would occur more nearly, suppose that 'A servant is good of the
wicked'; though perhaps it is not quite found even there: for a thing
may be 'good' and be 'X's' without being at the same time 'X's good'.
Nor is the saying that 'Man is of the animals' a phrase with a number
of meanings: for a phrase does not become possessed of a number of
meanings merely suppose we express it elliptically: for we express
'Give me the Iliad' by quoting half a line of it, e.g. 'Give me "Sing,
goddess, of the wrath..."' 

==== Part 25 ====


Those arguments which depend upon an expression that is valid of a
particular thing, or in a particular respect, or place, or manner,
or relation, and not valid absolutely, should be solved by considering
the conclusion in relation to its contradictory, to see if any of
these things can possibly have happened to it. For it is impossible
for contraries and opposites and an affirmative and a negative to
belong to the same thing absolutely; there is, however, nothing to
prevent each from belonging in a particular respect or relation or
manner, or to prevent one of them from belonging in a particular respect
and the other absolutely. So that if this one belongs absolutely and
that one in a particular respect, there is as yet no refutation. This
is a feature one has to find in the conclusion by examining it in
comparison with its contradictory. 

All arguments of the following kind have this feature: 'Is it possible
for what is-not to be? "No." But, you see, it is something, despite
its not being.' Likewise also, Being will not be; for it will not
he some particular form of being. Is it possible for the same man
at the same time to be a keeper and a breaker of his oath?' 'Can the
same man at the same time both obey and disobey the same man?' Or
isn't it the case that being something in particular and Being are
not the same? On the other hand, Not-being, even if it be something,
need not also have absolute 'being' as well. Nor if a man keeps his
oath in this particular instance or in this particular respect, is
he bound also to be a keeper of oaths absolutely, but he who swears
that he will break his oath, and then breaks it, keeps this particular
oath only; he is not a keeper of his oath: nor is the disobedient
man 'obedient', though he obeys one particular command. The argument
is similar, also, as regards the problem whether the same man can
at the same time say what is both false and true: but it appears to
be a troublesome question because it is not easy to see in which of
the two connexions the word 'absolutely' is to be rendered-with 'true'
or with 'false'. There is, however, nothing to prevent it from being
false absolutely, though true in some particular respect or relation,
i.e. being true in some things, though not 'true' absolutely. Likewise
also in cases of some particular relation and place and time. For
all arguments of the following kind depend upon this.' Is health,
or wealth, a good thing?' 'Yes.' 'But to the fool who does not use
it aright it is not a good thing: therefore it is both good and not
good.' 'Is health, or political power, a good thing?' 'Yes. "But sometimes
it is not particularly good: therefore the same thing is both good
and not good to the same man.' Or rather there is nothing to prevent
a thing, though good absolutely, being not good to a particular man,
or being good to a particular man, and yet not good or here. 'Is that
which the prudent man would not wish, an evil?' 'Yes.' 'But to get
rid of, he would not wish the good: therefore the good is an evil.'
But that is a mistake; for it is not the same thing to say 'The good
is an evil' and 'to get rid of the good is an evil'. Likewise also
the argument of the thief is mistaken. For it is not the case that
if the thief is an evil thing, acquiring things is also evil: what
he wishes, therefore, is not what is evil but what is good; for to
acquire something good is good. Also, disease is an evil thing, but
not to get rid of disease. 'Is the just preferable to the unjust,
and what takes place justly to what takes place unjustly? 'Yes.' 'But
to to be put to death unjustly is preferable.' 'Is it just that each
should have his own?' 'Yes.' 'But whatever decisions a man comes to
on the strength of his personal opinion, even if it be a false opinion,
are valid in law: therefore the same result is both just and unjust.'
Also, should one decide in favour of him who says what is unjust?'
'The former.' 'But you see, it is just for the injured party to say
fully the things he has suffered; and these are fallacies. For because
to suffer a thing unjustly is preferable, unjust ways are not therefore
preferable, though in this particular case the unjust may very well
be better than the just. Also, to have one's own is just, while to
have what is another's is not just: all the same, the decision in
question may very well be a just decision, whatever it be that the
opinion of the man who gave the decision supports: for because it
is just in this particular case or in this particular manner, it is
not also just absolutely. Likewise also, though things are unjust,
there is nothing to prevent the speaking of them being just: for because
to speak of things is just, there is no necessity that the things
should be just, any more than because to speak of things be of use,
the things need be of use. Likewise also in the case of what is just.
So that it is not the case that because the things spoken of are unjust,
the victory goes to him who speaks unjust things: for he speaks of
things that are just to speak of, though absolutely, i.e. to suffer,
they are unjust. 

==== Part 26 ====


Refutations that depend on the definition of a refutation must, according
to the plan sketched above, be met by comparing together the conclusion
with its contradictory, and seeing that it shall involve the same
attribute in the same respect and relation and manner and time. If
this additional question be put at the start, you should not admit
that it is impossible for the same thing to be both double and not
double, but grant that it is possible, only not in such a way as was
agreed to constitute a refutation of your case. All the following
arguments depend upon a point of that kind. 'Does a man who knows
A to be A, know the thing called A?' and in the same way, 'is one
who is ignorant that A is A ignorant of the thing called A?' 'Yes.'
'But one who knows that Coriscus is Coriscus might be ignorant of
the fact that he is musical, so that he both knows and is ignorant
of the same thing.' Is a thing four cubits long greater than a thing
three cubits long?' 'Yes.' 'But a thing might grow from three to four
cubits in length; 'now what is 'greater' is greater than a 'less':
accordingly the thing in question will be both greater and less than
itself in the same respect. 

==== Part 27 ====


As to refutations that depend on begging and assuming the original
point to be proved, suppose the nature of the question to be obvious,
one should not grant it, even though it be a view generally held,
but should tell him the truth. Suppose, however, that it escapes one,
then, thanks to the badness of arguments of that kind, one should
make one's error recoil upon the questioner, and say that he has brought
no argument: for a refutation must be proved independently of the
original point. Secondly, one should say that the point was granted
under the impression that he intended not to use it as a premiss,
but to reason against it, in the opposite way from that adopted in
refutations on side issues. 

==== Part 28 ====


Also, those refutations that bring one to their conclusion through
the consequent you should show up in the course of the argument itself.
The mode in which consequences follow is twofold. For the argument
either is that as the universal follows on its particular-as (e.g.)
'animal' follows from 'man'-so does the particular on its universal:
for the claim is made that if A is always found with B, then B also
is always found with A. Or else it proceeds by way of the opposites
of the terms involved: for if A follows B, it is claimed that A's
opposite will follow B's opposite. On this latter claim the argument
of Melissus also depends: for he claims that because that which has
come to be has a beginning, that which has not come to be has none,
so that if the heaven has not come to be, it is also eternal. But
that is not so; for the sequence is vice versa. 

==== Part 29 ====


In the case of any refutations whose reasoning depends on some addition,
look and see if upon its subtraction the absurdity follows none the
less: and then if so, the answerer should point this out, and say
that he granted the addition not because he really thought it, but
for the sake of the argument, whereas the questioner has not used
it for the purpose of his argument at all. 

==== Part 30 ====


To meet those refutations which make several questions into one, one
should draw a distinction between them straight away at the start.
For a question must be single to which there is a single answer, so
that one must not affirm or deny several things of one thing, nor
one thing of many, but one of one. But just as in the case of ambiguous
terms, an attribute belongs to a term sometimes in both its senses,
and sometimes in neither, so that a simple answer does one, as it
happens, no harm despite the fact that the question is not simple,
so it is in these cases of double questions too. Whenever, then, the
several attributes belong to the one subject, or the one to the many,
the man who gives a simple answer encounters no obstacle even though
he has committed this mistake: but whenever an attribute belongs to
one subject but not to the other, or there is a question of a number
of attributes belonging to a number of subjects and in one sense both
belong to both, while in another sense, again, they do not, then there
is trouble, so that one must beware of this. Thus (e.g.) in the following
arguments: Supposing to be good and B evil, you will, if you give
a single answer about both, be compelled to say that it is true to
call these good, and that it is true to call them evil and likewise
to call them neither good nor evil (for each of them has not each
character), so that the same thing will be both good and evil and
neither good nor evil. Also, since everything is the same as itself
and different from anything else, inasmuch as the man who answers
double questions simply can be made to say that several things are
'the same' not as other things but 'as themselves', and also that
they are different from themselves, it follows that the same things
must be both the same as and different from themselves. Moreover,
if what is good becomes evil while what is evil is good, then they
must both become two. So of two unequal things each being equal to
itself, it will follow that they are both equal and unequal to themselves.

Now these refutations fall into the province of other solutions as
well: for 'both' and 'all' have more than one meaning, so that the
resulting affirmation and denial of the same thing does not occur,
except verbally: and this is not what we meant by a refutation. But
it is clear that if there be not put a single question on a number
of points, but the answerer has affirmed or denied one attribute only
of one subject only, the absurdity will not come to pass.

==== Part 31 ====


With regard to those who draw one into repeating the same thing a
number of times, it is clear that one must not grant that predications
of relative terms have any meaning in abstraction by themselves, e.g.
that 'double' is a significant term apart from the whole phrase 'double
of half' merely on the ground that it figures in it. For ten figures
in 'ten minus one' and in 'not do', and generally the affirmation
in the negation; but for all that, suppose any one were to say, 'This
is not white', he does not say that it is white. The bare word 'double',
one may perhaps say, has not even any meaning at all, any more than
has 'the' in 'the half': and even if it has a meaning, yet it has
not the same meaning as in the combination. Nor is 'knowledge' the
same thing in a specific branch of it (suppose it, e.g. to be 'medical
knowledge') as it is in general: for in general it was the 'knowledge
of the knowable'. In the case of terms that are predicated of the
terms through which they are defined, you should say the same thing,
that the term defined is not the same in abstraction as it is in the
whole phrase. For 'concave' has a general meaning which is the same
in the case of a snub nose, and of a bandy leg, but when added to
either substantive nothing prevents it from differentiating its meaning;
in fact it bears one sense as applied to the nose, and another as
applied to the leg: for in the former connexion it means 'snub' and
in the latter 'bandyshaped'; i.e. it makes no difference whether you
say 'a snub nose' or 'a concave nose'. Moreover, the expression must
not be granted in the nominative case: for it is a falsehood. For
snubness is not a concave nose but something (e.g. an affection) belonging
to a nose: hence, there is no absurdity in supposing that the snub
nose is a nose possessing the concavity that belongs to a nose.

==== Part 32 ====


With regard to solecisms, we have previously said what it is that
appears to bring them about; the method of their solution will be
clear in the course of the arguments themselves. Solecism is the result
aimed at in all arguments of the following kind: 'Is a thing truly
that which you truly call it?' 'Yes'. 'But, speaking of a stone, you
call him real: therefore of a stone it follows that "him is real".'
No: rather, talking of a stone means not saying which' but 'whom',
and not 'that' but 'him'. If, then, any one were to ask, 'Is a stone
him whom you truly call him?' he would be generally thought not to
be speaking good Greek, any more than if he were to ask, 'Is he what
you call her?' Speak in this way of a 'stick' or any neuter word,
and the difference does not break out. For this reason, also, no solecism
is incurred, suppose any one asks, 'Is a thing what you say it to
be?' 'Yes'. 'But, speaking of a stick, you call it real: therefore,
of a stick it follows that it is real.' 'Stone', however, and 'he'
have masculine designations. Now suppose some one were to ask, 'Can
"he" be a she" (a female)?', and then again, 'Well, but is not he
Coriscus?' and then were to say, 'Then he is a "she",' he has not
proved the solecism, even if the name 'Coriscus' does signify a 'she',
if, on the other hand, the answerer does not grant this: this point
must be put as an additional question: while if neither is it the
fact nor does he grant it, then the sophist has not proved his case
either in fact or as against the person he has been questioning. In
like manner, then, in the above instance as well it must be definitely
put that 'he' means the stone. If, however, this neither is so nor
is granted, the conclusion must not be stated: though it follows apparently,
because the case (the accusative), that is really unlike, appears
to be like the nominative. 'Is it true to say that this object is
what you call it by name?' 'Yes'. 'But you call it by the name of
a shield: this object therefore is "of a shield".' No: not necessarily,
because the meaning of 'this object' is not 'of a shield' but 'a shield':
'of a shield' would be the meaning of 'this object's'. Nor again if
'He is what you call him by name', while 'the name you call him by
is Cleon's', is he therefore 'Cleon's': for he is not 'Cleon's', for
what was said was that 'He, not his, is what I call him by name'.
For the question, if put in the latter way, would not even be Greek.
'Do you know this?' 'Yes.' 'But this is he: therefore you know he'.
No: rather 'this' has not the same meaning in 'Do you know this?'
as in 'This is a stone'; in the first it stands for an accusative,
in the second for a nominative case. 'When you have understanding
of anything, do you understand it?' 'Yes.' 'But you have understanding
of a stone: therefore you understand of a stone.' No: the one phrase
is in the genitive, 'of a stone', while the other is in the accusative,
'a stone': and what was granted was that 'you understand that, not
of that, of which you have understanding', so that you understand
not 'of a stone', but 'the stone'. 

Thus that arguments of this kind do not prove solecism but merely
appear to do so, and both why they so appear and how you should meet
them, is clear from what has been said. 

==== Part 33 ====


We must also observe that of all the arguments aforesaid it is easier
with some to see why and where the reasoning leads the hearer astray,
while with others it is more difficult, though often they are the
same arguments as the former. For we must call an argument the same
if it depends upon the same point; but the same argument is apt to
be thought by some to depend on diction, by others on accident, and
by others on something else, because each of them, when worked with
different terms, is not so clear as it was. Accordingly, just as in
fallacies that depend on ambiguity, which are generally thought to
be the silliest form of fallacy, some are clear even to the man in
the street (for humorous phrases nearly all depend on diction; e.g.
'The man got the cart down from the stand'; and 'Where are you bound?'
'To the yard arm'; and 'Which cow will calve afore?' 'Neither, but
both behind;' and 'Is the North wind clear?' 'No, indeed; for it has
murdered the beggar and the merchant." Is he a Good enough-King?'
'No, indeed; a Rob-son': and so with the great majority of the rest
as well), while others appear to elude the most expert (and it is
a symptom of this that they often fight about their terms, e.g. whether
the meaning of 'Being' and 'One' is the same in all their applications
or different; for some think that 'Being' and 'One' mean the same;
while others solve the argument of Zeno and Parmenides by asserting
that 'One' and 'Being' are used in a number of senses), likewise also
as regards fallacies of Accident and each of the other types, some
of the arguments will be easier to see while others are more difficult;
also to grasp to which class a fallacy belongs, and whether it is
a refutation or not a refutation, is not equally easy in all cases.

An incisive argument is one which produces the greatest perplexity:
for this is the one with the sharpest fang. Now perplexity is twofold,
one which occurs in reasoned arguments, respecting which of the propositions
asked one is to demolish, and the other in contentious arguments,
respecting the manner in which one is to assent to what is propounded.
Therefore it is in syllogistic arguments that the more incisive ones
produce the keenest heart-searching. Now a syllogistic argument is
most incisive if from premisses that are as generally accepted as
possible it demolishes a conclusion that is accepted as generally
as possible. For the one argument, if the contradictory is changed
about, makes all the resulting syllogisms alike in character: for
always from premisses that are generally accepted it will prove a
conclusion, negative or positive as the case may be, that is just
as generally accepted; and therefore one is bound to feel perplexed.
An argument, then, of this kind is the most incisive, viz. the one
that puts its conclusion on all fours with the propositions asked;
and second comes the one that argues from premisses, all of which
are equally convincing: for this will produce an equal perplexity
as to what kind of premiss, of those asked, one should demolish. Herein
is a difficulty: for one must demolish something, but what one must
demolish is uncertain. Of contentious arguments, on the other hand,
the most incisive is the one which, in the first place, is characterized
by an initial uncertainty whether it has been properly reasoned or
not; and also whether the solution depends on a false premiss or on
the drawing of a distinction; while, of the rest, the second place
is held by that whose solution clearly depends upon a distinction
or a demolition, and yet it does not reveal clearly which it is of
the premisses asked, whose demolition, or the drawing of a distinction
within it, will bring the solution about, but even leaves it vague
whether it is on the conclusion or on one of the premisses that the
deception depends. 

Now sometimes an argument which has not been properly reasoned is
silly, supposing the assumptions required to be extremely contrary
to the general view or false; but sometimes it ought not to be held
in contempt. For whenever some question is left out, of the kind that
concerns both the subject and the nerve of the argument, the reasoning
that has both failed to secure this as well, and also failed to reason
properly, is silly; but when what is omitted is some extraneous question,
then it is by no means to be lightly despised, but the argument is
quite respectable, though the questioner has not put his questions
well. 

Just as it is possible to bring a solution sometimes against the argument,
at others against the questioner and his mode of questioning, and
at others against neither of these, likewise also it is possible to
marshal one's questions and reasoning both against the thesis, and
against the answerer and against the time, whenever the solution requires
a longer time to examine than the period available. 

==== Part 34 ====


As to the number, then, and kind of sources whence fallacies arise
in discussion, and how we are to show that our opponent is committing
a fallacy and make him utter paradoxes; moreover, by the use of what
materials solescism is brought about, and how to question and what
is the way to arrange the questions; moreover, as to the question
what use is served by all arguments of this kind, and concerning the
answerer's part, both as a whole in general, and in particular how
to solve arguments and solecisms-on all these things let the foregoing
discussion suffice. It remains to recall our original proposal and
to bring our discussion to a close with a few words upon it.

Our programme was, then, to discover some faculty of reasoning about
any theme put before us from the most generally accepted premisses
that there are. For that is the essential task of the art of discussion
(dialectic) and of examination (peirastic). Inasmuch, however, as
it is annexed to it, on account of the near presence of the art of
sophistry (sophistic), not only to be able to conduct an examination
dialectically but also with a show of knowledge, we therefore proposed
for our treatise not only the aforesaid aim of being able to exact
an account of any view, but also the aim of ensuring that in standing
up to an argument we shall defend our thesis in the same manner by
means of views as generally held as possible. The reason of this we
have explained; for this, too, was why Socrates used to ask questions
and not to answer them; for he used to confess that he did not know.
We have made clear, in the course of what precedes, the number both
of the points with reference to which, and of the materials from which,
this will be accomplished, and also from what sources we can become
well supplied with these: we have shown, moreover, how to question
or arrange the questioning as a whole, and the problems concerning
the answers and solutions to be used against the reasonings of the
questioner. We have also cleared up the problems concerning all other
matters that belong to the same inquiry into arguments. In addition
to this we have been through the subject of Fallacies, as we have
already stated above. 

That our programme, then, has been adequately completed is clear.
But we must not omit to notice what has happened in regard to this
inquiry. For in the case of all discoveries the results of previous
labours that have been handed down from others have been advanced
bit by bit by those who have taken them on, whereas the original discoveries
generally make advance that is small at first though much more useful
than the development which later springs out of them. For it may be
that in everything, as the saying is, 'the first start is the main
part': and for this reason also it is the most difficult; for in proportion
as it is most potent in its influence, so it is smallest in its compass
and therefore most difficult to see: whereas when this is once discovered,
it is easier to add and develop the remainder in connexion with it.
This is in fact what has happened in regard to rhetorical speeches
and to practically all the other arts: for those who discovered the
beginnings of them advanced them in all only a little way, whereas
the celebrities of to-day are the heirs (so to speak) of a long succession
of men who have advanced them bit by bit, and so have developed them
to their present form, Tisias coming next after the first founders,
then Thrasymachus after Tisias, and Theodorus next to him, while several
people have made their several contributions to it: and therefore
it is not to be wondered at that the art has attained considerable
dimensions. Of this inquiry, on the other hand, it was not the case
that part of the work had been thoroughly done before, while part
had not. Nothing existed at all. For the training given by the paid
professors of contentious arguments was like the treatment of the
matter by Gorgias. For they used to hand out speeches to be learned
by heart, some rhetorical, others in the form of question and answer,
each side supposing that their arguments on either side generally
fall among them. And therefore the teaching they gave their pupils
was ready but rough. For they used to suppose that they trained people
by imparting to them not the art but its products, as though any one
professing that he would impart a form of knowledge to obviate any
pain in the feet, were then not to teach a man the art of shoe-making
or the sources whence he can acquire anything of the kind, but were
to present him with several kinds of shoes of all sorts: for he has
helped him to meet his need, but has not imparted an art to him. Moreover,
on the subject of Rhetoric there exists much that has been said long
ago, whereas on the subject of reasoning we had nothing else of an
earlier date to speak of at all, but were kept at work for a long
time in experimental researches. If, then, it seems to you after inspection
that, such being the situation as it existed at the start, our investigation
is in a satisfactory condition compared with the other inquiries that
have been developed by tradition, there must remain for all of you,
or for our students, the task of extending us your pardon for the
shortcomings of the inquiry, and for the discoveries thereof your
warm thanks. 

THE END