by Aristotle
Those that depend upon whether something is said in a certain respect only or said without qualification occur 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 without qualification it is not white, without qualification. If, then, a man treats the admission that a thing is white in a certain respect as though it were said to be white without qualification, he does not effect a refutation, but merely appears to do so owing to ignorance of what [15] 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 given their name.13 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 [20] ‘defect in 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 clear through the definition. 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 [25] arguments which depend upon postulating 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 a swan), whereas the consequent [30] 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. (But this is not always true, e.g. suppose that they are the same accidentally; for both snow and the swan are the same as something white.) Or again, as in Melissus’ argument, a man assumes that to have [35] 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 [169a1] 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 of ignorance of what a refutation is, clearly so also does a refutation depending on the [5] consequent. We shall have further to examine this in another way as well.14
Those fallacies that depend upon the making of several questions into one consist in our failure to articulate the account of a proposition. For a proposition predicates a single thing of a single thing. For the same definition applies to one single thing only and to the thing without qualification, e.g. to man and to one single [10] man only; and likewise also in other cases. If, then, a single proposition is one which claims a single thing of a single thing, a proposition, without qualification, will be the putting of a question of that kind. Now since a deduction starts from propositions and a refutation is a deduction, a refutation, too, will start from propositions. If, then, a proposition predicates a single thing of a single thing, it is obvious that this fallacy too consists in ignorance of what a refutation is; for in it [15] 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. All the types of fallacy,15 then, fall under ignorance of what a refutation is, those dependent [20] on language because the contradiction, which is the proper mark of a refutation, is merely apparent, and the rest because of the definition of a deduction.
7 · The error comes about in the case of arguments that depend on homonymy and the account16 because we are unable to distinguish the various senses (for some terms it is not easy to distinguish, e.g. one, being, and sameness), [25] while in those that depend on combination and division, it is because we suppose that it makes no difference whether the phrase is 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 pitch upon a phrase seems not to alter its meaning—with [30] any phrase, or not with many. With those that depend on the form 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, and knows best how to assent) because we suppose every predicate of anything to be an individual [35] thing, and we understand it as being one thing; for it is to that which is one and to substances that individuality and being seem especially to belong. For this reason, too, this type of fallacy is to be ranked among those that depend on language; in the first place, because the error 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 err, even when inquiring by himself, when he takes speech as the basis of his inquiry; [169b1] moreover the error arises out of the likeness, and the likeness arises out of the language. With those fallacies that depend upon accident, error comes about because we cannot distinguish what is the same and what is different, what is one and what many, or what kinds of predicate have all the same accidents as their [5] subject. Likewise also with those that depend on the consequent; for the consequent is a branch of accident. Moreover, in many cases it seems and it is claimed that if this is inseparable from that, so also is that from this. With those that depend upon deficiency in the account of a refutation, and with those that depend upon the [10] difference between a qualified and an unqualified statement, the error 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 error lies in the smallness of the difference; for our failure to be quite [15] precise in our definition of propositions and of deductions is due to the aforesaid reason.
8 · Since we know on how many points apparent deductions depend, we know also on how many sophistical deductions and refutations may depend. By a sophistical refutation and deduction I mean not only a deduction or refutation [20] 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 in respect of the object and which prove the answerer to be ignorant, which was the function of the art of examination. Now the art of examining is a branch of dialectic; and this may deduce a false conclusion because of the ignorance of the [25] answerer. Sophistic refutations on the other hand, even though they deduce the contradictory of his thesis, do not make clear whether he is ignorant; for even men of knowledge are entangled by these arguments.
That we know them by the same line of inquiry is clear; for the same [30] considerations which make it appear to an audience that the conclusion was deduced by way of the questions, would make the answerer think so as well, so that false deductions 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 the [35] falsity, e.g. in fallacies that depend on language and on solecism. If then fallacious arguments for the contradictory of a thesis depend on their appearing to refute, it is clear that the c
onsiderations on which both deductions of false conclusions and 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 [170a1] depends on the failure of the conclusion to follow from the argument (the argument ad impossibile) and that which treats two questions as one and so depends upon a flaw in the proposition, 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 [5] consequent; moreover, 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, in violation of the principle of not reckoning in the original point. Thus we should have [10] the number of considerations on which fallacies depend; for they could not depend on more, but all will depend on the points aforesaid.
A sophistical refutation is a refutation not without qualification but relatively to someone; and so is a deduction, in the same way. For unless that which depends upon homonymy assumes that the term has a single meaning, and that which [15] depends on similarity of form assumes that terms signify nothing but individuals, and the rest in the same way, they will be neither refutations nor deductions, either without qualification or relatively to the answerer; whereas if they do assume these things, they will be, relatively to the answerer; but they will not be without qualification; 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.
[20] 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 single 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 [25] 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, we shall have to have scientific knowledge of everything; for some refutations depend upon the principles of geometry and the conclusions that follow from these, others upon those of medicine, and others upon those of the other [30] sciences. For the matter of that, false refutations likewise belong to the number of the infinite; for in respect of every art there is false deduction, e.g. in respect of geometry there is a geometrical one, and in respect of medicine a medical. By in respect of the art, I mean in respect of its principles. Clearly, then, it is not of all refutations, but only of those that depend upon dialectic that we need to grasp the [35] commonplace rules; for these are common to every art and faculty. And as regards the refutation that is in respect of 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 is real, what is the reason for it; whereas it is the business of dialecticians so to examine the refutation that proceeds from common principles and falls under no particular study. For if we grasp the starting-points of the reputable deductions on any subject we grasp those of the refutations. For a [170b1] refutation is a deduction of the contradictory, so that either one or two deductions of the contradictory constitute a refutation. We grasp, then, the number of considerations on which all such depend; and if we grasp this, we 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—[5] 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 common principles, of a refutation that is either real or apparent, i.e. either [10] dialectical or apparently dialectical, or suitable for an examination.
10 · It is no true distinction between arguments which some people draw when they say that some arguments are directed against the word, and others against the thought; for it is absurd to suppose that some arguments are directed against the word and others against the thought, and that they are not the same. For [15] what is failure to direct an argument against the thought except what occurs whenever a man does not use the word in the sense about which the person being questioned thought he was being questioned when he made the concession? And this is the same thing as to direct the argument against the word. On the other hand, it is directed against the thought whenever a man uses the word in the sense which the answerer had in mind when he made the concession. If now anyone (i.e. both the questioner and the person questioned), in dealing with a word with more than one [20] 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 word than against the thought of the person questioned? If, on the other hand, someone [25] supposes the word to have many meanings, it is clear that such a discussion will not be directed against the thought. For direction against the word and against the thought applies primarily to those arguments which have several meanings, but secondarily to any argument whatsoever; for the fact of being directed against the thought depends not on the argument, but on the special attitude of the answerer towards the points he concedes. Next, all of them may be directed to the word. For [30] to be directed against the word is in this doctrine not to be directed against the thought. For if not all are directed against either word or thought, there will be certain other arguments directed neither against the word nor against the thought, whereas they say that all must be one or the other, and divide them all as directed either against the word or against the thought, while others (they say) there are none. But in point of fact those that depend on the word are a branch of those deductions that depend on a multiplicity of uses. For the absurd statement has [35] actually been made that the description ‘dependent on the word’ 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 use.
It is altogether absurd to discuss refutation without first discussing deduction; [171a1] for a refutation is a deduction, so that one ought to discuss deduction before describing false refutation; for a refutation of that kind is a merely apparent [5] deduction of the contradictory of a thesis. Accordingly, the reason of the falsity will be either in the deduction or in the contradiction (for mention of the contradiction must be added), while sometimes it is in both, if the refutation is merely apparent. In the argument that speaking of the silent is possible it lies in the contradiction, not in the deduction; in the argument that one can give what one does not possess, it lies [10] in both; in the argument that Homer’s poem is a figure through its being a cycle it lies in the deduction. An argument that does not fail in either respect is a true deduction.
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 [15] 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 name bears many senses, while the answerer does not understand or suppose it to have them, surely the questioner h
ere 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 ‘Is speaking of the silent [20] possible or not?’ or ‘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 word. There is not, then, any definite kind of arguments that is directed against the thought. Some arguments are, indeed, directed against the word; but these do not [25] include all 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 anyone requires 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 [30] to require this is in the first place absurd (for sometimes the question does not seem to have several uses, and you cannot possibly draw a distinction which you do 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 use. For what is there to prevent the same thing also happening to us in cases where there is no17 double use? ‘Are the [35] units in four equal to the twos? Observe that some twos18 are contained in one way, some in another.’ Also, ‘Is the knowledge of contraries one or not? Observe that some contraries are known, while others are unknown.’ Thus the man who makes [171b1] this requirement 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.