Tractate III. Chapters IX-XV

CHAPTER IX. On the things that are preliminary for knowing the fallacy according to ignorance of refutation.

Concerning the fallacy which is called ignorance of refutation, which is placed after the fallacy according to qualifiedly and simply, because it is with a double determination, while that which is according to qualifiedly and simply is with one, it must first be noted what ignorance of refutation is; and then the cause of appearance in it can be known, and the cause of non-existence, which, taken specially and under a specific and proper difference, substantially and in species constitute the sophistical place or fallacy.

It must be noted that, although ignorance has many divisions both on the part of the thing ignored, and on the part of the one ignorant, and also on the part of the mode of being ignorant, nevertheless in that commonality in which it embraces all things dividing ignorance so and in so many modes as it is said, it is not taken here, when ignorance of refutation is spoken of.

On the part of the thing ignored it is divided into universal and particular, which some call ignorance of law and of fact: because ignorance of law is universal ignorance regulating in the parts; but ignorance of fact is particular ignorance, or ignorance of some particular circumstance, which is scarcely avoidable in the parts.

On the part of the one ignorant it is divided into invincible ignorance and vincible ignorance; and into ignorance of which we are the cause, and ignorance of which we are not the cause. Invincible ignorance is twofold. It is from nature, as the ignorance of a fool. But he is called a fool who is foolish through a vice of melancholic complexion. But invincible by accident is such as the ignorance of one insane from a wound, or from another accident of chance or of someone's impulse. But ignorance of which we are the cause is twofold, namely from an illicit or shameful deed, as the ignorance of him who becomes drunk; or from sexual things he falls into madness which is called ἔρως by a Greek name among physicians, and into fourfold curses, as Aristotle says in Ethics II. But ignorance of which we are not the cause is like ignorance which is from the infirmity of an accident. It is also divided into affected or voluntary ignorance, as of him who does not wish to learn when he can; and into ignorance not affected, but occurring from the fact that one cannot look around into singulars in which acts are, as are the ignorances of physicians and of those divining by the stars, who frequently are ignorant, because they cannot look around at all the things needing consideration, in which there are actions helping or impeding for divining or helping the sick person; and such are the ignorances of a judge and of advocates in examining causes, and the things which help toward considerations of causes.

But the division of ignorance in the mode of ignorance is twofold, or into two, namely ignorance of negation, which properly is called nescience, when a man knows absolutely nothing about a thing, neither in the universal, nor in the particular, nor in acting called knowledge; and into ignorance of bad or perverse disposition, and this is when someone is of a perverse disposition toward knowing something. And this is threefold according to knowledge, which is divided by Aristotle in the second book of the Prior Analytics into three: namely, to know in the universal through common things, and to know in proper nature through proper things, and to know in acting through comparison of principles to the conclusion. For in all these ways it happens that someone is perversely disposed, either through this, that he conceives contraries of principles as principles, as Heraclitus did; or because he badly takes proper or common things for proper things, as one who thinks gall to be honey, because he sees only through common things, namely that honey is saffron-colored, moist, and viscous; or because he badly adapts principles for concluding, either without mode and figure, or without a relation proving the consequence through a cause or a local relation.

But with all the said ignorances omitted, here alone ignorance of bad disposition toward knowing is spoken of, especially in acting, which is in the conclusion to be inferred according to the proof of what is proposed, and secondarily insofar as one is badly disposed toward knowing in proper nature, and thirdly insofar as one is badly disposed toward knowing in the universal, and especially in the major proposition insofar as in it is the principle of the syllogistic course. For from these things there is caused a bad contradicting through a syllogism produced from an impossible or a false thing for contradicting, and in a syllogism to the impossible. For Aristotle says that if a syllogism through the order of premises to a conclusion is good, the syllogism from the opposite of the conclusion with the other premise to the destruction of the other premise will also be good; and if one is faulty, the remaining one will also be faulty. Hence ignorance from those things which are required so that from the opposite of the conclusion there may follow the opposite of that which the respondent believes, whom the objector intends to refute, is this which is called ignorance of refutation, or the syllogism of contradiction.

With these things thus noted, one must know that a refutation is a syllogism of contradiction; and therefore it has certain things which belong to the syllogism, and certain things proper to contradiction. From the syllogism it has that it be from certain things posited and disposed in mode and figure, and from certain relations which are causes, either topically inferring a consequence, and proving that which has been inferred. To omit considering either all the things which have been said, or some, or one of them, because this occurs from every syllogistic speech, therefore this does not make a special fallacy. But the things which are proper to contradiction are four, namely that it be toward the same thing, according to the same thing, and similarly, at the same time; and to omit these inconsiderately in a syllogism of contradiction introduces a special mode of deception, and therefore makes a special fallacy, which is called ignorance of refutation, and not ignorance of syllogism, except perhaps by consequence and not primarily.

It must also be noted that a syllogism of contradiction, or a refutation, is twofold. One syllogizes the opposite of the inferred conclusion from opposite principles. But another, from the opposite of the conclusion with the other of the premises, concludes the opposite of the other premise. And each is called a refutation in the fallacy which is called ignorance of refutation.

CHAPTER X. On the difference between the fallacy according to qualifiedly and simply, and ignorance of refutation.

Having these things, the cause of appearance in this fallacy and the cause of non-existence must be considered. Therefore one must know that the cause of appearance in this fallacy is the apparent contradiction of the things which are concluded, because through the fact that the things which are concluded in two syllogisms appear to be contradictory, there seems to be a refutation, but according to the truth there is not a refutation. But the cause of defect or non-existence is a defect of a true syllogism or of contradiction. Hence there is a difference between this fallacy and the preceding one, which is according to qualifiedly and simply. Some, assigning the difference, said that this is the difference between the fallacy according to qualifiedly and simply and ignorance of refutation: that the paralogisms of the fallacy according to qualifiedly and simply are always taken with a single determination; but the paralogisms of the fallacy according to ignorance of refutation are taken with a double determination. The contrary of this has been determined in what came before, because Aristotle says that, when contraries are equally in something according to diverse halves, as in a shield when one half is white and one half black, in that which is according to qualifiedly and simply there are two determinations according to qualifiedly: as when it is said, the shield is white according to one half, and is black or not white according to one half; therefore it is white and black, and white and not white.

But others said that the difference is in this, that the paralogisms of this fallacy are always made with a proper determination which infers its simply; but the paralogisms of the fallacy according to qualifiedly and simply are always made with an improper determination which does not infer its simply. But this seems to be unsuitable, because if each premise can infer its simply, then in the conclusion an opposite is concluded concerning an opposite; and thus the conclusion will always be false; and since the conclusion is well inferred from a proper determination, the conclusion will have been well syllogized. And because the false follows only from the false, it is necessary that one of the premises, or both, be false; and thus the paralogisms of that fallacy will be true syllogisms, sinning in matter and not in form; and thus they will not be apparent syllogisms or paralogisms.

Hence one must know that there are three differences between the fallacy according to qualifiedly and simply and the fallacy according to ignorance of refutation. One is indeed that which has already been said a little before, because the paralogisms of ignorance of refutation always proceed with a double determination; but the paralogisms of the fallacy according to qualifiedly and simply sometimes proceed with one determination, and sometimes with two, as was said in the objection. But another difference is that which has also already been had: that the paralogisms of the fallacy according to qualifiedly and simply proceed with a proper determination, while the paralogisms of this fallacy proceed with a double and improper determination. And as to what was objected against what they say, that in the paralogisms of the fallacy of ignorance of refutation both premises are true, and they do not have contradictories in themselves except apparently, and therefore contradictories are not inferred from them except apparently. But the objection proceeds as if a true composition of contradictories were in the premises, and therefore it does not conclude. But the third difference follows from these two, namely that the paralogisms of the fallacy according to qualifiedly and simply always sin in following and proving; but the paralogisms of the fallacy according to ignorance of refutation never sin in following or proving, but always in contradicting.

For understanding these things better, it must also be noted that, when opposites are taken in the paralogisms of these paralogisms with determination, either both of the opposites are taken with determination, or only one; and one must consider whether the determination is proper or not proper. If one of the opposites is taken with a proper determination, then no fallacy is made in such a process, but there will be a sin in matter, because the other of the premises is false: as if I say, an Ethiopian is white according to the head, and is black; therefore white and not white; because from this, white according to the head, there follows that he is simply white, and with this it cannot stand that he is simply black; and thus by consequence there follows a true contradiction, that he is white and not white. But if that determination has been improper, then the fallacy according to qualifiedly and simply is made, and not ignorance of refutation, as here: an Indian is white as to the teeth, and is black; therefore he is white and not white; for the procedure is from whiteness according to the teeth and to whiteness simply, and the fallacy according to qualifiedly and simply occurs.

But if each of the opposites is taken with a determination, this can happen in three ways: because either each is taken with a proper determination, or one with a proper and the other with an improper, or each with an improper. But in two of the said ways, namely the first and third, the fallacy according to ignorance of refutation never happens, but the fallacy according to qualifiedly and simply does; for if each is taken with an improper determination, such is the process: a swan is black according to its feet, and is not black according to the remaining parts of its body, as by its wings. Or thus: Socrates is black according to his feet, and not black according to his feet; therefore he is black and not black. For in this process the fallacy according to qualifiedly and simply is made, by proceeding from each determination to simply. But an example of that in which one of the opposites is with a proper determination and the other with an improper is: Socrates is white according to the head, and is black according to the eyes or feet; therefore white and not white. For here one proceeds from an improper determination to simply. But the process is good in the other part, from a proper determination to simply.

But if each is taken with a proper determination, then one must consider whether the things to which the determinations are added are truly contradictory. If they are truly contradictory and the determinations are proper, then the fallacy according to ignorance of refutation never occurs; but sometimes with the other part of the process the fallacy of the consequent occurs, and sometimes no fallacy occurs, but there is only a sin in matter, as is clear if the process is made thus: A is double to B and is not double to C; therefore double and not double. For those two determinations, one of which is to B, and the other is signified by what is said as to C, are added to two truly contradictory things, which are being double and being not double; and from one side it follows well from inferior to superior, as, it is double to B; therefore it is double. But on the other side of the process, because it is negative, it does not follow; for when it is said, it is not double to C; therefore it is not double, one proceeds from destruction of the antecedent, or from inferior to superior by denying, which causes the fallacy of the consequent. Sometimes in such a process no fallacy is made, but there is only a sin in matter, as here: Socrates is white according to the head, and is black according to the hands; therefore he is white and not white. Here a good contradiction is inferred by consequence, but one of the premises is false, whichever happens, because one does not stand when the other is posited, whichever one it is.

But if the things to which true determinations are added are not truly contradictory, but only apparent, then the fallacy according to ignorance of refutation always occurs, as here: A is double to B, and A is not double to C; double to B is not contradictory to not double to C, and therefore when it is inferred that A is double and not double, it does not infer a true contradiction, but is ignorant of it according to this contradiction: because contradiction must be toward the same thing and according to the same thing; because ignorance of refutation, as was said, does not sin in following or in syllogistic consequence, but only in contradicting. From these things the difference between the fallacy according to ignorance of refutation and the fallacy according to qualifiedly and simply is received.

Nevertheless it can still be objected: because, since in the fallacy according to qualifiedly and simply there is one qualifiedly and one simply, but in ignorance of refutation there are two qualifiedlies and two simpllies, and one is part of two, nor does a part make a number with its whole, it would perhaps seem to someone that the fallacy according to qualifiedly and simply ought not make a number of fallacies with ignorance of refutation, but ought to be part of it. And to this one must say that qualifiedly and simply do not make a fallacy of the figure of diction, but the relation of that which is qualifiedly to that which is simply does. But the relation of one to one is different, and the relation of two to two or to one is different; for the relation of one to two is the relation of the half; but the relation of two to one is the relation of the double; and thus there are two relations of the middle to the whole, and of the whole to the half. And thus also the relation of two qualifiedlies to two simpllies is different, and the relation of one qualifiedly to one or two is different; and thus these fallacies are distinguished according to relations, and therefore they are different and make a number.

It must also be noted that both this fallacy and the fallacy according to qualifiedly and simply are solved by comparing the conclusion to the premises according to the contradiction of true contradiction; but they differ in this, that in this fallacy the true contradiction of the conclusion is compared to the apparent contradiction in the premises, which has the defect of true contradiction in each part of the contradiction; but in the fallacy according to qualifiedly and simply, the true contradiction which is in the conclusion is compared to the apparent contradiction in the premises, which does not have the effect of true contradiction except in one part of the contradiction; and therefore this differs from that.

CHAPTER XI. On the universal cause of the fallacy according to ignorance of refutation, and its manifestation through examples.

Therefore, determining concerning the fallacy according to ignorance of refutation, we shall say that the paralogisms which are made according to ignorance of refutation have their cause in this, that in the process toward contradiction it is not determined what is truly a syllogism and what is truly a refutation. For each must be determined, because a refutation is a syllogism of contradiction; and therefore it is both a syllogism and of contradiction. Hence a paralogism according to ignorance of refutation is made according to a diminution of the account of syllogism and of refutation; for the account of contradiction or refutation is that a refutation is a true contradiction of one and the same thing, not of the name only, but of the thing, and not of a synonymous name, but of the same name; because there is not a contradiction if I say, a sword cuts, and I say, a blade does not cut. It is an accident following by necessity of consequence from the premises from those things which have been given, not by counting together in the conclusion what was in the beginning, but by taking one thing in the conclusion and another in the premises, so that through what is in the premises, what is in the conclusion is proved, as the unknown or less known is proved through another known or more known thing; so that the contradiction is according to the same thing, and toward the same thing, and similarly, and at the same time. But in the same way, by the omission of any one of these conditions, it happens to lie in contradicting about something.

Hence some people according to ignorance of refutation seem indeed to argue a contradiction, but they do not act, omitting some condition or something from the things that have been said, and especially from the four last conditions said, which are according to the same thing, and toward the same thing, and similarly, and at the same time. And this is manifest in examples. For if someone argues thus: two are indeed double of one, and they are not double of three; therefore two are double and not double. He sins because he omits this condition, toward the same thing; for double and not double are not compared to the same thing, but double to one and not double to three.

Or if he argues thus, that the same thing of the same thing is double and not double, but he does not observe that it is double and not double according to the same thing; as if some surface of four cubits is double of a two-cubit surface according to length, and is not double to the same according to breadth, and so he concludes that the same thing is double and not double of the same thing, it is manifest that he omits this condition, according to the same thing; for according to length it is double, but according to breadth it is not double, and so he does not affirm and deny according to the same thing.

Or also in a third way, if he argues that the same thing of the same thing and according to the same thing is double and not double, but it does not follow; as if he argues that in a right-angled triangle the side opposite the right angle is not dimensionally equal to the two other sides, and yet virtually or potentially is equal to the two other sides, because its square is equal to the two squares of the other two sides; therefore it is equal and not equal. It does not follow, because he does not affirm and deny similarly, but denies that it is dimensionally equal, and affirms that it is virtually equal. Or thus: man is a species; no man is a species; therefore man is a species and not a species. He does not contradict, because man is not taken similarly in the premises in affirming and denying.

Or also fourth, if he seems to argue affirmation toward the same thing, and of the same thing, and according to the same thing, and similarly, but not at the same time together; as if someone first shows a closed hand, and immediately opening it, argues thus: my hand is closed, and he says, opening it, that my hand is open; therefore it is open and not open, or closed and not closed. For he does not affirm and deny the same thing toward the same thing, and according to the same thing, and similarly, and at the same time, but at diverse times and not together; and this is not unsuitable.

For in these four modes and not others, ignorance of refutation is made; and this is proved as follows. For if the defect of syllogism and contradiction here will exist only through an added determination, then either the determination is added to each part of the contradiction, or to the one. If only to the one, either that determination is proper or improper. If improper, then the contradiction is impeded, and with the contradiction the syllogism; but there is there the fallacy according to qualifiedly and simply, and no mode of ignorance of refutation, as is clear from the foregoing, because ignorance of refutation sins against contradiction and not against syllogism. But if that determination has been proper, then there is a contradiction by consequence; as if I say, Socrates is white according to the head, and is black; therefore he is white and not white; this is a contradiction by consequence, and contradiction simply is not impeded, but a certain one, which is by consequence. But if each part is taken with a determination, then either the same determination is added to each part of the contradiction, or a diverse one. If the same determination is added to each part of the contradiction, then the contradiction is not impeded, whether the determination is proper or not proper. As if I say: Socrates is white according to the head, and is not white according to the head.

But if a diverse determination is added to each part, this happens in one of three modes: either each determination will be improper, or one proper and the other improper, or each proper. If each has been improper, then both the syllogism and the contradiction alone are impeded; and therefore in such a process the fallacy according to qualifiedly and simply occurs. Similarly it happens if one is proper and the other improper; for still both the syllogism and the contradiction are impeded, and the fallacy according to qualifiedly and simply occurs. But if each determination has been proper, one must consider whether those determinations are added to opposites, namely to affirmation and negation, by reason of the other term, namely of the subject or the predicate, or by reason of composition. If they are added by reason of some term, this happens in one of two modes: for either they are added by reason of the term to which the comparison is made, or by reason of that term which is compared. If by reason of the term to which the comparison is made, then it is impeded by reason of that term, or of the contradiction which is toward the same thing. But if they are added by reason of the one who is compared, then the comparison is impeded with respect to the other contradiction, which is according to the same thing. But if determinations are added not by reason of some term, but by reason of composition, this happens in one of two modes: either they are added to the composition by reason of signification, or by reason of the consignified time in composition. If they are added by reason of what is signified in the composition, then the contradiction is impeded with respect to this condition which is similarly; as in the example said above, the side opposite the right angle is double to the other of the two remaining sides of the triangle, that is, to the two equal sides, virtually; and it is not double dimensionally; therefore it is double and not double. For here the contradiction fails by reason of that condition which is similarly. For here proper determinations are added to each part of the contradiction by reason of what is signified in their compositions, because an adverb determines a verb by reason of its own signification. But if proper determinations are added by reason of the consignified time to each composition of the opposites, then the contradiction is impeded by reason of the consignified time; and so there is a paralogism according to the defect of this condition which is at the same time. And thus against a refutation insofar as it is a refutation, it happens to sin in four ways; and therefore there are only four modes of paralogisms of this fallacy.

CHAPTER XII. Whether true opposites are concluded in a paralogism according to ignorance of refutation.

From the things said a question arises. For it seems that paralogisms according to ignorance of refutation always conclude true opposites. For Aristotle says in the second book of On Interpretation and at the end of the first book of the Prior Analytics that from an affirmative about an infinite predicate there follows a negative about a finite predicate, as: this is non-double; therefore this is not double. Therefore, since paralogisms of ignorance of refutation conclude, this is double and non-double, they will also conclude these: it is double, it is not double; and thus they conclude true opposites, because if they can infer the antecedent, they can also infer the consequent.

But to this one must say that it is not generally true that an affirmative about an infinite predicate can infer a negative about a finite predicate. For in every proposition some verb is predicated: therefore either an adjective verb or a substantive verb. If an adjective verb is predicated, an affirmative about an infinite predicate never infers a negative about a finite predicate, as is clear here: I see a non-white thing; therefore I do not see a white thing; for in such a process there is always the fallacy of the consequent. But if a substantive verb is predicated, this will either be of present time, or of another, namely past or future. And if a substantive verb of another time than present is predicated, then it never holds, but there is always the fallacy of the consequent, as here: you were non-white; therefore you were not white. Similarly here: you will be non-white; therefore you will not be white. But if a substantive verb of present time is predicated, then one must consider the term joined to it: for either it is of absolute signification, or of relative signification. If of relative signification, of which sort relatives are, then such a process never holds, but the fallacy of the consequent always occurs; as, it is non-similar; therefore it is not similar. Or, it is non-double; therefore it is not double. But if an infinite term is added to a substantive verb of present time, and it is made of absolute signification, thus it always holds; and in this mode alone the rule introduced is understood, that an affirmative about an infinite predicate infers a negative about a finite predicate, as: it is non-man; therefore it is not man.

Nevertheless, it seems that these two cannot stand together, this is double and this is non-double; because when something follows from another, with whatever the consequent cannot stand, neither can the antecedent stand with the same; but from this, it is non-double, there follows, it is not double. This is proved thus: because when something follows from another with some determination added on both sides, or when the same determination is removed on both sides, it still follows from that; but it follows: A is not double with respect to D; therefore it is not double with respect to B; still one follows from the other; and thus the proposed point is had, that it follows: A is non-double; therefore it is not double. And thus these two, A is double and A is non-double, cannot stand together, just as neither can these, that A is double and A is not double.

Further, when a form is removed from an absolute term, there follows the removal of it from any subject of that term, as here: it is non-man; therefore it is not this man, nor that man, and so of others; therefore similarly, when the form of a relative term is removed, there follows the removal of it from any supposit to which it sets a relation; and thus it follows: it is non-double; therefore it is not double of this or of that or of the other; and so further it follows: it is non-double; therefore it is double of none; but from this, A is double of none, this follows: therefore it is not double; therefore from first to last it seems to follow: it is non-double; therefore it is not double.

To these things one must say that it does not follow: A is non-double; therefore it is not double. But to what is first objected one must say that, when something follows from another with a determination posited on both sides, namely to antecedent and consequent, then, with the same determination removed, it still follows from that, if the same determination belongs wholly to the antecedent and consequent; but this is not so in the proposed case, because when it is said in the premise, A is not double with respect to B, this determination with respect to B is a proper determination which can infer; for it follows: A is non-double with respect to B; therefore it is non-double. But in the conclusion there is an improper determination, for it does not infer its simply, because this does not follow: A is not double with respect to B; therefore it is not double; but there is there the fallacy of the consequent.

But to that which is objected concerning the privation of a term of absolute signification and of a term of relative signification, one must say that it is not similar, because in the privation of a term of absolute signification and of a term of relative signification a universal negation is actually understood; this is clear from the fact that it follows: it is non-man; therefore it is not this man, or that one, and so of singulars; and by reason of that negation actually understood in the privation it follows: it is non-man; therefore it is not man; and it does not follow from privation except by accident, for it does not follow by reason of privation, but by reason of the negation understood in the privation. But in a relative term it is not so, because that is preserved with respect to one only; for it follows: it is non-double with respect to B; therefore it is non-double. And therefore the privation of that, since a universal negation is not understood in it, cannot infer a negative; as this follows well: A is non-double; therefore A is not double.

Those doing violence set down this fallacy as being outside the fallacies outside diction and among the fallacies in diction, for two reasons: namely because it sins against diction, like the fallacies in diction; for a fallacy in diction is made because by the same names or speeches we do not signify the same thing; but for contradiction identity of name and identity of thing are required. And again because the contradiction of speeches is of an affirmative and a negative; and therefore they said that this fallacy is a fallacy in diction.

CHAPTER XIII. On the preliminaries for knowing the fallacy according to begging the principle.

Concerning the fallacy according to begging that which is in the beginning, first it must be noted that principle, as it is taken here, is a premise in a dialectical syllogism. But the same thing which is in the beginning according to material and efficient cause is in some way the conclusion. But as was held in the foregoing of this logic, the conclusion is materially made from the major extreme, which is the predicate of the major proposition, and from the minor extreme, which is the subject of the minor proposition. And thus materially the conclusion is in the principles of the syllogism premised to the conclusion. And in this way, when the conclusion to be proved is begged as something necessary through itself from the premises, then that which is from the principle is begged, because the preposition from notes a material cause moved by an efficient cause; and in this way Aristotle often calls this fallacy begging of that which is from the principle. But because this preposition in notes containment, and the thing caused is contained within its cause, and the thing principled is contained within its principle, and not conversely, and the middle joining the extremes through its mediation is the efficient cause why the extremes are joined in the conclusion, therefore when the conclusion is begged in the premises as they are principles of the conclusion, then the conclusion as in a cause is begged in the premises; and therefore according to this account this fallacy is then called begging of that which is in the principle; and thus these two names, namely what is called begging of that which is in the principle, and begging of that which is from the principle according to Aristotle. Moreover it is called begging the principle.

But the same thing can be begged in two ways: for either it is the same in name and in thing, or by a carrying-over to another in thing or in name, as if it is argued thus: some man runs; therefore man runs. And then between the inferring and the inferred, and the proving and the proved, there is no diversity; and such a mode of arguing does not fall within art; and this is properly called begging the principle, and not of that which is from the principle, or of that which is in the principle, and there is no fallacy. And therefore this fallacy is not called by Aristotle begging the principle, because the preposition in or from notes some diversity; for no cause of appearance and cause of non-existence can be given in such an argument. Therefore, properly speaking, this fallacy cannot be called begging the principle, but it is called begging of that which is in the principle, or begging of that which is from the principle. Therefore the cause of appearance in this fallacy is the apparent diversity of the conclusion and of some premise. But the cause of non-existence is identity of the conclusion with the premise in every way according to the thing. If either of these is lacking, it falls away from the account of fallacy.

Again it must be noted that a merely inferring syllogism can infer the same from the same, and will not sin either in figure or in mode, as here: every man runs; every rational mortal animal is a man; therefore every rational mortal animal runs. And therefore this fallacy does not sin against an inferring syllogism. But in a proving syllogism, which is a syllogism contracted to dialectical or demonstrative matter, it is required that one thing be proving and more known, and another thing proved and less known. But in begging that which is in the principle, what is to be proved is begged in what proves, as accepted in it and as the same as it; and therefore this fallacy sins against a proving syllogism to the proposed point.

Again it must be noted that there is begging the principle according to truth, and there is begging the principle according to opinion. According to truth there is begging the principle when something to be proved and not known through itself is begged in that which must be accepted through itself and is known through itself, as when a first cause is proved through an effect; for an effect is not known through itself, but must be proved through another; and the cause is proving and known through itself, and afterward the effect is proved through the cause. Then, according to truth, the effect is proved through the effect, because what is a proving principle is proving of what is principled, and what is a principle of the principle is a principle of the thing principled; and then in such a process there is begging the principle according to truth. For a cause is not proved through an effect except perhaps by a demonstration that something is so, and not what it is and on account of what; and this is as if I say: the moon is in the head or tail of the dragon, and the earth is interposed; therefore the moon is eclipsed. And then there is begging the principle according to truth, because the same is proved through the same according to truth.

But according to opinion there is begging the principle when that which is not fitted to be shown through itself is shown through the same, because it is estimated to be another thing on account of another intention which it has, in which it is estimated to be more known and more probable than that; as an effect accepted in the cause is estimated to be more probable than in itself, and a cause accepted in the effect is sometimes more probable than in itself, at least according to the way of sense; and thus the cause shown through the effect shows the effect, and consequently the effect is shown through itself. And this indeed, if it is in diverse intentions, in which the showing and the shown, the more probable and the less probable, have no sin in the operations, because by diverse ways according to intellect and according to sense nothing prevents each, namely the showing and the shown, from being more probable and less probable than the other. On account of this nearly all dialectical places are circular. Yet this would be a sin in demonstratives, because demonstrations are not circular.

Therefore begging of that which is in the principle, or of that which is from the principle, is intended here according as it is in opinion and sins against the dialectical syllogism; but to beg a principle according as a premise is called a principle makes no sin, since in dialecticals one can be proved through the other and conversely, so that the whole dialectical syllogism is preserved. Yet a sin against the dialectical syllogism occurs here, insofar as in the same way of intellect or sense that which must be proved is begged without proof in that which is assumed for the proof of what is to be proved; because if this were done according to diverse ways, there would be absolutely no sin against the dialectical syllogism.

Hence begging of that which is in the principle is in a twofold intention: namely in the intention of a vice or defect to be avoided in dialecticals, and as to this it was spoken of at the end of the eighth book of the Topics. It is also from the appearance of the same thing which seems diverse in the intention of a deceiving and sophistical place; and thus it is determined here concerning it.

CHAPTER XIV. On the modes of paralogisms according as that which was in the beginning is begged.

With these things thus noted beforehand, it is not difficult to determine concerning the fallacy according to begging that which is in the beginning; for paralogisms which are made in that which is taken without proof, or in which that which was in the beginning is begged, are indeed made thus, as to the mode of formation, as often as it happens to beg that which is in the beginning. But this has already been determined at the end of the eighth book of the Topics. For it occurs in five modes.

The first mode is when the defined is begged in the definition, or conversely. As if it is asked whether man runs, and this is taken, a rational mortal animal runs, and it is inferred: therefore man runs. For there is doubt concerning the inherence of the predicate in the subject, and it is equally unknown whether the predicate inheres in the defined or in the definition, and neither is fitted to be made known through the other, because they differ only through implicit and explicit; and thus one is begged in the other.

The second mode is when the particular is begged in the universal actually distributed for the parts; because with the universal so taken, the particular is actually begged and taken in it. As if it is asked whether there is the same discipline of all contraries, which is one particular contained in the genus of opposites, and it is taken for proving that there is the same discipline of all opposites. For this same thing which is concluded is begged in the premises, because from the fact that the universal is actually distributed for the particulars, the universal is not outside the particular, and the particular is in the universal.

The third mode is the converse of this, when the universal is begged in the particular. As if it is asked whether there is the same discipline of all opposites, and it is taken for proving thus: there is the same discipline of all contraries, and there is the same discipline of all privatively opposed things, and there is the same discipline of all contradictories, and there is the same discipline of all relatively opposed things. For as in the universal actually distributed the particular is begged, so in all the parts the universal actually distributed is begged in that.

The fourth mode is when the conjoined is begged in the divided things, which is not in them by reason of conjunction, but by reason of the things conjoined. As if it is asked whether medicine is the science of the healthy and the sick, and it is begged that medicine is the science of the healthy, and medicine is the science of the sick; therefore medicine is the science of the healthy and the sick. For it is nothing other for medicine to be the science of the healthy, and medicine to be the science of the sick, than for medicine to be the science of the healthy and the sick.

The fifth mode is when one of correlatives is begged in the other, not as the term at which the relation is terminated, but as the account by which each is in the other through understanding. As if it is asked whether Socrates is the father of Plato, and it is taken for proving that Plato is the son of Socrates; therefore Socrates is the father of Plato. For one of these is not fitted to be proved through the other. But all the paralogisms introduced have a cause of appearance through which they seem to argue something by a proving syllogism, although they do not argue; because they seem to assume a diverse thing, which is the same, and they do not argue because that which seems to be diverse is the same. Hence they fail in a proving syllogism from this, that they cannot look into what in the proving and in the proved is the same and diverse.

But the number of those modes is taken thus: because begging of that which is in the beginning according to the respondent's opinion is taken either without association of itself with another, or with association of itself to another. If in the first way, it is taken either in itself or in its parts. If it is begged in itself, either it remains the same in name and thing, or it remains the same in thing and not in name. If what is begged remains the same in thing and name, thus there is the first mode. But if it is begged with association to another, thus there is the second mode, for what ought to be shown particularly is begged universally according to the opinion of the respondent. But if what is begged is begged in itself, not in its parts, then what is begged either has parts joined by copulation, and thus there is the fourth mode. But if it is begged in distributed parts, thus there is the third mode. But if it is begged while not remaining in the same name, thus there is the fifth mode, because then it is begged in the same thing which is said convertibly with it, and things of this kind are easy to take.

But one must know that for that which is in the beginning to be begged, it is necessary that the conclusion according to its whole self be begged in its premises, or in one of the premises. But since no whole according to its whole self is in any one of its parts, therefore although a subjective part may infer its whole, nevertheless the whole cannot be begged in a subjective part; and therefore no mode of begging that which is in the beginning is taken according to that mode.

One must also know that the two modes which are accepted according to the whole distributed into its parts, when the whole is begged in the parts, or conversely the parts in the whole, are understood concerning the whole which is distributed into parts, and concerning the whole in which the parts are joined, as is in the fourth mode.

One must also know that in the same argument the sophistical place, which is begging that which is in the beginning, and the dialectical place fall together; for it happens that, as to the opponent, it is more known that the major extreme is said of the middle than of the minor extreme, and in this way the premise is more known to the opponent than the conclusion. It also happens that in the same argument, as to the respondent, the conclusion is more known than the premise; and thus as to the respondent that which is in the beginning is begged, and as to the opponent it is a good dialectical syllogism. Hence one must always consider whether the major extreme is more known of the middle than of the minor, or conversely. For if it is more known of the middle, it is always a good dialectical syllogism. But if it is more known of the minor extreme than of the middle, it is always begging of that which is in the beginning.

CHAPTER XV. On the preliminaries for understanding the fallacy of the consequent.

For understanding the things that must be said about the fallacy of the consequent, one must first know what the antecedent is and what the consequent is, and what and how many consequences there are. Therefore let us say that the antecedent is that from which, when it is posited, the consequent is inferred from it either necessarily or probably. Necessarily, indeed, when the consequent in understanding and act is in the antecedent according to the first mode of saying through itself, the second, or the fourth. As, if man exists, animal exists; in that antecedent, man exists, this consequent, animal exists, is in act and understanding, because it is definitional of it. But the second mode of saying through itself is as if it is said: if a line exists, it is straight or curved; for line is definitional of what is straight or curved. Or thus: if number exists, it is even or odd; for number is in the definition of even and odd. But according to the fourth mode, as if I say: if an animal has been beheaded, it has perished because of beheading; and generally between a proper cause and its effect. But probably, when, with the adjuncts of something posited, that to which those things are adjuncts is inferred from it, as: if he is adorned or polluted, he is an adulterer. Or if a poor man speaks with a rich man, he asks something from him. Or both are friends if both are enemies of the same person, or something of this kind which it belongs to cleverness to discern.

But the consequent is that which is thus inferred from the antecedent. But consequence or argumentation is drawn from the relation of antecedent to consequent, and conversely from the relation of consequent to antecedent; and this is multiform. For according to the first division it is simple and composite. Simple is when from a simple antecedent a simple consequent is inferred, as if I say thus: if man exists, animal exists. Composite is when from one consequence another is inferred, and this is among opposites. And it is twofold. One is when from the antecedent the consequent is inferred, and from the opposite of the antecedent the opposite of the consequent is inferred; and this is among contraries. As: if justice is a virtue, injustice is a vice. And if fortitude is a virtue or praiseworthy, timidity is a vice or blameworthy. And this is called consequence in itself, because it is in the terms themselves and in the same order of the terms. But the other is when from the antecedent the consequent follows, and from the opposite of the consequent the opposite of the antecedent follows; and this is among contradictorily opposed things thus: if man is animal, non-animal is non-man. And the cause of this is that the negated consequent is a subjective part of the negated antecedent, just as the affirmed antecedent is a subjective part of the affirmed consequent; for non-animal is part of non-man. And therefore, just as the affirmed antecedent infers the consequent, so conversely the negated consequent infers the negated antecedent; and each of these is called consequence from the contrary, either of the antecedent or of the consequent.

But there is another division of consequence which Boethius intimates in his Topics, namely this: that one consequence is necessary and not probable, as in demonstratives; another is probable and not necessary, as in dialecticals; another necessary and probable, but not through the same middle; another is neither necessary nor probable, but only making suspicion, as in rhetoricals and poetics.

And just as consequence is commonly said of all consequences of this kind, so consequent, as the fallacy of the consequent is spoken of, which sins against consequence,