Commentary Aristotle Posterior Analytics
Lecture 27
How ignorance or deception bearing on first and immediate things can be induced by syllogism and lead one to suppose something to be which is not
b23. Ignorance, defined not as the negation of knowledge but as a positive state of mind, is error produced by inference. (1) Let us first consider propositions asserting a predicate’s immediate connexion with or disconnexion from a subject.
Here, it is true, positive error may befall one in alternative ways; for it may arise where one directly believes a connexion or disconnexion as well as where one’s belief is acquired by inference. The error, however, that consists in a direct belief is without complication; but the error resulting from inference—which here concerns us—takes many forms.
Thus, let A be atomically disconnected from all B: then the conclusion inferred through a middle term C, that all B is A, will be a case of error produced by syllogism. Now, two cases are possible. Either (a) both premises, or (b) one premise only, may be false. (a) If neither A is an attribute of any C nor C of any B, whereas the contrary was posited in both cases, both premises will be false.
(C may quite well be so related to A and B that C is neither subordinate to A nor a universal attribute of B: for B, since A was said to be primarily disconnected from B, cannot have a genus, and A need not necessarily be a universal attribute of all things. Consequently both premises may be false.)
On the other hand, (b) one of the premises may be true, though not either indifferently but only the major A-C since, B having no genus, the premise C-B will always be false, while A-C may be true. This is the case if, for example, A is related atomically to both C and B; because when the same term is related atomically to more terms than one, neither of those terms will belong to the other. It is, of course, equally the case if A-C is not atomic.
Error of attribution, then, occurs through these causes and in this form only — for we found that no syllogism of universal attribution was possible in any figure but the first.
Ignorance, defined not as the negation. After determining about the demonstrative syllogism through which science is acquired, the Philosopher here determines concerning the syllogism through which ignorance or deception is produced in us.
First, he shows what sort of ignorance can be induced by a syllogism.
Second, he shows the mode in which such a syllogism proceeds, at: here, it is true, positive error (79b28; [225]).
He distinguishes therefore first (79b23) a twofold ignorance, one of which is negative and the other a positive state.
There is ignorance in a negative way, when a man has no scientific knowledge at all about a thing. This ignorance consists in not attaining, as the Philosopher says in Metaphysics IX, and is exemplified in a peasant who knows absolutely nothing about whether a triangle has three angles equal to two right angles. But ignorance is present as a positive state, when one does have a definite opinion but it is unsound. For example, when he falsely thinks something about a thing, either because he thinks something to be which is not, or something not to be which is. And this ignorance is the same as error. Now the first ignorance is not produced by a syllogism, but the second can be, and then it is called deception.
Such ignorance or deception can concern two things.
First, those things which are first and immediate principles, namely, when a person opines things opposed to the principles. And although he cannot so opine inwardly in the mind, as has been stated above, because these things do not fall under apprehension, nevertheless he can contradict them orally and according to a false imagination, as is said in Metaphysics IV of some who deny the principles.
Second, it might be concerned with conclusions which are not first and immediate. Furthermore, the first of these ignorances or deceptions is opposed to the knowledge which is understanding, and the second to the knowledge which is science.
Each of these states of ignorance, whether concerned with things that are first or things not first, can befall a man in two ways.
In one way, simply, when independently of any process of reasoning he thinks a falsehood by affirming or denying.
In another way, when he is brought to his opinion through some syllogized reason.
Hence the Philosopher says in Metaphysics IV that some contradict the principles as though persuaded by reasons; but others, not as though persuaded by reasons, but through lack of erudition or through wilfullness which demands to have a demonstration in all matters.
Then, at: here, it is true, positive error (79b28) he shows how these ignorances are caused.
First, how the ignorance produced by a syllogism is caused.
Second, how ignorance befalls a man without syllogizing, at: it is also clear that the loss (81a38; [248]).
Concerning the first he does two things.
First, he states how ignorance in regard to first and immediate principles is engendered by a syllogism.
Second, how it is caused in regard to things not first and immediate, at: in the case of attributes (80b17; [240]).
Concerning the first he does two things.
First, he states how the ignorance is caused whereby that which is not is believed to be.
Second, that whereby that which is is believed not to be, at: on the other hand, an error (80a8; [233]).
Regarding the first he does three things.
First, he states how the aforesaid ignorance is generally caused.
Second, he assigns its various possible forms, at: it may occur when both premises (79b31; [227]).
Third, he answers a tacit question, at: error of attribution (80a6; [232]).
He says therefore first (79b28) that the deception according to false opinion which above was said to occur straightway is simple, that is, is engendered in only one way. For it is not caused by a reason, which might vary, but by the lack of a reason which [lack] is not diversified into various modes each having its own characteristics any more than other negations are. Yet because false reasons can be various and many, this ignorance, when it is engendered by a syllogism can occur in many ways according to the several ways in which a syllogism can be false. The common way is set forth when he says, Let A be in no B individually (79b29), that is, let this proposition be immediately true, “No B is A.” For two negations are stated in the place of one—for instance if we should say, “No quality is a substance”—according to the doctrine on immediate negative propositions presented above. Therefore, if someone were to conclude the opposite of this with a syllogism, taking C as a middle to show that every B is A, there will be a deception through syllogism.
Then, at: it may occur when both premises (79b31) he shows in how many ways this can vary.
And first of all it should be noted that a false conclusion is not concluded except when the syllogism is false. But a syllogism can be false in two ways: first, because it lacks syllogistic form, in which case it is not a syllogism but appears to be one. In a second way, because it employs false propositions, in which case it is a syllogism as to form, but it is a false one because of the false propositions used. Therefore, in a dialectical disputation, which bears on probables, use could be made of both types of false syllogism, because such a disputation proceeds from common premises. Consequently, error can arise in it both as regards the matter employed, which is common, and also as regards the form, which is common. But in a demonstrative disputation, which bears on necessary things, the type of syllogism used is the one which could be false only on account of the matter, because as it is stated in Topics I, a paralogism in a given discipline proceeds from things proper to the discipline, but not from true things. Hence, since syllogistic form must be counted among the common things, paralogism within a discipline—which is the matter under discussion-is not defective in form but only in matter, and furthermore in regard to proper and not in regard to common things.
Hence he first tells how such a syllogism might proceed from two false premises.
Second, how it might proceed from one or the other premise being false, at: on the other hand, one of the premises (79b40; [230]).
But since the first can occur in two ways, namely, the false proposition might be contrary to the true or contradictory to it, therefore:
First, he shows how such a syllogism might proceed from two false statements that are contrary to true statements.
Second, how a contradiction is accepted, at: C may quite well be so related to A and B (79b34; [229]).
First, then (79b30) he says that in a syllogism causing deception it sometimes happens that both premises are false, and sometimes only one. Let us take the case of two false premises, each contrary to what is true. For example, suppose that C is so related to A and to B, that no C is A and no B is C. Now, if we take the contraries of these, namely, that every C is A and every B is C, these two propositions will be completely false. For example, if I should say: “Every quality is a substance; every quantity is a quality: therefore, every quantity is a substance.”
Then, at: C may quite well be so related to A and B (79b34) he shows how both premises can be false and not contrary, but contradictory, to what is true. For example, if C is so related to A and to B, that it is neither contained totally under A nor is universally in B. Thus one might take C as 'perfect' or 'actual being,' and proceed in the following way: “Every perfect thing is a substance; every quantity is perfect: therefore, every quantity is a substance.” Now, although both are false, they are not entirely so, for their contradictories are true, namely, “Some perfect things are not substances,” and “Some quantity is not perfect”; but their contraries are false, namely, “No perfect thing is a substance,” and “No quantity is perfect.”
But that C is not in B universally (that is, that the statement, “Every quantity is perfect,” which was the minor, is not true), that is, that “Every B is C,” is not true he proves by the fact that B cannot be contained under any whole that might be predicated universally of it. And this is so because the proposition, “No B is A,” was said to be immediate, which means that A is universally not in B. But, as has been stated above, those negative propositions are immediate, neither of whose terms is under a whole.
Nevertheless, this proof does not seem sufficient, because something can be predicated universally even of that which is not under some whole as a species under a genus. For the genus and the difference are not the only things predicated universally, but a property is too.
But it must be said that although the proof in question is not efficacious generally speaking, it is in this case. Because, as it is stated in Topics I, a paralogism within a discipline—with which we are concerned here—proceeds from items that accord with the discipline. Hence he intends to use such middles as a demonstrator uses. But the middle of a demonstration is the definition, as has been stated above. Therefore, even in the syllogism of which he is speaking, he intends to use a definition as the middle. Now, a definition contains the genus and difference. Hence that which is predicated universally in this syllogism should contain that in which the subject is, as in a whole.
Again, that A is not in C universally, that is, that the statement, “Every perfect thing is a substance,” is not universally true is proved by the fact that it is not required of every universal that it be universally in all things that are: because no predicament is predicated of things contained under another predicament nor universally predicated of those items that commonly follow upon being, namely, act and potency, perfect and imperfect, prior and posterior, and the like.
Then, at: on the other hand, one of the premises (79b40) he shows how the aforesaid syllogism might proceed from one true and one false.
And he says that in the aforesaid syllogism we might take one true, that is, the major, which is AC, and the other false, namely, the minor, which is BC. That the minor proposition, which is BC, is always the false one he proves, as he did above, on the ground that B is in nothing as in a whole. But that this proposition AC could be true, while the other is false he proves in terms. Let A be in B and in C individually, that is, immediately, as a genus in its species; for example, as color is to whiteness and blackness. Now, under these conditions it is obvious that the major will be true, namely, “Every C is A,” for example, “Every whiteness is a color,” and the minor false, namely, “Every blackness is whiteness”: for when something is predicated first of several, none of the several is predicated of any other of them. For the first predication of a genus is of species which are opposite.
Here, too, a doubt arises, because from the terms used here, not a false but a true conclusion follows. For the conclusion will be that A is in B, it having also been assumed that it is in B individually.
But it must be answered that this example was used merely to illustrate how the major could be true and the minor false; although it is of no use in a case where a false conclusion is sought. Hence the Philosopher at once adds: it is equally the case of AC if not atomic. However, we could take terms such that A is not in B either individually or in any way, but is rather immediately removed from B. Neither is it necessary that it be in C individually, because it is not necessary that a demonstrator employ only immediate propositions: for he may use ones which are supported by immediate propositions. We can, therefore, take other terms pertaining to the present case, for example, “intellectual substance,” as the middle, for “Every intelligence is a substance,” and take as the false minor, “Every quantity is an intelligence.” Hence a false conclusion follows.
Then, at: error of attribution (80a6) he answers a tacit question. For someone might request that he exemplify the diversity of such a syllogism in the other figures. But he answers that a deception, which bears on being, that is, through which someone opines a false affirmative proposition, can be derived only by the first figure, because in the next figure, that is, in the second, an affirmative syllogism cannot be formed. As for the third figure, it has no bearing on the case, because it cannot conclude a universal, which is principally intended in demonstration and in this syllogism.