by Aristotle
To judge character from physical features, then, is possible in the first figure if the middle term is convertible with the first extreme, but is wider than the third term and not convertible with it: e.g. let A stand for courage, B for large extremities, [35] and C for lion. B then belongs to everything to which C belongs, but also to others. But A belongs to everything to which B belongs, and to nothing besides, but is convertible with B: otherwise, there would not be one sign for one affection.
**TEXT: W. D. Ross, OCT, Oxford, 1964
1‘Understanding’ here, and throughout the Analytics, translates ἐπιστήμη.
2‘Proposition’ here and hereafter translates πρότασις.
3‘Deduction’ here and hereafter translates συλλoγισμός.
4See Topics 102a27–30.
5See Posterior Analytics I 4–12.
6See Chapters 13–17.
7See Chapter 46.
8Ross excises the passage in brackets.
9Aristotle’s promise is not kept in any text we possess.
10Ross excises the passage in brackets.
11Ross excises the bracketed sentence (see 39a1).
12See Posterior Analytics I 19–22.
13Ross excises the passage in brackets.
14See Prior Analytics II 14.
15i.e. the Topics.
16Omitting τήν before πoδιαίαν and reading oὖσαν for oὔσας.
17This promise is not kept in Aristotle’s extant works.
18See 57a40–b17.
19Ross excises the bracketed phrases.
20Ross excises this paragraph.
21See Topics VIII 1.
22See Sophistical Refutations 167b21–36.
23See Plato, Meno 81B-86B.
24In the manuscripts, this sentence appears after ‘not together’, line 8: it was transposed by Pacius.
25Tredennick suggests this excision: Ross changes ‘whatever is bileless’ to ‘C’.
26Reading πρoσειληφέναι, τὴν AΓ.
27Excised by Ross.
28Some of these matters are considered in Rhetoric II 25.
29This sentence is transposed to the start of the chapter by Ross.
POSTERIOR ANALYTICS**
Jonathan Barnes
BOOK I
[71a1] 1 · All teaching and all intellectual learning come about from already existing knowledge. This is evident if we consider it in every case; for the mathematical sciences are acquired in this fashion, and so is each of the other arts. [5] And similarly too with arguments—both deductive and inductive arguments proceed in this way; for both produce their teaching through what we are already aware of, the former getting their premisses as from men who grasp them, the latter proving the universal through the particular’s being clear. (And rhetorical arguments [10] too persuade in the same way; for they do so either through examples, which is induction, or through enthymemes, which is deduction.)
It is necessary to be already aware of things in two ways: of some things it is necessary to believe already that they are, of some one must grasp what the thing said is, and of others both—e.g. of the fact that everything is either affirmed or [15] denied truly, one must believe that it is; of the triangle, that it signifies this; and of the unit both (both what it signifies and that it is). For each of these is not equally clear to us.
But you can become familiar by being familiar earlier with some things but getting knowledge of the others at the very same time—i.e. of whatever happens to be under the universal of which you have knowledge. For that every triangle has [20] angles equal to two right angles was already known; but that there is a triangle in the semicircle here became familiar at the same time as the induction. (For in some cases learning occurs in this way, and the last term does not become familiar through the middle—in cases dealing with what are in fact particulars and not said of any underlying subject.)
[25] Before the induction, or before getting a deduction, you should perhaps be said to understand in a way—but in another way not. For if you did not know if it is simpliciter, how did you know that it has two right angles simpliciter? But it is clear that you understand it in this sense—that you understand it universally—but you do not understand it simpliciter. (Otherwise the puzzle in the Meno1 will result; for [30] you will learn either nothing or what you know.)
For one should not argue in the way in which some people attempt to solve it: Do you or don’t you know of every pair that it is even? And when you said Yes, they brought forward some pair of which you did not think that it was, nor therefore that it was even. For they solve it by denying that people know of every pair that it is even, but only of anything of which they know that it is a pair.—Yet they know it of [71b]1 that which they have the demonstration about and which they got their premisses about; and they got them not about everything of which they know that it is a triangle or that it is a number, but of every number and triangle simpliciter. For no proposition of such a type is assumed (that what you know to be a number… or what you know to be rectilineal . . . ), but they are assumed as holding of every [5] case.
But nothing, I think, prevents one from in a sense understanding and in a sense being ignorant of what one is learning; for what is absurd is not that you should know in some sense what you are learning, but that you should know it in this sense, i.e. in the way and sense in which you are learning it.
2 · We think we understand a thing simpliciter (and not in the sophistic fashion accidentally) whenever we think we are aware both that the explanation [10] because of which the object is is its explanation, and that it is not possible for this to be otherwise. It is clear, then, that to understand is something of this sort; for both those who do not understand and those who do understand—the former think they are themselves in such a state, and those who do understand actually are. Hence [15] that of which there is understanding simpliciter cannot be otherwise.
Now whether there is also another type of understanding we shall say later; but we say now that we do know through demonstration. By demonstration I mean a scientific deduction; and by scientific I mean one in virtue of which, by having it, we understand something.
If, then, understanding is as we posited, it is necessary for demonstrative [20] understanding in particular to depend on things which are true and primitive and immediate and more familiar than and prior to and explanatory of the conclusion (for in this way the principles will also be appropriate to what is being proved). For there will be deduction even without these conditions, but there will not be demonstration; for it will not produce understanding.
Now they must be true because one cannot understand what is not the [25] case—e.g. that the diagonal is commensurate. And they must depend on what is primitive and non-demonstrable because otherwise you will not understand if you do not have a demonstration of them; for to understand that of which there is a demonstration non-accidentally is to have a demonstration. They must be both explanatory and more familiar and prior—explanatory because we only understand [30] when we know the explanation; and prior, if they are explanatory, and we are already aware of them not only in the sense of grasping them but also of knowing that they are.
Things are prior and more familiar in two ways; for it is not the same to be prior by nature and prior in relation to us, nor to be more familiar and more familiar [72a1] to us. I call prior and more familiar in relation to us what is nearer to perception, prior and more familiar simpliciter what is further away. What is most universal is [5] furthest away, and the particulars are nearest; and these are opposite to each other.
Depending on things that are primitive is depending on appropriate principles; for I call the same thing primitive and a principle. A principle of a demonstration is an immediate proposition, and an immediate proposition is one to which there is no other prior. A proposition is the one part of a contradiction,2 one thing said of one; it [10] is dialectical if it assumes indifferently either part, demonstrative if it determinatel
y assumes the one that is true.3 [A statement is either part of a contradiction.]4 A contradiction is an opposition of which of itself excludes any intermediate; and the part of a contradiction saying something of something is an affirmation, the one saying something from something is a denial.
[15] An immediate deductive principle I call a posit if one cannot prove it but it is not necessary for anyone who is to learn anything to grasp it; and one which it is necessary for anyone who is going to learn anything whatever to grasp, I call an axiom (for there are some such things); for we are accustomed to use this name especially of such things. A posit which assumes either of the parts of a [20] contradiction—i.e., I mean, that something is or that something is not—I call a supposition; one without this, a definition. For a definition is a posit (for the arithmetician posits that a unit is what is quantitatively indivisible) but not a supposition (for what a unit is and that a unit is are not the same).
[25] Since one should both be convinced of and know the object by having a deduction of the sort we call a demonstration, and since this is the case when these things on which the deduction depends are the case, it is necessary not only to be already aware of the primitives (either all or some of them) but actually to be better aware of them. For a thing always belongs better to that thing because of which it [30] belongs—e.g. that because of which we love is better loved. Hence if we know and are convinced because of the primitives, we both know and are convinced of them better, since it is because of them that we know and are convinced of what is posterior.
It is not possible to be better convinced than one is of what one knows, of what one in fact neither knows nor is more happily disposed toward than if one in fact knew. But this will result if someone who is convinced because of a demonstration is [35] not already aware of the primitives, for it is necessary to be better convinced of the principles (either all or some of them) than of the conclusion.
Anyone who is going to have understanding through demonstration must not only be familiar with the principles and better convinced of them than of what is [72b1] being proved, but also there must be no other thing more convincing to him or more familiar among the opposites of the principles on which a deduction of the contrary error may depend—if anyone who understands simpliciter must be unpersuadable.
3 · Now some think that because one must understand the primitives there is [5] no understanding at all; others that there is, but that there are demonstrations of everything. Neither of these views is either true or necessary.
For the one party, supposing that one cannot understand in another way,5 claim that we are led back ad infinitum on the grounds that we would not understand what is posterior because of what is prior if there are no primitives; and they argue correctly, for it is impossible to go through infinitely many things. And if [10] it comes to a stop and there are principles, they say that these are unknowable since there is no demonstration of them, which alone they say is understanding; but if one cannot know the primitives, neither can what depends on them be understood simpliciter or properly, but only on the supposition that they are the case.
The other party agrees about understanding; for it, they say, occurs only [15] through demonstration. But they argue that nothing prevents there being demonstration of everything; for it is possible for the demonstration to come about in a circle and reciprocally.
But we say that neither is all understanding demonstrative, but in the case of the immediates it is non-demonstrable—and that this is necessary is evident; for if it [20] is necessary to understand the things which are prior and on which the demonstration depends, and it comes to a stop at some time, it is necessary for these immediates to be non-demonstrable. So as to that we argue thus; and we also say that there is not only understanding but also some principle of understanding by which we become familiar with the definitions.
And that it is impossible to demonstrate simpliciter in a circle is clear, if [25] demonstration must depend on what is prior and more familiar; for it is impossible for the same things at the same time to be prior and posterior to the same things—unless one is so in another way (i.e. one in relation to us, the other simpliciter), which induction makes familiar. But if so, knowing simpliciter will not [30] have been properly defined, but will be twofold. Or is the other demonstration not demonstration simpliciter in that it comes from about what is more familiar to us?
There results for those who say that demonstration is circular not only what has just been described, but also that they say nothing other than that this is the case if this is the case—and it is easy to prove everything in this way. It is clear that [35] this results if we posit three terms. (For it makes no difference to say that it bends back through many terms or through few, or through few or two.) For whenever if A is the case, of necessity B is, and if this then C, then if A is the case C will be the case. Thus given that if A is the case it is necessary that B is, and if this is that A is (for that is what being circular is)—let A be C: so to say that if B is the case A is, is [73a1] to say that C is, and this implies that if A is the case C is. But C is the same as A. Hence it results that those who assert that demonstration is circular say nothing but that if A is the case A is the case. And it is easy to prove everything in this way. [5]
Moreover, not even this is possible except in the case of things which follow one another, as properties do. Now if a single thing is laid down, it has been proved6 that it is never necessary that anything else should be the case (by a single thing I mean [10] that neither if one term nor if one posit is posited . . .), but two posits are the first and fewest from which it is possible, if at all, actually to deduce something. Now if A follows B and C, and these follow one another and A, in this way it is possible to prove all the postulates reciprocally in the first figure, as was proved in the account [15] of deduction.7 (And it was also proved that in the other figures either no deduction comes about or none about what was assumed.) But one cannot in any way prove circularly things which are not counterpredicated; hence, since there are few such things in demonstrations, it is evident that it is both empty and impossible to say that demonstration is reciprocal and that because of this there can be demonstration [20] of everything.
4 · Since it is impossible for that of which there is understanding simpliciter to be otherwise, what is understandable in virtue of demonstrative understanding will be necessary (it is demonstrative if we have it by having a demonstration). Demonstration, therefore, is deduction from what is necessary. We must therefore [25] grasp on what things and what sort of things demonstrations depend. And first let us define what we mean by holding of every case and what by in itself and what by universally.
Now I say that something holds of every case if it does not hold in some cases and not others, nor at some times and not at others; e.g. if animal holds of every [30] man, then if it is true to call this a man, it is true to call him an animal too; and if he is now the one, he is the other too; and the same goes if there is a point in every line. Evidence: when asked if something holds of every case, we bring our objections in this way—either if in some cases it does not hold or if at some time it does not.
One thing belongs to another in itself both if it belongs to it in what it is—e.g. [35] line to triangle and point to line (for their substance depends on these and they belong in the account which says what they are)—and also if the things it belongs to themselves belong in the account which makes clear what it is—e.g. straight belongs to line and so does curved, and odd and even to number, and prime and [73b1] composite, and equilateral and oblong; and for all these there belongs in the account which says what they are in the one case line, and in the others number. And similarly in other cases too it is such things that I say belong to something in itself; [5] and what belongs in neither way I call accidental, e.g. musical or white to animal.
Again, what is not said of some other underlying subject—as what is walking is something different walking (and white),8 while a substance, and whateve
r signifies some ‘this,’ is just what it is without being something else. Thus things which are not said of an underlying subject I call things in themselves, and those which are said of an underlying subject I call accidentals.
[10] Again, in another way what belongs to something because of itself belongs to it in itself, and what does not belong because of itself is accidental—e.g. if it lightened when he was walking, that was accidental; for it was not because of his walking that it lightened, but that, we say, was accidental. But if because of itself, then in itself—e.g. if something died while being sacrificed, it died in the sacrifice since it [15] died because of being sacrificed, and it was not accidental that it died while being sacrificed.