Commentary Aristotle Posterior Analytics
Lecture 4. Nature of the demonstrative syllogism
71b9. We suppose ourselves to possess unqualified scientific knowledge of a thing, as opposed to knowing it in the accidental way in which the sophist knows,
71b10. when we think that we know the cause on which the fact depends, as the cause of that fact and of no other, and, further, that the fact could not be other than it is.
71b12. Now, that scientific knowing is something of this sort is evident—witness both those who falsely claim it and those who actually possess it, since the former merely imagine themselves to be, while the latter are also actually, in the condition described.
71b15. Consequently the proper object of unqualified scientific knowledge is something which cannot be other than it is.
71b16. There may be another manner of knowing as well—that will be discussed later.
71b17. What I now assert is that at all events we do know by demonstration. By demonstration I mean a syllogism productive of scientific knowledge, a syllogism, that is, the grasp of which is eo ipso such knowledge.
71b19. Assuming then that my thesis as to the nature of scientific knowing is correct, the premises of demonstrated knowledge must be true, primary, immediate, better known than and prior to the conclusion, which is further related to them as effect to cause.
71b22. Unless these conditions are satisfied, the basic truths will not be ‘appropriate’ to the conclusion.
71b23. Syllogism there may indeed be without these conditions, but such syllogism, not being productive of scientific knowledge, will not be demonstration.
71b25. The premises must be true: for that which is non-existent cannot be known—we cannot know, e.g., that the diagonal of a square is commensurate with its side.
71b26. The premises must be primary and indemonstrable; otherwise they will require demonstration in order to be known, since to have knowledge, if it be not accidental knowledge, of things which are demonstrable, means precisely to have a demonstration of them.
71b29. The premises must be the causes of the conclusion, better known than it, and prior to it; its causes, since we possess scientific knowledge of a thing only when we know its cause; prior, in order to be causes; antecedently known, this antecedent knowledge being not our mere understanding of the meaning, but knowledge of the fact as well.
Now, ‘prior’ and ‘better known’ are ambiguous terms, for there is a difference between what is prior and better known in the order of being and what is prior and better known to man. I mean that objects nearer to sense are prior and better known to man; objects without qualification prior and better known are those further from sense. Now, the most universal causes are furthest from sense and particular causes are nearest to sense, and they are thus exactly opposed to one another.
72a5. In saying that the premises of demonstrated knowledge must be primary, I mean that they must be the ‘appropriate’ basic truths, for I identify primary premise and basic truth.
We suppose ourselves to possess. After indicating the need for the demonstrative syllogism, the Philosopher now begins to settle questions concerning the demonstrative syllogism itself.
And his treatment is divided into two parts.
In the first he determines concerning the demonstrative syllogism.
In the second, he determines concerning the middle from which the demonstrative syllogism proceeds in book 2, at the kinds of question we ask (90b21; [407]).
In the first he determines concerning the demonstrative syllogism in itself.
In the second he compares demonstration to demonstration, at: since demonstrations may be either commensurately universal or particular (85a12; [323]).
In the first he determines concerning the demonstrative syllogism.
In the second he shows that one does not proceed to infinity in demonstrations, at: every syllogism is effected by means of three terms (81b10; [255]).
In the first he determines concerning the demonstrative syllogism through which we acquire science.
In the second he shows how we also acquire ignorance through a syllogism, at: ignorance, defined not as the negation of knowledge (79b23; [221]).
Concerning the first he does three things.
First, he determines concerning the demonstrative syllogism by showing what it is.
Second, he determines concerning the matter of the demonstrative syllogism, pointing out the nature and character of the matter out of which it is formed, at: since the object of pure scientific knowledge (73a21; [79]).
Third, he determines concerning the form of the syllogism, pointing out the figure in which it is chiefly presented, at: of all the figures the most scientific (79a17; [213]).
Concerning the first he does three things.
First, he shows what the demonstrative syllogism is.
Second, he clarifies certain terms that appear in the definition of the demonstrative syllogism, at: a basic truth in a demonstration (72a8; [44]).
Third, he excludes certain errors that could arise from his doctrine on the nature of demonstration, at: some hold that, owing to the necessity of knowing (72b5; [60]).
In regard to the first it should be noted that in all things which exist for an end, the definition which employs a final cause is both the explanation of the definition which expresses the material cause, and is the middle which proves the latter. For the reason why a house should be made of stone and wood is that it is a structure protecting us from the cold and heat. Along these lines, therefore, he gives two definitions of demonstration, one of which is expressed in terms of the end of demonstration, which is to know in a scientific manner. And from this one is concluded the other, which is drawn from the matter of a demonstration.
Hence he does three things in regard to this.
First, he defines what it is to know in a scientific manner.
Second, he defines demonstration in terms of its end, which is to know in a scientific manner, at: what I now assert is that at all events (71b18; [36]).
Third, from these two definitions he concludes to that definition of demonstration which is expressed in terms of the matter of demonstration, at: assuming then that my thesis (71b19; [37]).
Concerning the first he does five things.
First (71b9), he determines what the scientific knowing, which he intends to define, bears upon.
And in regard to this it should be recognized that we are said to know something in a scientific manner absolutely, when we know it in itself. On the other hand, we are said to know something in a scientific manner qualifiedly, when we know it in something else in which it exists either as a part in a whole (as we are said to know a wall through knowing the house), or as an accident in its subject (as in knowing Coriscus we are said to know who is coming toward us), or as an effect in its cause (as in the example given earlier, we know the conclusion in the principles), or indeed in any fashion similar to these. To know in these ways is to know incidentally, because we are said to know that which is somehow accidental to what is known of itself.
However, what the Philosopher intends to define here is scientific knowing in the strict sense and not according to an accident. For this form of knowing is sophistical, since Sophists use a form of argument typified by the following: “I know Coriscus; Coriscus is coming toward me: therefore, I know the person coming toward me”.
Then, at: when we think that we know the cause (71b10), he presents the definition of scientific knowing in the strict sense.
Apropos of this it should be noted that to know something scientifically is to know it completely, which means to apprehend its truth perfectly. For the principles of a thing’s being are the same as those of its truth, as is stated in Metaphysics II. Therefore, the scientific knower, if he is to know perfectly, must know the cause of the thing known. But if he were to know the cause by itself, he would not yet know the effect actually—which would be to know it absolutely—but only virtually, which is the same as knowing in a qualified sense and incidentally. Consequently, one who knows scientifically in the full sense must know the application of the cause to the effect. Again, because science is also sure and certain knowledge of a thing, whereas a thing that could be otherwise cannot be known with certainty, it is further required that what is scientifically known could not be otherwise.
To repeat: because science is perfect knowledge, he says, when we think that we know the cause; but because the knowledge through which we know scientifically in the full sense is actual, he adds, as the cause of that fact. Finally, because it is certain knowledge, he adds, and that the fact could not be other than it is (71b11).
Third, at: now, that scientific knowing (71b12), he explains the definition he laid down, appealing to the fact that both those who know scientifically and those who do not know in that way but believe that they do, take scientific knowing to be as above described. For those who do not know in a scientific manner but believe that they do, are convinced that they know in the manner described, whereas those who know in a scientific manner do know in the manner described.
Furthermore, this is the proper way to manifest a definition. For a definition is the notion which a name signifies, as it is stated in Metaphysics IV. But the signification of a name must be based on what is generally meant by those who employ the name. Hence it is stated in Topics II that names must be used as the majority of people use them.
Again, careful consideration would indicate that this explanation seems rather to show what the name signifies than to signify something directly. For he does not explain science, concerning which a definition could, properly speaking, be formed, since it is a species of some genus; rather he explains scientific knowing. Hence at the very beginning he said, we suppose ourselves to possess unqualified scientific knowledge (71b8; [28]) and not that scientific knowledge is such and such.
Fourth, at: consequently the proper object (71b15), he draws a corollary from the definition, namely, that that of which there is unqualified scientific knowledge must be something necessary, that is, which cannot be otherwise.
Fifth, at: there may be another manner of knowing (71b16), he answers a tacit question, namely, whether there is another way of knowing scientifically in addition to the way described here. And he promises to discuss this later. For it is possible to know scientifically through an effect, as will be explained below [192]. Furthermore, there is a sense in which we are said to know scientifically the indemonstrable principles to which no cause is ascribed. But the proper and perfect manner of knowing scientifically is the one we have described.
Then, at: what I now assert is that at all events (71b17) he defines the demonstrative syllogism in terms of its end, which is to know in a scientific manner.
In regard to this he does three things.
First, he asserts that scientific knowing is the end of a demonstrative syllogism or is its effect, since to know scientifically seems to be nothing less than to understand the truth of a conclusion through demonstration.
Second, at: by demonstration I mean a syllogism (71b18), he defines demonstration in terms of the end, saying that a demonstration is a sciential syllogism, that is, producing scientific knowledge.
Third (71b18), he explains, sciential, saying that a sciential syllogism is one according to which we know scientifically insofar as we understand it, and not in the sense of a syllogism yielding knowledge to be put to use.
Then, at: assuming then that my thesis (71b19) he concludes from the foregoing a definition of the demonstrative syllogism that is based on its matter.
Concerning this he does two things.
First, he concludes it.
Second, he clarifies it, at: the premises must be true (71b24; [40]).
Concerning the first he does three things.
First (71b20), he sets forth the consequent in which the material definition of demonstration is concluded from the premises laid down above. And he says that if scientific knowing is what we have stated it to be, namely, knowing the cause of a thing, etc., then it is necessary that demonstrative science, that is, science acquired through demonstration, proceed from propositions which are true, first, and immediate, that is, not demonstrated by some other middle but clear in virtue of themselves (they are called immediate, inasmuch as they do not have a middle demonstrating them, but first, in relation to other propositions which are proved through them); and which, furthermore, are better known than, prior to, and causes of, the conclusion.
Second, at: unless these conditions are satisfied (71b22), he justifies himself for not adding another element which, it might seem, should be added, namely, that demonstration proceeds from proper principles. But he says that this is understood in virtue of the elements he did state. For since the propositions of a demonstration are causes of the conclusion, they must be its proper principles. For effects require proportionate causes.
Third, at: syllogism there may indeed (71b23), he manifests the necessity of the aforesaid consequence, saying that although a syllogism does not require these conditions in the premises from which it concludes, a demonstration does require them, for otherwise it would not produce science.
Then, at: the premises must be true (71b25) he explains this definition as well as the subsequent statement that unless these conditions are fulfilled in a demonstration it cannot beget science.
First, therefore, he shows that a demonstration must proceed from true principles in order to beget science, because there cannot be scientific knowledge of that which does not exist, for example, that the diagonal is symmetrical, that is, commensurable with the side of the square. For those quantities are said to be incommensurable which lack a common measuring unit. These are quantities whose ratio to one another cannot be expressed in terms of one number to another number. That this is the case with the diagonal of a square and its side is plain from Euclid’s sixteenth proposition. Now, what is not true does not exist, for to be and to be true are convertible. Therefore, anything scientifically known must be true. Consequently, the conclusion of a demonstration which does beget scientific knowing must be true, and a fortiori its premises. For the true cannot be known in a scientific way from the false, although something true can follow as a conclusion from something false, as he will show later [118].
Second, at: the premises must be primary and indemonstrable (71b26), he shows that the demonstration is composed of first and immediate or indemonstrable principles. For no one can possess scientific knowledge unless he possesses the demonstration of things that can be demonstrated, and I am speaking essentially and not accidentally. He says this because it would be possible to know some conclusion without having a demonstration of the premises, even were they demonstrable; because one would know it through other principles, and this would be accidental.
Suppose, therefore, that a demonstrator syllogizes from demonstrable, that is, mediate, premises. Now, he either possesses a demonstration of those premises or he does not. If he does not, then he does not know the premises in a scientific way; nor consequently, the conclusion because of the premises. But if he does possess their demonstration, then, since one may not proceed to infinity in demonstrations, principles immediate and indemonstrable must be reached. And so it is required that demonstration proceed from principles that are immediate either straightway or through middles. Hence it is stated in Topics I that demonstration is composed of first and true statements or of statements made credible by these.
Third, at: the premises must be the causes of the conclusion (71b29), he proves that the propositions of a demonstration are the causes of the conclusion, because we know in a scientific manner when we know the causes.
And in virtue of this he shows that they are prior and better known, because every cause is by nature prior and better known than its effect. However, the cause of a demonstrated conclusion must be better known not only with respect to the knowledge of what it is, but also with respect to the knowledge that it is. For in order to demonstrate that there is an eclipse of the sun, it is not enough to know that the moon is interposed; in addition it is necessary to know that the moon is interposed between the sun and the earth.
Again, because prior and better known are taken in two ways, namely, in reference to us and according to nature, he says that the things from which a demonstration proceeds are prior and better known absolutely and according to nature, and not in reference to us.
To elucidate this he says that those things are prior and better known absolutely, which are farthest from sense, as are universals; but the prior and better known in reference to us are nearest to sense, namely, the singulars, which are opposed to universals in the way that the prior and the later are opposite, or in the way that the nearest and the farthest are opposite.
However, it seems that the contrary of this is found in Physics I where it is stated that universals are prior in reference to us and later according to nature.
But it should be said that there [in the Posterior Analytics] he is speaking of the order of singular to universal absolutely; and this order must be taken according to the order of sensitive and intellectual knowledge in us. Now, in us sensitive knowledge is prior to intellectual, because intellectual knowledge in us proceeds from sense. For this reason the singular is prior and better known in relation to us than the universal. But in Physics I he is not speaking of the order of the universal to the singular absolutely but of the order of the more universal to the less universal, for example of animal to man. In this case the more universal is prior and better known in reference to us. For in every instance of generation, that which is in potency is prior in time but is later according to nature; whereas that which is complete in act is prior by nature but later in time. Now, one’s knowledge of a genus is, as it were, potential in comparison to one’s knowledge of the species in which all the essentials of a thing are actually known. Hence, too, in the generation of our science, knowledge of the more common precedes knowledge of the less common.
Again, in the Physics it is stated that it is natural for us to proceed from what is better known to us. Therefore, it seems that a demonstration is composed not of things that are prior absolutely but in reference to us.
But it must be said that here he is speaking according to the fact that what is in the sense is better known in reference to us than what is in the intellect; but there he was speaking according to the fact that what is better known in reference to us is also in the intellect. But demonstrations do not proceed from singulars which are in the sense but only from universals, which are in the intellect.
Or it might be said that in every demonstration one must proceed from things better known to us, provided they are not singulars but universals. For something is made known to us only by that which is more known to us. But sometimes that which is more known in reference to us is also more known absolutely and according to nature, as happens in mathematics where on account of abstraction from matter the demonstrations proceed from formal principles alone. In this case the demonstrations proceed from things which are more known absolutely. But sometimes that which is more known in reference to us is not more known absolutely, as happens in natural sciences where the essences and powers of things are hidden, because they are in matter, but are disclosed to us through the things which appear outwardly. Hence in these sciences the demonstrations are for the most part made through effects which are better known in reference to us but not absolutely. But he is not now speaking of this form of demonstration, but of the first.
Finally, because in his explanation he neglected to point out that demonstration should proceed from proper principles, he hastens to add that this fact is easily ascertainable from what he did say. For from the fact that he stated that demonstration is from things which are first, it follows that it is from proper principles, as he stated above. For first and principle seem to be the same: for that which is first and highest in each genus is the cause of all the things that are after it, as it is stated in Metaphysics 2.