Commentary Aristotle Posterior Analytics
Lecture 21
The questions, responses and disputations peculiar to each science a36. If a syllogistic question is equivalent to a proposition embodying one of the two sides of a contradiction, and if each science has its peculiar propositions from which its peculiar conclusion is developed, then there is such a thing as a distinctively scientific question, and it is the interrogative form of the premises from which the ‘appropriate’ conclusion of each science is developed. Hence it is clear that not every question will be relevant to geometry, nor to medicine, nor to any other science: a42. only those questions will be geometrical which form premises for the proof of the theorems of geometry or of any other science, such as optics, which uses the same basic truths as geometry. Of the other sciences the like is true.
b2. Of these questions the geometer is bound to give his account, using the basic truths of geometry in conjunction with his previous conclusions; of the basic truths the geometer, as such, is not bound to give any account. The like is true of the other sciences.
b6. There is a limit, then, to the questions which we may put to each man of science; nor is each man of science bound to answer all inquiries on each several subject, but only such as fall within the defined field of his own science.
b8. If, then, in controversy with a geometer qua geometer the disputant confines himself to geometry and proves anything from geometrical premises, he is clearly to be applauded; if he goes outside these he will be at fault, and obviously cannot even refute the geometer except accidentally. One should therefore not discuss geometry among those who are not geometers, for in such a company an unsound argument will pass unnoticed. This is correspondingly true in the other sciences.
If a syllogistic question. After showing how demonstrative sciences function in relation to common principles, the Philosopher now shows how they employ proper principles.
And his treatment falls into two parts.
In the first he shows that in each science there are questions, responses and disputations peculiar to each.
In the second he shows how in each science there are deceptions, peculiar to each, at: since there are “geometrical” questions (77b16; [180]).
Concerning the first he does two things.
First, he shows that in each science there are its own questions.
Second, that each science employs the responses and disputations proper to it, at: there is a limit (77b6; [178]).
Concerning the first he does two things.
First, he shows that in each science there are questions peculiar to each.
Second, what these are, at: only those questions will be geometrical (77a42; [176]).
He shows the first (77a36) in the following way. A syllogistic question and a proposition which takes one definite side of a contradiction are the same as to content, but they have not the same function. (For the answer which one gives to the question is made to serve as a proposition in some syllogism). But in each of the sciences, the propositions from which a syllogism is formed, are peculiar to it, for it has been shown that every science proceeds from things proper to it. Therefore, in each science there are questions peculiar to it. Hence not any random question is pertinent to geometry or to medicine or to some one of the other sciences.
However, it should be noted that questioning occurs one way in demonstrative sciences and another way in dialectics. For in dialectics not only the conclusion but also the premises are open to question; but in demonstrative sciences the demonstrator takes premises as per se known or proved by such principles. Hence, he asks only about the conclusion. And when he has demonstrated it, he uses it as a proposition to demonstrate some other conclusion.
Then, at: only those questions will be geometrical (77a42) he explains which questions are peculiar to each science.
First, insofar as they are taken as propositions from which the demonstrator proceeds.
Second, when taken as conclusions, at: of these questions the geometer (77b2; [177]).
He says therefore first (77a42) that geometric questions are ones from which something is demonstrated pertaining to matters of geometry or pertaining to matters demonstrated from the principles of geometry—for example, the ones from which something is demonstrated in optical science, that is, perspective, which proceeds from the principles of geometry. And what is said of geometry applies to other sciences, namely, that a proposition or question is peculiar to a science, if it is one from which a demonstration in that science or in a subalternate science proceeds.
Then, at: of these questions the geometer (77b2) he analyzes geometric questions insofar as they are conclusions, saying that solutions to geometric questions must be proved by demonstrating their truth from geometric principles and from conclusions already demonstrated by those principles. (For sometimes the proofs of certain geometric demonstrations are not drawn from the first principles of geometry, but from matters concluded from those first principles). Hence when it is a matter of questions which are always conclusions in demonstrative sciences, the proof can be obtained in the science itself, but the proof of the principles cannot be drawn from geometry qua geometry. The same also applies to other sciences. For no science proves its own principles, as we have explained above. And he says, “from geometry qua geometry”, because it may happen that a science proves its own principles, insofar as that science assumes the principles of another science, as a geometer proves his own principles insofar as he assumes the role of first philosopher, that is, of metaphysician.
Then, at: there is a limit (77b6), he shows that each has its own responses and disputations.
First, that each has its own responses.
Second, its own disputations, at: if, then, in controversy (77b8).
He says therefore (77b6) that from the foregoing it is clear that each scientific knower does not ask just any question whatever. Hence it is also clear that he will not answer just any random question but only those which conform to his own science on the ground that a question and its answer pertain to the same science.
Then (77b8) because disputations are concerned with a question and its answer, he shows that there are disputations—peculiar to each science, saying that if a geometer disputes with a geometer precisely as geometer, that is, in matters pertaining to geometry, then obviously the disputation goes well if the disputation not only concerns a point of geometry but proceeds from the principles of geometry. But it does not go well, if the disputation in geometry does not proceed along these lines. For if someone disputes with a geometer in matters alien to geometry, it is clear that he does not argue, that is, does not convince, except accidentally: for example, if the dispute concerns music, and the geometer accidentally happens to be a musician. Hence it is clear that one should not dispute in geometry about matters not geometric, because it will not be possible to judge by the principles of that science whether the dispute went favorably or unfavorably: and the same holds for other sciences.