Commentary Aristotle Posterior Analytics
Lecture 5. First and immediate propositions
72a7. A basic truth in a demonstration is an immediate proposition.
72a8a. An immediate proposition is one which has no other proposition prior to it.
72a8b. A proposition is either part of an enunciation, that is, it predicates a single attribute of a single subject
72a9. If a proposition is dialectical, it assumes either part indifferently; if it is demonstrative, it lays down one part to the definite exclusion of the other because that part is true.
72a11. The term ‘enunciation’ denotes either part of a contradiction indifferently. A contradiction is an opposition which of its own nature excludes a middle. The part of a contradiction which conjoins a predicate with a subject is an affirmation; the part disjoining them is a negation.
72a14. I call an immediate basic truth of syllogism a ‘thesis’ when, though it is not susceptible of proof by the teacher, yet ignorance of it does not constitute a total bar to progress on the part of the pupil: one which the pupil must know if he is to learn anything whatever is an axiom. I call it an axiom because there are such truths and we give them the name of axioms par excellence.
72a18. If a thesis assumes one part or the other of an enunciation, that is, asserts either the existence or the non-existence of a subject, it is a hypothesis; if it does not so assert, it is a definition. Definition is a ‘thesis’ or a ‘laying something down’, since the arithmetician lays it down that to be a unit is to be quantitatively indivisible; but it is not a hypothesis, for to define what a unit is is not the same as to affirm its existence.
A basic truth in a demonstration. Because the Philosopher had stated above that demonstration is from first and immediate principles, but had not yet identified them, he now sets out to identify them (72a7).
And this is divided into three parts.
In the first part he shows what an immediate proposition is.
In the second part he shows that such propositions must be better known than the conclusion, at: now, since the required ground of our knowledge (72a25; [53]).
In the third part he excludes certain errors which arose from the foregoing, at: some hold that, owing to the necessity (72b5; [60]).
Concerning the first he does two things.
First, he shows what an immediate principle is.
Second, he divides them, at: I call an immediate basic truth (72a15; [49]).
With respect to the first he proceeds this way.
First (72a7), he recalls what has been said above, namely, that a principle of demonstration is an immediate proposition, for he had also stated above that a demonstration is composed of things which are first and immediate.
Second, at: an immediate proposition (72a8a), he defines the immediate proposition.
He says that an immediate proposition is one which has no other one prior to it. The reason underlying this description is clear from what has been said. For it has been said above that demonstration is composed of things that are prior. Accordingly, whenever a proposition is mediate, that is, has a middle through which the predicate is demonstrated of its subject, it is required that there be prior propositions by which this one is demonstrated. For the predicate of a conclusion is present in the middle previously to being present in the subject; in which, however, the middle is present before the predicate is. Therefore, it follows that that proposition which does not have some other one prior to it is immediate.
Third, at: a proposition is either part (72a8b), he shows what is the nature of the proposition which is mentioned in the definition of an immediate proposition.
Concerning this he does three things:
First, he defines absolutely what a proposition is, saying that it is one or the other part of an enunciation in which one thing is predicated of one thing. For the enunciation has two parts, namely, affirmation and negation. For anyone who syllogizes must propose one or the other of these parts but not both, for this latter procedure is characteristic of one who first raises a question. (Hence it is on this basis that proposition is distinguished from a problem). For just as one and only one thing is concluded in one syllogism, so the proposition which is a principle of the syllogism should be one—and it is one if one thing is stated of one thing. Hence in asserting that it is one of one, he distinguishes the proposition from the enunciation which is said to be of several, whether sundry things are said of one thing or of one thing sundry.
Second, at: if a proposition is dialectical (72a9), he lays down the difference between the dialectical and the demonstrative proposition, saying that whereas the demonstrative proposition takes one definite side of a question, the dialectical takes either side indifferently. For since dialectic begins with the probable, it can lead to each side of a contradiction. Hence when it lays down its propositions, it employs both parts of a contradiction and presents them in the form of a question.
But a demonstrative proposition takes one side definitively, because a demonstrator never has any other alternative but to demonstrate the truth. Hence in forming its propositions he always assumes the true side of a contradiction. On this account he does not ask but posits something as known in the demonstration.
Third, at: the term “enunciation” (72a11), he defines the term “enunciation,” which appeared in the definition of a proposition, saying that an enunciation embraces both sides of a contradiction, as is clear from what has been said.
Then he shows what contradiction is, saying that contradiction is a form of opposition between whose parts there is of itself no middle. For although between privation and possession and between immediate contraries there is no middle in a given subject, nevertheless, absolutely speaking, there is one; for a stone is neither blind nor seeing, and something white is neither even nor odd. Furthermore, whatever immediacy they have in relation to a definite subject is traced to their participation in contradiction, for privation is negation in a definite subject; and of two things that are immediately contrary, one has some of the marks of privation. But contradiction in the full sense lacks a middle in all cases. And this belongs to it of its very nature and not in virtue of something else. Hence he says that of itself it has no medium.
He then explains what the parts of a contradiction are. For contradiction is an opposition of affirmation and negation; hence one of its parts is affirmation, which asserts something of something, and the other is negation, which denies something of something.
Then, at: I call an immediate basic truth of syllogism (72a14), he divides immediate principle.
Concerning this he does two things.
First, he divides.
Second, he subdivides, at: if a thesis assumes one part or the other (72a19; [51]).
He says therefore first, that there are two types of immediate principles of a syllogism:
the first is called a “position” [thesis] and is said to be immediate because one does not demonstrate (neither is it required that the student, that is, the one being instructed in the demonstrative science, have it, that is, advert to it or assent to it);
the other is called a “dignity” or “maxim,” which anyone who is to be instructed must have in his mind and assent to. That there are such principles is clear from Metaphysics 4, where it is proved that one such is the principle that affirmation and negation are not simultaneously true, for no one can believe the contrary of this in his mind even though he should state it orally. To such principles we give the aforesaid name of ‘dignity’ or ‘maxim’ on account of their certainty in manifesting other things.
To clarify this division it should be noted that any proposition whose predicate is included within the notion of its subject is immediate and known in virtue of itself as it stands.
However, in the case of some of these propositions the terms are such that they are understood by everyone, as being and one and those other notions that are characteristic of being precisely as being: for being is the first concept in the intellect. Hence it is necessary that propositions of this kind be held as known in virtue of themselves not only as they stand but also in reference to us. Examples of these are the propositions that ‘It does not occur that the same thing is and is not’ and that ‘The whole is greater than its part’, and others like these. Hence all the sciences take principles of this kind from metaphysics whose task it is to consider being absolutely and the characteristics of being.
On the other hand, there are some immediate propositions whose terms are not known by everyone. Hence, although their predicate may be included in the very notion of their subject, yet because the definition of the subject is not known to everyone, it is not necessary that such propositions be conceded by everyone. Thus the proposition, ‘All right angles are equal’, is in itself a proposition which is immediate and known in virtue of itself, because equality appears in the definition of a right angle. For a right angle is one which a straight line forms when it meets another straight line in such a way that the angles on each side are equal. Therefore, such principles are received as being posited or laid down.
There is yet another way, and according to it certain propositions are called ‘suppositions’. For there are some propositions which can be proved only by the principles of some other science; therefore, they must be supposed in the one science, although they are proved by the principles of the other science. Thus the geometer supposes that he can draw one straight line from one point to another, but the philosopher of nature proves it by showing that there is one straight line between any two points.
Then, at: if a thesis assumes one part or the other (72a18) he subdivides a member of the original division, namely, ‘position’, and says that there is one type of position which takes one side of an enunciation, namely, either affirmation or negation. He refers to this type when he says, that is, asserts either the existence or non-existence of a subject. Such a position is called a ‘supposition’ or ‘hypothesis’, because it is accepted as having truth.
Another type of position is the one which does not signify existence or non-existence: in this way a definition is a position. For the definition of ‘one’ is laid down in arithmetic as a principle, namely, that one is the quantitatively indivisible. Nevertheless a definition is not called a supposition, for a supposition, strictly speaking, is a statement which signifies the true or the false. Consequently, he adds that the definition of ‘one’, inasmuch as it signifies neither the true nor the false, is not the same as ‘to be one’, which does signify the true or the false.
Now it might be asked how it is that definition is set down as a member of the subdivision of immediate proposition, if a definition is not a proposition signifying either existence or non-existence.
One might answer that in this subdivision he was not subdividing immediate proposition but immediate principle; and the principle of the syllogism can be said to be not only the proposition but also the definition.
Or one might answer that although a definition as such is not an actual proposition, it is one virtually, because once a definition is known, it becomes clear that it is truly predicated of the subject.