Scriptum super libros Posteriorum

by Walter Burleigh

translated by John Longeway, from

the edition of Pamphilius de Montebononiensis, Venice 1514

      Chapter 17

          [I.23 84b31-85a12] (43rb) “When there is a need to etc.” (Cum autem indigeat etc.) This is the twentieth conclusion of this book, that for a <negative> conclusion it is necessary to have only one negative element. This conclusion is proved thus: Say a conclusion is concluded from mediated premisses of which one is affirmative and the other negative. The affirmative cannot be demonstrated except from two affirmatives. And if the negative needs to be demonstrated, since it cannot be demonstrated from two negatives, for nothing follows syllogistically from two negatives, therefore it is necessary that it be demonstrated from one affirmative and one negative. And if this negative is immediate we have what was proposed, for there is only on elementary proposition for the negative conclusion. But if it is mediated then there is a beginning to demonstration, therefore one does not proceed indefinitely. It is necessary at last to arrive at one immediate elementary propostion, that is, a negative <immediate proposition> from which a mediated negative is demonstrated. And thus there will not be many elementary propositions, <neither in general>, nor for any negative conclusion.

      Chapter 18

          [1.24] “Now since demonstration arises etc.” (Cum autem fit demonstratio etc.) In this chapter Aristotle intends to prove that universal demonstration is more powerful and better than particular demonstration. And this is the twenty-first conclusion thus shown.

          Universal demonstration produces knowing more than particular demonstration, therefore etc. The antecedent is obvious, for knowing is the cognizing of a reality through its cause. But universal demonstration produces knowing through the cause more than particular demonstration. Therefore universal demonstration without qualification produces knowing more than particular demonstration.

          It must be understood that there is a difference between universal and particular demonstration, for in universal demonstration its proper passion is concluded of its subject primarily, as with a demonstration in which having three angles is concluded of triangle.

          [1.25] The twenty-second conclusion is this, that an affirmative demonstration is from stronger propositions than is a negative demonstration, therefore etc. Proof of the antecedent: For affirmative demonstration is more powerful than negative demonstration. This conclusion is proved thus: Affirmative demonstration is from stronger propositions than negative demonstration, therefore etc. Proof of the antecedent: For affirmative demonstration is from affirmative propositions, but an affirmative proposition is stronger than a negative proposition, for an affirmative proves a negative, but not vice versa.

          [I.26] The twenty-third proposition of this book is that direct demonstration (demonstratio ostensiva) is more powerful and nobler than indirect demonstration (demonstratio ducens ad impossibilem). This conclusion is proved thus: That demonstration is more powerful that is from stronger propositions. But direct demonstration is from stronger propositions than indirect demonstration. Therefore etc.

          The twenty-fourth conclusion of this book is that knowledge from prior <principles> is more certain. This conclusion is proved thus: Knowing is cognizing through the cause, but among those that are prior there are found more fundamental causes (magis sunt causae), therefore etc.

          [I.27] The twenty-fifth conclusion of this book: That the science that produces knowledge of the fact and the reason why is more certain and better than that which produces knowledge of either of these alone. This conclusion is proved thus: That science is better that produces knowing more, but that which produces knowledge of the fact and the reason why produces knowing more than that which produces knowledge of either of these alone; therefore etc.

          The twenty-sixth conclusion of this book is that that is more certain which is about simpler realities than that is which is about composite realities. This conclusion is proved thus: What is simpler is prior according to nature, and is more certain and better according to nature, therefore that science is more certain and better which is about simpler realities.

          The twenty-seventh conclusion of this book, which is about two sciences that are raised up on abstract realities, therefore that science which is raised up on simpler realities is more certain than <that which is raised up> on composite <realities>. And this is proved as in the preceding.

      Chapter 19

          [1.28] “Now since knowledge etc.” (Quia autem scientia etc.) Having seen how one science is more certain than another, the Philosopher explains in this chapter what is required for the unity of a science. He says that three things are required for the unity of a science, namely, the unity of the subject from which demonstration arises, and, in the second place, it is required that the subject have principles from which (43va) demonstrations can be made, and, in the third place, it is required that the subject have appearances (species) or per se accidents from which a demonstration or demonstrative conclusion can be constructed.

          [I.29] The twenty-eighth conclusion is that there can be several demonstrations of one conclusion, and several middle terms. This conclusion is proved thus: It is the same reality from which a reality has the ordered principles or the ordered middle terms received in these principles. Thus one conclusion can be obtained through different middle terms not ordered to one another. And consequently there can be several demonstrations of one conclusion.

          [I.30] The twenty-ninth conclusion is that demonstration does not arise from what is only by chance (res casuales). This conclusion is proved thus: Every demonstration is either of a fact (rei) that is always the case or of a fact that is for the most part the case. But what happens by chance is not always, nor for the most part, the case. Therefore there is neither science nor demonstration of what is only by chance.

          [I.31] The thirtieth conclusion is this, that from sensibles realities insofar as they are sensible there does not arise any demonstration. This conclusion is proved thus: Demonstration is of universals, but sensible realities are all singular, since the senses are of singulars, and the intellect of universals. Therefore demonstration does not arise from sensibles.

          [I.32 88a18-88b15] The thirty-first conclusion is that it is not possible for everything to be demonstrated from the same principles, which is proved thus: Not every syllogism has the same principles, for some are from true terms and some from false. But the same principles are not both true and false. Therefore etc.

          Again, not every false syllogism has the same principles, for the principles of some false syllogisms are contrary, and contraries are not the same. In the same way, not every true syllogism has the same principles, nor every demonstrative syllogism. For there are necessarily different principles for realities that do not have a genus in common, as for instance, there are different principles in geometry and arithmetic, namely the point and unity.

          [I.32. 88b15-19] The thirty-second conclusion is that one conclusion is not demonstrated from every principle, which is proved thus: For if it is, then everything can be demonstrated, which was disproved in the beginning.

      Chapter 20

          [I.33, 34] “Now a knowable etc.” (Scibile autem etc.) In this chapter Aristotle determines the facts about the habits of science, namely knowledge (scientia) and opinion (opinio), understanding (intellectus) and acumen (solertia). Knowledge differs from opinion since it concerns what is universal and necessary, and opinion concerns what is contingent and not necessary. This much is obvious. For understanding, which is the habit of principles, is not of contingent things, but of necessary things. But every <true> habit is either understanding, knowledge, or opinion. Hence opinion is of contingent things, for opinion, according to the Philosopher, is the reception of a proposition immediately, and not necessarily. Acumen is a certain subtlety in discovering the middle <of demonstration> quickly.