In this lesson, we study the second chapter of Aristotle’s Prior Analytics, the third book of the Organon. For tutorial resources on this lesson, please see the Academy YouTube channel. This lesson is studied in the Academy’s Classical Reasoning II course. The text below is adapted from Thomas Taylor’s translation of Aristotle’s Prior Analytics[efn_note]Aristotle, Prior Analytics. Translated by Thomas Taylor (1819). https://classicalliberalarts.com/resources/TAYLOR_PRIOR_ANALYTICS.pdf[/efn_note]
Since, however, every proposition is either of that which is simply present, or of that which is present from necessity, or of that which may happen to be present; and of these, some are affirmative but others negative, according to each appellation; and again, since of affirmative and negative propositions, some are universal, others particular, and others indefinite.
Conversion of Simple Propositions
This being the case, it is necessary that the universal negative proposition of that which is present should be converted in its terms. Thus, for instance, if “No pleasure is good.”, then, “No good is pleasure.”
And it is necessary that a universal affirmative proposition should be converted, but not universally, but particularly. For instance, if “All pleasure is good.”, then it would be necessary that “Some good is pleasure.”
And of particular propositions, it is necessary that an affirmative particular proposition should be converted particularly; for if “Some pleasure is good.”, then, “Some good is pleasure.”. But it is not necessary that a negative particular proposition should be converted. For it does not follow that if “Some animal is not man.”, that “Some man is not animal.”.
Let the proposition A B be the first negative universal. Hence, if A is present with no B (that is, “No B is A”.), neither will B be present with any A (that is, “No A is B.”). For if B should be present with some A, as for instance, with C, it will not be true that A is present with no B; since C is something of B.
But if A is present with every B, B will be present with some A. For if with no A, neither will A be present with any B; but it was supposed to be present with every B.
Conversion also is in a similar manner produced, if the proposition is particular. For is A is present with some B, it is also necessary that B should be present with some A. For if it is present with no A, neither will A be present with any B. But if A is not present with some B, it is not necessary that B also should not be present with A. For instance, if B is animal, but A is man; man, indeed, is not present with every animal (i.e., is not participated by every animal), but animal is present with every man.