Philoponus: On Aristotle's Prior Analytics

The non-convertible referring to a type of sign that does not work in both directions is likely, as in the case of being pale and being pregnant. He says that the "sign" is intended to be a demonstrative proposition. He used the word "intended" well, for one who reasons through a sign uses it as if it were a demonstrative proposition. Yet it is not demonstrative, not even if the sign is necessary. For if the sign follows that of which it is a sign, then demonstration proceeds not only from known things but also from primary and immediate ones. Of signs, some are necessary, such as smoke for fire; others are reputable, such as paleness for pregnancy. Again, signs either indicate that a thing is present when it is present, as smoke indicates fire, or that it has come to be when it has come to be, as ash indicates fire, or that it will come to be when it will come to be, as spontaneous pains indicate diseases.

(f. 351v Z) + Regarding the enthymeme + (p. 70a 10) The enthymeme is a syllogism from probabilities or [signs]: Of Philoponus in margin Z: Wishing to show what an enthymeme is, since it is taken from probabilities and signs, he anticipates the teaching regarding these and says that a probability is a reputable proposition. inc. f. 174r Y For what is agreed upon by all to occur, or not to occur, or to be or not to be, as a general rule, this is a probability. For example, hating the envious. For every one who is envied hates those who envy him. This is a reputable proposition according to probability. And everyone who envies hates the one being envied, which is also a matter of necessity. It must be known that the enthymeme is a single-premise rhetorical syllogism. It is called single-premise because one proposition is uttered by the speaker or writer, and the other is passed over. As for instance, "So-and-so wanders by night; he is a thief." For he omitted the major premise that says, "Everyone who wanders by night is a thief." Again, "So-and-so won the Olympic games." Conclusion: "He won a sacred contest." For here too the major premise was omitted, which says, "Everyone who wins the Olympic games wins a sacred contest." Because of this, it is called an enthymeme, because the omitted proposition is considered enthymeisthai to keep in mind/think over and is understood by the listener for themselves.

f. 182r (om. Z). Of John Philoponus.

Such a mean referring to harmonic proportion was called harmonic because the five musical ratios are considered within it, as we will show in the examples that Nicomachus mentions. It must be known that some are considered only in the terms themselves, others in the differences of the ratios, and others in both the differences and the terms. Therefore, one must exercise the logic on the first example, which is the 6, 4, 3. For here is the "through five" the interval of a perfect fifth, that is, the hemiolic ratio ratio of 3:2 of 6 to 4. And the "through four" the interval of a perfect fourth, that is, the epitritic ratio ratio of 4:3 of 4 to 3. And the "through all" the octave, that is, the double ratio of the extreme terms to each other, such as 6 to 3. And the "through all and through five" the perfect twelfth, an octave plus a fifth, that is, the triple ratio of the greater extreme to the difference between the greater and the mean. And the "twice through all" the double octave, that is, the quadruple ratio, comes from the mean compared to the difference of itself and the lesser. And thus, in the first example, we have demonstrated all the ratios. On the second, again, we have the same things to demonstrate, for the 6, 3, 2. For it is possible to observe here also the "through all," that is, the double ratio, for 6, 4, 3, the double of 3; and the "through five," that is, the hemiolic. For 3 is hemiolic to 2. Likewise also the "through all," that is, the double ratio. For 6 is double of 3. And the "through five," that is, the triple. For 6 is triple of 2. And the "twice through all," that is, the quadruple ratio, can be found if you compare the difference of the greater to the lesser with the difference of the mean to the lesser. For example, the difference of the greater to the lesser is 4. For 6 compared to 2 has a difference of 4. The difference of the mean to the lesser is 1. For 3 differs from 2 by 1. And 4 is quadruple of 1. Thus we have also found the quadruple ratio. And the "through four," that is, the epitritic, is found if you compare the difference of the extremes to the mean term. For the difference of the extremes is 4. And the mean term is 3. And 4 is epitritic to 3.