Universa Philosophia

Ascent and descent are called by some argumentatio, by others consequentia, by others inductio. Ascent is a consequence from singulars sufficiently enumerated to the universal. That phrase, sufficiently enumerated, is put in place of the constantia of the old Summulists: for which the most constant is Soto, 2nd part of the introduction, chapter 3, lecture 1, notable 4. which Toletus and Villalpandus rightly omitted: But if the singulars are not enumerated sufficiently, the consequence will be inept, e.g. if someone were to say to the Master, all Scholastics have studied, and proved it because Peter studied, and likewise Paul, if he did not count Francis, the consequence is null, because he might not have studied. Hence the argument from induction in universal concepts is very weak, and not in the least formal: for all the singulars are impossible for man to enumerate. For if someone proves that every fire heats, because all fires in Spain heat, someone will say that there are some fires in Belgium which do not heat; for who would persuade the Ethiopian that there are white men? or the Indians that there are bearded men? It is necessary therefore to have recourse to some account which has the same force in each.

Descent is a consequence from the universal to singulars, as omnis homo currit has consequences to each one, and it can be proved that individual men run, because every man runs. It serves for verifying universal propositions, for which the individuals must be run through one by one: and for showing their falsity, for which it suffices to descend to one alone; for example, if someone says every man runs, for its falsity it is enough if Peter does not run: ascent is so called because the universal concept embraces all singulars, and because from one and another enumerated the universal consequence embraces the singulars which had been recounted in particular: which is to ascend; on the contrary descent, because from all taken together it turns down to the singulars one by one.

The Summulists divide ascent and descent fourfold, into copulate and copulative; disjunct and disjunctive. Copulative is when descent is made from the universal to singulars, as omnis homo currit, ergo et Petrus currit, et Paulus currit: because, they say, one proposition is coupled to the others. But this descent is distributive, because we distribute the common predicate to each of the inferior terms. They call descent copulate when one descends from the superior to the inferiors not one by one and separately, but collected: as all the Apostles are twelve, thus by descent it is explained, therefore Peter, Andrew, and the other Apostles are twelve, a true doctrine, but this descent is the same as copulative; for I have shown that the difference between copulate and copulative cannot be sought without trifling. They call descent disjunctive when one descends from the common account to singulars with a disjunction, or, as a man, or some man runs, therefore either Peter runs, or Paul runs. This doctrine I approve. They call it disjunct when one descends from the common account to particulars, not stopping in the singulars by themselves, but descending to all under a disjunction, as a horse is required for riding, it infers, therefore either this one, or that one, or another is required; for none is required in particular.

This distinction of descent from disjunctive has been impugned at §30 against Father Fonseca; and it is impugned against the other Summulists: because that proposition Aliquo equo equitatur has a disjunctive descent according to the opinion of the Summulists, but it also has the descent which they call disjunct, therefore these descents are not distinguished. I prove the minor: in it descent is made to all the singular horses recounted under a disjunction, so that it does not stop determinately in any one, therefore it is a copulate descent. I prove the antecedent: because descent is a consequence from the universal to the singular; but from that proposition there is no consequence from the universal to some singular by stopping determinately in it, but descent is made to all with the disjunction or, but to none in particular, therefore. The minor is proved, because this is a bad consequence, aliquis homo currit, ergo Petrus currit: but this consequence is good, ergo, vel Paulus, vel aliquis alius currit, because one descends to all individuals taken vaguely, but to none in singular.

You will say that in the copulative descent the truth of the proposition is taken from one determinate individual by stopping in it, without need to proceed to the others; therefore aliquo equo equitatur is a true proposition, because now Bucephalus is ridden, but in the disjunct sense it is false, because Bucephalus is not required for riding in particular, because without him one can ride. Wherefore this proposition, aliquis equus requiritur ad equitandum, is not true in any determinate individual, but vaguely; because in particular none is required; but it is required vaguely. On the contrary I showed at §30 that by that proposition it is not signified that some horse is required in particular; and since this is not signified, descent cannot be made to particulars in particular; but it is made confusedly similarly in this, aliquo equo equitatur: because although on the part of the thing Phoebus is ridden, yet that is not inferred, neither by that proposition nor by its descent: for it is a bad consequence, ergo Phaebo equitatur: but this is good, ergo Phaebo aut Brunello equitatur, aut alio equo, therefore the descent is the same in both propositions. I gave the reason a priori at §30. and indeed the consequence in descent is not taken from things as they are: for on the part of the thing there is no vague individual, but every one is determinate, but confusion is in the intellect: whence the account in the ascent and descent of a confused proposition must be weighed from the mode of conceiving.

Note that descent preserves the signification of the universal proposition from which they are derived, otherwise the consequence will be inept, e.g. every man in particular runs, has the consequence, therefore Peter in particular runs, and John, and so on: similarly this proposition, aliquo equo curritur, does not have this descent, aliquo equo in particulari curritur: but it has this descent, therefore either Brunellus in particular is run, or Phoebus in particular is run, because in that universal proposition the running is signified as actually existing, which cannot be except in particular, and from a particular cause: but the word aliquis does not denote indetermination in the running itself, but confusion in the mode of conceiving, on account of which confusion the singular existing running is not well penetrated; which confusion is retained in the descent signified by the disjunctions vel, aut, and because the consequence is a note of inference, or of intellection deduced from the antecedent: therefore in the descent one does not stop in any singular, but all are run through under disjunction, because from the force of the antecedent and of the mode by which it is signified, the intellect cannot infer that Peter runs in particular, even though he runs in reality, because consequences do not so much stop in the things themselves as in the mode by which they are deduced from the antecedent cognition. But in this proposition, aliquis equus requiritur ad cursum, confusion is not signified on the part of the mode of conceiving, but indetermination is signified on the part of the object, because although I see all horses most clearly, and in that mode of conceiving there is no confusion, I can say, some one is required, because it makes this sense, without a horse one cannot run, yet one can without this one and without that one: whence no necessity of any one in particular is signified; so that here one is necessary to such a degree that without it one cannot run, for in the others there is the power to run. Behold in what way, with the signification of the universal proposition retained, one descends disjunctively, and disjunctly to all singulars, and in no way does the disjunct descent differ from the disjunctive, just as there is no difference between these descents, every man in particular runs, therefore Peter in particular, and so on. likewise, every man runs, therefore Peter runs.

But because the Summulists by disjunct and disjunctive descent signify those two modes of suppositing for an individual confusedly known, and for an individual signified indeterminately on the part of the object, that is, when in each individual there is found whatever is necessary for the truth of the proposition: so that it is not found in one alone, but in all, on account of which some one of them is required, yet not this one, so that without it it cannot be done, as some eye is required for seeing, yet the right eye is not required, so that one cannot see with the left also. Let us not depart from the common opinion, but let us admit those two descents, observing this one thing, that in this disjunct supposition no vague individual is signified, which on its own part is vague, but that there is signified a power of running in any horse whatever, not however in one alone, for it is also in several other horses, and because that power is in others, none in singular is necessary. But when it is said, some horse is required for running, it has this sense, one can run with any horse whatever, but none in particular is required, but any one is sufficient, it is just as if the power of running is in all and each.

From this it follows that none in singular is necessary, because when it is removed, there can be another by which one runs: but if that power were in one alone, that one would be required in particular, as God is required for creating, because he alone has creative power, but in these no confusion is found, although by the word aliquis it seems to be signified, because by it we more frequently signify a confused mode of conceiving: observe these things, however, because from their confused knowledge many things are handed down less clearly. Likewise note that in a particular proposition signifying an act, the consequence holds in one singular with the others excluded, e.g. Some man runs, if Peter does not run, and there is no other but Paul, it follows well, therefore Paul runs, because there the thing is signified as exercised on the part of the thing, which is necessarily determinate: but in a particular proposition denoting a power, that exclusion of the others cannot be made, e.g. Some horse is required, one cannot say: Bucephalus is required, if the others are not required: because the power of running is found in the others as in Bucephalus, but the running is found in Paul alone, and the others can be excluded.

There is therefore in reality a threefold descent: distributive, from a universal proposition to singulars with the conjunction and, or the disjunction nec, which they call copulative: the second is copulative, or coupled, from the universal to singulars taken together, which they call copulate: the third disjunct, or disjunctive, from a confused universal to singulars also confusedly. This, on account of the Summulists, I divide in two; one is called disjunctive, when one descends from the confused universal to singulars; whose truth is found in one determinate singular, as aliquis homo currit has its truth in Peter alone running: the other which they call disjunct, as aliquis oculus requiritur ad visum, whose truth is found in no determinate one, but in all in the sense explained at §38. and just as they call the distributed descent copulative, because one descends to singulars in particular without the conjunction of one with another, but they call it copulate when one descends not to one but to several conjoined; so they call it disjunctive when one singular suffices without the others, but disjunct when none suffices, but all confusedly. There are no more descents, because the common terms from which one descends supposit in these three modes.

There are just as many ascents, because from singulars copulated, or disjoined, one ascends to a common proposition, and in just as many modes does one ascend from them to the universal, as one descends from the universal to singulars, as Peter, or Paul runs, therefore some man runs. Likewise Peter runs, Paul, and so on, therefore every man runs. Here many rules are handed down, but without advantage, for one descends or ascends from those terms which are either distributed, or copulated, or disjoined, and not from others, which is seen from the proposition itself, as every servant of the college sleeps, therefore this servant of the college, and that one and so on, as every servant grounds the descent, for that term is distributed, but the college does not ground the descent there, whence it would be badly inferred, therefore this servant of this colleague sleeps, because he is not a servant of the college, therefore servant of the college is not distributed through that, but through the individual servants of the whole college.