Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Since every ascent and descent proceeds from singulars to common terms and conversely, according to the different quantity and supposition of a term—whether it is universal or particular, supposing determinately or confusedly—ascent and descent are applied in different ways.

Two things must therefore be observed. First, which kind of ascent and descent belongs to this or that supposition. Second, what order of descending or ascending under a term is immediate or mediate; this is to resolve the term.

As to the first, there are three rules. First: A term supposing distributively requires conjunctive ascent and descent. Second: A term supposing determinately requires disjunctive ascent and descent. Third: A term supposing confusedly only in a conjunctive way requires compounded ascent and descent; a term supposing confusedly in a disjunctive way requires disjoined ascent and descent. Nevertheless, this compounded or disjoined ascent is not properly resolutory but manifests the truth; for it remains equally unknown to posit a term that supposes confusedly or is enumerated disjunctively. Therefore such a term remains simply unresolved and fixed—that is, it cannot be moved or proceeded through by resolution from singulars to universals or conversely.

As to the second, when a proposition contains several terms supposing in different ways, one cannot descend or ascend under each of them equally immediately. Three rules therefore help us determine this. First: Under a term supposing determinately with respect to a distributed term, one must ascend before descending under the distributed term, although one can descend immediately under the distributed term. The contrary is a fallacy called “from several determinates to a single determinate.” Thus, for ascending, a term supposing determinately is always more suitable; for descending, a distributed term is more suitable. For example, if you say, “Some man is not white,” you cannot rightly descend immediately under the distributed term by saying, “Some man is not this white thing, nor that white thing; therefore some man is not white.” Yet under the particular term supposing determinately you can descend immediately under the distributed term; thus, as to ascent, the resolution depends on that prior step, but not as to descent.

Second rule: Under a term supposing confusedly in a disjunctive way with respect to an antecedent universality, a disjunctive descent is not permitted before descending under the universal term; ascent, however, is valid. For example, if you say, “Every man is an animal,” “Therefore every man is this animal or that animal,” etc., does not follow; but the ascent does follow: “Every man is this animal, or every man is that animal; therefore every man is an animal.” Thus, in descending, the resolution of the confused term depends on resolving the antecedent distributed term. The contrary is the fallacy from one distribution to several, discussed below in chapter 13.

Third rule: If all terms suppose either distributively or determinately, resolution can immediately begin with any term in ascent or descent, insofar as this follows from the force of supposition, unless an impediment arises from another source. For example, in the distributive case, “No man is a stone,” or in the determinate case, “Some man is white”: you can begin with any term. Accordingly, in the ascent of terms, which serves to prove truth, the order is this: first resolve the term standing determinately, second the distributed term. In descent, however, we can begin immediately with a distributed term; with a confused term, only after descending under the distributed term. Ascent and descent are always understood to occur with logical properties unchanged, including kind of supposition, restriction, ampliation, appellation, etc. This is especially to be observed in complex terms, particularly those consisting of a determination and what is determined; differences in restriction are a major obstacle to immediate or mediate resolution, as we shall touch on below when treating the defects of consequences¹ and below in question 7, article 2.

Finally, there are two rules for relatives. First: With a reciprocal relative, one may not perform resolution by ascent or descent before resolving under the antecedent, because it supposes with the same supposition as its antecedent; this is called a sealed supposition. Second: A non-reciprocal relative does not necessarily depend on its antecedent for its resolution. For example, if you say, “Every man is an animal, and that is rational,” one may descend or ascend under “that” before doing so under “every man” or “animal,” just as with a term placed in a separate proposition.