Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

The reduction of modals to propositions de inesse is nothing other than proving or regulating the truth of a modal by the truth of a proposition de inesse. For if it is true that Peter possibly disputes, that is because the proposition de inesse “Peter disputes” has possibility. Note that every modal, if true, is a necessary proposition and an eternal truth, because it applies a mode suited to the proposition’s truth on account of an intrinsic connection. Thus, if you say, “That Peter runs is contingent,” this very proposition is necessary, because contingency necessarily belongs to Peter’s running. From this you may learn how the first cause can cause freedom and contingency in us by acting infallibly: for it causes not only the things themselves but also their modes, giving each its own mode. Thus, divine causation does not entail, for example, that Peter’s walking is necessary, but that Peter’s walking occurs freely and contingently is infallible and necessary, because freedom and contingency belong to that walking intrinsically and necessarily. And because in a compound modal the dictum is posited almost immovably and constitutes one extreme with respect to the mode, in order to resolve a compound modal by descending under the dictum, it must be reduced to its divided modal, to which it is equipollent, as “It is necessary that a man run,” “A man necessarily runs”; then one descends under “man.”

To see how modal propositions are to be reduced to their propositions de inesse, note that “proposition de inesse” is said in two ways. In one way, it lacks modes affecting it and is opposed to a modal proposition; in the other, it is present-tense and is opposed to a proposition about the past or future, which is called one of extrinsic time.

A modal is therefore reduced to its proposition de inesse by forming a proposition de inesse and showing that the mode posited in the modal proposition belongs to it. Thus, if you say, “Peter contingently runs,” it is reduced to its proposition de inesse as follows: “The proposition ‘Peter runs’ is contingent.” This is called the officiating proposition of that modal; the modal is said to be proved or reduced by the officiating proposition de inesse, that is, by showing through a proposition that its own proposition de inesse has such a mode of possibility or contingency belonging to it.

With this supposed, the several rules given for reducing and regulating modals, or propositions of extrinsic time, to their propositions de inesse come down to this: For the truth of a modal proposition or a proposition of extrinsic time that can be reduced immediately to its proposition de inesse, it is sufficient and required that the corresponding mode, or temporal difference, belong to and be verified of its proposition de inesse. For example, for “Peter possibly disputes” to be true, it is sufficient that “Peter disputes” be possible; for “Peter necessarily is a man” to be true, “Peter is a man” must be necessary; and for “Adam existed” to be true, it is sufficient that “Adam is” was true at some time, which is its proposition de inesse; and so in all other cases. I said “a proposition reducible immediately,” because sometimes a prior resolution or explanation of a term is required before it is reduced to its proposition de inesse. For example, “What is white was black” is not verified immediately by “What is white is black” having been true at some time; rather, it is verified by resolving the amplified subject as follows: “This is or was white,” and “this”—namely, what is white—“was black at some time.” Similarly, where there is a double copula, as in “Peter was and will be white,” each copula must first be resolved into its own copulative proposition, and then each categorical proposition is reduced or regulated by its own proposition de inesse.