Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

It is certain, assuming that metaphysical grades are distinguished only by reason, as we determined above,¹ that the reality which is a difference and which is a genus are not really and materially distinct from one another, and consequently that the generic difference is not distinct from the specific difference in the same subject. But THE DIFFICULTY IS whether, according to formal predication, a higher and generic difference stands to a lower one in such a way that it is predicated of it and included in it as a predicate constitutive of it.

The resolution is negative, and is more common among the doctors. On this question see Sanchez here, book 3, q. 28; Cabero, treatise 3, disputation 4, doubt 3; and the Carmelite Course, disputation 7, q. 4. This is drawn from St. Thomas in Metaphysics III, lecture 8, section He objects to the present point,² and in Against the Gentiles I, chapter 17, because a genus cannot be predicated of a difference: a difference does not participate in a genus, as is said in Topics IV.³ For then the genus would be included in the differences and would become analogical, as we shall prove in the treatise on Analogy.⁴ The same reasoning applies to a generic difference, because it constitutes a genus and is a quidditative part of it.

The point is further explained. In contracting a genus, a specific difference also contracts the generic difference itself, from which the quiddity of the genus is constituted. But a difference that contracts a genus is outside the concept of the genus; therefore it is also outside the concept of the generic difference, since it contracts that difference by contracting the genus.

The minor premise is proved from the Philosopher, Metaphysics III,⁵ and St. Thomas there, lecture 8,⁶ because if a genus were included in differences, it could not be included in them as a contractible part, but only as the whole and complete difference. For a difference, being simple, is not composed of genus and difference, nor of something contractible and something contracting; otherwise there would be a process to infinity. If a difference consisted of genus and difference, then the difference by which it is constituted would in turn consist of genus and difference, and one would ask again about that other difference, since the same reasoning would apply to it. Therefore, if a genus or generic difference is included in a specific difference, it is not included as a contractible, generic part; rather, since the difference itself is simple and without parts, it will be the whole difference. The genus would thus be analogical, partly the same—insofar as the species agree in it—and partly diverse, insofar as it signifies the entire difference by which the species differ from one another. Similarly, if a generic difference is included in a specific difference not as a part (for a difference, being simple, lacks parts), the generic difference would be the whole and complete specific difference. It would follow that one lowest species differed from another by that very generic difference, with nothing else added; this is impossible. For in that case the same difference would constitute the genus insofar as it is a generic difference, and divide the genus because it would be wholly and completely the specific difference.

THE ARGUMENTS ARE ANSWERED.

First, an objection is made from Aristotle, who in Metaphysics VII, text 43,⁷ lecture 12 in St. Thomas,⁸ says that common differences are divided into other differences, as having feet, which is a difference of certain animals, is divided into having split feet and unsplit feet. Indeed, he says of the difference of split-footedness that a higher difference is predicated of it; for it is true to say that splitting of the feet is a kind of footedness. Therefore higher differences are predicated of lower ones. Again, at the end of Metaphysics X, text 23,⁹ lecture 9,¹⁰ St. Thomas shows that in genera under which contraries are found, intermediate differences are composed of contrary differences. Our foundation would then collapse—the claim that generic differences are not included in specific differences, because they are not composite.

This is confirmed by the familiar syllogism: Every human being is sensitive; every human being is rational; therefore some rational being is sensitive. It is in a valid figure, namely Darapti, and the premises are true; therefore so is the conclusion.

If you say that the conclusion does not entail that the rational is sensitive formally, but materially or identically.

On the contrary: first, that predication is formal: “The rational is sensitive,” just like the predications in the premises. Second, one can make the syllogism by adding the word “formally”: Every human being is formally rational; therefore some rational being is formally sensitive.

THE REPLY to Aristotle’s first passage is that common differences are divided into other differences not formally but materially—that is, not by reason of themselves, but by reason of the genus constituted by higher differences. For a genus cannot be divided by lower differences unless the very differences constituting the genus are also divided. Aristotle said instead that the higher differences themselves are divided, rather than the genus constituted by them, to show which differences belong to a genus per se and which belong to it accidentally. When a genus is divided by lower differences because, by its own intrinsic constituent difference, that genus is in potency to them, it is divided by differences per se and not accidentally. For example, by its very notion of being two-footed, a two-footed animal is in potency to having split or unsplit feet; therefore it is divided per se into these differences. But when a genus is in potency to inferiors not by reason of its own constitutive difference but from some other source, that division is not by differences per se but accidentally—for example, if a two-footed animal is divided into white and black. From this, however, one cannot conclude that those common differences are formally predicated of the lower differences. Rather, they are divided by them, not predicated of them. And because they are divided by them, what is divided is the genus as constituted by that difference, together with the difference itself. This is the plain explanation of that text given there by St. Thomas, lecture 12 cited above,¹¹ where he says that “in this way the difference ‘having feet’ is to be divided: among animals of this kind, one has split feet, another unsplit feet.” Here not only the notion of two-footedness, or the difference of having feet, but the animal itself is divided. Thus, when it is said that splitting is a kind of footedness, St. Thomas says, “this is the same as being contained under ‘having feet’”;¹² and so it is contained under footedness as differences are contained under the genus of which the generic difference is a part.

The reply to the second authority from Metaphysics X is similar: the intermediate differences there are not differences that are the third predicable, but opposed species under the same genus—not opposed as extreme contraries, but as intermediates. Such species are called intermediate differences because they differ or are opposed not as contraries at the extremes, but as intermediate contraries.

In reply to the confirmation, there is no difficulty in the first syllogism: the inferred conclusion “The rational is sensitive” is verified identically, not formally. Nor must a conclusion inferred from premises verified in the formal sense also be true in the formal sense; it suffices that it be true in the identical sense, as often happens in the third figure. For example: “All milk is white; all milk is sweet; therefore something sweet is white”; “This man runs; this man is just; therefore the just man runs.” These conclusions are true only in the identical sense. In the second syllogism, where the word “formally” is added, the reference plainly shifts because that word is applied differently. In the premises it makes the predication formal. In the conclusion, however, the extremes are verified identically, so that word “formally” has no place there. For a syllogism to be valid, it suffices that if the antecedent is true, the consequent also be true; it is not required that they be verified in the same sense and relation. The antecedent can be true according to formal predication, and the consequent according to identical predication, as we have seen. The reason is that the word “formally” must always be understood relatively and under some reference: what is formal with respect to one thing may not be formal with respect to another. Therefore the reference under which it is formal must remain unchanged whenever the word “formally” is added. A human being is formally rational and sensitive because he receives these predicates as formal attributes; but “the rational is sensitive” is verified only through identification in the same subject. They therefore cannot be verified under the same formal aspect; if “formally” is added, its reference shifts.

But if you object: This syllogism is valid in Celarent—“No rational being is formally sensitive; every human being is formally rational; therefore no human being is sensitive.” Here there is no shift in reference, and yet, even if “formally” is removed from the conclusion, it is false; therefore the proposed solution is insufficient.

The reply is that the reference shifts in the same way because of the word “formally,” which always gives a sense that is not absolute but qualified by some restriction, dependence, or relation—namely, insofar as the extremes fall under that formality and relation. What is not joined or in agreement under one formality and relation may nevertheless agree under another. Hence one cannot infer from a negation under one relation a negation under another relation, or an absolute negation. Thus, from the fact that the rational, formally—that is, under the concept and formality of rationality—is in no way sensitive, one cannot infer that, under the concept and formality of a human being, a human being, who is identical with the rational, is not sensitive. This variation of formal aspects and references must be carefully observed in many other subject matters. For example, this does not follow: “Given a precept, Christ here and now can act and not act, because he acts freely; and if he did not act, he would sin; therefore he can sin and not sin.” I say that it does not follow, because he can refrain from acting under the aspect and formality of action, as required for freedom, but not under the formality and concept of sin, as though sinning were part of the nature of freedom.

Finally, an argument is made: A lower specific difference has some common and higher predicates; for example, rational is living and is a substance, etc. Therefore it has something common to it as a genus and higher predicate; therefore such a generic difference or genus can be predicated of a lower difference.

It is confirmed that the concept of a difference admits some composition, since it has something potential, as a created thing, whereas only pure act is altogether simple. Therefore it can be resolved into a common or generic concept and a specific or differential one. But that higher concept is a subordinate difference, since a lower difference has a nature and operation subordinate to the generic difference. For example, neighing in a horse is a kind of sensitive operation, and is consequently subordinate to the common sensitive, which is the generic difference of animal.

THE REPLY is that those higher predicates belong to a difference not in a formal and direct line, but reductively and according to a certain relation or connotation. For the rational is called a substance or living, not because it is in itself a substance or living thing, but because the form from which it is taken is a principle of substance, of living things, or of another grade. A form is not that which something is, but that by which something is; just as matter and form are substances as principles of substance, or incomplete substances. Differences likewise are something incomplete in their own category. Thus it is not the complete higher notion, nor generic differences themselves, that are predicated of them, but the incomplete notion of that category—for example, substance insofar as it abstracts from the complete and incomplete—which is included transcendentally in everything that pertains to and is reduced to that category.

In reply to the confirmation, a difference is not composed of these things but is composed with them, since it is a part or functions as a part. A part is not simple like pure act, with the simplicity of perfection, but with the simplicity of negation—that is, it is not fully perfect. The simplicity of negation has more potentiality, because the part can be composed with something else by which it is perfected. Yet it is not composed by being resolved into several concepts of which it consists, except perhaps analogically, because being is included in all things, even in differences. Nor is a lower difference formally and directly subordinate to a higher one as to a genus, though it presupposes it, just as it presupposes the genus constituted by it. Thus: “Neighing is a principle of sensitive operation”—I distinguish: if “sensitive” is taken suppositively and materially, I concede; if formally and directly, I deny. That is, the sensitive is presupposed for something to be neighing, but neighing is not formally the sensitive.