A Prolegomenon Concerning the Objectivity of Second Intentions, Part 5 (The Third Act of the Intellect in its Speculative Operation)

“Syllogism, which is produced by the third operation of the intellect, is the principal object of logic; among syllogisms, [scientific] demonstration is principal on account of its matter.”¹ Logic is the speculative art of human reasoning, and therefore it is not surprising to find John of St. Thomas stating a position that one can find echoed in earlier scholasticism, even if not always with such straightforward clarity. If the general subject of logic is second intentional relations in genere, logic’s primary subject of consideration will be that kind of second intentional relation that is most perfective of the human mind precisely as human and ratiocinative, most perfectly second intentional, most quintessentially human and discursive: reasoning. Even though all reasoning begins from an insight and ends in a terminal insight expressed in a propositional statement,² nonetheless, the discourse of reason represents the human mode of quasi-temporally passing from one statement-proposition to another by means of some form of inference. (For the purposes of this article, syllogism will be taken both in its somewhat imperfect form as hypothetical or in its categorical form, even though the latter will receive more attention. Also, the important distinctions between scientific and sapiential reasoning will be in the background, but only partly developed in explicit form.)

Human reason must win its way toward the truth. And, therefore, when we seek to know something discursively, we must form a series of relations that are new among the various objects of our knowledge. Just as definitional objects of knowledge became subjects and predicates as they passed from the first operation of the intellect to the second, so too the knowledge attained by the first and the second operations of the intellect will come to be transmuted by the third. First and foremost, we find that definitions, as well as subjects and predicates, now properly become terms, in the sense of termini, beginnings and ends of reason:

Every human is a political being.

Every political being reasons in relation to a common good.

Therefore, every human reasons in relation to a common good.

Here, human, political being, and reasons in relation to a common good no longer stand on their own. They are no longer mere essences that we are seeking to articulate with clearer definitions or even to combine appropriately in propositions. They have become termini.

This transmutation is clear when we consider the “major” and “minor” termini of this syllogism: human and reasons in relation to a common good. They are the beginning and end of our reasoning chain. In their sentential-enunciated combination, our mind comes to rest at a new truth that we have explained for ourselves through the discourse of reasoning. But, there is another term, a crucial term, in bold above: political being. Presupposing that we have done all of the labor necessary for defining our terms, this essence has become the bridge that enables us to bind together the subject and the predicate of our conclusion. This term, political being, is the “middle term” of this ratiocination. Although the middle term disappears in the conclusion of our syllogism, it is precisely what enables us to infer the conclusion. In fact, as I have already stated in earlier articles, we understand the conclusion precisely in light of this middle term.³ In short, the direct objects of our apprehension have now become terms, just as they had become subjects and predicates in the products of the second operation of the intellect. And in a categorical syllogism, the new relation is precisely as follows: a major term relates to a minor term on the basis of a shared foundation in the relational structure mediated by a middle term.

Moreover, although we often speak of statements and propositions as though they are the same thing, it is important to understand that there is at least a somewhat unique sense in which we can use the designation proposition, namely, to indicate those statements which function as major premises, minor premises, or conclusions within a syllogism or, for example, as antecedents and consequents in conditional syllogisms. Although not all draw this distinction between statement (second operation) and proposition (third operation, at least implicitly), I think it helps one to be sensitive to the new relational structure involved as statements are taken up into reasoning (or at least are considered as proximately-potentially included in the activity of the third operation of the intellect).

This structure of relations between propositions is also found in hypothetical syllogisms, whether disjunctive, conditional, etc. Let us only consider the classic case of a “modus tollens” argument style:

If active yeast is placed into appropriately wet flower, the mixture grows.

But, the mixture has not grown.

Therefore, active yeast was not placed into appropriately wet flower.

In this argument structure, we have several propositions which are placed in relation with each other. The argument presupposes an already-existing scaffolding of investigation, establishing the relation between the propositions stated in the initial conditional statement. Based on the particular subsumed claim (The mixture has not grown) we can argue that we know that the antecedent must be false if the consequent is false. All I wish to pay heed to is that we see that the truth of the various propositions has a structural pattern based upon the given conditional statement form that our intellect fashions between the various previously known statements. By means of the activity of the third operation of the intellect, these statements take up a new relation to each other, a relation that is a new kind of second intention, which has its own properties and can be explained by the rules of logic.⁴

A course in formal logic takes up the important question regarding the valid form of syllogistic inference. Through the second operation of the intellect, we know many things about the extension, distribution, quantity, quality, mode, and inter-opposition of our propositions and terms. However, gathering together the various statement types, we now find a new task at hand. According to the logic of the third, discursive operation of the intellect we see that we can analyze the structure among various propositions in order to see whether or not the conclusion we claim can be said to structurally follow from the major and minor premises that we offer. Anybody who has taken a logic class should have some experience with this procedure, whether with the somewhat limited modern tool of Venn diagrams, or with the classical rules enabling one to sift out the syllogistic validity of the various combinations of statements: AAA, AOO, EAO, IAI…

Moreover, the matter of our argumentation can be affected by the particular character of the principle-propositions used to guide our reasoning and the perseity of our attributional structure. For example, when we fashion for ourselves reasoning that is based upon necessary matter, ultimately founded upon principles that are self-evident on the force of the terms of those very propositions, we find ourselves to be within the domain of science when we use those propositions in “per se” attributions. Such demonstrations are very difficult to fashion, especially outside of mathematics. But they are possible, and when we do so, we make use of very carefully defined terms. This process of definition involves carefully selecting the characteristics of reality that answer to our particular discipline under consideration, so that we might appropriately focus upon the given aspect of reality that belongs to our science.⁵ As John of St. Thomas remarks, although abstraction (“diverse immateriality”) is the source of the distinction of the sciences, nonetheless, diversity of definition does reflect diversity of abstraction.⁶

In short, the relation between the premises within a given discipline will mark the very character of the terms themselves: scientific terms will strive to tightly define, themselves in a way that will reflect the particular abstraction necessary for isolating a given scientific body of knowledge; dialectical terms will make use of common principles that do not properly belong to the subject under consideration but are relevant insights concerning common characteristics that this subject shares with other entities;⁷ and rhetorical and poetic argumentation will use terms whose basis is far more marked by the affective and personal resonances of the disputation in which such terms are used. Therefore, the logic of simple terms is yet again altered by the inclusion of these terms within syllogistic reasoning. How greatly is the relational structure of the first operation expanded by the vistas that definition takes up now in the service of ratiocination!⁸

Merely to add one last example of a kind of relation formed by the third operation of the intellect, we could consider the distinction between various kinds of inferential and non-inferential syllogisms. First, there are those that are completely non-inferential (or non-illative), known as “expository” syllogisms, which function more like the furnishing of an example:

Judas became a traitor.

However, Judas was an apostle.

Therefore, an apostle became a traitor.⁹

Here, the conclusion does not state a new truth but, instead, only provides an example that illustrates what is, in fact, already contained within the premises. This is one unique sort of categorical-syllogistic relation structure.

Or, there are inferential syllogisms that, nonetheless, are explicative in form, such that the conclusion is in itself (quoad se, “objectively”) identical to the major premise of the argument, although the minor premise enables us (quoad se, “subjectively”) to re-express the terms in a more explicit manner:

Every man is mortal.

However, every rational animal is a man.

Therefore, every rational animal is mortal.¹⁰

This is another unique sort of categorical-syllogistic relation structure. And, of course, there is the standard categorical form which is properly inferential (“objectively illative”), leading to a new conclusion at the ultimate terminus of reasoning. This too involves a different kind of categorical-syllogistic relation structure.

In this article, I am only looking to tease out some basic characteristics of the third operation of the intellect as it forms syllogistic relations between definitions and statements. By far, prioristic (“formal”) and posterioristic (“material”) analyses of second intentions are the most important labors of logical science. Here, a whole host of new relations are formed among propositions and terms, bearing witness to the fact that the human mind, although marked by the temporality from which it emerges, is able to overcome multiplicity in order to regain unity through the discourse of reason. We live our intellectual life amid such rational processes, from a rather young age, reasoning from one truth to another, either in hypothetical or categorical form. And all of the various relations formed in the midst of this reasoning are a unique domain of second intention. Such relations are fashioned by a unique operation of the intellect, discursive reasoning, which bears witness at once to the poverty of our particular kind of intellectuality and yet also to the majesty of our capacity for pushing onward toward truth, whether scientifically, dialectically, rhetorically, or poetically grasped.

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1. John of St. Thomas, Material Logic, trans. Yves Simon et al. (Chicago: University of Chicago Press, 1955), q. 1, a. 3 (p.26).↩︎

2. See ST II-II, q. 8, a. 1, ad 2: “The discoursing of reason [rationis] always begins from an understanding [ab intellectu] and terminates in an understanding [ad intellectum].” See Maritain, Bergsonian Philosophy and Thomism, 2^nd ed., trans. Mabelle N. Andison and J. Gordon Andison (New York: Philosophical Library, 1955), 53; Maritain, “No Knowledge Without Intuitivity”, Untrammeled Approaches, trans. Bernard Doering, Vol. 20 (Notre Dame, IN: University of Notre Dame, 1997), 316.↩︎

3. There are in the background, here, technical questions regarding the scientific demonstration of a conclusion and whether or not, it can be understood—when scientifically understood—only through one particular, proper middle term. But I will not going to engage in that question here, as it is deserving of a full-form scholarly article.↩︎

4. For the purposes of this essay, I am setting aside the question regarding the degree to which various hypothetical syllogisms can be reduced to categorical form. See my previous article for citations from Maritain, who held that there is a unique character to hypothetical statements rendering them incompletely reducible to categorical form.↩︎

5. See the relevant citations regarding definition provided in the earlier article dedicated to the first operation of the intellect.↩︎

6. John of St. Thomas, Material Logic, q. 27, a. 1, 554ff; Jaques Maritain, Degrees of Knowledge, trans. by Gerald B. Phelan et al. (Notre Dame, IN: University of Notre Dame Press, 1995), 39n26, 190n69; The Philosophy of Nature, trans. Imelda C. Byrne (New York: Philosophical Library, 1951), 90–92.↩︎

7. Concerning this matter, see the various articles by Ambroise Gardeil concerning probable certainty and also De locis theologicis posted here on To Be a Thomist. Also see the various works cited in my translator comments to these texts by Gardeil.↩︎

8. To note one more sort of third-operational second intention extension of the first operation: as I have hinted in an earlier article (and also in several footnotes in passing in physical publications), arguably, the processes involved in analogical (imperfect) abstraction (“analogicity”) involve all three operations of the intellect to form the unique “non-generic superiority” belonging to analogical terms.↩︎

9. See Jacques Maritain, Formal Logic, trans. Imelda Choquette (New York: Sheed and Ward, 1946), 233–235.↩︎

10. The example is almost anodyne. One can find several explicit examples of such syllogisms throughout the works of Garrigou-Lagrange, himself drawing upon Reginald Schultes (in the midst of debates regarding dogmatic development). This is a topic still deserving, much development within scholastic logic. This topic is deserving of a complete academic article, given its importance within debates related to the logical form taken on by statements involved in dogmatic development.↩︎