A Prolegomenon Concerning the Objectivity of Second Intentions, Part 4 (The Second Act of the Intellect in its Speculative Operation)

We come now to the second operation of the intellect and the relations that the latter forms as part of its natural activity. The perfection of this particular operation, shared with the third operation, is the formation of judgments. For this reason, truth and falsity will be at the center of the concerns of logic dedicated to these two kinds of acts, in which we assert or deny something about reality. Technically, in the knowledge we have by way of defining, there is a kind of primordial, truthfulness—the manifesting of reality in its essential character.¹ Nonetheless, for our limited intellect, a full assertion about reality only takes place in the second and third operation of the intellect.² Before I turn to this pivotal topic concerning truth, I would like to begin by teasing out the novelty of this “second operation,” by considering the particular “judicative synthesis”³ formed by the human intellect in its second operation by drawing on a set of examples that are likely familiar to someone who has taken a basic logic class.

In logic, one learns about the square of opposition:⁴ every human is political; some human is able to play the piano; no human is photosynthetic; some human is not male. Based on a simple medieval pneumonic, these statements⁵ were respectively labeled: A(ffirmo), (aff)I(rmo), (n)E(go), and (neg)O. And as anybody who has done logic homework knows, there are various ways that these statements relate to each other.

But before we consider those relationships, we must consider something of capital importance for this article. Let us consider, for example, the statement no human is photosynthetic. This complex synthesis (which is a kind of conceptual-objective separation) involves two objects of knowledge being interrelated (in the form of a denial): human and photosynthetic. By means of the first operation of the intellect, we labor to form as clear and distinct a definition as possible for both of these terms. But here, in the second operation of the intellect, we take these two objects and bring them together to make an assertion about a single reality. The entire theory of speculative truth, as a kind of adaequatio of the mind to reality, hinges on understanding this point: the attainment of truth is nothing other than the uniting of two objects that are asserted as belonging to one reality that has been experienced. As we will see, the basis for such assertion is manifold (sometimes immediate, sometimes discursive). What is essential for now is to see that in judgment, the mind makes use of two objectified realities in order to assert (by means of the verb to be) something concerning the being of the reality in question, in which those objects are either conjoined or not. I will provide a footnote with all of the relevant texts to be consulted regarding this particular understanding of the theory of speculative truth, which I believe is the only path forward for a mature Thomistic epistemology, at least, as regards the great and essential outlines of such a theory.⁶

We will come back to truth very soon. However, I would like to return again to what is most familiar to most readers: the square of opposition.

So, we consider again the statement: no human is photosynthetic. Let us take for granted, in a critiqued way, that we can assert that this is true on the basis of experience. We would say that we have at least a kind of dialectical and probable certainty concerning this truth. Therefore, we can consider another statement using the same terms, the same objects, though forming a new relation between them: every human is photosynthetic. The example is almost trivial. The mind sees, by way of a so-called⁷ immediate inference, that if we can truly say no human is photosynthetic, then it would be false to say that every human is photosynthetic. In other words, in the vocabulary of classical logic, we see that an A statement is related to an O statement by means of a relation of contradiction. When one of them is true, the other is false.

Now, merely on the basis of this one example, let us appreciate several things that are of pivotal importance. As the human intellect strives to form statements that are the basis for judgment,⁸ it so to speak transmutes the basic definitions and terms that we form by means of the first operation of the intellect. In definition, we are concerned with the manifesting of an essence; here, we are taking up the great task of manifesting a truth about reality. And under these conditions, what were basic concepts⁹ in the first operation now become subjects and predicates of statements. Somewhat like how elements are taken up and changed into parts by becoming either parts of compounds or parts of biological systems, so too defined universals (or reflexively formed particular notions—Matthew, a tree, Pittsburgh, etc.) become parts of a statement, with all the various properties that belong to subjects and predicates, whether nominal or verbal.¹⁰ (Moreover, although we cannot take this up here, it is in view of this use in statements that concepts take on the property of what later medieval logicians referred to as suppositio.¹¹)

And once this new relation of predicate to subject is formed, this statement-complex also, itself, has various properties. There are the properties of quality and quantity for the statements¹² in question. And, of course, there are the properties of opposition that characterize them in relation to each other. All of these relations—that is, all these second intentions—are newly formed by this operation: subject, predicate, noun, verb, suppositio (with all of its various species), quantity, quality, mode (possibility, impossibility, contingence, necessity), opposition (contradiction, sub-alternation, contrariety, sub-contrariety), etc.

Likewise, there are further kinds of immediate relations between statements, some of which the reader might recall from logic class as well. There are the various kinds of valid conversion, by which we see the relationship between two statements, maintaining the same quantity, but reversing the subject and predicate: No Arians are orthodox believers can convert to No orthodox believers are Arians. Likewise, there are obversions, in which the quality of judgment is changed and the predicate negated: No heresy is good obverts to Every heresy is evil. And finally, there is the more complex case of contraposition: thus, Every Byzantine Catholic is an Eastern Catholic can be contraposed to Every Non-Eastern Catholic is a Non-Byzantine Catholic.¹³ There are various valid (and invalid) cases of conversion, obversion, and contraposition. All of these are properties of statements that form the basis of our judgments, and given the essential and unchanging nature of each of these, they furnished the basis for a scientific approach to the art of logic.¹⁴

And finally, I am sure that some readers will have noted at this point that we have only spoken of one sort of statement, namely, categorical statements. However, the second operation of the intellect can also form compound statements, made up of two statements together in a relationship that is, for example copulative (Humans are political and ants are merely social), disjunctive (We will eat food or we will die of starvation), or conditional (If you practice an instrument then you become at least somewhat better).¹⁵ Note very well that, in each of these statements, we have not yet begun the process of reasoning. We have formed relations among statements, compounded relations which can be considered in themselves and analyzed as holding true. (A clear example of this would be: if you practice an instrument then you will lose your mind. By itself, this statement is not valid or invalid; it is false.) This unique relationship between two statements serves as the basis for “hypothetical syllogizing,” which ultimately represents an irreducible and unique kind of reasoning (which we will consider briefly in our next article).¹⁶

But let us now turn our attention to a very important second intention that has been in the background throughout our discussion heretofore: namely, the second intention of truth. We must be clear that there is a sense of truth that is not merely “logical” or, more exactly, second intentional.¹⁷ Speaking in the register of metaphysical cognition, we can say that truth is the “manifest intelligibility of being.” In metaphysical discourse, the analogous notion of truth considers being not as ordered to existence but, rather, as ordered to intelligible manifestability. And this is the ultimate foundation for any sort of notion of “logical” or second intentional truth.

Nonetheless, let us note very well the case of the assertion of a truth: every human is a cultural being (at least in potency, exception made for exceptional cases). When we consider this judgment, we think something like the following: “The statement, ‘Every human is a cultural being,’ is true.” And this is not merely a question of asserting something about words in quotation marks. What we are asserting, by way of judgment, is that the synthesis of the subject (human) and predicate (cultural being) by means of a positive, universal, categorical statement¹⁸ is true: that the cognitional synthesis of these two objects of knowledge in fact—as the mind itself sees in the very act of judgment (or believes that it sees, but wrongly, in the case of erroneous judgment)—are, although different and dual as objects, nonetheless one in reality.¹⁹ We are saying: this intellectual synthesis is true; this statement is true. When we speak of “truth” here, we are talking about something attributed to statements, which exist as objects of knowledge or “intentionally.” For this reason, truth in this sense (but not exhaustively as regards what truth is) is a second intention, the relation that binds a given judicative synthesis to extramental reality.

Now, if we are correct in our judgment, we could perhaps also say that the metaphysical manifestability of reality here brings about the unity of being between the truth of the judgment and the truth of the reality in question, known under this particular aspect of objective synthesis. That is: humanity manifests its formal richness in the synthesis by which we state to ourselves Every human is a cultural being. And the correlate to this manifestation of reality to the mind is truth, a property of the judgment in question, by which it is now related to reality as synthesizing (whether by combination or by division) two objects in such a way that the judgment is faithfully related to reality. (And the privation of this truth is also a relation, a kind of second intention as well: falsehood.)

But not all truth is marked by the same degree of certainty. In fact, certainty itself is a kind of second intention, attributed to statements, depending upon the evidence that has been marshaled in their regard. In point of fact, this certainty-intention will be formed by both the second and third operations of the intellect.

The pivotally important domain of certainty that is established purely by the second operation of the intellect is so-called “per se nota” or “self-evident” certainty.²⁰ Such statements are certain on their own merits. On the basis of the subject and predicate term, sufficiently understood, the statement in question stands as something that can be known without essentially²¹ calling for any sort of reasoning. To be per se notum, therefore, is a second intention pertaining to the second operation of the intellect. Moreover, the distinction between those things that are “per se notum to all” and those that are only “per se notum to the wise” offers a very interesting subject for logical investigation. The rules, properties, and even signs or notes of such “self-evidence” are of pivotal importance to a robust and mature logic. (And one’s entire logical apparatus concerning the nature of science hinges, at least in an important part, on how one understands the logical rules pertaining to such per se notum statements.)

However, such certainty now opens the door for an entirely new domain of second intentions that will be the subject of the next article, namely, those that are formed by the third operation of the intellect. For the sake of ensuring that these two articles are sufficiently connected in the mind of the reader, however, allow a few words concerning the other sorts of certainty that can belong to judgments. Consideration of them will help to solidify what we have said about self-evident (per se notum) certainty.

When a conclusion is known precisely as a conclusion, we find ourselves faced with the activity of reasoning. As we will see in the next article, this means that we are faced with those second intentions that are syllogistic in nature. This next statement is very important (and very often underappreciated): conclusions are known precisely in light of the fact that they are propositions drawn through a series of reasoning. As it was put by John of St. Thomas, the truth of the conclusion-proposition is marked with a particular discursive modality. It is not truth per se nota. No, the judgment that terminates syllogistic reasoning—especially what is referred to as “objectively inferential” or “objectively illative” reasoning (reasoning to a new conclusion-truth)—is known per medium, through a middle term.²²

In fact, most of our intellectual life is lived in the midst of such syllogistic reasoning. Really, we could say that the majority of our intellectual life is deployed in such ratiocination. Such discursive rationality is the proper and natural exercise of our intelligence qua human.²³ The certainty that we draw by means of such reasoning, will sometimes be unbreakable. It will be the certainty of science, where we know the strict definitions, proper effects, and properties of the subjects under consideration. Such certainty will not be per se notum. These conclusions will be known in light of the premises that enable us to draw them. But if they are truly scientific, they will ultimately rest upon first principles which stand in themselves for their truthfulness (i.e., per se notum principles pertaining to the abstractive visualization of the science in question).²⁴

But more frequently, we live in the midst of likeliness, of “verisimilitude,” of opinion and probable certainty.²⁵ We very often know truths on the basis of authority, signs, and confirmations, but not their per se causes and principles. This domain of probable certainty plays an immensely important role in our intellectual life as we work toward a definitive grasping of the truth. In fact, probability already involves a kind of inclination toward a more certain grasp of the truth. The classic, if awkward, term “verisimilitude” bears witness to this aspect of probable certainty: such certainty has a weighty likeness (-similitude) to the truth (veri-).

We could also consider, of course, rhetorical certainty and even a kind of poetic certainty which establishes a loose likeness to the truth (something not unimportant in the domain of rhetoric as well). Likewise, we could also justify a consideration of the “logic of practico-moral truth,” something that is quite importantly connected to the logic of rhetoric, whether we are considering individual or collective moral decisions. However, all of these discursive forms of certainty fall to the subject of the next article, namely, concerning the second intentions formed by the third operation of the intellect. If I have made a remark about discursive second intentions here, it is only to note that the truth that is grasped by the second operation of the intellect also takes on modalities as the intellect enunciates statements that are not only the subject of judgment but also the subject of conclusion-judgments.

I have not even here considered all of the possible second intentions that one could encounter in a logic course regarding statements formed by the second operation of the intellect. However, I believe we nonetheless have a rather full panoply to consider, a host of relations formed by the intellect as it labors in the conquest of truth: subject, predicate, noun, verb, suppositio, quantity, quality, statement (categorical, hypothetical, copulative, disjunctive, conditional, exclusive, etc.), mode (possibility, impossibility, contingence, necessity), opposition (contradiction, sub-alternation, contrariety, sub-contrariety), truth, falsity, certainty (per se notum, per alium seu per medium notum, the latter being subdivided in a way that we will take up in the next lecture), etc. I have heard some Thomists reflect that perhaps really there is nothing unique about the second operation of the intellect which could not, in the end, merely be reduced to the first and its grasping of the intelligibility by means of the intelligible species—sometimes going so far as to deny the role played by the verbum!) I believe, however, merely on the force of common sense deployed in relation to the topics considered in this article, that the reader can see why that would be such a disastrous reduction of the human intellect’s vitality. And in the next article, we will turn to the third operation of the intellect, which at once marks the poverty of our discursion and yet highlights the majesty of our capacity to overcome multiplicity in order to grasp the truth of reality.

---

1. I here have in mind, partly, certain remarks found in Kurt Pritzl, “Being True in Aristotle's Thinking,” Proceedings of the Boston Area Colloquium in Ancient Philosophy 14 (1998): 177–201.↩︎

2. Technically, angelic knowledge, and, above all, divine knowledge, are immediate and free from the kind of composition involved due to our human, abstractive cognitional modality. Nonetheless, the perfection of asserting, or denying something about reality that our judgment manifests is ultimately what is primordial, even in such divine or angelic knowledge. This is noted, for example, by Yves Simon (in his Introduction to the Metaphysics of Knowledge) and by Jean-Hervé Nicolas (in his supplementary volume to his Synthèse dogmatique, to be published in English in 2025 by The Catholic University of America Press). But we are not concerned with angelic logic, or uncreated logic. It is human logic that we are concerned with and (to repeat again, appoint that I’ve made multiple times) the relations naturally formed by the human intellect in its speculative operation.↩︎

3. The language is taken from Simon (and perhaps also from Maritain. Regarding the simplicity of the judgment, see Maritain Jacques Maritain, Formal Logic, trans. Imelda Choquette (New York: Sheed and Ward, 1946), 90–93. Also, see the following text, cited by Garrigou-Lagrange (from the Tabula aurea of Peter of Bergamo?) in The Order of Things: The Realism of the Principle of Finality, trans. Matthew K. Minerd (Steubenville, OH: Emmaus Academic, 2020), 316n69: “There is more in the signification of a composite term than in the signification of the components. Signification is essential to an enunciation (i.e., formed by the second operation of the intellect). The signification of an expression (orationis) in relation to the thing signified is simple, inasmuch as it signifies one thing, namely a composition; although, in relation to the parts of the expression (orationis) it may seem to be composite, nonetheless, their significations exist as a material disposition to the signification of the whole.”]↩︎

4. We will presume that, when it is understood aright, the Aristotelian square (both in its simple form and in its fully modal form) holds good against certain claims regarding the problem of existential implication. See Maritain, Formal Logic, 61–63 and 225–233.↩︎

5. The reader will note that, by way of a kind of methodological scruple, I have chosen to use “statement” to refer to the syntheses formed solely by the second operation of the intellect, reserving “proposition” for statements that have become part of syllogistic reasoning, whether as premises or as conclusions.↩︎

6. See Yves R. Simon, Introduction to Metaphysics of Knowledge, trans. Vukan Kuic and Richard J. Thompson (New York: Fordham University Press, 1990), 136–49; John C. Cahalan, “The Problem of Thing and Object in Maritain,” The Thomist 59, no. 1 (1995): 21–46; Jacques Maritain, The Degrees of Knowledge, trans. Gerald Phelan et al. (Notre Dame, IN: University of Notre Dame, 1995), 96–107. The central nucleus for all of these thinkers can be found in Reginald Garrigou-Lagrange, Thomistic Common Sense, trans. Matthew K. Minerd (Steubenville, OH: Emmaus Academic, 2021), 54–55, 105–6, 147n34, 156, 160n67, 281. If I am here neglecting certain more-contemporary studies about this matter, this is because I believe that the position found in the texts cited here is the clearest and most philosophically well-founded that the reader can find. Caveat lector: parvus error in principio magnus in fine!↩︎

7. Maritain explains well why inferences referred to as “immediate inferences” are not, properly speaking, inferences. See Maritain, Formal Logic, 162–9. I suspect that the logic of such “immediate inferences” actually plays an interesting role in, for example, the logic involved in the development of doctrine (in accord with the arguments made by Schultes).↩︎

8. Concerning the distinction between a statement (or “enunciation”) and a judgment, see Maritain, Formal Logic, 82–90.↩︎

9. Note that I am not using the word terms here, as I would like to reserve term to designate a concept serving in a syllogism (as a major term, major term, or middle “term” – the last being placed in quotation marks because technically the middle is not a terminus for the reasoning, but rather a kind of via for the joining of the major and minor).↩︎

10. See the text from Maritain cited in note 8 above.↩︎

11. For a brief introduction, see Maritain, Formal Logic, 59–79.↩︎

12. That is: their affirmative or negative character (quality) or their universal, particular, or singular extension (quantity).↩︎

13. And one might also add, with Maritain, conversion per accidens, when the quantity is changed.↩︎

14. One could also take up the topic of “equipollence” here. Although only briefly treated in Maritain, I suspect that the equipollence of statements plays an occasional role in the logical form involved in the development of doctrine.↩︎

15. Concerning these and the various other kinds of hypothetical statements, see Maritain, Formal Logic, 100–111.↩︎

16. Here, I am following Maritain’s argument that one cannot completely reduce hypothetical syllogisms to categorical ones. See Maritain, Formal Logic, 235–247.↩︎

17. Here, one must recognize the problematic conclusions reached by Fr. Lawrence Dewan regarding the transcendental of true.↩︎

18. A statement requires, as we saw in the last article, a unique kind of internal word to be spoken by the intellect, statement-word serving the judgment.↩︎

19. Because of the importance of this remark, I ask the reader to consider consulting the works cited in note 6 above. The distinction between thing and object is also key in this matter, as I discuss in this article on To Be a Thomist. In particular, see the texts cited in note 6 of this latter article.↩︎

20. I discussed this topic at greater length in an earlier article on To Be a Thomist.↩︎

21. It is possible, however, by means of a reductio ad absurdum and, perhaps also, some variant on arguments ex convenentia, to argue on behalf of such premises. But, in the end, in such cases, the middle term is referred to as an “extrinsic” middle term because it does not function to reveal the truth of the conclusion itself but, rather, some related truth or falsity following from the denial or affirmation of the statement in question.↩︎

22. In these articles, we will only be able to briefly note the distinction between those sorts of syllogisms that are non-illative (expository categorical syllogisms), those which are subjectively illative (explicative categorical syllogisms) and objectively illative syllogisms (categorical syllogisms, properly so called). This is, however, a point of capital importance, so much so that I here anticipate the third operation of the intellect merely to repeat the content regarding this division of categorical syllogisms.↩︎

23. And yet, in the supernatural order, the very nature of supernatural faith presses us beyond this human limitations. On the one hand, yes, discursive theology is the supernatural wisdom that is most human: inferential, discursive, and methodological; it is for wayfarers a kind of “dilation” of the Truth of God over many truths (a “dilation” that already begins in the revelation of various truths in the deposit of faith itself). But, on the other hand, without ever leaving behind the conceptual knowledge that serves as the basis of the superanalogical judgment of faith, this very faith demands to pass into the silence of love here-below—not by a denial of the conceptual, but by its apotheosis, anticipating (at yet an infinite, still-wayfaring distance) the union to be experienced by the blessed in the hereafter. For brief but penetrating reflections on this topic, see the admirable volume by Charles Journet, The Dark Knowledge of God (Providence, RI: Cluny Media, 2020). One should, of course, also see the various relevant works of Garrigou-Lagrange, Arintero, Gardeil, Nicolas, et al.↩︎

24. Such per se nota principles can, however, be per se nota for another person (as in the case of subalternate sciences), even if we only receive those principles as certain, without evidence of their certainty. The importance of this topic is immense, both in the sciences in general and also for understanding the scientific status of theology in our wayfaring state.↩︎

25. The sense of probable certainty implied here is that which is described by Fr. Gardeil, in line with a solid Thomist and Aristotelian tradition. See the translation of his work on probable certainty, available here on To Be a Thomist.↩︎