Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

This most difficult question has always been regarded as such, and the opinions and explanations of various authors have made it more involved.

BUT IN ORDER TO SEPARATE WHAT IS CERTAIN FROM WHAT IS UNCERTAIN, we do not treat here in the first place of practical sciences, but of speculative ones. For practical sciences derive their species from the different end to which they are ordered, as St. Thomas observes, Opusc. 70, q. 5, art. 1.¹ Speculative sciences, however, have truth for their end, precisely insofar as it is knowable. Hence the difficulty lies in assigning the species of diverse knowability. For each thing is knowable insofar as it is immaterial, and a different account of knowability results from a different mode of immateriality. Further, it pertains to the account of what is scientifically knowable that the object be necessary and immobile, and proceed from necessary principles to illuminate conclusions. The present difficulty, then, is to order all these features so that from them we may fully derive the species of the sciences.

Second, it is certain that sciences, like all other habits, derive their species from their object, as is clear from On the Soul II, text 33.² St. Thomas determines this in Ia, q. 77, art. 3; and thus the unity and distinction of a power or habit must always be proportioned and conformed to the unity or distinction of its object precisely as object.

Finally, it is certain that this specification of the sciences is not taken from the unity or distinction of the object in its being as a thing, but in its being as an object; that is, not from the object considered materially and entitatively in itself, but as it is suited or proportioned to a given habit or power. Hence Cajetan rightly cautioned, Ia, q. 1, art. 3, that the account of an object as object, or in its formal character, differs from its account in the being of a thing; and the species of things in their being as things differ from their species in their being as objects, as the examples themselves clearly show. For color, in its being as a quality, is a genus divided into various species, yet as visible it has one and the same species of object for sight. All bodies have the same species in the account of the object of physics, and all beings in the account of the object of metaphysics, although in their entitative account of body and being they are divided into very many species. Conversely, the same color is reached in different ways by sight and intellect; the same thing is reached as good by the will and as true by the intellect; the same earth is reached as round by the astronomer and as mobile by the physicist, and so in many other cases. Hence it is clear that the specific account of a thing differs from that of an object in its being and formal account as object.

Therefore, almost THE WHOLE DIFFICULTY at issue comes down to investigating what formal account specifically constitutes an object as an object of scientific knowledge, and makes it differ from another in its very specific account. As we said in the preliminary question 1, art. 3, the formal account of an object is usually distinguished into the formal aspect which is reached and the formal aspect under which it is reached. This distinction should not be rejected, as Vazquez does in Ia, disp. 7, ch. 3. For in the very object reached by different habits or powers, some aspect must be designated that is specially reached by one and another aspect specially reached by another. The aspect specially attained is called the formal aspect which—that is, what is attained, as distinguished from the material object determined by that special aspect so as to be attained. The formal aspect under which is the aspect that actualizes the others and contains them under itself, so that a power may attain them. Since what is formal with respect to one thing can be material with respect to another, the ultimate formality under which the others are contained is called the formal account under which without qualification. Just as, on the side of the knowable object, we consider the formality that is reached and the ultimate formal account under which the others are made reachable—and which usually coincides with the ultimate account which—so on the side of the power there corresponds the formal account under which it reaches the object: the light or actuality by which the power is ordered and actualized toward that object. Sight provides a clear example. A body, such as a wall or stone, is what is materially seen; what formally determines it for sight rather than hearing is color, the formal aspect that is seen. Color, in turn, is actualized and formed by light, which is the ultimate formality that makes it visible and under which the other aspects are ordered to sight. On the side of the eye, there is the light under which the actualized power proceeds to see.

Applying this in the same way to the object of scientific knowledge and to science, the knowable object is something complex, consisting of a subject of which some property or attribute is demonstrated. This object—the truth of the inferred conclusion—must be illuminated by some middle term, posited in the premises as a principle from which that truth is inferred and, in the very act of inference, illuminated. Definitions, then, which function as principles or middle terms for demonstrating attributes, must have the role of determining the knowability of the inferred object by illuminating it. If each object-as-object were known adequately and just as it is in itself, each would ground a science distinct from every other with respect to its attributes. It is plausible, for example, that Christ’s infused knowledge was distinguished according to the distinction among the species representing quiddities, as St. Thomas indicates in IIIa, q. 11, art. 6. But our intellect is univocal and abstracting, and does not understand every nature just as it is adequately in itself; rather, it coordinates and joins one nature with another, and understands one and the same thing in different ways. Consequently, different natures can belong to the same science, and the same nature can be considered in different sciences. We must therefore assign some account by which several natures are united in one science, or several accounts by which they are considered in different ways by different sciences.

Although there are many opinions of the learned on this matter, they can all be reduced to THREE PRINCIPAL VIEWS:

The first is that this unity in each conclusion³ is a distinct partial unity, as will be treated more fully in the following article; nevertheless, all these parts are united in one science because of the unity of the principal subject, to which the others are referred or on which they depend as something more principal. Thus in logic, for example, the syllogism or mode of knowing gives unity to the whole science. Father Suarez seems finally to hold this view in his Metaphysics, disp. 44, sect. 11; see also the Conimbricenses, Posterior Analytics I, ch. 23, single question, art. 1, against this view. Scotus and his school nevertheless hold it, as Father Merinero follows and explains it in disp. 1, preliminary question on logic, q. 5. They derive the unity of a science from the unity of its subject, in which all the truths of that science are contained. Thus, if all the properties pertaining to a science can be demonstrated by virtue of that subject and its definition, there will be one science in the lowest species. But if not all the truths can be reached by virtue of that subject and its definition without other definitions intervening—for example, if the subject is something generic and the species contained under it are defined by means of other definitions—then that science will be one generically and will contain several sciences distinct in species. Hence, for these authors, the specific unity of a science, strictly speaking, is derived from the unity of the definition and quiddity of the thing under discussion.

The second view derives the unity or diversity of sciences from the unity or diversity of the middle term, insofar as it makes conclusions knowable in different ways. Some understand this diversity of knowability as an extrinsic denomination in the object arising from the science; others as a diversity of light, which amounts to the same thing if light is taken to mean the habit of science.

The third view, very common among authors, especially in the school of St. Thomas, derives the unity or diversity of sciences from their different modes of abstracting from matter, taking abstraction not as the intellect’s act of abstracting one thing from another, but as the object’s capacity for abstraction, or its immateriality.

There are three kinds of matter from which abstraction can be made, as St. Thomas teaches in Ia, q. 85, art. 1, ad 2: individual matter, which makes a thing individual and singular; sensible matter, which makes it subject to sensible accidents, at least in general; and intelligible matter, which is substance insofar as it underlies quantity even without the other accidents. From abstraction from, or the differing absence of, these kinds of matter, three genera of sciences are derived: physics, which abstracts only from individual matter and treats of sensible matter; mathematics, which also abstracts from sensible matter and treats of quantity; and metaphysics, which also abstracts from intelligible matter and treats of substance or being. Since different species of sciences are contained under these genera, however, this view does not readily explain how those species are derived from abstraction.

I SAY FIRST: The unity or distinction of a science is not derived solely from the unity of its principal subject, insofar as that subject contains or causes the truths of the science, or insofar as all those truths are ordered to such a subject, as the first view maintains.

The REASON is that different sciences can treat of one and the same subject: God, for example, in the beatific and infused knowledge, in theology, and in metaphysics; and the heavens in astronomy and physics; and so in many cases. Therefore, a formal account must be assigned of why several sciences are distinguished even when they concern the same subject.

They say it is because the subject has a different definition. For a definition is a middle term in demonstration; since the subject is defined in one way in one science and in another way in another science, a different account is assigned for belonging to one science or another.

However, this is said inadequately. For it remains to explain what that different way of defining consists in, in one science as compared with another—for example, why the physicist defines quantity differently from the mathematician. But a different account and manner of definition cannot be assigned except from a different mode of immateriality and abstraction, according to which something is apprehended and defined in different ways, as we shall show below from St. Thomas.

Again, since different definitions are found within one science, just as different things or quiddities are, as is clear in physics and mathematics, and even more so in metaphysics, which ranges over such varied things and defines each by a different definition, one cannot adequately explain why all these definitions, and the things demonstrated by means of them, are reduced to one science.

For if this is because of their coordination and dependence on one more principal subject, it remains to explain whence this coordination, which constitutes that unity, is derived. The things coordinated are not different attributes of one nature, but different natures and definitions ordered within the same science. Nor is the definition of the principal subject alone sufficient for this, since the same subject can be defined in different ways in different sciences, as we have said. Thus this unity or diversity would ultimately be reduced to a different manner of defining, and that different manner can be reduced only to a different immateriality, as we shall show; for there is no other way to assign a different manner of defining the same quiddity.

If, as some say, the science that defines its principal subject in such a way that it also contains several definitions under itself for demonstrating different truths contained under that subject is one only generically and contains several specific sciences, the objection is this: either those definitions and demonstrated truths are coordinated and connected with the principal subject, or they are not. If they are not connected or coordinated, then they do not regard it as their principal subject, and so they will be several sciences unrelated to one another. There will then be no need to seek their unity, but rather their diversity.⁴ But if all those truths are coordinated and subordinated to that principal subject, and derive their specific or generic unity or distinction from this coordination and subordination, it remains to explain what this subordination is, and how truths defined in one way are subordinated to that subject while truths defined in another way are not—unless this is reduced to a different manner of defining in respect of different immateriality.

Therefore, it must be categorically denied that the principal subject of a science can immediately contain all the truths of that science sufficiently for demonstrating them. Particular definitions of the different quiddities treated in that science must necessarily intervene. The unity that comes from subordinating such truths to that principal subject cannot be derived solely from the subject’s unity in its being as a thing, but from the formality and mode of the subject’s differing knowability, which ultimately is reduced to a different mode of immateriality, as we shall now say.

I SAY SECOND: Generally speaking, the unity and distinction of sciences in their character as things scientifically knowable is derived from differing immateriality and abstraction, as these are first found in the principles or middle terms of demonstration and from there extend to illuminate conclusions in different ways.

Thomists generally agree on this conclusion. On it, see Cajetan, Ia, q. 1, art. 3; Ferrara, Against the Gentiles II, ch. 4; the Carmelite Course, disp. 19, q. 4; and the Conimbricenses, Posterior Analytics I, ch. 23, single question, art. 1.

It should be noted that here we do not take abstraction to mean the intellect’s act of abstracting, nor the extrinsic denomination that follows from that act. That would be circular, since a different science that abstracts would be derived from a different object abstracted and denominated by the science, and what is differently knowable from a different science abstracting. Rather, abstraction means the object’s capacity for abstraction, insofar as the object has a foundation for terminating and representing a different immateriality. Nor are we speaking of total abstraction, which abstracts something as predicable of its inferiors; for this abstraction is a common condition of the sciences, which treat not of singulars but of universals. We are speaking instead of formal abstraction, which abstracts formal accounts from material or potential ones, and so constitutes or grounds intelligibility. The more or less something is removed from matter and material conditions, the differently it is made intelligible. St. Thomas discusses this difference among abstractions in Ia, q. 4, art. 3, and Cajetan at the beginning of On Being and Essence.

Thus explained, the conclusion follows plainly from St. Thomas. His various passages, which seem to speak differently about the unity and diversity of sciences, can be reconciled: they do not have different meanings, but explain the same matter, which cannot be explained in only one way. At times he derives the distinction of sciences absolutely from differing abstraction from matter, as in the prologue to On Sense and the Sensible⁵ and very well in Opusc. 70, q. 5, art. 1.⁶ At times he derives it from a diversity of middle terms, from which the formal account of demonstration is taken, as in IIa IIae, q. 1, art. 1, and Ia IIae, q. 54, art. 2, ad 2. At times from a different definition and manner of defining, since one proceeds from a definition as from a principle to demonstrated conclusions, as in Metaphysics VI, lect. 1⁷ and Posterior Analytics I, lect. 41,⁸ where the diversity of sciences is derived from the diversity of principles. All these passages perfectly explain for us what the unity and diversity of sciences must be derived from. For St. Thomas assumes as a foundational principle that each thing is intelligible to the extent that it is separable from matter, since the intelligible is the same as the spiritual and immaterial, and the principle of spirituality is removal from matter. Since matter thus obscures and impedes intelligibility, an object is illuminated and made apparent insofar as it is separated from matter in different ways. We must add to this foundation that what is scientifically knowable adds to being intelligible a certain mode of knowing: something is understood not simply, but inferentially, by proceeding from causes or premises to conclusions. To know scientifically is to know the cause on account of which a thing is, and so forth.

From this it is plainly deduced that if immateriality is the root of intelligibility, and differing immateriality consequently the root of differing intelligibility, then differing immateriality or abstraction will likewise be the root and principle of differing scientific knowability—not considered absolutely and simply, but insofar as it proceeds from premises to conclusions. In the sciences, the premises or demonstrative middle terms are the first principles themselves or definitions by which the subject’s proper attributes are demonstrated. These definitions and principles are different when they define or explain a quiddity in different ways or according to different immaterialities. For the root of understanding something is immateriality, and the root of understanding in different ways is differing immateriality; therefore, understanding a quiddity in different ways—that is, defining it—also involves differing immateriality. Thus a different manner of defining or understanding a quiddity is a different immateriality. Where a different manner of defining is maintained, a different manner of demonstrating also follows, since demonstration in the sciences proceeds through definitions as principles. All principles that proceed according to the same mode of understanding, or the same abstraction, are considered to belong to the same species. Thus the different definitions found in one science, although they define quiddities distinct in species in the being of things, are said to belong to the same species in their mode of understanding and defining if they proceed according to the same mode of definition. The physicist defines in the same way everything treated in physics, namely under the same abstraction, including sensible matter subject to motion. Therefore all those definitions are alike and of the same species in their mode of definition, although they differ on the side of the things defined. This is St. Thomas’s reasoning in Metaphysics VI, lect. 1,⁹ where he says: “Since definition is the middle term of a demonstration, and consequently a principle of knowing, a diversity in the sciences of speculation must follow a diversity in the manner of defining.” He discusses this at length there, showing that the different manner of defining depends on the different manner of including matter in the things defined.

From this it is evident that it is most true that the unity and distinction of sciences is derived from the diversity of middle terms or principles through which scientific illumination occurs. In turn, the diversity of middle terms or principles must be derived from different modes of defining or understanding; this diversity of understanding, whether in definitions and causes or in effects, must be reduced to differing immateriality according to which a thing is understood. This immateriality must first be found in the principles, so that from there it may be drawn out to conclusions, since it is scientific. Because these principles, thus understood, are said to illuminate conclusions, one can also say that the diversity of sciences is derived from a different light—not a light on the side of the power, which is the habit itself or the specific science, but on the side of the principles, which are the objective light determining how conclusions are to be proved scientifically.

I SAY FINALLY: The ultimate species of sciences is not derived from the material diversity of objects in their being as things, but from a different degree of immateriality acquired through abstraction; in sciences of the supernatural order, it is derived from a different access to or participation in divine knowledge itself.

The FIRST PART of the conclusion, which is negative, is taken explicitly from St. Thomas, Posterior Analytics I, lect. 41,¹⁰ where he derives not only the genera of sciences but also their species from a different mode of knowability, not from different things known considered materially, as some suppose. St. Thomas says: “Genera of knowables are distinguished according to a different mode of knowing, as things defined with matter are known in one way, and those without matter in another. Hence one genus of knowables is natural body and another is mathematical body, and each of these genera is divided into different species of knowables according to different modes and accounts of knowability.” So says St. Thomas, whose words sufficiently clearly prove this part.

The point is clarified as follows. In one science of a single ultimate species, different things materially distinct in species and in their being as things can be treated, as is clear in metaphysics, logic, physics, or any other science, however specifically ultimate its species. There is not a distinct science for every species of thing, just as there is not a distinct power of sight for every species of color. Sciences, therefore, cannot be specifically distinguished according to the distinction of quiddities or things in their being as things. Ultimately this is all because our sciences are imperfect and are not fully proportioned to things themselves, nor do they comprehend them adequately. For if each thing were perfectly comprehended, each thing would ground a science proper to itself and specifically distinct from every other; science would not require a coordination of species, but each thing, perfectly represented by its own adequate species, would demonstrate its own attributes. On this basis St. Thomas effectively concludes in IIIa, q. 11, art. 6, that the infused knowledge in Christ the Lord was distinguished by different habits, because he had different species by which he understood the natures of things. That infused knowledge did not consist in coordinating different species ordered under the same mode and immateriality; rather, each species, because it represented each thing perfectly and adequately, grounded a science distinct from the others. But when a science is not proportioned adequately to each thing known—because it does not comprehend a single thing perfectly or exclusively, but reaches several things under some common aspect, and therefore coordinates several species under the same account of knowing and understanding—it is not divided according to the entitative division of things, but comprehends several quiddities under one and the same specific account. The specific formal account of a science, then, encompasses several species of things, and is not derived from being proportioned to each individual species.

The SECOND PART of the conclusion is to be explained from what Master Báñez teaches in the Prologue to the books On Generation, around the fourth main point, where he seems to have grasped St. Thomas’s mind. The point is clarified as follows. In material things, which are made intelligible and immaterial by being separated from matter and material conditions, abstraction itself is like a kind of motion in which a terminus from which and a terminus toward which are considered: formally in the very act of abstraction, but fundamentally and objectively in the object capable of being abstracted. On the side of the terminus from which there is a departure from matter, which is threefold, as we said above, and thus three genera of abstraction are constituted. On the side of the terminus toward which there is a different degree of immateriality, or spirituality, which the thing so abstracted can acquire. St. Thomas calls this the distinction of different species in each genus of what is scientifically knowable according to different modes of knowability, in lect. 41.¹¹ Therefore, the formal and specific account of sciences is derived not only from a departure from matter, but also from an approach to a determinate degree of immateriality, by which some object is specifically assigned and made intelligible. Likewise, in angels, their different species are derived not only from departure from corporeity, but from an approach to a determinate mode of having spirituality and immateriality and to pure act, as St. Thomas notes near the end of ch. 6 of On Being and Essence.¹² Thus we find in mathematics that, although in general it abstracts from sensible matter, a different mode of immateriality is reached in continuous quantity than in discrete quantity. Discrete quantity involves materiality less, since it depends less on place and time than continuous quantity, which joins its parts in place. Therefore two sciences are constituted: geometry and arithmetic. Likewise, physics and medicine are two sciences: although both abstract from individual matter, medicine is more concerned with the body as something to be healed than physics is with the body as mobile as such. In logic and metaphysics there is a departure from sensible and intelligible matter on the side of the terminus from which, but each reaches a different mode of immateriality. Theology considers God himself as known through the divine light of virtual revelation; metaphysics considers him according to the first and highest account of being, as it abstracts from created and uncreated being. Logic, however, considers intentions as grounded in objects of the intellect; these have no immateriality of their own except negative immateriality, since they are not something real.

Therefore, since the ultimate specification of sciences is the final account of what is scientifically knowable, which is no longer divisible, if the formal account of scientific knowability is derived from immateriality, its ultimate and specific account must be derived determinately from the terminus toward which that abstraction proceeds, at which abstraction finally rests and is determined. Thus it is not derived from mere separation from matter, considered as the terminus from which of abstraction; rather, the specific and determinate account of scientific knowability consists in the ultimate determination of immateriality.

But in sciences of the supernatural order, since they are not derived by abstraction from things, but by participation in and derivation from the very light of divine knowledge, their specific and determinate account must be derived from different modes of participation. Thus the revelation of faith is participated in one way, as testimony; prophecy in another way, which may be obscure or clear depending on whether revelation merely testifies or also represents and declares what is revealed; infused knowledge in another way, since it knows supernatural quiddities quidditatively; and beatific knowledge in another way, since it reaches God clearly in himself. In each of these, God knows how participation can be multiplied in different ways.

THE ARGUMENTS ARE ANSWERED.

First it is argued. The primary object does not confer unity or diversity on a science by virtue of abstraction; therefore.

The antecedent is proved by many examples in which several sciences are found under the same immateriality, while conversely a single science reaches its objects under different immaterialities. First, moral science and logic do not derive their specification from abstraction, for no such abstraction can be assigned. Again, natural philosophy has a single abstraction, namely from individual matter, yet it contains sciences distinct in species, such as the books On the Heavens and On the Soul, and so forth. The same holds in mathematics, which abstracts from sensible matter, yet contains different species such as geometry, arithmetic, and so on. Indeed, music and the other subaltern sciences are of one species, yet do not have a single abstraction. For music considers the number of sounds, and with respect to number has mathematical abstraction, while with respect to sound it has physical abstraction. Finally, if differing immateriality distinguishes sciences, it will also distinguish the habits of first principles and the habits of opinion. There is no stronger reason for one than for the other. Yet it is clear that the same habit of first principles reaches all principles, however diverse their abstractions, such as the principles of metaphysics, physics, or mathematics. Conversely, the same immateriality found in the principles of physics and in physics itself does not constitute the same habit, since principles belong to the habit of principles, whereas physics belongs to the habit of science. Therefore, the same immateriality does not always constitute the same habit, nor does a different immateriality always constitute a different one.

THE REPLY is to deny the antecedent. To explain the examples adduced, it should be noted that the immateriality of an object constitutes its intelligibility in itself. But it is not always applied to the intellect according to the intelligibility that it grounds in itself; it may be applied according to another intelligibility. In that case, the account of the object is constituted according to the intelligibility under which it is applied. The immateriality it has and grounds in itself will then be incidental; if it were applied according to that immateriality, it would constitute different sciences.

As to the first example, the rational science that is logic derives its unity from its abstraction, which is indeed similar to metaphysics’ abstraction but differs from it, since it is only negative abstraction. For logic concerns the intentions of reason insofar as they are instruments of speculation. This is an abstraction of a being of reason—not insofar as it is opposed simply to real being in general, for in that respect it belongs secondarily to metaphysics, but insofar as it is grounded in things understood; from things’ being as known it receives its abstraction. Rhetoric and grammar are either not sciences, because they do not proceed demonstratively, or they are not rational sciences but sciences of discourse. If moral science is taken practically, it is the same as prudence and so does not belong to speculative habits, but to practical ones, which are not at issue here. If, however, it is taken speculatively as ethical science, which treats the nature of the virtues, it belongs to philosophy and is a part of it; since philosophy treats the intellectual soul, it must consequently treat its moral acts.

As to the second example, there are two opinions about the parts of philosophy, as will be said in Physics I, q. 1.¹³ Some distinguish them as ultimate species; on that view, different specific abstractions are posited. Although all abstract from individual matter as their point of departure, they nevertheless take on a different determinate abstraction, as it were on the side of the terminus toward which they proceed, insofar as matter is more or less involved in the principles used in these distinct parts of philosophy. Others say that the same specific abstraction is found in all parts of philosophy. On this view, the books On the Heavens and On the Soul, and even the ethical part treating virtues, are reduced to the same abstraction, namely the account of mobile being, insofar as they involve or depend on some motion of a bodily thing. These subjects are divided among different parts within the same science, just as theology has one treatise on God, another on angels, and another on human beings. Which of these opinions is truer will be said in the cited place in the Physics.

As for mathematics, it is certain that there are sciences distinct in species within the same abstraction from sensible matter, since that abstraction is only generic and admits different ranges and degrees in the principles of continuous or discrete quantity, as was said above.

As for what is added about music and the other subaltern sciences, the reply is that they do not have a double abstraction but a single one. The principles of a higher science, when applied to such matter, are made less abstract and consequently pertain to a different species within the genus of the knowable. The abstraction they take on in such matter is one; therefore, such sciences are neither purely mathematical nor purely physical, but partake of both, while having a single abstraction—just as one existing middle term is said to partake of the extremes.

As to the final point concerning the habit of principles, the reply is that the habit of principles naturally acquired in us cannot be diversified on the basis of the different immaterialities of things in themselves, but according to the way it is applied to the intellect. Just as immateriality contributes to the unity or diversity of sciences only insofar as it lies on the side of the illuminating middle term or principle, so in first principles themselves the different immaterialities of things in themselves contribute to specific diversity only insofar as truth is made known through the terms. This way of illuminating things through their terms, without any proof, is the same in all necessary first principles, because it is grounded in the same account: the immediate connection of predicate to subject. It is like an intuitive and immediate vision of truth in itself. Therefore, all principles are reached by one habit, since the mode of knowing is the same: seeing truth in itself. Scientific illumination, by contrast, manifests a hidden thing through a demonstrative middle term; hence, the higher and more intelligibly it is manifested, the more different the mode of knowing. Higher intelligibility is derived from greater immateriality. If principles are reached through different modes and immaterialities in the very character of vision, they require different habits and lights, as do principles seen by angels or by human beings through supernatural or natural light. Finally, there is no difficulty in saying that habits of opinion, just as they are distinguished by different demonstrative middle terms, are also distinguished by different modes of immateriality—not necessary immateriality, but contingent.

Second it is argued that this abstraction is either taken in the object as an extrinsic denomination arising from the act of science, or taken fundamentally as the object’s very capacity for abstraction. In the first way, it is not that from which the specification of a science is derived, since it presupposes a science that is already specified, and that denomination is derived from the act of science. If it is taken in the second way, it cannot be the formal account under which sciences are specified, since God is always immaterial in the same way, yet there are sciences of him that differ in species, such as theology and metaphysics. Similarly, one science of a single species, metaphysics, treats things of differing immateriality, such as angels and bodies.

It is confirmed that science a priori and a posteriori differ in species, and yet they can proceed from the same thing under the same immateriality: for example, demonstrating that a human being is capable of laughter because rational, or from the effect because he laughs. The immateriality is the same, yet the sciences are different.

THE REPLY is that if things were known adequately as they are in themselves, the immateriality of the thing in itself would be the same as its immateriality insofar as it is subject to the means of cognition. But it happens that a thing of the same immateriality is known through different means, or according to different connotations and effects that do not illuminate and make the object appear in the same way. Therefore, different sciences can be given of the same immaterial thing when it is not known by the same immaterial mode and means, because it is subject to different formal immaterialities—that is, to different principles or means that illuminate and infer the conclusion under different immaterialities. The species of sciences is therefore derived from a different objective or foundational immateriality, not insofar as it exists entitatively in the thing itself, but insofar as it shines forth in the middle term or principle through which it appears to and is demonstrated to the intellect. Likewise, things that are in themselves of different abstractions, such as angels and bodies, can be united under some account or means superior to both, such as the account of being, which the metaphysician considers through a single abstraction from sensible and intelligible matter.

In reply to the confirmation, it is said that even in these sciences a different specific abstraction is found, because to demonstrate through causes and through effects is not of the same immateriality in intelligible being. Although cause and effect are of the same spirituality in the being of beings, these sciences proceed a posteriori and with respect to whether a thing is, only insofar as their effects fall under experience and induction, from which they originate. Experimental cognition does not involve the intelligible abstraction by which a thing is known through its quiddity, especially since experience among us always depends on some sensibles. Thus the science that proceeds a priori has a different abstraction, considered as such.

Third it is argued to prove that the unity or diversity of sciences is not derived from the side of the middle terms or principles. For it would follow that anything derived from common principles of some thing would be contained under the same science. For example, since the principles of human beings and horses are contained under the common principles of animal, human beings and horses would belong to the same science. Therefore, spiritual and bodily things would likewise be contained under one science, since they are derived from the same principles of substance; and discrete and continuous quantity would be contained under the same mathematical abstraction from the common principles of quantity. Therefore, all these would belong to the same science by reason of the same abstraction.

It is confirmed that, since different definitions and means of demonstration are found in one science, they must be reduced to some unity for the science to be called one. But they are not reduced to some common definition, as is self-evident; therefore, they are reduced to something common that is not a definition and consequently is not a middle term. Therefore, the formal account of the unity or diversity of sciences is not derived from middle terms or principles, but from some other source.

THE REPLY is to deny the consequence. To the proof, it is said that for some things to belong to one science, it is not enough that they be derived from common principles that are common in any way whatsoever—namely, in the being of a thing or according to total universality, which is universality in predication. Rather, the principles must be common in their being as objects and within the same formal abstraction. For the account of scientific knowability is derived from formal abstraction, not total abstraction. Thus human beings and horses agree in the common principles of animal not only with respect to generic total abstraction, but also with respect to the same formal abstraction, as found in physics under the account of mobile being, which involves sensible matter and excludes only the individual. Angels and bodily things, however, do agree under the common account of substance, but not under the same formal abstraction of mobile being; they do agree under the same metaphysical abstraction, and under it are united in the same science. Likewise, discrete and continuous quantity agree in the same quantity according to the same essential account, but not according to the same account of mathematical formal abstraction, which considers a greater or lesser abstraction from sensible matter in the mode of measuring: number does not measure with as much concretion as continuous quantity, as was said above. Likewise, theology and metaphysics treat of God under different abstractions: theology through participation in divine knowledge and supernatural light; metaphysics insofar as God is known from natural effects. Nevertheless, both agree in the generic account of abstraction with respect to the point of departure.¹⁴

In reply to the confirmation, it is said that the several definitions of one science agree not in one common definition, nor in one thing defined, but in one mode of defining, as St. Thomas says in Metaphysics VI, lect. 1.¹⁵ This is to agree formally in the same middle term, insofar as a thing defined in such a way and according to this or that abstraction also illuminates inferred truths in a corresponding way. Hence, although different things or quiddities are treated in one science—things that can have different perfections and abstractions in themselves, as metaphysics does when treating of God and the categories, or physics when treating of an element or the soul—the mode of defining is nevertheless always the same. For just as an element is defined as mobile, so the soul is defined as the actuality of a mobile thing; and just as the categories are treated insofar as they participate in the account of being, so God is treated as the first cause of all being. This is to treat them all under the same order, just as within the same body there are different parts with different perfections, yet all agree in being informed by the same soul.

But if you say: A middle term or definition does not express the very account under which, but the account which is known, for it is a certain thing known. Therefore, it is not itself the ultimate account distinguishing sciences. Similarly, it is not something intrinsic to the very demonstrated truth, since the definition is outside the conclusion; therefore, it is not that truth’s formal account.

The reply is that a definition formed according to this mode of abstraction is the formal account under which the conclusion is illuminated by it, although in itself it is also a formal account which, when grasped by the habit of principles or taken by science as a premise. For example, light has the role of the formal account under which colors are illuminated, although in itself it is also visible as a formal account which. The definition itself is an intrinsic middle term to the conclusion and inferred truth—not as a predicate constituting it, but as something necessarily connected and necessarily entailing it, just as the essence entails attributes distinct from itself.