ABSTRACTION

Generally, a mental separation of things, not or at least not necessarily, separated in the real. Looked at from this point of view, abstraction is understood as the psychological act of discarding all but one facet of a thing (or things) to cognize that facet without the others. To be legitimate, this psychological act presupposes an appropriate object: the facet cognized through abstraction must in itself be knowable, apart from that which it is mentally separated. Just as the term abstraction is used to name the psychological act of mentally separating one thing from another, it can also be used to name the abstractability of that which is mentally separated. Thus one may speak of a man abstracting a given object from certain nonessential data, and one may speak of that object itself abstracting from these data. This article first considers the abstraction of the intelligible from the sensible, as well as alternative theories in the history of thought that propose to account for the discovery of the intelligible. It then explains how the intelligible as abstracted is universal, and concludes with a consideration of the various kinds of abstraction.

Abstraction Of The Intelligible. Of the different, though not necessarily unrelated, instances of abstraction the most radical is the abstraction of the intelligible object from the data of sense experience. This abstraction is meaningful, of course, only within a philosophical frame that sees such a thorough difference between the sensible and the intelligible, that they are recognized as objects pertaining to irreconcilably different orders. And even among those who admit this difference there is an abstraction only so long as the sensible and intelligible are somehow given together, with the intelligible somehow cognized by way of an insight in and through the sensible. The sensible is the fluctuating, kaleidoscopic data of man's original cognitive contact with the things of the physical world: their colors and shapes, their sounds, odors and flavors, their temperatures and weights, their motions and rest, and the like. The intelligible, on the other hand, is the stable, definable, potentially scientific object of a cognitive vision radically different from an experience of the sensible. If the sensible is the phenomenal in things, the intelligible is the meaningful in them. The sensible as a datum of experience is exclusively singular, tied to an individual thing in this place at this time. The intelligible is, at least as the object of the direct act of intellection, universal; i.e., it can be said of many, indifferent to individual differences, indifferent to shifts in place and time.

Empiricist View. For those who fail to admit the distinction between the sensible and the intelligible there is no question of the abstraction of an intelligible object from sense data. This is the case, for example, with those empiricists (such as J. locke and D. hume) who limit knowledge effectively to the realm of sense experience. They may speak of an abstraction, but at best they mean some more or less subtle reworking of sense impressions that yield an image involving an outline simple enough to stand for many things. This notion also underlies the use of the term abstraction by those working in cybernetics. The refined impressions spoken of here, remain on the same plane as the impressions from which they came, the plane of the sensible. There is no question of penetrating to the radically different plane of the meaningful. Therefore, in this there can be no abstraction from the sensible to the intelligible.

Nonabstractive Theories. There are some in the history of thought, however, who do admit the radical difference between the sensible and the intelligible, but they nevertheless explain man's knowledge of each without recourse to a theory of abstraction. Plato and St. Augustine are two such people.

For plato, envisioning the intelligible is not the result of seeing into and through the data of sense experience to an underlying intelligibility, but rather, of turning from what is sensible, to the intelligible that is defined apart from and exists independently of the sensible. Plato distinguishes between preexistence in a realm of pure intelligibles, wherein a vision of these intelligibles has once been achieved, and this life, in which there takes place, by way of reminiscence, a conversion from the data of sense experience to these intelligibles. If Plato can be taken literally, for him learning is but a process of remembering ideas from another existence, temporarily forgotten in this existence, but innately present nonetheless.

For St. augustine, the intelligible is not innate; it is not apprehended by way of reminiscence, but neither is it seen by way of abstraction from sensible data. In his view, there is a realm of intelligibles to which the human intellect is naturally subject and which a man can know so long as his intellectual vision functions in virtue of an incorporeal light supplied by God. The intellect is thought to be related through this divine illumination to the intelligible as the sense of sight is related through corporeal light to the visible. For St. Augustine, as well as for Plato, there is an infinite metaphysical distance between the sensible and the intelligible, but there is no abstraction because the intelligible is not known in and through the sensible. For aristotle and for St. thomas aquinas, there is an infinite metaphysical distance between the sensible and the intelligible, and yet the latter can only be cognized through the former; for them a theory of abstraction is a noetic necessity.

Thomistic Account. According to the Thomistic epistemology, some things are endowed sensibly as well as intelligibly, for example, men, trees and rocks; others, such as angels, are endowed only intelligibly. Men can know both, but the human condition is such that the latter are known only as a function of the former, and the intelligible in the former is known only as a function of the sensible. In other words, the sensible characteristics of the sensibly endowed things are immediately knowable, but the intelligible characteristics are knowable only mediately by way of the sensible.

In Thomistic terms, a thing is said to be actually sensible and only potentially intelligible. As actually sensible it can be actually sensed as it stands; but the potentially intelligible part must be rendered actually intelligible before it can be actually understood. The senses are capacities for actually sensing the actually sensible; the intellect (that is, the possible intellect) is the capacity for actually understanding the actually intelligible. The senses need no help since the thing as it stands is actually sensible. The possible intellect stands in need of another capacity on the intellectual level that is able to make the potentially intelligible actually intelligible. This capacity is called the agent intellect. The thing—which is potentially intelligible—is originally present in knowledge through its sensory representation, which is called the phantasm. Through this phantasm in sensory experience, only the sensible characteristics of the thing are actually presented to the knower; but just as the thing, while being actually sensible, is potentially intelligible, so through the phantasm the intelligible aspect of the thing is potentially present to the knower. The agent intellect is a spiritual light that, by illuminating the phantasm, actualizes the intelligible so that it can be actually cognized by the possible intellect.

The possible intellect, like the senses, is a passive power, able to operate only after being reduced from potency to act. The thing as it stands, as physical, is able to reduce the senses, themselves in a way physical, from potency to act: no agent sense is needed. But the thing itself, as physical, cannot reduce the wholly spiritual possible intellect to act: only something spiritual can do this, and this is the agent intellect. But the agent intellect is an unspecified light; and since there is no knowing except of something determinate, that which actualizes the possible intellect must simultaneously specify it for the act of knowing something determinate. Thus the agent intellect, as principal cause, uses the phantasm of the thing as instrumental cause (see instrumental causality). Together they actualize the possible intellect, which—once reduced from potency to act in reference to a given intelligible aspect of some thing—can posit the act of knowing that intelligible object. The intelligible remains an object irreducibly other than the sensible. Intellection is never reduced to sensation. But the intelligible is known only in and through sense experience by way of an intuitive penetration that is most strictly an abstractive act.

The Intelligible As Universal. The object cognized in the abstractive intuition just described can be distinguished from the data of sense experience in several ways, as has already been noted. Perhaps the most obvious difference is that the characteristics present in sense knowledge are incorrigibly singular, while the object intellectually cognized is characteristically universal. This difference demands further comment. For one thing, though this is an obvious difference between the sensible and the intelligible in man's experience, it is not the essential difference. If it were, the intellect would be defined as an appetite for the universal; it is, rather, an appetite for the meaningful. In fact, there is an inverse ratio between the meaningful content of an object and its universality (man being an object much richer in content than substance, but considerably less general). If one were to define the intellect as transcendentally related to universality rather than to intelligible content or meaning, this would strongly suggest that the crowning achievement of the intellectual life would come in the possession of an object involving next to nothing in the way of intelligible content.

It remains true, however, that the object cognized intellectually is, as cognized, universal. The reason is that that which in the thing shrouds its intelligibility (so that it is only potentially intelligible) is matter, and this coincidentally is the principle of the individuation of the physical thing. To get to the intelligible, man must (and does, through the light that is the agent intellect) slough off matter as a principle of nonintelligibility. In doing so, of course, he also sloughs off the principle of individuation and cognizes an object that is universal. The intellect is essentially ordered to the intelligible, but the price of knowing the intelligible is knowing it as a universal.

Further comment is required in reference to the universal character of the object of intellection. It might seem, perhaps, that since in the realm of real subjects only singulars exist, the abstraction that renders an object universal somehow precludes the possibility of knowing things as they are. The question is: Is there something inherently falsifying in the process of abstraction? Not at all. A quiddity that is universal in the mind as object, need not be in itself intelligibly different from this same quiddity individualized in things. Natures or quiddities in themselves are neither singular nor universal, but as such are open to either state. In things, in a first existence outside the mind natures are in the state of singularity; in the mind in a second existence, as objects, they are invested with the relation of reason that is the form of universality. Universality is not real; it is a being of reason. But the nature as known, to which universality accrues in the process of being known, need in no sense be itself intelligibly de-realized simply because it takes on a nonreal relation in the mind. The nature of the thing remains unchanged. However, even though abstraction does not falsify things, man does pay a price because he knows by way of abstraction. Things as they exist as subjects, independently of the mind's knowing them, are highly sophisticated complexes of many intelligible aspects as well as all that is sensible in them and the existential act that makes them be more than a mere possibility. In any given act of abstractive intuition some one (more or less meaningful) intelligible aspect, abstracted from all else, is cognized. Thus knowledge by way of abstraction, in any given instance of abstractive intuition, may be seriously incomplete. However, there is an infinite difference between knowledge that is incorrigibly false and knowledge that is less than complete. (see universals.)

Kinds of Abstraction. The discussion thus far has been limited to the abstraction of the intelligible from the sensible. There are other abstractions to consider and certain distinctions to be made, namely, between abstraction by way of simple consideration and abstraction by way of negative judgment, between precisive and nonprecisive abstraction, between total abstraction and formal abstraction, and between the abstraction of the whole, the abstraction of the form and separation.

Simple Consideration vs. Negative Judgment. One important distinction between different types of abstraction is between abstraction by way of simple consideration and abstraction by way of negative judgment. To abstract one thing from another by way of simple consideration is to cognize it without simultaneously cognizing the other. This is legitimate only if the first is definable or able to be understood without the other entering into its definition or meaning. There is no need here for the first to be existentially independent of the other. Some things (for example, the nature of man) are definable apart from other things (such as individuating characteristics) without being able to exist apart from them. They can, of course, be abstracted from these by way of abstraction through simple consideration.

To abstract one thing from another by way of negative judgment is not simply to cognize it independently of the other but to think that it exists without the other. An abstraction of this sort is legitimate only if what is abstracted from another is not only independent in meaning from the other but even existentially independent. The nature of man cannot be abstracted by way of negative judgment from individuating characteristics because, though man is definable apart from them, man cannot exist apart from them. However, man can be abstracted from a tree by way of negative judgment because man is independent of the tree both in meaning and in existence; for a tree does not enter into the definition of man, and men can exist without trees. This distinction is important, as the examples should make clear, for any solution to the problem of the universal. As Aquinas frequently points out, it was a failure to distinguish between abstraction by way of simple consideration and abstraction by way of negative judgment that forced Plato to posit existing Forms and Mathematicals.

Precisive vs. Nonprecisive Abstraction. Another distinction between types of intellectual abstraction is that between precisive abstraction that renders an object abstractly expressed and nonprecisive abstraction that renders an object concretely expressed. The difference between "man" and "humanity" (for an example from the category of substance) and between "pious" and "piety" (for an example of an accident) is at stake. "Pious" and "piety" do not differ in intelligible content; their difference is one of mode of conception. The formality that is precisely "piety" is conceived as belonging to a bearer (in general) in the conception of "pious." "Pious" is equivalently "subject-having-piety." Identically this same formality, but abstracted from any reference to a bearer—that is, positively cut off from any subject—is conceived in the notion of "piety." "Pious" names a whole, that is, the whole subject that is the bearer of piety, but only from the point of view of its piety. "Piety" names the formality as a part, which, with other parts, makes up the whole. "Pious" can be said of a concrete subject, such as Tom, so long as Tom has piety. "Piety" cannot be said of Tom; though it is no less real than "pious," it is conceived in such fashion as to be, as conceived, cut off from concrete subjects.

Formal vs. Total Abstraction. Important among the traditional distinctions between types of intellectual abstraction is that between formal abstraction and total abstraction. In this matter it is necessary to clarify the usage of terms, for "total abstraction" and "formal abstraction" are used by different philosophers to stand for a variety of different abstractions. Reference here is exclusively to the use to which T. de Vio cajetan and john of st. thomas put them when they discuss abstraction in reference to the specification of the sciences (see sciences, classification of). Although these commentators on St. Thomas claim to be repeating a distinction already made by St. Thomas, a careful investigation of the relevant texts in St. Thomas suggests this is not the case. Be that as it may, the point they make is consonant with the Thomistic theory of science and helpful in understanding it.

Formal abstraction (abstractio formalis ) is the abstraction of an intelligible content of thought from the matter that shrouds its intelligibility. Total abstraction (abstractio totalis ) is the abstraction of a logical whole from its subjective parts. Formal abstraction yields an object qua intelligible; total abstraction, qua universal. Given the inverse ratio between meaningful content and universality the two abstractions work in opposite directions. And yet they are both necessary for human science (scientia ). Human science, as science, needs an object able to be intellectually analyzed. For science, the real must be present to the mind in abstraction from whatever matter stands in the way of its being understood. Formal abstraction abstracts from matter as a principle of nonintelligibility to yield an object rich enough in intelligible content to satisfy the scientific mind. Human science, as human, is achieved in discourse. The objects of scientific analysis must be present to the mind as being able to fit into a discursive pattern: they must be present in the state of universality or of communicability. Total abstraction abstracts from matter as the principle of incommunicability to yield an object that is universal and as such able to fit into a discursive pattern.

To the extent that objects are differently freed from the restrictions of matter as a principle of nonintelligibility they are differently scientific. Freedom from individual sensible matter yields an object that is scientifically relevant on the level of natural science. Freedom from all sensible matter yields an object that is scientifically relevant on the level of mathematics. And freedom from all matter yields the object of metaphysical inquiry. Thus one may speak of the first order of formal abstraction, that is, physical abstraction; the second order of formal abstraction, that is, mathematical abstraction; and the third order of formal abstraction, that is, metaphysical abstraction. These three orders or degrees of formal abstraction respectively constitute the different levels of theoretical science.

Total abstraction admits of different degrees also: some objects are more general and some less general than others. These differences do not constitute differences among sciences; they function exclusively within a given science. Two objects on the same level of formal abstraction are studied in the same science, but the more general is studied before the more specific. Total abstraction does not help to specify the sciences, but it is a common condition for all the sciences; and, within a given science, it determines the order of proceeding in its particular subject matter.

Abstraction vs. Separation. In distinguishing between the types of speculative science, St. Thomas speaks of an abstraction of the whole (abstractio totius ) that yields the object of natural science, of an abstraction of the form (abstractio formae ) that yields the object of mathematics, and a separation (separatio ) that yields the object of metaphysics. The first two of these are called abstractions in a strict sense because they are abstractions by way of simple consideration. The third is more sharply referred to as a separation because it is an instance of the more radical abstraction by way of negative judgment.

The first of these three abstractions is the abstraction of the whole essence of the natural thing from the matter that individuates it. It yields an object sufficiently free from matter to be intelligible, but an object defined nevertheless in terms of common sensible matter. The second yields the form of quantity that is abstracted from all matter save common intelligible matter. The third yields an object abstracted from all matter and an object seen to be independent of matter both in meaning and existence. The significantly different stances in reference to matter for these objects—resulting in significantly different modes of defining—put each on a different level of theoretical science. St. Thomas, with his distinctions between the abstraction of the whole, the abstraction of the form, and separation, covers the same ground as do Cajetan and John of St. Thomas with their distinctions between physical abstraction (the first degree of formal abstraction), mathematical abstraction (the second degree of formal abstraction), and metaphysical abstraction (the third degree of formal abstraction).

See Also: knowledge, process of; knowledge, theories of; knowledge; epistemology; universals

Bibliography: thomas aquinas, The Division and Methods of the Sciences: Questions 5 and 6 of Commentary on the De Trinitate of Boethius, tr. with introd. and notes, a. maurer (Toronto 1953), bibliography 86–93. j. f. peifer, The Concept in Thomism (New York 1952). e. d. simmons, "In Defense of Total and Formal Abstraction," The New Scholasticism, 29 (1955) 427–440; "The Thomistic Doctrine of the Three Degrees of Formal Abstraction," Thomist, 22 (1959) 37–67. c. de koninck, "Abstraction from Matter," Laval Théologique et Philosophique, 13 (1957) 133–196; 16 (1960) 53–69, 169–188. f. a. cunningham, "A Theory on Abstraction in St. Thomas," The Modern Schoolman, 35 (1958) 249–270. l. ferrari, "Abstractio totius and abstractio totalis," Thomist, 24 (1961) 72–89. m.d. phillipe, "'A φαίρεσι[symbol omitted], πρόσθεσι[symbol omitted], χωρίζειν dans la philosophie d'Aristote," Revue thomiste, 48 (1948) 461–479. g. van riet, "La Théorie thomiste de l’abstraction," Revue philosophique de Louvain, 50 (1952) 353–393. l. b. geiger, "Abstraction et séparation d'après S. Thomas: In De Trinitate, q.5, a.3," Revue des sciences philosophiques et théologiques, 31 (1947) 3–40.

[e. d. simmons]

ab·strac·tion / abˈstrakshən/ • n. 1. the quality of dealing with ideas rather than events. ∎  something that exists only as an idea.2. freedom from representational qualities in art.3. a state of preoccupation: his momentary abstraction.4. the process of considering something independently of its associations, attributes, or concrete accompaniments: they tend to interpret Jesus's words in abstraction from any historical context.5. the process of removing something, esp. water from a river or other source.

abstraction The principle of ignoring those aspects of a subject that are not relevant to the current purpose in order to concentrate solely on those that are. The application of this principle is essential in the development and understanding of all forms of computer system. See data abstraction, procedural abstraction.

ABSTRACTION

Taking from someone with an intent to injure or defraud.

Wrongful abstraction is an unauthorized and illegal withdrawing of funds or an appropriation of someone else's funds for the taker's own benefit. It may be a crime under the laws of a state. It is different from embezzlement, which is a crime committed only if the taker had a lawful right to possession of the money when it was first taken.

abstraction (extraction) The artificial removal of water from a well, reservoir, or river.