Writings of Charles S. Peirce: A Chronological Edition, Volume 2. Charles S. Peirce

and throughout suppose a previous synthesis, since they themselves represent something which is only given by sensuous impressions, something sensible; as, the concept of red colour. In this signification, neither pure intuitions (Space and Time) nor pure intellectual concepts (as Substance, Cause, Totality) are to be termed abstract concepts, since they are not contained as sensuously given constituents in the concrete concepts of sensuous objects, but first make these themselves possible, that is, are conditions which must be present in the cognitive power itself, in order to be empirically intuited or thought by the latter. The prescinded consciousness of them, however, supposes the operation of abstraction, since we at first become acquainted with them only by their immediate application to individual objects, and therefore in concreto. Hence arises the illusion of their being sensuously abstracted. That A, from which something else B is abstracted as a mark, we must still be able to represent to ourselves after the abstraction has taken place. But if, for instance, we abstract space from a body, every other representation which belongs to the body, vanishes along with Space.” See further under the verb to abstract.

      4. The immediate object of an abstract representation is termed an abstract form or attribute, &c.

      See Logical, Metaphysical, Physical.

      Abstract concept. Abstract, as applied to concept, is commonly used in the second of the above senses. More properly in the first sense; by Kant sometimes in the third.

      “The use of some logicians which identifies abstract and universal is not to be commended. Grammar distinguishes the two sharply. Wolff, also, has the more proper terminology which agrees with that of grammar since he (Logik, §110) defines the abstract notion as that which represents something which is in a certain thing (to wit, the attributes, modes, relations, of things) apart from the thing which it is in, but the universal notion as that which represents what is common to several things.” Überweg.

      Abstract freedom “consists in that indetermination or equality of the ego with itself, wherein there is a determination only so far as it makes it its own or puts it into itself.” Hegel.

      Abstract knowledge. Used by Hamilton (Reid, p. 812) in place of abstractive knowledge, q.v.

      Abstract name. 1. “The question is whether a denominative name signifies the same as an abstract one, to wit, a form only.” Scotus, Quaestiones in Praedicamentis, Qu. 8. Abstract is here used in the first sense.

      2. “A practice has grown up in more modern times, which, if not introduced by Locke, has gained currency chiefly from his example, of applying the expression ‘abstract name’ to all names which are the result of abstraction or generalization, and consequently to all general names, instead of confining it to the names of attributes. The metaphysicians of the Condillac school,… have gone on imitating him in this abuse of language, until there is now some difficulty in restoring the word to its original signification. A more wanton alteration of the meaning of a word is rarely to be met with; for the expression ‘general name’, the exact equivalent of which exists in all languages … was already available for the purpose to which abstract has been misappropriated, while the misappropriation leaves that important class of words, the names of attributes, without any compact distinctive appellation. The old acceptation, however, has not gone so completely out of use, as to deprive those who still adhere to it of all chance of being understood.” Mill, Logic.

      Abstract Logic “considers the laws of thought as potentially applicable to the objects of all the arts and sciences, but as not actually applied to those of any.” Hamilton.

      Abstract object. The object of an abstract concept in the first or second sense.

      TO ABSTRACT

      “It is necessary here to note the very great ambiguity of the word abstract. For we should properly say ‘to abstract from anything’ not ‘to abstract anything’. The former denotes that we do not attend in a certain concept to others in any way bound up with it, but the latter that it is not given unless in the concrete and so that it may be separated from the things conjoined with it. Hence, an intellectual concept abstracts from all that is sensitive, but is not abstracted from sensitive objects; and perhaps it would be more correct to call it abstrahent than abstract. Wherefore, it is better to name intellectual concepts pure ideas, but those which are only given empirically abstract.” Kant, De mundi sensibilis atque intelligibilis forma et principiis.

      It is difficult to see what ground there is for saying that the expression to abstract anything has the implication here attributed to it. It is certainly improper to speak, as Berkeley does, of abstracting things apart; but the opinion that some entertain that mentem is the understood object of abstrahere is neither supported by the original metaphor, nor by good usage in any age of the world.

      The following are examples of the use by Scotus, who chiefly formed the modern custom with reference to the derivatives of abstractio. “Intellectus noster in cognoscendo abstrahet ab hic et nunc”; “Prius cognoscit intellectus singulare quam universale; impossibile est enim, quod rationem universalis ab aliquo abstrahet, nisi id, a quo abstrahit, praecognoscat.” Of course ratio does not here mean reason; ratio universalis is the mode of the universal.

      ABSTRACTION

      Abstractio is the translation by Boëthius of

      1. Abstraction is the separation in thought of an attribute or relation from its subject, by neglecting the latter. This seems to be its sense, in Aristotle.

      2. Mental separation of any elements by neglect of one and attending to the other; that is, by supposing one not to exist.

      3. Such a separation of matter and form, or of certain characters from others, but not of one thing from another.

      4. Any sort of mental separation.

      5. Any separation, mental or real.

      6. The power of performing mental abstraction. See Concrete, Formal, Logical, Mathematical, Metaphysical, Modal, Objective, Partial, Physical, Real, Ultimate.

      ABSTRACTIVE

      Abstractive cognition. The distinction between abstractive and intuitive cognition is found in St. Anselm (Monologium, Caps. 62, 63, 66, 67), but the word first occurs in Scotus.

      1. “In order that I may use brief words, I will call that cognition abstractive, which is of the quiddity itself as it is abstracted from existence and non-existence.” Scotus, lib. 2, dist. 3, qu. 9, p. 197.

      2. “Abstractive knowledge is the cognition of a thing not as it is present; for example, the knowledge by which I know Socrates when absent, and that by which an astronomer in the house considers an eclipse which he does not observe, supposing that he knows that at that time the earth is between the moon and the sun. And also, that by which the philosopher from creatures knows that God is. For although these cognitions are directed to the thing as to its existence, yet they are not so directed to it that the presence of their object is discerned.” Conimbricenses, De Anima, lib. 2, cap. 6, qu. 3, art. 1.

      ABSTRAHENT

      This term was often used in the 12th century (see the treatise De intellectibus. Cousin, Fragments Philosophiques, p. 481). Kant has suggested the revival of the term to denote pure concepts of the understanding.

      Abstrahentium non est mendacium. This is an awkward way of saying that a quality which is abstracted from is not denied. If abstraction is not denial, far less is generalization. Yet the two seem to be confounded by Hegel when he says that being and nothing are the same because they are equally the absence of all determination.

      ABSURD

      1. That which involves an error obvious to common sense.

      2. That which would