The terms “prescision” and “abstraction,” which were formerly applied to every kind of separation, are now limited, not merely to mental separation, but to that which arises from attention to one element and neglect of the other. Exclusive attention consists in a definite conception or supposition of one part of an object, without any supposition of the other. Abstraction or prescision ought to be carefully distinguished from two other modes of mental separation, which may be termed discrimination and dissociation. [—]
Prescision is not a reciprocal process. It is frequently the case, that, while A cannot be prescinded from B, B can be prescinded from A. This circumstance is accounted for as follows. Elementary conceptions only arise upon the occasion of experience; that is, they are produced for the first time according to a general law, the condition of which is the existence of certain impressions. Now if a conception does not reduce the impressions upon which it follows to unity, it is a mere arbitrary addition to these latter; and elementary conceptions do not arise thus arbitrarily. But if the impressions could be definitely comprehended without the conception, this latter would not reduce them to unity. Hence, the impressions (or more immediate conceptions) cannot be definitely conceived or attended to, to the neglect of an elementary conception which reduces them to unity. On the other hand, when such a conception has once been obtained, there is, in general, no reason why the premisses which have occasioned it should not be neglected, and therefore the explaining conception may frequently be prescinded from the more immediate ones and from the impressions.
…even in cases where two conceptions cannot be separated in the imagination, we can often suppose one without the other, that is we can imagine data from which we should be led to believe in a state of things where one was separated from the other. Thus, we can suppose uncolored space, though we cannot dissociate space from color. I call this mode of separation Prescission.
…even in the very first passage in which abstraction occurs as a term of logic, two distinct meanings of it are given, the one the contemplation of a form apart from matter, as when we think of whiteness, and the other the thinking of a nature indifferenter, or without regard to the differences of its individuals, as when we think of a white thing, generally. The latter process is called, also, precision (or better, prescission): and it would greatly contribute to perspicuity of thought and expression if we were to return to the usage of the best scholastic doctors and designate it by that name exclusively, restricting abstraction to the former process by which we obtain notions corresponding to the “abstract nouns.” [—] …prescission, if accurately analyzed, will be found not to be an affair of attention. We cannot prescind, but can only distinguish, color from figure. But we can prescind the geometrical figure from color; and the operation consists in imagining it to be so illuminated that its hue cannot be made out (which we easily can imagine, by an exaggeration of the familiar experience of the indistinctness of hues in the dusk of twilight). In general, prescission is always accomplished by imagining ourselves in situations in which certain elements of fact cannot be ascertained. This is a different and more complicated operation than merely attending to one element and neglecting the rest.
Precision. [—] (1) A high degree of approximation, only attainable by the thorough application of the most refined methods of science.
(2) Its earlier meaning, still more or less used by logicians, is derived from a meaning given to praecisio by Scotus and other scholastics: the act of supposing (whether with consciousness of fiction or not) something about one element of a percept, upon which the thought dwells, without paying any regard to other elements. Precision implies more than mere discrimination, which relates merely to the essence of a term. Thus I can, by an act of discrimination, separate color from extension; but I cannot do so by precision, since I cannot suppose that in any possible universe color (not color-sensation, but color as a quality of an object) exists without extension. So with triangularity and trilaterality. On the other hand, precision implies much less than dissociation, which, indeed, is not a term of logic, but of psychology. It is doubtful whether a person who is not devoid of the sense of sight can separate space from color by dissociation, or, at any rate, not without great difficulty; but he can, and, indeed, does do so, by precision, if he thinks a vacuum is uncolored. So it is, likewise, with space and tridimensionality.
A decrease of supposed information may have the effect of diminishing the depth of a term without increasing its information. This is often called abstraction; but it is far better to call it prescission; for the word abstraction is wanted as the designation of an even far more important procedure, whereby a transitive element of thought is made substantive, as in the grammatical change of an adjective into an abstract noun.
Separation of Secondness, or Secundal Separation, called Precission, consists in supposing a state of things in which one element is present without the other, the one being logically possible without the other. Thus, we cannot imagine a sensuous quality without some degree of vividness. But we usually suppose that redness, as it is in red things, has no vividness; and it would certainly be impossible to demonstrate that everything red must have a degree of vividness.
Abstraction names two wholly different operations. One of them consists in supposing some feature of the fact to be absent, or at least leaving it out of account. I call that prescissive abstraction.
The second mode consists in supposing that one component of the Phaneron is present in a given subject, while making no supposition whatever in regard to another. Thus, I may suppose that a star shines with an intense light without making any supposition at all in regard to the color of the light, further than that it has some color. We thus separate luminosity from hue. I called this mode of analysis prescission.