The most ordinary fact of perception, such as “it is light,” involves precisive abstraction, or prescission. But hypostatic abstraction, the abstraction which transforms “it is light” into “there is light here,” which is the sense which I shall commonly attach to the word abstraction (since prescission will do for precisive abstraction) is a very special mode of thought. It consists in taking a feature of a percept or percepts (after it has already been prescinded from the other elements of the percept), so as to take propositional form in a judgment (indeed, it may operate upon any judgment whatsoever), and in conceiving this fact to consist in the relation between the subject of that judgment and another subject, which has a mode of being that merely consists in the truth of propositions of which the corresponding concrete term is the predicate. Thus, we transform the proposition, “honey is sweet,” into “honey possesses sweetness.”
We shall […] do much to relieve the stem “abstract” from staggering under the double burden of conveying the idea of prescission as well as the unrelated and very important idea of the creation of ens rationis out of an ἔπος πτερόεν – to filch the phrase to furnish a name for an expression of non-substantive thought – an operation that has been treated as a subject of ridicule – this hypostatic abstraction – but which gives mathematics half its power.
From EP 2: The Greek means "winged word"
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 other changes ‘This man is shy’ to ‘This man is affected with shyness’. [—] In non-prosaic language it changes a predicate into a subject (extending the term subject beyond the subject nominative to the subject accusative and subject dative, – in short, to what are called the direct and indirect objects of the verb). “The rose smells very sweetly” is by hypostatic abstraction converted into “The rose possesses a delightful perfume.” So “Cain killed Abel” is changed to “Cain caused the death of Abel.” Perfume and death are hypostatical abstractions. They denote entia rationis, whatever that may mean.
That wonderful operation of hypostatic abstraction by which we seem to create entia rationis that are, nevertheless, sometimes real, furnishes us the means of turning predicates from being signs that we think or think through, into being subjects thought of.
When we speak of the depth, or signification, of a sign we are resorting to hypostatic abstraction, that process whereby we regard a thought as a thing, make an interpretant sign the object of a sign. It has been a butt of ridicule since Molière’s dying week, and the depth of a writer on philosophy can conveniently be sounded by his disposition to make fun of the basis of voluntary inhibition, which is the chief characteristic of mankind. For cautious thinkers will not be in haste to deride a kind of thinking that is evidently founded upon observation, – namely, upon observation of a sign. At any rate, whenever we speak of a predicate we are representing a thought as a thing, as a substantia, since the concepts of substance and subject are one, its concomitants only being different in the two cases. It is needful to remark this in the present connexion, because, were it not for hypostatic abstraction, there could be no generality of a predicate, since a sign which should make its interpreter its deputy to determine its signification at his pleasure would not signify anything, unless nothing be its significate. But hypostatic abstraction (the product of which may be termed a hypostasis) renders general classes of predicates possible, and classes of those classes, and so on, in a manner which the dull and lazy brood of modern logicians has failed to investigate sufficiently, not to say altogether.