In philosophy
Abstraction in philosophy is the process (or, to some, the alleged process) in concept formation of recognizing some set of common features in individuals, and on that basis forming a concept of that feature. The notion of abstraction is important to understanding some philosophical controversies surrounding empiricism and the problem of universals. It has also recently become popular in formal logic under predicate abstraction. Another philosophical tool for the discussion of abstraction is thought space.
John Locke defined abstraction in An Essay Concerning Human Understanding:
"So words are used to stand as outward marks of our internal ideas, which are taken from particular things; but if every particular idea that we take in had its own special name, there would be no end to names. To prevent this, the mind makes particular ideas received from particular things become general; which it does by considering them as they are in the mind—mental appearances—separate from all other existences, and from the circumstances of real existence, such as time, place, and so on. This procedure is called abstraction. In it, an idea taken from a particular thing becomes a general representative of all of the same kind, and its name becomes a general name that is applicable to any existing thing that fits that abstract idea." (2.11.9)
Danish philosopher and existentialist Søren Kierkegaard argued that, since human thought always works by abstracting from a concrete existent, i.e., whenever one thinks of some concrete thing, he must transform it into an abstract generality (the impossibility of cognizing every single detail about any concrete thing, among other reasons, makes this necessary), it is impossible for any thinker "to think existence per se." This makes Kierkegaard repudiate "Hegel's reply to Kant," the latter of which Kierkegaard acknowledges as being right about the impotence of human thought to grasp the "thing-in-itself." According to Kierkegaard, Hegel, instead of reminding Kant that thought "has nothing to do with actuality," attempts to answer the latter using pure thinking, an attempt Kierkegaard sees as categorically defunct. In Concluding Unscientific Postscript he writes:
Instead of admitting that idealism is in the right—but, please note, in such a way that one would reject the whole question about actuality (about a self-withholding an sich) in relation to thinking as a temptation, which like all other temptations cannot possibly be canceled by surrendering to it—instead of putting a stop to Kant's deviation, which brought actuality into relation to thinking, instead of referring actuality to the ethical, Hegel certainly went further, inasmuch as he became fantastical and overcame the skepticism of idealism by means of pure thinking... The dubiousness of "the method" is already apparent in Hegel's relation to Kant. A skepticism that confiscates thinking itself cannot be halted by being thought through, because this must indeed be done by thinking, which is on the side of the mutineer. It must be broken off. To reply to Kant within the fantastical Schattenspiel [shadow play] of pure thinking is precisely not to reply to him. —The only an sich that cannot be thought is existing, with which thinking has nothing at all to do. But how would it be possible for pure thinking to be able to cancel this difficulty, since as pure thinking it is abstract? But from what does pure thinking abstract? From existence, consequently from what it is supposed to explain.
Since thought abstracts from existence, Kierkegaard identified Descartes' "cogito ergo sum," as well as Anselm's ontological argument, as circular in nature. He writes:
The Cartesian cogito ergo sum [I think therefore I am] has been repeated often enough. If the I in cogito is understood to be an individual human being, then the statement demonstrates nothing: I am thinking ergo I am, but if I am thinking, no wonder, then, that I am; after all, it has already been said, and the first consequently says even more than the last.
Similar argument is also advanced against Anselm's proof of God:
When, for example, it is said: God must have all perfections, or the highest being must have all perfections, to be is also a perfection; ergo the highest being must be, or God must be—the whole movement is deceptive. That is, if in the first part of this statement God actually is not thought of as being, then the statement cannot come off at all. It will then run somewhat like this: A supreme being who, please note, does not exist, must be in possession of all perfections, among them also that of existing; ergo a supreme being who does not exist does exist. This would be a strange conclusion. The highest being must either not be in the beginning of the discourse in order to come into existence in the conclusion, and in that case it cannot come into existence; or the highest being was, and thus, of course, it cannot come into existence, in which case the conclusion is a fraudulent form of developing a predicate, a fraudulent paraphrase of a presupposition.
