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What are your views on the reality of abstractions? Are they the same as Deutsch’s? Are they compatible with Ayn Rand’s? Are there any differences between Rand’s view and Deutsch’s view on this matter?

“The guiding principle is, as always, to reject bad explanations in favour of good ones. In regard to what is or is not real, this leads to the requirement that, if an entity is referred to by our best explanation in the relevant field, we must regard it as really existing. And if, as with the force of gravity, our best explanation denies that it exists, then we must stop assuming that it does.” (Deutsch, BoI, p. 107)

Do David Deutsch’s views on the nature of abstractions fall into one of the four schools described by Ayn Rand in the foreword to Introduction to Objectivist Epistemology ?

“In the history of philosophy, there are, essentially, four schools of thought on this issue:

  1. The “extreme realists” or Platonists, who hold that abstractions exist as real entities or archetypes in another dimension of reality and that the concretes we perceive are merely their imperfect reflections, but the concretes evoke the abstractions in our mind. (According to Plato, they do so by evoking the memory of the archetypes which we had known, before birth, in that other dimension.)
  1. The “moderate realists,” whose ancestor (unfortunately) is Aristotle, who hold that abstractions exist in reality, but they exist only in concretes, in the form of metaphysical essences, and that our concepts refer to these essences.
  1. The “nominalists,” who hold that all our ideas are only images of concretes, and that abstractions are merely “names” which we give to arbitrary groupings of concretes on the basis of vague resemblances.
  1. The “conceptualists,” who share the nominalists’ view that abstractions have no actual basis in reality, but who hold that concepts exist in our minds as some sort of ideas, not as images. (There is also the extreme nominalist position, the modern one, which consists of declaring that the problem is a meaningless issue, that “reality” is a meaningless term, that we can never know whether our concepts correspond to anything or not, that our knowledge consists of words—and that words are an arbitrary social convention.)” (Rand, IToE, p. 1)

And in the Q&A section Rand says this:

“And more than that; the fact that Aristotle is right and not Plato is very relevant here: abstractions, as such, do not exist. Only concretes exist. We could not deal with a sum of concrete objects constantly without losing our grasp of them. But what do we do conceptually? We substitute a concrete—a visual or auditory concrete—for the unlimited, open-ended number of concretes which that new concrete subsumes.” (Rand, IToE, p. 64)

And finally:

“AR: May I point out something here? I said, in this sentence, an abstraction one step further removed from perceptual reality. Now, remember, abstractions also are real. Abstraction itself is only our epistemological process, but that which it refers to exists in reality; but it would not be available to us by direct perceptual means. And, therefore, the term “perceptual reality” is very important here. I don’t mean that higher abstractions are a step removed from reality. I mean they cannot be perceived by perceptual means; in order to grasp them, we need concepts.” (Rand, IToE, p. 78)