STEPHEN - Yes, the Berkeley idea seems the same, but in other terms. And a lot of Objectivist types when thinking about the nature of mathematics come down rather like Berkeley. I disagree with them both on the mathematical situation. We do have physical applications of complex numbers. But we did not have any such applications (i.e., physical structures known to coincide with the structure of complex numbers) at the time complex numbers were first thought up. They were never ungrounded in rationally grasped realities, even before physical application was found for them. And there are other things mathematically sensible that to this day we’ve found no physical instantiation of, and perhaps there is no such instantiation.
Rand wrote against the idea of a system of free-market private protective agencies replacing government in the primary functions of the latter: “Nor can one call it a floating abstraction, since it is devoid of any contact with or reference to reality and cannot be concretized at all, not even roughly or approximately.” Here she seemed to think of floating abstractions as having some weak connection to reality. Although, presumably, that could still leave them of limited use and even detrimental for knowledge.
On the NOT side, it occurs to me that I’ve NOT noticed any Objectivist writings taking Platonic Ideas as floating abstractions. The fact that such Ideas have regular relations to concretes may perhaps be enough to save them from being the sleaze of floating abstractions, even though we do not obtain them by abstraction from concretes perceived by the senses.
In the 1960’s while articulating Objectivism, together with Rand and others, Barbara Branden gave a lecture series called “Principles of Efficient Thinking.” Therein she spoke in a kind of psychological-type way of persons who characteristically think in terms of floating abstractions. She said they don’t see the trees for the forest. There’s “nothing in his head but floating abstractions—that is, abstractions which he’s unable to concretize, which he believes, without any idea of what they would actually mean in reality. / An example of this kind of thinking is a meeting at which a political candidate declares that he stands for a balanced budget, decreased taxes, and increased government spending; and his audience bursts into applause. No one who understood concretely what these abstractions meant could possibly applaud. / A man who holds floating abstractions understands words not in terms of what they denote, but in terms of what they connote. Words connote things to him. They call up pleasant or unpleasant emotions, associations, memories. They suggest; they do not denote. His abstractions float in space, untied to meanings, to facts, to reality.” (Transcribed on p. 178 of the book THE VISION OF AYN RAND.)
In the 1980’s Leonard Peikoff gave a lecture series called “Understanding Objectivism.” I notice there that he thought of Leibniz, and presumably Rationalists more generally as dealing in floating abstractions (which is rather the idea you get of Rand’s view of Rationalism in her “For the New Intellectual” even though she doesn’t use the name ‘floating abstraction’ there so far as I’ve found). Peikoff mentions a type of psychosis “which has some elements of being concrete-bound, and has some elements of floating abstractions (certain schizophrenics will build castles in the air), but still they are crazy, and Leibniz wasn’t.” (Transcribed on p. 265 of the book UNDERSTANDING OBJECTIVISM.)
The quotation on floating abstractions you found in Peikoff’s OPAR is helpful. Thanks. There he seems to be back to thinking about persons not very philosophical in their thinking. (Cf. Rand’s ITOE 75-76; also p. 214 of Harry Binswanger’s HOW WE KNOW.) Gregory Salmieri maintains that floating abstractions are one possible result of not taking the dependency relations of concepts into one’s thinking. He seemed to have in mind the dependency chain of concepts ultimately to “first-level concepts” (presumably elementary concepts of kinds of concretes ordinary in perception). “A floating abstraction is a concept that has become detached in one’s mind from its basis in perception and has therefore lost its meaning (Peikoff 1991, 96).” (p. 71 in CONCEPTS AND THEIR ROLE IN KNOWLEDGE – REFLECTIONS ON OBJECTIVIST EPISTEMOLOGY.)