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In view of the confusion that exists in the 20th century with regard to the meaning of “abstraction” and “abstract” it is necessary to begin by recalling what is genuine abstraction and by stating what should be expected from a theory of abstraction today (section 1). Since Boethius and till the late 19th century abstraction enjoyed a peaceful life (except for some attacks from the British empiricists), within logic, metaphysics and psychology, under the reign of the great masters of abstraction (2). Aside from neo-scholasticism, only a few individual authors carried the torch of genuine abstraction in our century; for example: Husserl and Piaget; within modern logic: Weyl, and especially Lorenzen. Probably because of Frege and Russell, abstraction disappeared from the mainstream of modern logic and analytic philosophy (3). The void was filled by a proliferation of pseudo-uses of the terms “abstraction” and “abstract”: the usurpers (4). The survival of abstraction in modern logic (“modern abstraction”, Lorenzen) was unfortunately associated with nominalism (5). Nominalism shuns the challenge of having to say something about the nature of abstracta (6). But, thanks to nominalism, modern abstraction turns out to be immune to a recent criticism (7). Signs of a renewed interest in abstraction are mentioned (8). The final reflection is that philosophers have the right to reject abstraction, but then no pseudo-uses of the word should be introduced (9).

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