The logic of impossible quantities

Abstract
In a ground-breaking essay Nagel contended that the controversy over impossible numbers influenced the development of modern logic. I maintain that Nagel was correct in outline only. He overlooked the fact that the controversy engendered a new account of reasoning, one in which the concept of a well-made language played a decisive role. Focusing on the new account of reasoning changes the story considerably and reveals important but unnoticed similarities between the development of algebraic logic and quantificational logic
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DOI 10.1016/0039-3681(91)90014-J
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References found in this work BETA
Two Dogmas of Empiricism.Willard V. O. Quine - 1951 - Philosophical Review 60 (1):20–43.
Posterior Analytics. Aristotle - 1994 - Clarendon Press.
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Mathematics and Reality.Stewart Shapiro - 1983 - Philosophy of Science 50 (4):523-548.
The Wake of Berkeley's Analyst: Rigor Mathematicae?David Sherry - 1987 - Studies in History and Philosophy of Science Part A 18 (4):455-480.

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Citations of this work BETA
On Mathematical Error.D. Sherry - 1997 - Studies in History and Philosophy of Science Part A 28 (3):393-416.

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