By A. Korhonen
ISBN-10: 1137304855
ISBN-13: 9781137304858
ISBN-10: 1349366854
ISBN-13: 9781349366859
Good judgment as common technology bargains a close reconstruction of the underlying philosophy within the rules of arithmetic exhibiting how Russell sought to bring a dying blow to the dominant Kantian view that formal good judgment is a concise and dry technological know-how and not able to amplify our knowing.
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Additional info for Logic as Universal Science: Russell’s Early Logicism and Its Philosophical Context
Sample text
These resulted in a transformation that is readily comparable to what occurred in logic; in both cases one is justified in speaking about ‘a transformation so profound that it is not too much to call it the second birth of the subject’ (Stein 1988, 238). The mathematical development had two sides to it. First, mathematicians extended their research to new areas, which resulted in the discovery of entire fields of mathematics; the nineteenth century saw the introduction of such new areas of mathematics as projective and non-Euclidean geometry, set theory and transfinite mathematics, complex and imaginary numbers, infinitely distant points and points with imaginary coordinates and algebraic numbers – even though in some cases, like projective and non-Euclidean geometry, the beginnings had been laid by earlier mathematicians.
The symbols have been multiplied and admit of varied combinations, which are no longer of limited number. Have we any right to give this extension to the meaning of the word logic? It would be useless to examine this question and quarrel with Mr. Russell merely on the score of words. We will grant him what he asks; but we must not be surprised if we find that certain truths which had been declared to be irreducible to logic, in the old sense of the word, have become reducible to logic, in its new sense which is quite different.
Precisely delineated concepts and rigorous proofs may not only improve our mathematical understanding but also increase the degree of certainty that we attach to mathematics. Nevertheless, the semantic sense of rigour is what we find in the early Russell, and in what follows, the focus will be on it to the exclusion of the epistemic sense. Rigour and mathematical understanding: Russell and Kant The early Russell is clearly assuming the semantic sense of ‘rigour’ when he argues in PoM and elsewhere that ‘modern mathematics’, with its pursuit of rigour, has first made it possible to attain clarity on a number of important philosophical issues.
Logic as Universal Science: Russell’s Early Logicism and Its Philosophical Context by A. Korhonen
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