Bertrand Russell's 1897 critique of the traditional theory of measurement

Synthese 110 (2):257-276 (1997)
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The transition from the traditional to the representational theory of measurement around the turn of the century was accompanied by little sustained criticism of the former. The most forceful critique was Bertrand Russell''s 1897 Mind paper, On the relations of number and quantity. The traditional theory has it that real numbers unfold from the concept of continuous quantity. Russell''s critique identified two serious problems for this theory: (1) can magnitudes of a continuous quantity be defined without infinite regress; and (2) can additive relations between such magnitudes exist if magnitudes are not divisible? The present paper shows how the traditional theory answers these questions and compares the traditional and representational theories as contributions to our understanding of the logic of application.



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Ethics without numbers.Jacob M. Nebel - 2024 - Philosophy and Phenomenological Research 108 (2):289-319.
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References found in this work

Frege.Michael Dummett - 1975 - Teorema: International Journal of Philosophy 5 (2):149-188.
Introduction to mathematical philosophy.Bertrand Russell - 1920 - Revue de Métaphysique et de Morale 27 (2):4-5.

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