Abstract
IT is recorded that when a pupil asked Confucius what he would do first if he had absolute power, the Master replied “I should reform language”. (The development of the theme in the text of the “Analecta” is scarcely worthy of it, but incorporations are suspected.) The history of mathematical logic since “Principia Mathematica” affords an admirable illustration. Even before that great work, the need for unambiguous definitions and for the explicit statement of even the most harmless hypotheses was a main source of inspiration; but later investigators have found that ambiguities remained. In particular, there was a confusion between a symbol and the thing designated by it, and a prepositional function was sometimes a property and sometimes what Prof. Willard Van Orman Quine in his recent book, “Mathematical Logic”*, calls a “statement matrix”, that is, an expression that would become a statement if it contained names in place of variables. It was hoped also, especially in Russell's popular works, that the actual existence of numbers could be demonstrated in terms of the theory of classes.
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JEFFREYS, H. ASPECTS OF MATHEMATICAL LOGIC. Nature 148, 396–397 (1941). https://doi.org/10.1038/148396a0
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DOI: https://doi.org/10.1038/148396a0