Apart from the mis-representation ( which Russell partly rectified by explaining his own view of the role of arithmetic in mathematics ), the passage is notable for the word which he put in quotation marks, but their presence suggests nervousness, and he never used the word again, so that'logicism'did not emerge until the later 1920s " ( G-G 2002 : 434 ).
42.
Kerry Walter s describes this ideology in her essay Beyond Logicism in Critical Thinking, A logistic approach to critical thinking conveys the message to students that thinking is legitimate only when it conforms to the procedures of informal ( and, to a lesser extent,, formal ) logic and that the good thinker necessarily aims for styles of examination and appraisal that are analytical, abstract, universal, and objective.
43.
Often cited for his work on the twentieth-century philosopher Bertrand Russell, Irvine has argued in favour of physicalism and against several commonly held views in the history of modern philosophy, including the claim that Gottlob Frege succeeded in developing a workable theory of mathematical platonism and the claim that Bertrand Russell was an advocate of epistemic logicism, a claim that one commentator has concluded is now thoroughly debunked .
44.
Despite the negative nature of the incompleteness theorems, G�del's completeness theorem, a result in model theory and another application of mathematics to logic, can be understood as showing how close logicism came to being true : every rigorously defined mathematical theory can be exactly captured by a first-order logical theory; Frege's proof calculus is enough to " describe " the whole of mathematics, though not " equivalent " to it.
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