By G. P. Baker, P. M. S. Hacker(auth.)
Read Online or Download Wittgenstein: Rules, Grammar and Necessity: Essays and Exegesis of §§185-242, Volume 2, Second Edition PDF
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Additional info for Wittgenstein: Rules, Grammar and Necessity: Essays and Exegesis of §§185-242, Volume 2, Second Edition
Mathematicians say “Surely it is not just the numeral, it is something more” ’ (LSD 111). ). In both cases this response is misleading. It leads the mathematician to the idea that arithmetical equations describe relations among abstract objects and that they are true in virtue of corresponding to a mathematical reality. This generates a debate between ‘formalism’ and ‘contentful mathematics’ (as Frege put it) in which both sides make unwarranted assertions at variance with their ordinary practice (PG 293).
The very question, W. responds, contains mistakes – a misunderstanding of what is meant by ‘determined by the formula’ and a misconception that a rule determines the steps that accord with it by a mechanism of some kind. This having been clarified, §190 concedes that, of course, the teacher meant the pupil to continue the series by writing ‘1000, 1002, 1004, . . ’. But his meaning it, correctly understood, presupposes and does not provide a standard of correctness for the expansion of the series.
Began a preliminary examination of the example of mastering the technique of developing an arithmetical series according to a rule. The rule for a series here is akin to an explanation of meaning that constitutes a rule for the use of a word, the development of the series akin to the applications of a word in accordance with the explanation of its meaning, and the internal relation between the rule for the series and any given step in its extension analogous to the internal relation between a word and its correct application.
Wittgenstein: Rules, Grammar and Necessity: Essays and Exegesis of §§185-242, Volume 2, Second Edition by G. P. Baker, P. M. S. Hacker(auth.)