Chapter

Logicism without Classes

Mathieu Marion

in Wittgenstein, Finitism, and the Foundations of Mathematics

Published in print August 2008 | ISBN: 9780199550470
Published online September 2011 | e-ISBN: 9780191701559 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199550470.003.0002
Logicism without Classes

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  • History of Western Philosophy
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The notion of operation plays a pivotal role in the symbolism of the Tractatus Logico-Philosophicus: on the one hand, truth-functions are based on truth-operations; on the other, numbers are exponents of an operation. Considering that operations seem to be so central, it is amazing to notice how little is understood of Ludwig Wittgenstein's remarks: not enough attention has been paid in the past to the curious piece of symbolism of 6.01. What Wittgenstein says about the notion of operation very much resembles informal explanations of the notion of operator. Two differences with the set-theoretic notion of function were mentioned in Chapter 1: firstly, an operator is defined by describing how it transforms an input without defining the set of inputs, that is without defining its domain. Secondly, there is no restriction on the domain of some operators.

Keywords: logicism; Ludwig Wittgenstein; operations; symbolism; truth-functions; exponents; arithmetic; generality; infinity; predicativity

Chapter.  11618 words. 

Subjects: History of Western Philosophy ; Philosophy of Mathematics and Logic

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