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Wittgenstein, Finitism, and the Foundations of Mathematics$
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Mathieu Marion

Print publication date: 2008

Print ISBN-13: 9780199550470

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199550470.001.0001

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Logicism without Classes

Logicism without Classes

(p.21) 2 Logicism without Classes
Wittgenstein, Finitism, and the Foundations of Mathematics

Mathieu Marion (Contributor Webpage)

Oxford University Press

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

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