The philosophy of mathematical information

Authored by: Marcello D’Agostino

The Routledge Handbook of Philosophy of Information

Print publication date:  June  2016
Online publication date:  June  2016

Print ISBN: 9781138796935
eBook ISBN: 9781315757544
Adobe ISBN: 9781317633495

10.4324/9781315757544.ch15

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Abstract

It is somewhat ironical that, for some philosophically sophisticated readers, the very topic of this chapter, the concept of mathematical information, should be empty. Indeed, according to a time-honored philosophical tradition, there is no such thing as “mathematical information.” This tradition, which started with the Vienna Circle and later became known as “logical neopositivism” or “logical empiricism” or also “logical positivism,” maintained that the trademark of logical and mathematical statements, which separates them from all the other scientific statements, is that they are “tautological” and convey no information. This view was one of the basic tenets of the Vienna Circle, as clearly stated in the manifesto of logical neopositivism:

The conception of mathematics as tautological in character, which is based on the investigations of Russell and Wittgenstein, is also held by the Vienna Circle. It is to be noted that this conception is opposed not only to apriorism and intuitionism, but also to the older empiricism (for instance of J.S. Mill), which tried to derive mathematics and logic in an experimental-inductive manner as it were.

(Hahn et al., 1973, p. 311)

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