Article ID: CBB837308592

Hobson’s Conception of Definable Numbers (2020)

unapi

In this paper, I explore an intriguing view of definable numbers proposed by a Cambridge mathematician Ernest Hobson, and his solution to the paradoxes of definability. Reflecting on König’s paradox and Richard’s paradox, Hobson argues that an unacceptable consequence of the paradoxes of definability is that there are numbers that are inherently incapable of finite definition. Contrast to other interpreters, Hobson analyses the problem of the paradoxes of definability lies in a dichotomy between finitely definable numbers and not finitely definable numbers. To bypass this predicament, Hobson proposes a language dependent analysis of definable numbers, where the diagonal argument is employed as a means to generate more and more definable numbers. This paper examines Hobson’s work in its historical context, and articulates his argument in detail. It concludes with a remark on Hobson’s analysis of definability and Alan Turing’s analysis of computability.

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Authors & Contributors
Gray, Jeremy
Wang, Chang
Chambris, Christine
Nobrega, Hugo
Wang, Xiaofei
Viana, Petrucio
Concepts
Philosophy of mathematics
Number theory; number concept
Mathematics
Logic
Philosophy of science
Algebraic geometry
Time Periods
19th century
20th century, early
21st century
20th century
18th century
Places
France
Germany
Institutions
University of Chicago
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