Mathematics and essence

Authors

  • Tiago Tranjan

Keywords:

Philosophy of mathematics. Mathematical necessity. Counting systems. Linguistic necessity. Wittgenstein on mathematics.

Abstract

Arithmetic seems to provide philosophers and mathematicians with the typical domain where it makes sense to talk about “essences”, “essential properties” and “necessary propositions”. In this paper I try to examine the subject, following the lines of investigation suggested by Wittgenstein from his middle period on. Beginning with a specific question – Is it part of the essence of the number 3 to be followed by the number 4? –, I intend to examine different aspects of the problem, with three main goals at sight: 1) Understanding more thoroughly the role and limits of formal analysis in philosophical questions, particularly those related to the philosophy of mathematics; 2) Correctly locating the note of “essentiality” and/or “necessity” commonly associated with arithmetic; and 3) Suggesting a general way of understanding the idea of essence and necessity, in its strict connection with human language and experience.

Author Biography

Tiago Tranjan

Doutor e Professor de Filosofia da UNIFESP

Downloads

Published

2013-12-22

Issue

No. 10

Section

Philosophy of Logic and Mathematics

License

Argumentos magazine is licensed under an International Creative Commons Attribution License.

The Magazine uses CC BY inclusion

1) The authors retain the copyright granted to the magazine or the right to initial publication, with the work regularly licensed under the Creative Commons Attribution, which allows the sharing of the work with acknowledgment of authorship and initial publication in this magazine.

2) The authors are authorized to contract additional applicable contracts, for non-exclusive distribution of the version of the work published in this journal (for example, publication in the institutional repository or as a chapter of the book), recognition of authorship and initial publication in this journal.

3) Authors are authorized and encourage to publish and distribute their work online (for example, in institutional repositories or on their personal pages) at any time before or during the editorial process, as they can generate productive changes, as well as increase the impact and reference of published work.