Citation
- Type
- article
- Author
- Pourciau, Sarah
- Title
- A/Logos: An Anomalous Episode in the History of Number
- Short title
- A/Logos
- Journal
- MLN
- Volume
- 134
- Number
- 3
- Pages
- 616--642
- Year
- 2019
- DOI
- 10.1353/mln.2019.0046
- ISSN
- 1080-6598
- Abstract
- ``Mathematics is the science of the infinite'' (Weyl, ``The Current Epistemological Situation'' 123).1 With this pronouncement, the German mathematician Hermann Weyl opens his 1925 diagnostic essay, ``The Current Epistemological Situation in Mathematics'' (Die heutige Erkenntnislage in der Mathematik), which takes the measure of a contemporary situation identified elsewhere by Weyl as a ``foundational crisis'' (``On the New Foundational Crisis of Mathematics''). At issue for Weyl, as for many of his fellow mathematicians---whose positions he attempts to reconcile in his paper ---is the ongoing battle for dominion over an infinitely divisible continuum. That unbroken flow of experiential time and space, within which, as the Presocratic philosopher Anaxagoras had already observed by the 5th century BC, there is no smallest part of what is small, since there is always a smaller (Curd 38, fragment 3), poses seemingly insurmountable difficulties for an attempt to analyze the world into discrete, and thus calculable or measurable units. On the one hand: to eschew all such analysis is to relinquish the possibility of science, and perhaps even of language, since both activities would appear to depend on an intellectual capacity for delimiting particular phenomena. On the other hand: the contradictions generated by ignoring Anaxagoras' prohibition against a carved-up continuum (``the things in the one kosmos have not been separated from one another, nor hacked apart with an axe'' [Curd 51, fragment 8]) have dogged both philosophers and mathematicians for millenia. Weyl, who
- Langid
- english