The Infinite within Descartes’ Mathematical Physics
Keywords:
Descartes, infinity, mathematical physics, space, matterAbstract
Descartes’ philosophy contains an intriguing notion of the infinite, a concept labeled by the philosopher as indefinite. Even though Descartes clearly defined this term on several occasions in the correspondence with his contemporaries, as well as in his Principles of Philosophy, numerous problems about its meaning have arisen over the years. Most commentators reject the view that the indefinite could mean a real thing and, instead, identify it with an Aristotelian potential infinite. In the first part of this article, I show why there is no numerical infinity in Cartesian mathematics, as such a concept would be inconsistent with the main fundamental attribute of numbers: to be comparable with each other. In the second part, I analyze the indefinite in the context of Descartes’ mathematical physics. It is my contention that, even with no trace of infinite in his mathematics, Descartes does refer to an actual indefinite because of its application to the material world within the system of his physics. This fact underlines a discrepancy between his mathematics and physics of the infinite, but does not lead a difficulty in his mathematical physics. Thus, in Descartes’ physics, the indefinite refers to an actual dimension of the world rather than to an Aristotelian mathematical potential infinity.
In fact, Descartes establishes the reality and limitlessness of the extension of the cosmos and, by extension, the actual nature of his indefinite world. This indefinite has a physical dimension, even if it is not measurable.
Downloads
Published
Issue
Section
License
Authors who publish with this journal agree to the following terms:1. The Author retains copyright in the Work, where the term "Work" shall include all digital objects that may result in subsequent electronic publication or distribution.
2. Upon acceptance of the Work, the author shall grant to the Publisher the right of first publication of the Work.
The Author shall grant to the Publisher a nonexclusive perpetual right and license to publish, archive, and make accessible the Work in whole or in part in all forms of media now or hereafter known under a Creative Commons 3.0 License Attribution-NonCommercial 3.0 Unported CC BY-NC 3.0, or its equivalent, which, for the avoidance of doubt, allows others to copy, distribute, and transmit the Work under the following conditions: (a) Attribution: Other users must attribute the Work in the manner specified by the author as indicated on the journal Web site;(b) Noncommercial: Other users (including Publisher) may not use this Work for commercial purposes;
4. The Author is able to enter into separate, additional contractual arrangements for the nonexclusive distribution of the journal's published version of the Work (e.g., post it to an institutional repository or publish it in a book), as long as there is provided in the document an acknowledgement of its initial publication in this journal.
5. Authors are permitted, and Eidos promotes, to post online the preprint manuscript of the Work in institutional repositories or on their Websites prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (see The Effect of Open Access). Any such posting made before acceptance and publication of the Work is expected be updated upon publication to include a reference to the Eidos's assigned URL to the Article and its final published version in Eidos.
