Addendum

Note from the Editors

The following piece is a short objection that was sent to us by undergraduate student Gabriel Rivas in response to the paper “The Problem of Infinity” by Ashlyn Molyneaux published in the Spring 2018 edition of Kalopsia. Since this is our first time publishing work of this nature, we want to establish our purpose and intentions in doing so.

It is one of our goals as an undergraduate philosophy journal to provide a space for undergraduate students to be in dialogue with one another and encourage each other to grow. Addressing mistakes, highlighting objections, and having conversations or even disagreements are aspects of practicing philosophy, and we would love to show that process in our journal. Undergraduates are not perfect, and it's not our position that that means we shouldn't be published and recognized for our hard work. On the contrary, we believe that giving undergraduates a voice opens up the possibility for learning and furthers our philosophical goals, especially in consideration of our mistakes rather than in spite of them.

With those values in mind and after communication with both authors, the response is published below. It is our hope that the inclusion of this addendum will encourage readers to send us their thoughts, responses, and possible concerns or objections with the work they encounter in our journal and not discourage future authors from submitting their work.

-H.B.

A Short Objection to “The Problem of Infinity” by Ashlyn Molyneaux in the Spring 2018 Edition of Kalopsia

By Gabriel Rivas

In the essay "The Problem of Infinity," Ashlyn Molyneaux gives a mistaken account of Aristotle's definition of actual and potential infinity. Molyneaux claims that "Potential infinity is a group of numbers or things that continue on forever and ever without end whereas actual infinity is a set of infinite numbers or things within a confined space with a beginning and end." This gets Aristotle's definition backwards. Aristotle defined actual infinity as a completed series, and potential infinity as a series that can always be added to. In Molyneaux's example, then, a spatial magnitude of potential infinity exists in a finite space which could theoretically be divided indefinitely, but at any one instant, only exists as a finite magnitude. Conversely, actual infinite magnitude lacks borders so to speak, and any division of such a magnitude would yield another actually infinite magnitude.

Sources:

Stanford Encyclopedia of Philosophy, Aristotle and Mathematics, "12. The Infinite", and the article's supplement, "Aristotle's classification of infinite series." https://plato.stanford.edu/archives/spr2017/entries/aristotle-mathematics/#12 https://plato.stanford.edu/archives/spr2017/entries/aristotle-mathematics/supplement3.html