| Title | Realism and the Infinite |
|---|---|
| Contributor | Paul M. Livingston (author) |
| DOI | https://doi.org/10.21983/P3.0032.1.16 |
| Landing page | https://punctumbooks.com/titles/speculations-4-speculative-realism/ |
| License | https://creativecommons.org/licenses/by-nc-sa/3.0/ |
| Copyright | Livingston, Paul M. |
| Publisher | punctum books |
| Published on | 2013-06-05 |
| Long abstract | In his 1951 Gibbs lecture, drawing out some of the “philosophical consequences” of his two in-completeness theorems and related results, Kurt Gödel outlines a disjunctive alternative which, as I shall try to show, captures in a precise way the contemporary situation of reflective thought in its ongoing consideration of the relationship of formalism to the real:Either mathematics is incompletable in [the] sense that its evident axioms can never be comprised in a finite rule, i.e. to say the human mind (even within the realm of pure mathematics) infinitely surpass-es the powers of any finite machine, or else there exist absolutely unsolvable Diophantine problems of the type specified...2A consequence of this aporeatic situation of con-temporary thought, as I shall try to show, is that the longstanding philosophical debate over the relative priority of thought and being that finds expres-sion in discussions of “realism” and “anti-realism” (whether of idealist, positivist, or conventionalist forms) can only be assayed from the position of a metaformal reflection on the relationship of the forms of thought to the real of being. Moreover, if Gödel’s argument is correct and can be generalized beyond the epistemology of mathematics itself, it is also not neutral on this question of relative priority, but rather suggests a new kind of realism—what I shall call “metaformal” realism—that differs markedly both from “metaphysical realism” and from the newer varieties of “speculative realism” on offer today. |
| Page range | pp. 99–107 |
| Print length | 9 pages |
| Language | English (Original) |