This past July I presented my first philosophy of mathematics paper at Tyndale’s conference at Cambridge University. In brief discussions with others this paper seems a bit controversial since I’m defending the possibility of an actual infinite set of things existing. Below is the abstract for “The Extent of Existents: Ontologies and Infinities”.
Abstract: There seems to be an intrinsic rationality to the universe that is not simply extrinsically projected by the knowing subject. The consilience between mathematics and physics is inherent to nature and is inductively depended upon by every person. What makes the question of infinities interesting is whether there actually are such existent sets. Theists are often inclined to deny that actual infinites exist and explain such things as useful fictions of conceptually existent in the mind of God—but there can be no actual infinite set (ℵ) of existents [or anything]. I will, of course, address the concrete or abstract nature and [the so-called] indispensability of such sets but that is a peripheral concern, as the infinite set of quarks or strings does not necessarily depend on the existence of the correlate abstracta. I will then survey some rejoinders such as Hilbert’s Hotel and other ‘incoherence’ arguments against actual infinites and how they are limited in applicable scope. Cantorian and ZFC semantics will be used, as they are mathematically canonical. I will conclude that theists are wholly consistent in their philosophy of mathematics and science, which will, in turn, compose a stronger theology of nature by affirming actual infinites. A theological and scientific consilience will be argued from Thomas Aquinas’ doctrine of variety and G. W. Leibniz’s principle of plenitude. I will conclude that having a theology and philosophy that permits an actual infinite set of existents will not conflict with [examples in] theoretical physics such as many cosmological models and some mechanics in quantum physics—though this is not to be considered a driving motivator; rather, it’s an example of some of the consequences for one allowing the possibility of an actual infinite of existents to one’s ontological framework.