The negative theology of absolute infinity: Cantor, mathematics, and humility (original) (raw)
Related papers
Absolute Infinity, Knowledge, and Divinity
Ontology of Divinity, ed. M. Szatkowski, De Gruyter, Berlin, 2024
This historical essay compares the views of Nicholas of Cusa ('Cusanus') and Georg Cantor on the topics of infinity, divinity, and mathematical knowledge. Echoing Nicholas and neo-Platonism, Cantor says in his Grundlagen (1883) that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, which can only be acknowledged but never known. Moreover, Cantor envisions his transfinite set theory as providing the analytical methods and techniques necessary for a complete philosophy of nature. Cantor's novel mathematics is presented as part of a long tradition, to which Cusanus, Bruno, Spinoza, Leibniz and others belong, in which the infinite character of organic life forms is appreciated and is taken to be in some sense a mirror and symbol of the divine. The doctrine of symbolism present in both Cusanus and Cantor enables these thinkers to articulate a transcendental apophatic approach to divinity.
Cantorian Infinity and Philosophical Concepts of God
European Journal for Philosophy of Religion
It is often alleged that Cantor’s views about how the set theoretic universe as a whole should be considered are fundamentally unclear. In this article we argue that Cantor’s views on this subject, at least up until around 1896, are relatively clear, coherent, and interesting. We then go on to argue that Cantor’s views about the set theoretic universe as a whole have implications for theology that have hitherto not been sufficiently recognised. However, the theological implications in question, at least as articulated here, would not have satisfied Cantor himself.
This was a talk at "Theology in Mathematics?" (Kraków, Poland, June 8-10, 2014). The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern is nineteenth-century mathematics. Theology was present in modern mathematics not through its objects or methods, but mainly through popular philosophy, which absolutized mathematics. Moreover, modern pure mathematics was treated as a sort of quasi-theology; a long-standing alliance between theology and mathematics made it habitual to view mathematics as a divine knowledge, so when theology was discarded, mathematics naturally took its place at the top of the system of knowledge. It was that cultural expectation aimed at mathematics that was substantially responsible for a great resonance made by set-theoretic paradoxes, and, finally, the whole picture of modern mathematics.
The challenge of bad infinity: A restatement of Hegel's critique of mathematics
Hegel's critique of mathematics cannot be reduced to mathematics alone. At least this is the stake of the present paper: to argue that a comprehensive understanding of the matter cannot be confined strictly to the philosophy of science. Indeed, Hegel's philosophy of mathematics pervades his entire ontology and, within the system, his political philosophy. Starting with Hegel's logic, the article advances towards the fact that Hegel did not reject mathematics in itself, nor he denied the incalculable merits of exact sciences made possible by applied mathematics. What he considered risky regarding mathematics was its revindication of the explanation of movement to the disadvantage of philosophy. Hence, the possibility of a technocratic world incapable of seeing and going beyond itself.
Infinity as a transformative concept in science and theology
The paper shows the histroy of the concept of in infinity starting with the Aristotelian understanding and the way it was perceived by the church fathers. The watershed in the writings of Nicolaus of Cusa (Cusanus) is elucidated and show how continually it changes from theology to metaphysics and mathematics culminating in Georg Cantors revolutionary mathematics
On the Implications of the Idea of Infinity for Postmodern Fundamental Theology
Pacifica Vol. 25, 2012
This essay provides a dimensional analysis of the variousmanners in which mathematics, phenomenology, and theology claim tomake present or mediate infinity. Edmund Husserl’s 1935 lecture, Philosophy and the Crisis of European Humanity, because engaged witheach discipline to various degrees, will function as our primary,preparatory text. Husserl’s discussion of the ideal objects of mathematicsand the Greek attitude will call for further analysis of the relation between mathematics and infinity. Similarly, intentional infinities,insofar as related to transcendental phenomenology, will be compared to Jean-Luc Marion’s distinct phenomenology of the icon. Next, the ways inwhich the infinite God is conceptualised by Husserl and Marion will be juxtaposed in order to demonstrate their disparate, theological thinking.Finally, the notion of multiple infinities will be analogically extendedfrom set theory to the discursive wholes of mathematics, phenomenology, and theology in order to suggest a novel understandingof the role of the infinite within postmodern fundamental theology.
In search of aleph-null: how infinity can be created
In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.
This was a talk at "Theology in Mathematics?" (Kraków, Poland, June 8-10, 2014). The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern in the second part of this paper is the early-twentieth-century foundational crisis of mathematics. The hypothesis that pure mathematics partially fulfilled the functions of theology at that time is tested on the views of the leading figures of the three main foundationalist programs: Russell, Hilbert and Brouwer.