This paper discusses the treatment of "infinity" in philosophy of religion, including its use in discussions of divine attributes, and its use in various arguments about the existence of God (including the kalam cosmological argument and Pascal's wager). The aim of the paper is to set out -- and where possible, to resolve -- various foundational problems about infinity.

Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty ordinal construction and his fundamental powerset description of the continuum, Cantor has also left to us his obsessive presumption that the universe of sets should be subjected to laws similar to those governing the set of natural numbers, including the universal principles of cardinal comparability (...) and well-ordering -- and implying an ordinal re-creation of the continuum. During the last hundred years, the mainstream set-theoretical research -- all insights and adjustments due to Kurt G\"odel's revolutionary insights and discoveries notwithstanding -- has compliantly centered its efforts on ad hoc axiomatizations of Cantor's intuitive transfinite design. We demonstrate here that the ontological and epistemic sustainability} of this design has been irremediably compromised by the underlying peremptory, Reductionist mindset of the XIXth century's ideology of science. (shrink)

In the philosophical works of Emmanuel Levinasʼs early career, it is in a phenomenology of Eros that he claims to have uncovered the site of what he calls ʻtranscendenceʼ. This is no small claim. According to the argument of the later Totality and Infinity (1961), the history of Western philosophy is to be thought as the history of the ʻphilosophy of the sameʼ. Within this polemical generalization almost the whole of Western philosophy is characterized as a totalizing discourse which aims (...) to reduce everything to the categories of a thematizing consciousness. Conceptual structures are employed (or presupposed) in order to make diverse phenomena commensurable within a system, and according to Levinas this operation always constitutes a reduction of what is ʻotherʼ to the order of the ʻsameʼ. In agreement with a certain transcendentalism which is itself implicated in Levinasʼs critique, these structures of thought are then equated with consciousness itself; the thematizing project is one of mastery in which noemata will of necessity conform to noesis, in which the object is constituted for and by the subject. The experience of transcendence, so rare in this version of philosophyʼs history, is the experience of whatever is and truly remains other than me, recalcitrant to mastery through conceptualization and to the transcendental project of the subject to construe everything as originating from within itself. If, then, it is first of all in the erotic relation that the possibility of the experience of transcendence is said to arise, Eros can in no sense be dismissed as an unimportant or peripheral theme for Levinas, and a full investigation is warranted, especially given the current interest in Levinasʼs work, interest which is not limited to the discipline of philosophy. Furthermore, as the notion of Eros is closely associated, textually and conceptually, with what Levinas calls ʻthe feminineʼ, critical attention has been excited amongst feminist scholars of various persuasions, with claims – both positive and negative – being made for Levinasʼs significance as a resource for feminist philosophy and feminist politics. If assertions of a ʻLevinasianʼ feminism, no matter how qualified, tend to rest on the idea that Levinasʼs phenomenology of Eros, and analyses of ʻthe feminineʼ mark a break in or a new departure from a ʻmasculinistʼ tradition, this article seeks, in part, to argue to the contrary. (shrink)

In a recent article, Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of study. In practice, this means excluding as (...) inadmissible all those real numbers whose decimal expansions cannot be calculated in as much detail as one would like by some rule. We argue against Ormell that the classical realist account of the continuum has explanatory power in mathematics and should be accepted, much in the same way that "dark matter" is posited by physicists to explain observations in cosmology. In effect, the indefinable real numbers are like the "dark matter" of real analysis. (shrink)

In this essay I consider the end-of-art thesis in its metaphysical and empirical versions. I show that both use the correspondence theory of truth as the basis for their conception of the history of art. As a counterpart to these theories I have chosen Patočka’s conception of the history of art. His theory is based also on the relationship between art and truth, but he conceives truth in the phenomenological sense of manifestation. In the rest of the essay I seek (...) to show the consequences Patočka’s conception has for the history of art. In the rst part, I set out to show Patocka’s critique of Hegel’s aesthetics as a system based on the correspondence theory of truth. In particular, I endeavour to explain his critique of some intrinsic problems of Hegel’s aesthetics, the general failure of Hegel’s system to achieve its goal, and, lastly, Hegel’s giving up on the meaning of the art in the present. I also seek to show that Danto’s version runs into the same problems and conclusions as Hegel’s. In the second part I discuss Patočka’s analysis of modern art and the aesthetic attitude, where he nds a hidden a nity between art and aletheia, which Hegel overlooked. e last part of the essay focuses on the consequences that the conception of the truth of art as aletheia have for the history of art. I conclude that art in such a conception represents an independent eld of the manifestation of being in history beside philosophy. Moreover, modern and contemporary art do not mean the end of art; rather, they have their place in art history based on aletheia, since they are more focused on the manifestation itself than on what is manifested. Unlike Hegel and Danto, therefore, Patočka retains the historical meaning of modern and contemporary art. His conception of the history of art, summed up under the idea of aletheia, has greater explanatory potential than Hegel’s and Danto’s conceptions, and it retains the historical meaning of modern and contemporary art. (shrink)