This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand (...) Tarski’s and Gödel’s work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy’s mathematical naturalism and Shapiro’s mathematical structuralism. Last but not least, the book introduces Biancani’s Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century. (shrink)

The paper discusses problems which arise in attempts to axiomatize parts of religion or religious belief systems. Besides those problems already investigated by Bochenski, like that of the propositional content or the meaning of religious discourse there are several further ones. This paper deals with the question whether full Classical Logic is suitable, whether one universe of discourse is sufficient, how to use definitions and analogous concepts and whether justifications satisfy credibility criteria.

Rob Lovering has recently argued that since theists have been unable, by means of philosophical arguments, to convince 85 percent of professional philosophers that God exists, at least one of their defining beliefs must be either false or meaningless. This paper is a critical examination of his argument. First we present Lovering’s argument and point out its salient features. Next we explain why the argument’s conclusion is entirely acceptable for theists, even if, as we show, there are multiple problems with (...) the premises. (shrink)

Semen Frank (1877–1950) was one of the first and most ardent advocates of the ontological argument in the twentieth century. He proposed an original interpretation of the ontological argument based on its analogy to Descartes’ Cogito. Frank believed that it is possible to develop Cogito ergo sum into Cogito ergo est ens absolutum. In this paper, I analyze his version of the ontological argument. First, I propose a simple reconstruction of his reasoning, paying attention to its hidden premise. Second, departing (...) from the classical logical interpretations of Descartes’ argument, I show that for Frank the claim that God exists had the same logical properties as Cogito. As a result, it seems that his argument was formally correct, though based on a premise which could hardly be convincing for a non-believer. This should not be surprising, however, since Frank, as most Russian religious philosophers, was not interested in the project of philosophical theology. His main concern was rather the development of philosophy based on religious premises, which might be called “theological philosophy”. (shrink)

Semyon Frank opposed the Neo-Kantian School and admitted the real existence of the objects of cognition. He treated ontologism as essential to the entire movement of Russian religious philosophy. For Frank, one can only know about something thanks to the absolute, which exists prior to the knowing subject. Ontologism, affirming the priority of being over cognition, has a great significance not only for metaphysics and epistemology, but also for the philosophy of religion. In particular, Frank taught that the most privileged (...) mode of cognition of God is intuition, an immediate experience of God or faith. Intuition is at the heart of the ontological proof, which can be found in St. Anselm, Descartes, and Frank himself. Frank dedicated a number of articles to this topic: “K istorii ontologicheskogo dokazatel’stva”, “Ontologicheskoe dokazatel’stvo bytiya Boga”, as well as texts recently discovered at the Bakhmeteff Archive, including “Dokazatel’stvo bytiya Boga”. In this way, Russian ontologism leads to a new interpretation of the traditional ontological proof, one which acknowledges the existence of God, not on the basis of arguments resting on His definition, but on the basis of the intuitive recognition of His being. (shrink)

Latest version of my SEP entry on ontological arguments, which first appeared in 1996. General discussion of ontological arguments. Includes a brief historical overview, a taxonomy of different kinds of ontological arguments, a brief survey of objections to the different kinds of ontological arguments identified in the taxonomy, and more extended discussions of Anselm's ontological argument (Proslogion 2), Godel's ontological argument, and Plantinga's ontological argument.