EXPANDED EDITION (eBook): -/- Infinity Is Not What It Seems...Infinity is commonly assumed to be a logical concept, reliable for conducting mathematics, describing the Universe, and understanding the divine. Most of us are educated to take for granted that there exist infinite sets of numbers, that lines contain an infinite number of points, that space is infinite in expanse, that time has an infinite succession of events, that possibilities are infinite in quantity, and over half of the world’s population believes (...) in a divine Creator infinite in knowledge, power, and benevolence. -/- According to this treatise, such assumptions are mistaken. In reality, to be is to be finite. The implications of this assessment are profound: the Universe and even God must necessarily be finite. -/- The author makes a compelling case against infinity, refuting its most prominent advocates. Any defense of the infinite will find it challenging to answer the arguments laid out in this book. But regardless of the reader’s position, FOREVER FINITE offers plenty of thought-provoking material for anyone interested in the subject of infinity from the perspectives of philosophy, mathematics, science, and theology. -/- This electronic edition of FOREVER FINITE is offered free online for all and is expanded with content that does not appear in the published edition due to print production page limitations. From the Introduction to the Conclusion, Chapters 1–27 are identical to the published print edition, including the page numbering for the chapters. This electronic edition adds an appendix and associated content—specifically, updates to the book’s back matter (68 new endnotes, 17 new bibliographic references, 3 new figure credits, 14 new glossary terms) and front matter (an updated table of contents and this preface note). (shrink)

This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...) volume includes 35 contributions. It is divided into nine parts: 1. Who Created the Concept of God; 2. Omniscience, Omnipotence, Timelessness and Spacelessness of God; 3. God and Perfect Goodness, Perfect Beauty, Perfect Freedom; 4. God, Fundamentality and Creation of All Else; 5. Simplicity and Ineffability of God; 6. God, Necessity and Abstract Objects; 7. God, Infinity, and Pascal's Wager; 8. God and (Meta-)Mathematics; and 9. God and Mind. (shrink)

Nicholas of Cusa was first of all a theologian but he was interested also in mathematic and natural sciences. In fact philosophico-theological and mathematical ideas were intertwined by him, theological and philosophical ideas influenced his mathematical considerations, in particular when he considered philosophical problems connected with mathematics and vice versa, mathematical ideas and examples were used by him to explain some ideas from theology. In this paper we attempt to indicate this mutual influence. We shall concentrate on the following problems: (...) the role and place of mathematics and mathematical knowledge in knowledge in general and in particular in theological knowledge, ontology of mathematical objects and their origin, in particular their relations to God and their meaning for the description of the world and physical reality, infinity in mathematics versus infinity in theology and their mutual relations and connections. It will be shown that—according to Nicholas—mathematics and mathematical thinking are tools of rationalization of theology and liberating it in a certain sense from the trap of apophatic theology. (shrink)

In this article, we evaluate various responses to a noteworthy objection, namely, the infinite God objection to the kalām cosmological argument. As regards this objection, the proponents of the kalām argument face a dilemma—either an actual infinite cannot exist or God cannot be infinite. More precisely, this objection claims that God’s omniscience entails the existence of an actual infinite with God knowing an actually infinite number of future events or abstract objects, such as mathematical truths. We argue, however, that the (...) infinite God objection is based on two questionable assumptions, namely, that it is possible for an omniscient being to know an actually infinite number of things and that there exist an actually infinite number of abstract objects for God to know. (shrink)

The paper is devoted to the philosophical and theological as well as mathematical ideas of Nicholas of Cusa. He was a mathematician, but first of all a theologian. Connections between theology and philosophy on the one side and mathematics on the other were, for him, bilateral. In this paper we shall concentrate only on one side and try to show how some theological ideas were used by him to answer fundamental questions in the philosophy of mathematics.