This book uncovers how we make meaning of abstraction, both historically and in present times, and examines abstract images as a visual language. The contributors demonstrate that abstraction is not primarily an artistic phenomenon, but rather arises from human beings’ desire to imagine, understand and communicate complex, ineffable concepts in fields ranging from fine art and philosophy to technologies of data visualization, from cartography and medicine to astronomy. The book will be of interest to scholars working in image studies, visual studies, art history, philosophy and aesthetics.

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Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Gödel's writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Gödel's three philosophical heroes - Plato, Leibniz, and Husserl - and his engagement with Kant, and supplements close readings of Gödel's texts on foundations with materials from Gödel's Nachlass and from Hao Wang's discussions with Gödel. As well as providing discussions of Gödel's views on the philosophical significance of his technical results on completeness, incompleteness, undecidability, consistency proofs, speed-up theorems, and independence proofs, Tieszen furnishes a detailed analysis of Gödel's critique of Hilbert and Carnap, and of his subsequent turn to Husserl's transcendental philosophy in 1959. On this basis, a new type of platonic rationalism that requires rational intuition, called 'constituted platonism', is developed and defended. Tieszen shows how constituted platonism addresses the problem of the objectivity of mathematics and of the knowledge of abstract mathematical objects. Finally, he considers the implications of this position for the claim that human minds ('monads') are machines, and discusses the issues of pragmatic holism and rationalism.

Prominent scientists and philosophers of science address contemporary debates on the nature of Time. Their contributions freely discuss its unity and reality, its compatibility with the orders of classical philosophy (present, past and future) and with the disputed idea of free will (Volume 1). They also present a detailed and updated state of the role of Time in the so-called exact sciences: biology — or more precisely genetics, evolution, neurosciences, natural and artificial intelligence (Volume 2) , and physics — relativity, quantum mechanics and quantum gravity, and cosmology (Volume 3).

The present volume of Time and Science series is devoted to Physical Sciences and Cosmology. Today more than ever, the question 'is Time an ontological property, a necessary ingredient for the physical description of the world, or a purely epistemological element, relative to our situation in the world?' worry physicists and cosmologists alike. For many of them, Relativity (and particularly General Relativity), as well as its reconciliation with quantum mechanics in the elaboration of a quantum theory of gravitation, points to a negative answer to the first alternative, and leads them to deny the objective reality of time. For others, the answer is nuanced by the evidence of an emerging temporal property when one climbs the scales of the complexity of systems and/or the applicability of the statistical laws of thermodynamics. But for some, the illusion of the unreality of time comes from certain confusions that they denounce, and plead for the re-establishment of time at the heart of physical theories.

Neopragmatism is a very general language-first approach to questions about the existence or nature of various traditionally philosophically troubling entities or properties. It rejects metaphysical questions about these things by instead focusing our attention on our practices of using the relevant words: words like 'true', 'four', 'immoral', 'necessary', 'art', and so on. Once we have unmysterious naturalistic explanations of our practices of making assertions with these sorts of words, and of assessing those assertions as true or false, metaphysical worries about them should simply fade away. Neopragmatism differs from more common expressivist accounts of the same sorts of vocabulary because expressivism is almost always offered as a local view, presented against a more general representationalist background. Neopragmatists, on the other hand, defend a global view that endorses deflationary accounts of the whole constellation of representational and semantic notions such as reference, truth, belief, assertion, and proposition. A general deflationism of this sort makes it impossible to draw a contrast between representational and non-representational propositions, assertions, or beliefs. While neopragmatism has been on the scene since the 1980's, it has generally only been visible to theorists working on the very general issue of the relation of language to reality. When it comes to first-order philosophical issues such as the nature of time, or the various modals, or color, or art, neopragmatism often seems simply not to be on the radar. This volume takes up the task of exploring the implications - direct and indirect - of the neopragmatist perspective for various first order philosophical issues.