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The philosophical approach of this volume is mainly structuralist, using logical tools to investigate the formal structure of various kinds of objects in our world, as characterised by language and as systematised by philosophy. This volume mainly analyses the structural properties of collections or pluralities (with applications to the philosophy of set theory), homogeneous objects like water, and the semantics and philosophy of events. This book thereby complements algebraic work that has been done on other philosophical entities, i.e. propositions, properties, relations, or situations. Located in the triangle of language, logic and philosophy, this volume is unique in combining the resources of different ¹elds in an interdisciplinary enterprise. Half of the fourteen chapters of this volume are original papers, complementing the collection of the author's previously published essays on the subject.

A classic on mind, matter, and the unified world model

C. G. Jung's work in his later years suggested that the seemingly divergent sciences of psychology and modern physics might, in fact, be approaching a unified world model in which the dualism of matter and psyche would be resolved into “one world” or Unus Mundus. Jung believed that the natural integers are the archetypal patterns that regulate the unitary realm of psyche and matter, and that number serves as a special instrument for man's becoming conscious of this unity.

Written in a clear style and replete with illustrations which help make the mathematical ideas visible, Number and Time is a piece of original scholarship which introduces a view of how "mind" connects with "matter" at the most fundamental level.
 

Ranging from math to literature to philosophy, Uncountable explains how numbers triumphed as the basis of knowledge—and compromise our sense of humanity.

Our knowledge of mathematics has structured much of what we think we know about ourselves as individuals and communities, shaping our psychologies, sociologies, and economies. In pursuit of a more predictable and more controllable cosmos, we have extended mathematical insights and methods to more and more aspects of the world. Today those powers are greater than ever, as computation is applied to virtually every aspect of human activity. Yet, in the process, are we losing sight of the human? When we apply mathematics so broadly, what do we gain and what do we lose, and at what risk to humanity?

These are the questions that David and Ricardo L. Nirenberg ask in Uncountable, a provocative account of how numerical relations became the cornerstone of human claims to knowledge, truth, and certainty. There is a limit to these number-based claims, they argue, which they set out to explore. The Nirenbergs, father and son, bring together their backgrounds in math, history, literature, religion, and philosophy, interweaving scientific experiments with readings of poems, setting crises in mathematics alongside world wars, and putting medieval Muslim and Buddhist philosophers in conversation with Einstein, Schrödinger, and other giants of modern physics. The result is a powerful lesson in what counts as knowledge and its deepest implications for how we live our lives.