• Offers insights into leading issues in the philosophy of mathematics

• Discusses a wide range of topics

• Contributors include some of the most distinguished scholars in the philosophy of mathematics

This book offers a unique perspective on one of the deepest questions about the world we live in: is reality multi-leveled, or can everything be reduced to some fundamental ‘flat’ level? 

This deep philosophical issue has widespread implications in philosophy, since it is fundamental to how we understand the world and the basic entities in it. Both the notion of ‘levels’ within science and their ontological implications are issues that are underexplored in the philosophical literature. The volume reconsiders the view that reality contains many levels and opens new ways to understand the ontological status of the special sciences. The book focuses on major open questions that arise at the foundations of cognitive science, cognitive psychology, brain science and other special sciences, in particular with respect to the physical foundations of these sciences. For example: Is the mental computational? Do brains compute? How can the special sciences be autonomous from physics, grounded in, or based on, physics and at the same time irreducible to physics? 

The book is an important read for scientists and philosophers alike. It is of interest to philosophers of science, philosophers of mind and biology interested in the notion of levels, but also to psychologists, cognitive scientists and neuroscientists investigating such issues as the precise relation of the mental to the underlying neural structures and the appropriate approach to study it.

This book subjects the traditional concept of law of nature to critical examination. 

There are two kinds of reasons that invite this reexamination, one deriving from philosophical concerns over the traditional concept, the other motivated by theoretical and practical changes in science. One of the philosophical worries is that the idiom of law of nature, especially when combined with the notion of laws 'governing' individual events and processes, is no longer as intelligible as it used to be in the theistic context in which the formulation of laws became central to science. The traditional concept is also challenged in various ways by contemporary scientific theories such as quantum mechanics, chaos theory and the general theory of relativity. It is no longer clear that there are any universal laws, laws do not always guarantee predictability, and the border between physical and mathematical considerations is constantly shifting. The most difficult challenge, perhaps, is to come up with a scientific explanation of the origin of laws. 

Wrestling with these intriguing problems, the papers in this volume broaden both our understanding of the natural order and our desiderata of scientific explanation. 

This book explores relationships and maps out intersections between discussions on causation in three scientific disciplines: linguistics, philosophy, and psychology. The book is organized in five thematic parts, investigating connections between philosophical and linguistic studies of causation; presenting novel methodologies for studying the representation of causation; tackling central issues in syntactic and semantic representation of causal relations; and introducing recent advances in philosophical thinking on causation.

Beyond its thematic organization, readers will find several recurring topics throughout this book, such as the attempt to reduce causality to other non-causal terms; causal pluralism vs. one all-encompassing account for causation; causal relations pertaining to the mental as opposed to the physical realm, and more.

This collection also lays the foundation for questioning whether it is possible to evaluate available philosophical approaches to causation against the variety of linguistic phenomena ranging across diverse lexical and grammatical items, such as bound morphemes, prepositions, connectives, and verbs. Above all, it lays the groundwork for considering whether the fruits of the psychological-cognitive study of the perception of causal relations may contribute to linguistic and philosophical studies, and whether insights from linguistics can benefit the other two disciplines.

This volume provides a broad perspective on the state of the art in the philosophy and conceptual foundations of quantum mechanics. Its essays take their starting point in the work and influence of Itamar Pitowsky, who has greatly influenced our understanding of what is characteristically non-classical about quantum probabilities and quantum logic, and this serves as a vantage point from which they reflect on key ongoing debates in the field. Readers will find a definitive and multi-faceted description of the major open questions in the foundations of quantum mechanics today, including: Is quantum mechanics a new theory of (contextual) probability? Should the quantum state be interpreted objectively or subjectively? How should probability be understood in the Everett interpretation of quantum mechanics? What are the limits of the physical implementation of computation? The impact of this volume goes beyond the exposition of Pitowsky’s influence: it provides a unique collection of essays by leading thinkers containing profound reflections on the field.

Aleph is devoted to the exploration of the interface between Judaism and science in history. We welcome contributions on any chapter in the history of science in which Judaism played a significant role, or on any chapter in the history of Judaism in which science played a significant role. Science is conceived very broadly, including the social sciences and the humanities. History of science is also broadly construed within its social and cultural dimensions.

Aleph is published in partnership with the Sidney M. Edelstein Center for the History and Philosophy of Science, Technology and Medicine at The Hebrew University of Jerusalem