This book develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics in the same terms as it accounts for more traditional aesthetic phenomena. Building upon a view advanced by James McAllister, the assertion is that beauty in science does not confine itself to anecdotes or personal idiosyncrasies, but rather that it had played a role in shaping the development of science. Mathematicians often evaluate certain pieces of mathematics using words like beautiful, elegant, or even ugly. Such evaluations are prevalent, however, rigorous investigation of them,...

This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia.

The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details...

The main purpose of the present volume is to advance our understanding of the notions of knowledge and context, the connections between them and the ways in which they can be modeled, in particular formalized - a question of prime importance and utmost relevance to such diverse disciplines as philosophy, linguistics, computer science and artificial intelligence and cognitive science.

Bringing together essays written by world-leading experts and emerging researchers in epistemology, logic, philosophy of language, linguistics and theoretical computer science, the book examines the...

This collection of papers investigates the most recent debates about individualism and holism in the philosophy of social science. The debates revolve mainly around two issues: firstly, whether social phenomena exist sui generis and how they relate to individuals. This is the focus of discussions between ontological individualists and ontological holists. Secondly, to what extent social scientific explanations may and should, focus on individuals and social phenomena respectively. This issue is debated amongst methodological holists and methodological individualists.

In social...

This volume is the first systematic and thorough attempt to investigate the relation and the possible applications of mereology to contemporary science. It gathers contributions from leading scholars in the field and covers a wide range of scientific theories and practices such as physics, mathematics, chemistry, biology, computer science and engineering. Throughout the volume, a variety of foundational issues are investigated both from the formal and the empirical point of view.

The first section looks at the topic as it applies to physics. The section addresses questions of...

This volume provides an overview of applications of conceptual spaces theory, beginning with an introduction to the modeling tool that unifies the chapters. The first section explores issues of linguistic semantics, including speakers' negotiation of meaning. Further sections address computational and ontological aspects of constructing conceptual spaces, while the final section looks at philosophical applications. Domains include artificial intelligence and robotics, epistemology and philosophy of science, lexical semantics and pragmatics, agent-based simulation, perspectivism, framing,...

This monograph presents Azzouni's new approach to the rule-following paradox. His solution leaves intact an isolated individual's capacity to follow rules, and it simultaneously avoids replacing the truth conditions for meaning-talk with mere assertability conditions for that talk.

Kripke's influential version of Wittgenstein's rule-following paradox--and Wittgenstein's views more generally--on the contrary, make rule-following practices and assertions about those practices subject to community norms without which they lose their cogency.

Azzouni summarizes and develops...