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A sound philosophy of mathematical physics balances a philosophy of mathematics with a philosophy of physics, sharpening the general applicability problem of mathematics by also taking care of: (i) the early modern `mathematization of the world picture'; (ii) the theory-laden character of the targets of mathematical models of modern physics; and (iii): Wigner's `unreasonable effectiveness of mathematics in the natural sciences'. Guided by a historical survey, I propose that theories of mathematical physics are meaning-constitutive a priori constructions, conventional but far from arbitrary and best described as hypothetical. Their models subsequently mediate between theory and nature, that is, between the a priori and the a posteriori. Models mediate by playing the role of Wittgensteinian yardsticks or objects of comparison to be held against nature as represented by data models, where the comparison is made via surrogative inference. This balancing act compromises realism.

A sound philosophy of mathematical physics balances a philosophy of mathematics with a philosophy of physics, sharpening the general applicability problem of mathematics by also taking care of: (i) the early modern `mathematization of the world picture'; (ii) the theory-laden character of the targets of mathematical models of modern physics; and (iii): Wigner's `unreasonable effectiveness of mathematics in the natural sciences'. Guided by a historical survey, I propose that theories of mathematical physics are meaning-constitutive a priori constructions, conventional but far from arbitrary and best described as hypothetical. Their models subsequently mediate between theory and nature, that is, between the a priori and the a posteriori. Models mediate by playing the role of Wittgensteinian yardsticks or objects of comparison to be held against nature as represented by data models, where the comparison is made via surrogative inference. This balancing act compromises realism.

This book presents a multidisciplinary perspective on chance, with contributions from distinguished researchers in the areas of biology, cognitive neuroscience, economics, genetics, general history, law, linguistics, logic, mathematical physics, statistics, theology and philosophy. The individual chapters are bound together by a general introduction followed by an opening chapter that surveys 2500 years of linguistic, philosophical, and scientific reflections on chance, coincidence, fortune, randomness, luck and related concepts.A main conclusion that can be drawn is that, even after all this time, we still cannot be sure whether chance is a truly fundamental and irreducible phenomenon, in that certain events are simply uncaused and could have been otherwise, or whether it is always simply a reflection of our ignorance. Other challenges that emerge from this book include a better understanding of the contextuality and perspectival character of chance (including its scale-dependence), and the curious fact that, throughout history (including contemporary science), chance has been used both as an explanation and as a hallmark of the absence of explanation. As such, this book challenges the reader to think about chance in a new way and to come to grips with this endlessly fascinating phenomenon.

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.This book is Open Access under a CC BY licence.

This book presents a multidisciplinary perspective on chance, with contributions from distinguished researchers in the areas of biology, cognitive neuroscience, economics, genetics, general history, law, linguistics, logic, mathematical physics, statistics, theology and philosophy. The individual chapters are bound together by a general introduction followed by an opening chapter that surveys 2500 years of linguistic, philosophical, and scientific reflections on chance, coincidence, fortune, randomness, luck and related concepts.A main conclusion that can be drawn is that, even after all this time, we still cannot be sure whether chance is a truly fundamental and irreducible phenomenon, in that certain events are simply uncaused and could have been otherwise, or whether it is always simply a reflection of our ignorance. Other challenges that emerge from this book include a better understanding of the contextuality and perspectival character of chance (including its scale-dependence), and the curious fact that, throughout history (including contemporary science), chance has been used both as an explanation and as a hallmark of the absence of explanation. As such, this book challenges the reader to think about chance in a new way and to come to grips with this endlessly fascinating phenomenon.