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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 ian 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 ian 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.

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.