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This Element discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain the (defeasible) justification of our mathematical beliefs ('the justificatory challenge'), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the challenge to explain their reliability ('the reliability challenge'), arises to the extent that we could have easily had different beliefs. The Element shows that mathematical facts are not, in general, empirically accessible, contra Quine, and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is unmysterious. The Element concludes with a complementary 'pluralism' about modality, logic and normative theory, highlighting its surprising implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap's pragmatism, transposed to the key of realism.

Mathematics --- Philosophy. --- Logic of mathematics --- Mathematics, Logic of --- Objectivism (Philosophy). --- Pluralism. --- Realism. --- Empiricism --- Philosophy --- Universals (Philosophy) --- Conceptualism --- Dualism --- Idealism --- Materialism --- Nominalism --- Positivism --- Rationalism --- Monadology --- Monism --- Reality

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As probably the most successful scientific theory ever created, quantum theory has profoundly changed our view of the world and extended the limits of our knowledge. It has impacted on the theoretical interpretation of a tremendous range of phenomena and the practical development of a host of new technologies. Yet for all its success, aspects of quantum theory remain baffling. Quantum Reality: Theory and Philosophy, Second Edition cuts through much of the confusion to provide readers with an exploration of quantum theory that is as authoritatively comprehensive as it is intriguingly comprehensible. It presents a thorough grounding in the theoretical machinery of quantum physics. Fully updated throughout to include the latest results in quantum entanglement, quantum computing, and an introduction to quantum cosmology and quantum gravity. Without needing an extensive physics and mathematics background, the book requires only an interest in understanding how quantum theory came to be and the myriad ways it both explains how our universe functions and extends the reach of human knowledge. The world beneath the one that we experience with our senses is profoundly mysterious, and while we may never completely unravel that mystery, quantum theory allows us to come closer than ever to understanding where the science leaves off and the mystery begins. Quantum Reality: Theory and Philosophy, Second Edition makes that understanding accessible to anyone possessing a quest for knowledge and a sense of awe. Written by well-known physics author and teacher Dr. Jonathan Allday, this highly engaging work : offers a whistle-stop tour through the early part of the 20th century when the founding fathers of quantum theory forever altered the frontiers of human thought, provides an example-filled interpretation of the theory, its applications, and its pinnacle in Quantum Field Theory (QFT), which is crucial in shaping ideas about the nature of reality, and separates fact from speculation regarding quantum physics' ability to provide a starting point for philosophical queries into ultimate understanding and the limits of sciencer.

Quantum theory. --- Quantum theory --- Théorie quantique. --- Théorie quantique --- Philosophie et physique. --- Physique --- Philosophy. --- Philosophie. --- Philosphie. --- Planck, Max, --- Einstein, Albert, --- Bohr, Niels, --- Heisenberg, Werner, --- Broglie, Louis de, --- Schrödinger, Erwin, --- Dirac, P. A. M. --- Planck, Max, --- Einstein, Albert, --- Bohr, Niels, --- Heisenberg, Werner, --- Broglie, Louis de, --- Dirac, Paul A. M., --- Schrödinger, Erwin, --- Criticism and interpretation. --- Criticism and interpretation. --- Criticism and interpretation. --- Criticism and interpretation. --- Criticism and interpretation. --- Criticism and interpretation. --- Criticism and interpretation. --- Critique et interprétation --- Critique et interprétation --- Critique et interprétation --- Critique et interprétation --- Critique et interprétation --- Critique et interprétation