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Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premises have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even if the principles behind it remain intuitive. Jan von Plato provides an accessible but rigorous introduction to an important aspect of contemporary logic: its deductive machinery. He shows that when the forms of logical reasoning are analysed, it turns out that a limited set of first principles can represent any logical argument. His book will be valuable for students of logic, mathematics and computer science.
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Mathematics --- Logic, Symbolic and mathematical. --- Philosophy.
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Computer science --- Mathematics --- Logic, symbolic and mathematical
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The scientific method is one of the most basic and essential concepts across the sciences, ensuring that investigations are carried out with precision and thoroughness. The scientific method is typically taught as a step-by-step approach, but real examples from history are not always given. This book teaches the basic modes of scientific thought, not by philosophical generalizations, but by illustrating in detail how great scientists from across the sciences solved problems using scientific reason. Examples include Christopher Columbus, Joseph Priestly, Antoine Lavoisier, Michael Faraday, W
Science --- Methodology. --- History. --- Scientific method --- Logic, Symbolic and mathematical
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This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.
Lambda calculus. --- Calculus, Lambda --- Logic, Symbolic and mathematical
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Logic, Symbolic and mathematical --- Mathematics --- Analysis (Philosophy) --- Philosophy --- Frege, Gottlob,
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Forcing (Model theory) --- Model theory --- Model theory. --- Logic, Symbolic and mathematical
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This book models and simulates metaphysics by presenting the metaphysics of a model. The small size of the model makes it possible to treat metaphysical matters with a more than usual systematicity and comprehensiveness. In the mirror of sustained analogy, simulation-metaphysics offers a wealth of insights on the real thing: on the doctrines, the methods, and the epistemology of metaphysics.
Metaphysics. --- Model theory. --- Logic, Symbolic and mathematical --- Philosophy --- God --- Ontology --- Philosophy of mind --- Metaphysics --- Model theory
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The Asian Logic Conference is one of the largest meetings, and this volume represents work presented at, and arising from the 12th meeting. It collects a number of interesting papers from experts in the field. It covers many areas of logic.
Logic, Symbolic and mathematical --- Asia. --- Asian and Pacific Council countries --- Eastern Hemisphere --- Eurasia
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Paul Feyeraband famously asked, what's so great about science? One answer is that it has been surprisingly successful in getting things right about the natural world, more successful than non-scientific or pre-scientific systems, religion or philosophy. Science has been able to formulate theories that have successfully predicted novel observations. It has produced theories about parts of reality that were not observable or accessible at the time those theories were first advanced, but the claims about those inaccessible areas have since turned out to be true. And science has, on occasion, advanced on more or less a priori grounds theories that subsequently turned out to be highly empirically successful. In this book the philosopher of science, John Wright delves deep into science's methodology to offer an explanation for this remarkable success story.
Science --- Scientific method --- Logic, Symbolic and mathematical --- Normal science --- Philosophy of science --- Philosophy. --- Methodology. --- Methodology --- Philosophy
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