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This open access book is the first ever collection of Karl Popper's writings on deductive logic. Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics. This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.

Logic --- Popper, Karl --- Karl R. Popper --- Deductive Logic --- Logical Constants --- Proof-theoretic Semantics --- Classical Logic --- Non-classical Logic --- Inferential Definitions --- Mathematical Logic --- Negation --- Modalities --- History of Logic --- L.E.J. Brouwer --- Paul Bernays --- Rudolf Carnap --- Alonzo Church --- Kalman Joseph Cohen --- Henry George Forder --- Harold Jeffreys --- Stephen Cole Kleene

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This open access book is the first ever collection of Karl Popper's writings on deductive logic. Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics. This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.

Lògica --- Argumentació --- Dialèctica (Lògica) --- Lògica deductiva --- Filosofia --- Intel·ligència --- Psicologia --- Abstracció --- Alteritat (Filosofia) --- Categories (Filosofia) --- Certesa --- Condicionals (Lògica) --- Definició (Lògica) --- Dilema --- Evidència --- Hipòtesi --- Inconsistència (Lògica) --- Inducció (Lògica) --- Intenció (Lògica) --- Judici lògic --- Lògica deòntica --- Metodologia --- Modalitat (Lògica) --- Nominalisme --- Positivisme lògic --- Probabilitats --- Raó suficient --- Sil·logisme --- Sofismes --- Teoria del coneixement --- Universals (Filosofia) --- Metodologia de la ciència --- Pensament --- Raonament --- Karl R. Popper --- Deductive Logic --- Logical Constants --- Proof-theoretic Semantics --- Classical Logic --- Non-classical Logic --- Inferential Definitions --- Mathematical Logic --- Negation --- Modalities --- History of Logic --- L.E.J. Brouwer --- Paul Bernays --- Rudolf Carnap --- Alonzo Church --- Kalman Joseph Cohen --- Henry George Forder --- Harold Jeffreys --- Stephen Cole Kleene --- Logic. --- Mathematical logic. --- Language and languages --- Mathematical Logic and Foundations. --- Stylistics. --- Style. --- Linguostylistics --- Stylistics --- Literary style --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Methodology

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A facsimile edition of Alan Turing's influential Princeton thesisBetween inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912–1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world—including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene—were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton.A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal—a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine.Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science.

Logic, Symbolic and mathematical. --- Turing, Alan, --- Alan Perlis. --- Alan Turing. --- Algorithm. --- Alonzo Church. --- Applicable mathematics. --- Automated theorem proving. --- Axiomatic system. --- Boolean algebra. --- Boolean satisfiability problem. --- C++. --- Calculus of constructions. --- Cantor's diagonal argument. --- Central limit theorem. --- Church–Turing thesis. --- Computability theory. --- Computability. --- Computable function. --- Computable number. --- Computation. --- Computer architecture. --- Computer program. --- Computer science. --- Computer scientist. --- Computer. --- Computing Machinery and Intelligence. --- Computing. --- Coq. --- Cryptography. --- Decision problem. --- Donald Gillies. --- EDVAC. --- ENIAC. --- Enigma machine. --- Entscheidungsproblem. --- Formal system. --- Foundations of mathematics. --- Georges Gonthier. --- Gödel's incompleteness theorems. --- Haskell Curry. --- Howard Aiken. --- Instance (computer science). --- Iteration. --- J. Barkley Rosser. --- John Tukey. --- John von Neumann. --- Kenneth Appel. --- Kepler conjecture. --- Konrad Zuse. --- Lecture. --- Lisp (programming language). --- Logic for Computable Functions. --- Logic in computer science. --- Logic. --- Logical framework. --- Marvin Minsky. --- Mathematica. --- Mathematical analysis. --- Mathematical logic. --- Mathematical proof. --- Mathematician. --- Mathematics. --- Model of computation. --- Monotonic function. --- Natural number. --- Notation. --- Number theory. --- Numerical analysis. --- Oswald Veblen. --- Parameter (computer programming). --- Peano axioms. --- Peter Landin. --- Presburger arithmetic. --- Probability theory. --- Processing (programming language). --- Programming language. --- Proof assistant. --- Quantifier (logic). --- Recursion (computer science). --- Recursion. --- Result. --- Rice's theorem. --- Riemann zeta function. --- Satisfiability modulo theories. --- Scientific notation. --- Simultaneous equations. --- Skewes' number. --- Solomon Feferman. --- Solomon Lefschetz. --- Systems of Logic Based on Ordinals. --- The Unreasonable Effectiveness of Mathematics in the Natural Sciences. --- Theorem. --- Theory of computation. --- Theory. --- Topology. --- Traditional mathematics. --- Turing Award. --- Turing machine. --- Turing's proof. --- Variable (computer science). --- Variable (mathematics).