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This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?

Consciousness. --- Parapsychology. --- Constructive mathematics --- Ontology --- Mathematics --- Philosophy --- Philosophy & Religion --- Physical Sciences & Mathematics --- Logic --- Mathematical Theory --- Philosophy. --- Logic of mathematics --- Mathematics, Logic of --- Epistemology. --- Logic. --- Ontology. --- Mathematics. --- History. --- Mathematical logic. --- Mathematical Logic and Foundations. --- History of Mathematical Sciences. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Annals --- Auxiliary sciences of history --- Math --- Science --- Being --- Metaphysics --- Necessity (Philosophy) --- Substance (Philosophy) --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Psychology --- Reasoning --- Thought and thinking --- Epistemology --- Theory of knowledge --- Mental philosophy --- Humanities --- Methodology --- Logic, Symbolic and mathematical. --- Genetic epistemology. --- Developmental psychology --- Knowledge, Theory of --- Martin-Löf, Per, --- Löf, Per Martin-, --- Martin-Löf, P.

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This volume contains several invited papers as well as a selection of the other contributions. The conference was the first meeting of the Soviet logicians interested in com- puter science with their Western counterparts. The papers report new results and techniques in applications of deductive systems, deductive program synthesis and analysis, computer experiments in logic related fields, theorem proving and logic programming. It provides access to intensive work on computer logic both in the USSR and in Western countries.

Computer science --- Logic, Symbolic and mathematical --- Mathematics --- Congresses. --- -Logic, Symbolic and mathematical --- -681.3*D12 --- 681.3*D24 --- 681.3*F4 --- 681.3*I23 --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Informatics --- Science --- -Congresses --- Congresses --- Automatic programming--See also {681.3*I22} --- Program verification: assertion checkers; correctness proofs; reliability; validation (Software engineering)--See also {681.3*F31} --- Mathematical logic and formal languages (Theory of computation) --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*F4 Mathematical logic and formal languages (Theory of computation) --- 681.3*D24 Program verification: assertion checkers; correctness proofs; reliability; validation (Software engineering)--See also {681.3*F31} --- 681.3*D12 Automatic programming--See also {681.3*I22} --- 681.3*D12 --- Mathematics&delete& --- Information theory. --- Logic, Symbolic and mathematical. --- Computer science. --- Artificial intelligence. --- Theory of Computation. --- Mathematical Logic and Foundations. --- Philosophy of Science. --- Mathematical Logic and Formal Languages. --- Artificial Intelligence. --- Programming Techniques. --- Philosophy. --- Normal science --- Philosophy of science --- Communication theory --- Communication --- Cybernetics --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Computer science - Mathematics - Congresses --- Logic, Symbolic and mathematical - Congresses