Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The period in the foundations of mathematics that started in 1879 with the publication of Frege's Begriffsschrift and ended in 1931 with Gödel's Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I can reasonably be called the classical period. It saw the development of three major foundational programmes: the logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. In this period, there were also lively exchanges between the various schools culminating in the famous Hilbert-Brouwer controversy in the 1920s. The purpose of this anthology is to review the programmes in the foundations of mathematics from the classical period and to assess their possible relevance for contemporary philosophy of mathematics. What can we say, in retrospect, about the various foundational programmes of the classical period and the disputes that took place between them? To what extent do the classical programmes of logicism, intuitionism and formalism represent options that are still alive today? These questions are addressed in this volume by leading mathematical logicians and philosophers of mathematics. The volume will be of interest primarily to researchers and graduate students of philosophy, logic, mathematics and theoretical computer science. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields.

Intuitionistic mathematics. --- Mathematics -- Philosophy -- History. --- Mathematics. --- Intuitionistic mathematics --- Mathematics --- Mathematical Theory --- Physical Sciences & Mathematics --- History --- Philosophy --- History. --- Math --- Epistemology. --- Logic. --- Ontology. --- Language and languages --- Mathematical logic. --- Mathematical Logic and Foundations. --- Philosophy of Language. --- History of Mathematical Sciences. --- Philosophy. --- Science --- Constructive mathematics --- Logic, Symbolic and mathematical. --- Linguistics --- Genetic epistemology. --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Psychology --- Reasoning --- Thought and thinking --- Being --- Metaphysics --- Necessity (Philosophy) --- Substance (Philosophy) --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Developmental psychology --- Knowledge, Theory of --- Methodology --- Language and languages—Philosophy. --- Annals --- Auxiliary sciences of history --- Epistemology --- Theory of knowledge

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Domain theory is an established part of theoretical computer science, used in giving semantics to programming languages and logics. In mathematics and logic it has also proved to be useful in the study of algorithms. This book is devoted to providing a unified and self-contained treatment of the subject. The theory is presented in a mathematically precise manner which nevertheless is accessible to mathematicians and computer scientists alike. The authors begin with the basic theory including domain equations, various domain representations and universal domains. They then proceed to more specialized topics such as effective and power domains, models of lambda-calculus and so on. In particular, the connections with ultrametric spaces and the Kleene-Kreisel continuous functionals are made precise. Consequently the text will be useful as an introductory textbook (earlier versions have been class-tested in Uppsala, Gothenburg, Passau, Munich and Swansea), or as a general reference for professionals in computer science and logic.

Computer science --- Approximation theory. --- Numerical analysis. --- Mathematics.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The period in the foundations of mathematics that started in 1879 with the publication of Frege's Begriffsschrift and ended in 1931 with Gödel's Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I can reasonably be called the classical period. It saw the development of three major foundational programmes: the logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. In this period, there were also lively exchanges between the various schools culminating in the famous Hilbert-Brouwer controversy in the 1920s. The purpose of this anthology is to review the programmes in the foundations of mathematics from the classical period and to assess their possible relevance for contemporary philosophy of mathematics. What can we say, in retrospect, about the various foundational programmes of the classical period and the disputes that took place between them? To what extent do the classical programmes of logicism, intuitionism and formalism represent options that are still alive today? These questions are addressed in this volume by leading mathematical logicians and philosophers of mathematics. The volume will be of interest primarily to researchers and graduate students of philosophy, logic, mathematics and theoretical computer science. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields.

Metaphysics --- Mathematical logic --- Theory of knowledge --- Logic --- Mathematics --- Philosophy of language --- geschiedenis --- epistomologie --- taalfilosofie --- kennisleer --- metafysica --- wiskunde --- logica