Choose an application

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

Space and time. --- General relativity (Physics) --- Geometry --- Physics --- Philosophy. --- -Space and time --- Space of more than three dimensions --- Space-time --- Space-time continuum --- Space-times --- Spacetime --- Time and space --- Fourth dimension --- Infinite --- Metaphysics --- Philosophy --- Space sciences --- Time --- Beginning --- Hyperspace --- Relativity (Physics) --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Mathematics --- Euclid's Elements --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Geometry. --- General relativity (Physics). --- Space and time --- Physics - Philosophy.

Choose an application

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

Truth --- Conviction --- Logic --- Metaphysics --- Belief and doubt --- Philosophy --- Skepticism --- Certainty --- Necessity (Philosophy) --- Pragmatism --- Truth.

Choose an application

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

Volume 5 has three parts, dealing with General Relativity, Epistemological Issues, and Quantum Mechanics. The core of the first part is Hilbert's two semester lecture course on ˜The Foundations of Physics' (1916/17). This is framed by Hilbert's published ˜First and Second Communications' on the ˜Foundations of Physics' (1915, 1917) and by a selection of documents dealing with more specific topics like ˜The Principle of Causality' or a lecture on the new concepts of space and time held in Bucharest in 1918. The epistemological issues concern the intricate relation between nature and mathematical knowledge, in particular the question of irreversibility and objectivity (1921) as well as the subtle question whether what Hilbert calls the ˜world equations' are physically complete (1923). The last part deals with quantum theory in its early, advanced and mature stages. Hilbert held lecture courses on the mathematical foundations of quantum theory twice, before and after the breakthrough in 1926. These documents bear witness to one of the most dramatic changes in the foundations of science.

Choose an application

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

The core of Volume 3 consists of lecture notes for seven sets of lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and 1926. These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical work: the emergence of modern mathematical logic; the explicit raising of questions of completeness, consistency and decidability for logical systems; the investigation of the relative strengths of various logical calculi; the birth and evolution of proof theory, and the parallel emergence of Hilbert’s finitist standpoint. The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen Logik (1928), and several shorter lectures by Hilbert from the later 1920s. These documents, which provide the background to Hilbert and Bernays’s monumental Grundlagen der Mathematik (1934, 1938), are essential for understanding the development of modern mathematical logic, and for reconstructing the interactions between Hilbert, Bernays, Brouwer, and Weyl in the philosophy of mathematics.

Mathematics. --- History. --- Mathematical logic. --- History of Mathematical Sciences. --- Mathematical Logic and Foundations. --- Arithmetic --- Logic. --- Foundations.