Conceived of philosophically, the foundations of mathematics concern various metaphysical and epistemological problems raised by mathematical practice, its results and applications. Most of these problems are of ancient ...
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Philosophy of logic can be roughly characterized as those philosophical topics which have emerged either from the technical development of symbolic (mathematical) logic, or from the motivations that ...
Putnam’s work spans a broad spectrum of philosophical interests, yet nonetheless reflects thematic unity in its concern over the question of realism. A critic of logical positivism, Putnam ...
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L.E.J. Brouwer was a mathematician and philosopher. He graduated from the University of Amsterdam in 1907 and remained there, from 1913 to 1951, as full professor. Brouwer was ...
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REVISED
Putnam’s work spans a broad spectrum of philosophical interests, yet nonetheless reflects thematic unity in its concern over the question of realism. The dynamic nature of Putnam's thought ...
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Hilbert is commonly regarded as one of the two leading mathematicians of the early 20th century, the other being Henri Poincaré (1854–1912). Hilbert made important contributions to a ...
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Logical positivism (logical empiricism, neo-positivism) originated in Austria and Germany in the 1920s. Inspired by late nineteenth- and early twentieth-century revolutions in logic, mathematics and mathematical physics, it ...
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Ultimately, mathematical intuitionism gets its name and its epistemological parentage from a conviction of Kant: that intuition reveals basic mathematical principles as true a priori. Intuitionism’s mathematical lineage ...
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A conceptual analysis of measurement can properly begin by formulating the two fundamental problems of any measurement procedure. The first problem is that of representation, justifying the assignment ...
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Leopold Kronecker was one of the most influential German mathematicians of the late nineteenth century. He exercised a strong sociopolitical influence on the development of mathematics as an ...
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According to Herbrand’s theorem, each formula F of quantification theory can be associated with a sequence F1, F2, F3,… of quantifier-free formulas such that F is provable just ...
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In classical mechanics a measurement process can be represented, in principle, as an interaction between two systems, a measuring instrument M and a measured system S, ...
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Von Neumann was one of the great mathematical minds of the twentieth century. His work has affected philosophy on several fronts, including logic and the philosophy of science. ...
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In the first, geometric stage of Hilbert’s formalism, his view was that a system of axioms does not express truths particular to a given subject matter but rather ...
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The effective calculability of number-theoretic functions such as addition and multiplication has always been recognized, and for that judgment a rigorous notion of ‘computable function’ is not required. ...
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The various attitudes that have been taken to mathematics can be split into two camps according to whether they take mathematical theorems to be true or not. Mathematicians ...
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The topic of quantum logic was introduced by Birkhoff and von Neumann (1936), who described the formal properties of a certain algebraic system associated with quantum theory. To ...
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Quantum mechanics developed in the early part of the twentieth century in response to the discovery that energy is quantized, that is, comes in discrete units. At the ...
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The least abstract form of mathematics, geometry has, from the earliest Hellenic times, been accorded a curious position straddling empirical and exact science. Its standing as an empirical ...
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Proof theory is a branch of mathematical logic founded by David Hilbert around 1920 to pursue Hilbert’s programme. The problems addressed by the programme had already been formulated, ...
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Utilizing the formalization of mathematics and logic found in Whitehead and Russell’s Principia Mathematica (1910), Hilbert and Ackermann (1928) gave precise formulations of a variety of foundational and ...
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The term ‘Polish logic’ was coined by McCall to signal the important contributions to modern logic by logicians from Poland between the wars. There were several centres of ...
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The term ‘theory’ is used variously in science to refer to an unproven hunch, a scientific field (as in ‘electromagnetic theory’), and a conceptual device for systematically characterizing ...
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