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Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathematical objects are purely abstract entities or are in some way concrete, and in what the relationship ...
Mathematics is the science that draws necessary conclusions. [10] Benjamin Peirce 1870. All Mathematics is Symbolic Logic. [8] Bertrand Russell 1903. Peirce did not think that mathematics is the same as logic, since he thought mathematics makes only hypothetical assertions, not categorical ones. [11]
Frontispiece of Operum Mathematicorum Pars Prima (1657) by John Wallis, the first volume of Opera Mathematica including a chapter entitled Mathesis Universalis.. Mathesis universalis (from Greek: μάθησις, mathesis "science or learning", and Latin: universalis "universal") is a hypothetical universal science modelled on mathematics envisaged by Descartes and Leibniz, among a number of ...
The distinction between the quantitative exact sciences and those sciences that deal with the causes of things is due to Aristotle, who distinguished mathematics from natural philosophy [10] and considered the exact sciences to be the "more natural of the branches of mathematics."
Mathematical Platonism is the metaphysical view that (a) there are abstract mathematical objects whose existence is independent of us, and (b) there are true mathematical sentences that provide true descriptions of such objects. The independence of the mathematical objects is such that they are non physical and do not exist in space or time.
Philosophy of science is the branch of philosophy concerned with the foundations, methods, and implications of science. Amongst its central questions are the difference between science and non-science , the reliability of scientific theories, and the ultimate purpose and meaning of science as a human endeavour.
Logicism is a school of thought, and research programme, in the philosophy of mathematics, based on the thesis that mathematics is an extension of logic or that some or all mathematics may be derived in a suitable formal system whose axioms and rules of inference are 'logical' in nature.
Russell's work contributed to philosophy of science's development into a separate branch of philosophy. Much of Russell's thinking about science is expressed in his 1914 book, Our Knowledge of the External World as a Field for Scientific Method in Philosophy, [20] which influenced the logical positivists.