عنوان

An Aristotelian realist philosophy of mathematics :

1137400722

9781137400727

dltt

An Aristotelian realist philosophy of mathematics :

[Book]

mathematics as the science of quantity and structure /

James Franklin

x, 308 pages :

illustrations ; 23 cm

Includes bibliographical references and index

Part I. The science of quantity and structure. The Aristotelian realist point of view -- Uninstantiated universals and 'semi-Platonist' Aristotelianism -- Elementary mathematics : the science of quantity -- Higher mathematics : science of the purely structural -- Necessary truths about reality -- The formal sciences discover the philosophers' stone -- Comparisons and objections -- Infinity -- Geometry : mathematics or empirical science? -- Part II. Knowing mathematical reality. Knowing mathematics : pattern recognition and perception of quantity and structure -- Knowing mathematics : visualization and understanding -- Knowing mathematics : proof and certainty -- Explanation in mathematics -- Idealization : an Aristotelian view -- Non-deductive logic in mathematics -- Epilogue : mathematics, last bastion of reason

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"An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge."--Page 4 of cover

Aristotle

Mathematics-- Philosophy

Franklin, James,1953-

20150901112820.0

rda

[Book]

Y