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An Aristotelian realist philosophy of mathematics :mathematics as the science of quantity and structure /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	510.1
書名/作者:	An Aristotelian realist philosophy of mathematics : : mathematics as the science of quantity and structure // James Franklin.
作者:	Franklin, James,
面頁冊數:	1 online resource.
標題:	Mathematics - Philosophy.
ISBN:	1137400730 (electronic bk.)
ISBN:	9781137400734 (electronic bk.)
書目註:	Includes bibliographical references and index.
內容註:	PART I: THE SCIENCE OF QUANTITY AND STRUCTURE -- 1. The Aristotelian Realist Point of View -- 2. Uninstantiated Universals and 'Semi-Platonist' Aristotelianism -- 3. Elementary Mathematics: Quantity and Number -- 4. Higher Mathematics: Science of the Purely Structural -- 5. Necessary Truths about Reality -- 6. The Formal Sciences Discover the Philosophers' Stone -- 7. Comparisons and Objections -- 8. Infinity -- 9. Geometry: Mathematics or Empirical Science? -- PART II: KNOWING MATHEMATICAL REALITY -- 10. Knowing Mathematics: Pattern Recognition and Perception of Quantity and Structure -- 11. Knowing Mathematics: Visualization -- 12. Knowing Mathematics: Understanding and Proof -- 13. Explanation in Mathematics -- 14. Idealization: An Aristotelian View -- 15. Non-Deductive Logic in Mathematics -- Epilogue: Mathematics, Last Bastion of Reason.
摘要、提要註:	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.
電子資源:	http://www.palgraveconnect.com/doifinder/10.1057/9781137400734

An Aristotelian realist philosophy of mathematics :mathematics as the science of quantity and structure /
Franklin, James,1953-

An Aristotelian realist philosophy of mathematics :mathematics as the science of quantity and structure /James Franklin. - 1 online resource.

Includes bibliographical references and index.

PART I: THE SCIENCE OF QUANTITY AND STRUCTURE -- 1. The Aristotelian Realist Point of View -- 2. Uninstantiated Universals and 'Semi-Platonist' Aristotelianism -- 3. Elementary Mathematics: Quantity and Number -- 4. Higher Mathematics: Science of the Purely Structural -- 5. Necessary Truths about Reality -- 6. The Formal Sciences Discover the Philosophers' Stone -- 7. Comparisons and Objections -- 8. Infinity -- 9. Geometry: Mathematics or Empirical Science? -- PART II: KNOWING MATHEMATICAL REALITY -- 10. Knowing Mathematics: Pattern Recognition and Perception of Quantity and Structure -- 11. Knowing Mathematics: Visualization -- 12. Knowing Mathematics: Understanding and Proof -- 13. Explanation in Mathematics -- 14. Idealization: An Aristotelian View -- 15. Non-Deductive Logic in Mathematics -- Epilogue: Mathematics, Last Bastion of Reason.

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.

ISBN: 1137400730 (electronic bk.)

Source: 746474Palgrave Macmillanhttp://www.palgraveconnect.com

Nat. Bib. Agency Control No.: 016698290UkSubjects--Personal Names:

372752
Aristotle.
Subjects--Topical Terms:

379760
Mathematics
--Philosophy.Index Terms--Genre/Form:

336502
Electronic books.

LC Class. No.: QA8.4

Dewey Class. No.: 510.1

An Aristotelian realist philosophy of mathematics :mathematics as the science of quantity and structure /
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520 $a 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.
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