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

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	An Aristotelian realist philosophy of mathematics :James Franklin.
其他題名:	mathematics as the science of quantity and structure /
作者:	Franklin, James,
面頁冊數:	1 online resource.
標題:	MathematicsPhilosophy.
電子資源:	https://link.springer.com/book/10.1057/9781137400734
ISBN:	1137400730 (electronic bk.)

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:

176560
Aristotle.
Subjects--Topical Terms:

187658
Mathematics
--Philosophy.Index Terms--Genre/Form:

214472
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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505 0 $a 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.
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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