標(biāo)題: Titlebook: An Aristotelian Realist Philosophy of Mathematics; Mathematics as the S James Franklin Book 2014 Palgrave Macmillan, a division of Macmilla [打印本頁] 作者: 厭氧 時間: 2025-3-21 19:58
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作者: Creatinine-Test 時間: 2025-3-21 23:27
Uninstantiated Universals and ‘Semi-Platonist’ Aristotelianism physical world, so that mathematics is a science of aspects of the world, as much as biology is. The principal objection to that thesis is, ‘Some of the objects of mathematics are . realized in the physical world, such as large infinite numbers’. It may be that the world is finite, in which case in作者: 錯誤 時間: 2025-3-22 00:57
Elementary Mathematics: The Science of Quantityticularly necessary since it is much less obvious what the answer is for mathematics than it is for sciences like physics, biology or sociology. It is clear enough what properties of things physics studies – properties such as mass and attraction (even if it is hard to say what they have in common t作者: 膠狀 時間: 2025-3-22 06:16 作者: 釋放 時間: 2025-3-22 09:53 作者: Emmenagogue 時間: 2025-3-22 15:35 作者: commonsense 時間: 2025-3-22 19:19 作者: Ophthalmologist 時間: 2025-3-22 23:10 作者: anthesis 時間: 2025-3-23 05:14 作者: 訓(xùn)誡 時間: 2025-3-23 08:42 作者: dyspareunia 時間: 2025-3-23 12:34 作者: 戰(zhàn)勝 時間: 2025-3-23 16:49
Non-Deductive Logic in Mathematics addition to methods special to mathematics such as proof, there ought to be a role for ordinary scientific methods such as experiment, conjecture and the confirmation of theories by observations. Those methods should work in mathematics just as well as in science. Mathematics has extra and more cer作者: muscle-fibers 時間: 2025-3-23 21:30 作者: 冬眠 時間: 2025-3-23 23:00 作者: 額外的事 時間: 2025-3-24 02:23
Stephanie Schiemann,Robert W?stenfeldizations. Aristotle himself described the Platonists arguing that geometry studies perfect lines and circles, which cannot be realized in the physical world and hence must exist in some non-physical realm:作者: ablate 時間: 2025-3-24 08:33
https://doi.org/10.1007/978-3-642-91079-1er than complex structures, its concern with infinities before small finite structures, its epistemological impasse over how to know about ‘a(chǎn)bstract’ objects – comes from its oscillation between Platonism and nominalism, as if those were the only alternatives. So it is desirable to begin with a brie作者: 外表讀作 時間: 2025-3-24 14:44
https://doi.org/10.1007/978-3-642-91079-1 physical world, so that mathematics is a science of aspects of the world, as much as biology is. The principal objection to that thesis is, ‘Some of the objects of mathematics are . realized in the physical world, such as large infinite numbers’. It may be that the world is finite, in which case in作者: Prosaic 時間: 2025-3-24 15:13
https://doi.org/10.1007/978-3-642-91079-1ticularly necessary since it is much less obvious what the answer is for mathematics than it is for sciences like physics, biology or sociology. It is clear enough what properties of things physics studies – properties such as mass and attraction (even if it is hard to say what they have in common t作者: fiscal 時間: 2025-3-24 21:14
https://doi.org/10.1007/978-3-642-91079-1ct-matter, structure or pattern. We survey the historical development with an eye to philosophically significant examples, then address the crucial philosophical question of characterizing precisely what ‘structure’ is.作者: FLACK 時間: 2025-3-25 01:31 作者: animated 時間: 2025-3-25 05:00 作者: Missile 時間: 2025-3-25 10:46 作者: Host142 時間: 2025-3-25 12:40
Stephanie Schiemann,Robert W?stenfeldal things as symmetry and continuity, it should be possible to observe those properties in things, and so the epistemology of mathematics should be no more problematic than the epistemology of colour. An Aristotelian point of view should solve the epistemology problem at the same time as it solves t作者: OREX 時間: 2025-3-25 18:40 作者: Hiatus 時間: 2025-3-25 20:11
https://doi.org/10.1007/978-3-658-13887-5endently of each other. For example, the . articles on ‘Scientific explanation’. and ‘Explanation in mathematics’. barely mention any common issues and have only three items in common in their extensive bibliographies. That is strange, since . explanation works much the same way in mathematics and i作者: AVERT 時間: 2025-3-26 01:37 作者: 表示問 時間: 2025-3-26 07:03 作者: Admire 時間: 2025-3-26 08:33 作者: 流出 時間: 2025-3-26 14:19
Kunststoffe aus reinen NaturerzeugnissenBecause the main body of philosophy of mathematics since Frege has moved along a path unsympathetic to Aristotelian views, it is natural to collect in one place the comparisons of the present point of view with standard philosophy of mathematics.作者: 不舒服 時間: 2025-3-26 17:19 作者: Mindfulness 時間: 2025-3-26 23:31
https://doi.org/10.1007/978-3-658-13887-5If a mathematical truth is too complex to be visualized and so understood at one glance, it may still be established conclusively by putting together two glances. Or three, or .. That is, it may be proved by a chain of inferences, each of which is clear individually, even if the whole is not clear simultaneously. That is the idea behind proof.作者: Cabinet 時間: 2025-3-27 03:57
Stephanie Schiemann,Robert W?stenfeldThe twentieth century – and we hardly need a longer perspective to see this – was beset by, and in cultural life almost defined by, an unteachable .. From Dadaism to the 1960s to postmodernism, it was sufficient to throw tomatoes at tradition to get a full-page spread from the intellectual paparazzi.作者: BRAWL 時間: 2025-3-27 07:42
IntroductionAccording to the philosophy of mathematics to be defended here, mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative and structural or patterned aspects of things.作者: Exclude 時間: 2025-3-27 11:26
Comparisons and ObjectionsBecause the main body of philosophy of mathematics since Frege has moved along a path unsympathetic to Aristotelian views, it is natural to collect in one place the comparisons of the present point of view with standard philosophy of mathematics.作者: coagulate 時間: 2025-3-27 13:38 作者: folliculitis 時間: 2025-3-27 20:45 作者: Acetabulum 時間: 2025-3-27 23:00
Epilogue: Mathematics, Last Bastion of ReasonThe twentieth century – and we hardly need a longer perspective to see this – was beset by, and in cultural life almost defined by, an unteachable .. From Dadaism to the 1960s to postmodernism, it was sufficient to throw tomatoes at tradition to get a full-page spread from the intellectual paparazzi.作者: mettlesome 時間: 2025-3-28 02:06
Higher Mathematics: Science of the Purely Structuralct-matter, structure or pattern. We survey the historical development with an eye to philosophically significant examples, then address the crucial philosophical question of characterizing precisely what ‘structure’ is.作者: 轉(zhuǎn)折點 時間: 2025-3-28 07:57
Infinityer sets and the like. When those methods are fed finite sets they yield finite sets and when they are fed infinite sets they (can) yield infinite sets. But there is no way to build an infinite set from finitely many finite sets. The ZF axioms cope with that limitation by adding a bald ‘Axiom of Infinity’, which states ‘there is an infinite set’.作者: 樹上結(jié)蜜糖 時間: 2025-3-28 10:36 作者: induct 時間: 2025-3-28 17:47
structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.978-1-349-48618-2978-1-137-40073-4作者: metropolitan 時間: 2025-3-28 20:26 作者: Chameleon 時間: 2025-3-28 23:31 作者: 單片眼鏡 時間: 2025-3-29 03:40 作者: 縮短 時間: 2025-3-29 09:54 作者: 投射 時間: 2025-3-29 12:18 作者: 愛好 時間: 2025-3-29 16:41 作者: critic 時間: 2025-3-29 19:56 作者: genesis 時間: 2025-3-30 03:02
Stephanie Schiemann,Robert W?stenfeldhimpanzees are not surprised by that fact.. They are incapable of being surprised by that, because they cannot understand it. They lack the relevant cognitive abilities - the same intellectual cognitive abilities that are needed for reading diagrams, visualizing, using mathematical symbols, and understanding proofs.作者: radiograph 時間: 2025-3-30 06:53
https://doi.org/10.1007/978-3-658-13887-5d have only three items in common in their extensive bibliographies. That is strange, since . explanation works much the same way in mathematics and in science. An account of scientific explanation is incomplete if it does not cover explanation in mathematics (or at least include some reasoning on why the mathematical case is different).作者: Feigned 時間: 2025-3-30 09:58 作者: 得意人 時間: 2025-3-30 16:08 作者: 消耗 時間: 2025-3-30 19:19
Knowing Mathematics: Pattern Recognition and Perception of Quantity and Structure more problematic than the epistemology of colour. An Aristotelian point of view should solve the epistemology problem at the same time as it solves the problem of the applicability of mathematics, by showing that mathematics deals directly with properties of real things..作者: 不可磨滅 時間: 2025-3-30 23:01 作者: laparoscopy 時間: 2025-3-31 00:57 作者: 變化 時間: 2025-3-31 08:27
Non-Deductive Logic in Mathematics the confirmation of theories by observations. Those methods should work in mathematics just as well as in science. Mathematics has extra and more certain methods of its own, but that should not prevent ordinary scientific methods from working.作者: Carcinogen 時間: 2025-3-31 12:58 作者: 作嘔 時間: 2025-3-31 14:44
https://doi.org/10.1007/978-3-642-91079-1tence of infinite sets that are so huge that they simply dwarf garden variety infinite sets, like the set of all the natural numbers. There is just no plausible way to interpret this talk of gigantic infinite sets as being about physical objects.’. Or as Shapiro writes:
