Titlebook: An Aristotelian Realist Philosophy of Mathematics; Mathematics as the S James Franklin Book 2014 Palgrave Macmillan, a division of Macmilla

Mindfulness

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.

Cabinet

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.

BRAWL

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.

Exclude

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.

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folliculitis

Acetabulum

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.

mettlesome

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.

轉折點

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’.

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