Download e-book for kindle: An Aristotelian Realist Philosophy of Mathematics: by J. Franklin

By J. Franklin

ISBN-10: 1137400730

ISBN-13: 9781137400734

ISBN-10: 1349486183

ISBN-13: 9781349486182

Arithmetic is as a lot a technological know-how of the genuine global as biology is. it's the technology of the world's quantitative elements (such as ratio) and structural or patterned points (such as symmetry). The ebook develops an entire philosophy of arithmetic that contrasts with the standard Platonist and nominalist innovations.

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Additional resources for An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure

Example text

The volumes of the elephant and the Italian, or the Hottentot and the hummingbird, will be ‘more different’ than their surface areas. There are several distinct relationships present; furthermore, there are distinctive ways in which these relationships differ from one another. There are also distinctive relationships among these relationships. These facts have consequences of physical significance: for instance, with regard to problems of heat regulation. 35 kilograms in mass’. Pairs of lengths can stand in that same ratio, as can pairs of time intervals.

In particular, such physical properties stand in relations of proportion to one another. There is a relation between the surface area of the humming-bird and that of the Hottentot; and this may or may not be the same as the relationship that holds between the surface areas of an Italian and an elephant. Relationships such as proportion will hold not only between surface areas but also between volumes. Conceivably, the relationship between the surface areas of two objects might be the same as the relationship between volumes for two other objects.

It could be argued however that allowing indefinite iterability creates a bloated ontology. Thus Chihara argues, of Maddy’s view that sets of physical objects are located where their members are, there is on my desk, not only the apple and the unit set whose only member is the apple, but also the unit set whose only element is this unit set whose only element is the apple. Clearly, by this line of reasoning, we can infer that there are infinitely many such objects on my desk. 31 The implication that the desk is becoming overcrowded with objects and hence that we should not believe in them is unreasonable.

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An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure by J. Franklin

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