By J. Franklin
Arithmetic is as a lot a technology of the true international as biology is. it's the technological know-how of the world's quantitative points (such as ratio) and structural or patterned points (such as symmetry). The ebook develops a whole philosophy of arithmetic that contrasts with the standard Platonist and nominalist strategies.
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Additional resources for An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure
Colour is a determinable, while an exact shade of colour such as Cambridge Blue is a determinate – a precise way of being a colour, among the wide range of possible ways of being a colour. 57 metres a determinate length. The way in which determinables are divided into determinates is unlike the way in which classification works via genus and differentia. While (in the traditional example) humans are of the genus animal with the differentia of rationality added, Cambridge Blue is not colour with some differentia added (other than Cambridge Blue itself).
32 Those are genuine questions but they should be left to the metaphysics of states of affairs to deal with. Provided that the concept of states of affairs is sound, the philosophy of mathematics can accept whatever answers metaphysics delivers about whether states of affairs Elementary Mathematics: The Science of Quantity 43 Fa should be said to possess, for example, the causal powers of the individual a and the property F. 33 If I open an egg carton and see that there are three eggs in it, I perceive both the pale curved surface of the egg-heap and that it is structured by ‘being an egg’ into three parts, each an egg.
The structuralist theory of mathematics has, like the quantity theory, some initial plausibility, in view of the concentration of modern mathematics on structural properties like symmetry and the purely relational aspects of systems both physical and abstract. It is supported by the widespread concentration of modern pure mathematics on ‘abstract structures’ such as groups and topological spaces. Elementary Mathematics: The Science of Quantity 33 In view of the underlying philosophical similarity between these two realist theories of mathematics, it is surprising that questions have not been asked about the relation between them, or about the relation between the concepts of quantity and structure.
An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure by J. Franklin