Combining Texts

Ideas for 'Structures and Structuralism in Phil of Maths', 'The Laws of Thought' and 'What are Sets and What are they For?'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

10165	'Analysis' is the theory of the real numbers [Reck/Price]
	Full Idea: 'Analysis' is the theory of the real numbers.
	From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
	A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work.

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics

14246	If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
	Full Idea: If mathematics was purely concerned with mathematical objects, there would be no room for applied mathematics.
	From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1)
	A reaction: Love it! Of course, they are using 'objects' in the rather Fregean sense of genuine abstract entities. I don't see why fictionalism shouldn't allow maths to be wholly 'pure', although we have invented fictions which actually have application.