Combining Texts

Ideas for 'The Gettier Problem', 'A Priori' and 'The Principles of Art'

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2 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers

17715	The truth of the axioms doesn't matter for pure mathematics, but it does for applied [Mares]
	Full Idea: The epistemological burden of showing that the axioms are true is removed if we are only studying pure mathematics. If, however, we want to look at applied mathematics, then this burden returns.
	From: Edwin D. Mares (A Priori [2011], 11.4)
	A reaction: One of those really simple ideas that hits the spot. Nice. The most advanced applied mathematics must rest on counting and measuring.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

17716	Mathematics is relations between properties we abstract from experience [Mares]
	Full Idea: Aristotelians treat mathematical facts as relations between properties. These properties, moreover, are abstracted from our experience of things. ...This view finds a natural companion in structuralism.
	From: Edwin D. Mares (A Priori [2011], 11.7)
	A reaction: This is the view of mathematics that I personally favour. The view that we abstract 'five' from a group of five pebbles is too simplistic, but this is the right general approach.