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Ideas for 'Thinking About Mathematics', 'Structures and Structuralism in Phil of Maths' and 'A Philosophy of Boredom'

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2 ideas

12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
If subjective and objective begin to merge, then so do primary and secondary qualities [Svendsen]
     Full Idea: It is doubtful whether the traditional dichotomy between the strictly subjective and the strictly objective can still be maintained; if not, we must also revise the distinction between primary and secondary qualities.
     From: Lars Svendsen (A Philosophy of Boredom [2005], Ch.3)
     A reaction: Very perceptive. The reason why I am so keen to hang onto the primary/secondary distinction is because I want to preserve objectivity (and realism). I much prefer Locke to Hume, as empiricist spokesmen.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
     Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1)
     A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach.