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Ideas for 'Thinking About Mathematics', 'The Philosophy of Philosophy' and 'Lewis on Perdurance versus Endurance'

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4 ideas

12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
There are 'armchair' truths which are not a priori, because experience was involved [Williamson]
     Full Idea: There is extensive 'armchair knowledge' in which experience plays no strictly evidential role, but it may not fit the stereotype of the a priori, because the contribution of experience was more than enabling, such as armchair truths about our environment.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], 5.5)
     A reaction: Once this point is conceded we have no idea where to draw the line. Does 'if it is red it can't be green' derive from experience? I think it might.
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.
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence [Williamson]
     Full Idea: Crude rationalists postulate a special knowledge-generating faculty of rational intuition. Crude empiricists regard intuition as an obscurantist term of folk psychology. Linguistic/conceptual philosophy says it reveals linguistic or conceptual competence.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], Intro)
     A reaction: Kripke seems to think that it is the basis of logical competence. I would use it as a blank term for any insight in which we have considerable confidence, and yet are unable to articulate its basis; roughly, for rational thought that evades logic.
When analytic philosophers run out of arguments, they present intuitions as their evidence [Williamson]
     Full Idea: 'Intuition' plays a major role in contemporary analytic philosophy's self-understanding. ...When contemporary analytic philosophers run out of arguments, they appeal to intuitions. ...Thus intuitions are presented as our evidence in philosophy.
     From: Timothy Williamson (The Philosophy of Philosophy [2007], p.214-5), quoted by Herman Cappelen - Philosophy without Intuitions 01.1
     A reaction: Williamson says we must investigate this 'scandal', but Cappelen's book says analytic philosophy does not rely on intuition.