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Ideas for 'Thinking About Mathematics', 'Reflections on my Critics' and 'There is No A Priori (and reply)'

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3 ideas

12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
How could the mind have a link to the necessary character of reality? [Devitt]
     Full Idea: What non-experiential link to reality could support insights into its necessary character?
     From: Michael Devitt (There is No A Priori (and reply) [2005], 4)
     A reaction: The key to it, I think, is your theory of mind. If you are a substance dualist, then connecting to such deep things looks fine, but if you are a reductive physicalist then it looks absurdly hopeful.
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
Some knowledge must be empirical; naturalism implies that all knowledge is like that [Devitt]
     Full Idea: It is overwhelmingly plausible that some knowledge is empirical. The attractive thesis of naturalism is that all knowledge is; there is only one way of knowing.
     From: Michael Devitt (There is No A Priori (and reply) [2005], 1)
     A reaction: How many ways for us to know seems to depend on what faculties we have. We lump our senses together under a single heading. The arrival of data is not the same as the arrival of knowledge. I'm unconvinced that naturalists like me must accept this.
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.