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2 ideas
| 8725 | 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. |
| 14830 | Intuition only recognises what is possible, not what exists or is certain [Nietzsche] |
| Full Idea: 'To intuit' does not mean to recognise the existence of a thing to any extent, but rather to hold it to be possible, in that one wishes or fears it. 'Intuition' takes us not one step farther into the land of certainty. | |
| From: Friedrich Nietzsche (Human, All Too Human [1878], 131) | |
| A reaction: I like this remark. I am sympathetic to the view that the actual world has modal properties (in opposition to Sider, for example). To apprehend dispositions is precisely to apprehend possibilities. Intuition is a thousand interwoven inductions. |