3 ideas
| 14248 | We could accept the integers as primitive, then use sets to construct the rest [Cohen] |
| Full Idea: A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities. | |
| From: Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For? | |
| A reaction: I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world. |
| 3193 | Turing showed that logical rules can be specified computationally and mechanically [Turing, by Rey] |
| Full Idea: Turing showed that any formal process can be specified computationally, and captured by a Turing Machine. Hence logical rules (and arithmetic) could be obeyed not by someone representing and following them, but by causal organisation of the brain. | |
| From: report of Alan Turing (works [1935]) by Georges Rey - Contemporary Philosophy of Mind 8.2 | |
| A reaction: It is questionable whether logic is an entirely formal process, if it involves truth. You would need an entirely formal notion of truth for that. But a brain can do whatever a flow diagram can do. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |