3 ideas
| 8754 | Logic is dependent on mathematics, not the other way round [Heyting, by Shapiro] |
| Full Idea: Heyting (the intuitionist pupil of Brouwer) said that 'logic is dependent on mathematics', not the other way round. | |
| From: report of Arend Heyting (Intuitionism: an Introduction [1956]) by Stewart Shapiro - Thinking About Mathematics 7.3 | |
| A reaction: To me, this claim makes logicism sound much more plausible, as I don't see how mathematics could get beyond basic counting without a capacity for logical thought. Logic runs much deeper, psychologically and metaphysically. |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| Full Idea: A whole must possess an attribute peculiar to and characteristic of it as a whole; there must be a characteristic relation of dependence between the parts; and the whole must have some structure which gives it characteristics. | |
| From: Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2 | |
| A reaction: Simons says these are basically sensible conditions, and tries to fill them out. They seem a pretty good start, and I must resist the temptation to rush to borderline cases. |
| 20992 | Right and wrong concerns what other people cannot reasonably reject [Scanlon] |
| Full Idea: Thinking about right and wrong is, at the most basic level, thinking about what could be justified to others on grounds that they, if appropriately motivated, could not reasonably reject. | |
| From: Thomas M. Scanlon (What We Owe to Each Other [1998], Intro) | |
| A reaction: The tricky bit is that the acceptance by others must be 'reasonable', so we need a reasonably objective view of rationality. Don't picture your neighbours, picture the locals when you are on holiday in a very different culture. Other Nazis? |