display all the ideas for this combination of texts
2 ideas
| 16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
| Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
| From: Plato (Parmenides [c.364 BCE], 144a) | |
| A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |
| 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. |