display all the ideas for this combination of texts
3 ideas
| 23252 | Socrates first proposed that we are run by mind or reason [Socrates, by Frede,M] |
| Full Idea: It would seem that historically the decisive step was taken by Socrates in conceiving of human beings as being run by a mind or reason.. …He postulated an entity whose precision nature and function then was a matter of considerable debate. | |
| From: report of Socrates (reports of career [c.420 BCE]) by Michael Frede - Intro to 'Rationality in Greek Thought' p.19 | |
| A reaction: This is, for me, a rather revelatory idea. I am keen on the fact the animals make judgements which are true and false, and also that we exhibit rationality when walking across uneven ground. So pure rationality is a cultural construct! |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| Full Idea: Cantor (in his exploration of infinities) pushed the bounds of conceivability further than anyone before him. To discover what is conceivable, we have to enquire into the concept. | |
| From: report of George Cantor (works [1880]) by Michèle Friend - Introducing the Philosophy of Mathematics 6.5 | |
| A reaction: This remark comes during a discussion of Husserl's phenomenology. Intuitionists challenge Cantor's claim, and restrict what is conceivable to what is provable. Does possibility depend on conceivability? |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| Full Idea: Cantor thought that we abstract a number as something common to all and only those sets any one of which has as many members as any other. ...However one wants to see the logic of the inference. The irony is that set theory lays out this logic. | |
| From: comment on George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: The logic Hart has in mind is the notion of an equivalence relation between sets. This idea sums up the older and more modern concepts of abstraction, the first as psychological, the second as logical (or trying very hard to be!). Cf Idea 9145. |