display all the ideas for this combination of texts
4 ideas
| 3967 | Absence of all rationality would be absence of thought [Davidson] |
| Full Idea: To imagine a totally irrational animal is to imagine an animal without thought. | |
| From: Donald Davidson (Davidson on himself [1994], p.232) | |
| A reaction: This wouldn't be so clear without the theory of evolution, which suggests that only the finders of truth last long enough to breed. |
| 3974 | Our meanings are partly fixed by events of which we may be ignorant [Davidson] |
| Full Idea: What we mean by what we say is partly fixed by events of which we may be ignorant. | |
| From: Donald Davidson (Davidson on himself [1994], p.235) | |
| A reaction: There is 'strict and literal meaning', which is fixed by the words, even if I don't know what I am saying. But 'speaker's meaning' is surely a pure matter of a state of mind? |
| 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. |