5 ideas
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| Full Idea: Philosophy says it is not right even to stretch out a finger without some reason. | |
| From: Epictetus (fragments/reports [c.57], 15) | |
| A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!). |
| 16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
| Full Idea: Geometrical concepts appear to depend in some way on a spatial ability. Although one can translate geometrical propositions into algebraic ones and produce equivalent models, the meaning of the propositions seems to me to be thereby lost. | |
| From: Tyler Burge (Frege on Apriority (with ps) [2000], 4) | |
| A reaction: I think this is a widely held view nowadays. Giaquinto has a book on it. A successful model of something can't replace it. Set theory can't replace arithmetic. |
| 16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
| Full Idea: In the Peano axiomatisation, arithmetic seems primitively to involve the thought that 0 is a number. | |
| From: Tyler Burge (Frege on Apriority (with ps) [2000], 5) | |
| A reaction: Burge is pointing this out as a problem for Frege, for whom only the logic is primitive. |
| 17555 | 'One' can mean undivided and not a multitude, or it can add measurement, giving number [Aquinas] |
| Full Idea: There are two sorts of one. There is the one which is convertible with being, which adds nothing to being except being undivided; and this deprives of multitude. Then there is the principle of number, which to the notion of being adds measurement. | |
| From: Thomas Aquinas (Quaestiones de Potentia Dei [1269], q3 a16 ad 3-um) | |
| A reaction: [From a lecture handout] I'm not sure I understand this. We might say, I suppose, that insofar as water is water, it is all one, but you can't count it. Perhaps being 'unified' and being a 'unity' are different? |
| 16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |
| Full Idea: Whereas Leibniz and Frege predicate apriority primarily of truths (or more fundamentally, proofs of truths), Kant predicates apriority primarily of cognition and the employment of representations. | |
| From: Tyler Burge (Frege on Apriority (with ps) [2000], 1) |