5 ideas
| 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. |
| 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) |
| 3214 | The models we use in reasoning may be more like perceptions than like language [Johnson-Laird] |
| Full Idea: The models that people use to reason are more likely to resemble perception or conception of the events (from a God's-eye view) than a string of symbols directly corresponding to the linguistic form of the premises and then applying rules of inference. | |
| From: P. Johnson-Laird (Mental Models [1983], p.53), quoted by Georges Rey - Contemporary Philosophy of Mind 10.1.2 | |
| A reaction: My intuition is that imagination is the single most important faculty in any conscious mind, and that even small animals have an inkling of the God's-eye view. Decisions need 'what-if' scenarios. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |