7 ideas
8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
Full Idea: Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths. | |
From: Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2 | |
A reaction: Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time! |
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? |
18228 | An end can't be an ultimate value just because it is useless! [Korsgaard] |
Full Idea: If what is final is whatever is an end but never a means, ...why should something be more valuable just because it is useless? | |
From: Christine M. Korsgaard (Aristotle and Kant on the Source of Value [1986], 8 'Finality') | |
A reaction: Korsgaard is offering this as a bad reading of what Aristotle intends. |
18225 | If we can't reason about value, we can reason about the unconditional source of value [Korsgaard] |
Full Idea: If you can only know what is intrinsically valuable through intuition (as Moore claims), you can still argue about what is unconditionally valuable. There must be something unconditionally valuable because there must be a source of value. | |
From: Christine M. Korsgaard (Aristotle and Kant on the Source of Value [1986], 8 'Three') | |
A reaction: If you only grasped the values through intuition, does that give you enough information to infer the dependence relations between values? |
18224 | Goodness is given either by a psychological state, or the attribution of a property [Korsgaard] |
Full Idea: 'Subjectivism' identifies good ends with or by reference to some psychological state. ...'Objectivism' says that something is good as an end if a property, intrinsic goodness, is attributed to it. | |
From: Christine M. Korsgaard (Aristotle and Kant on the Source of Value [1986], 8 'Three') | |
A reaction: Not sure about 'objectivism' here, as attributing a 'property'. A tomato is not intrinsically good. Hopeless for building walls. |
18233 | Contemplation is final because it is an activity which is not a process [Korsgaard] |
Full Idea: It is because contemplation is an activity that is not also a process that Aristotle identifies it as the most final good. | |
From: Christine M. Korsgaard (Aristotle and Kant on the Source of Value [1986], 8 'Activity') | |
A reaction: Quite a helpful way of labelling what Aristotle has in mind. So should we not aspire to be involved in processes, except reluctantly? I take the mind itself to be a process, so that may be difficult! |
18226 | For Aristotle, contemplation consists purely of understanding [Korsgaard] |
Full Idea: Contemplation, as Aristotle understand it, is not research or inquiry, but an activity that ensues on these: an activity that consists in understanding. | |
From: Christine M. Korsgaard (Aristotle and Kant on the Source of Value [1986], 8 'Aristotle') | |
A reaction: Fairly obvious, when you read the last part of 'Ethics', but helpful in grasping Aristotle, because understanding is the objective of 'Posterior Analytics' and 'Metaphysics', so he tells you how to achieve the ideal moral state. |