8 ideas
| 6408 | Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling] |
| Full Idea: In order to deduce the theorems of mathematics from purely logical axioms, Russell had to add three new axioms to those of standards logic, which were: the axiom of infinity, the axiom of choice, and the axiom of reducibility. | |
| From: A.C. Grayling (Russell [1996], Ch.2) | |
| A reaction: The third one was adopted to avoid his 'barber' paradox, but many thinkers do not accept it. The interesting question is why anyone would 'accept' or 'reject' an axiom. |
| 6414 | Two propositions might seem self-evident, but contradict one another [Grayling] |
| Full Idea: Two propositions might contradict each other despite appearing self-evident when considered separately. | |
| From: A.C. Grayling (Russell [1996], Ch.2) | |
| A reaction: Russell's proposal (Idea 5416) is important here, that self-evidence comes in degrees. If self-evidence was all-or-nothing, Grayling's point would be a major problem, but it isn't. Bonjour explores the idea more fully (e.g. Idea 3704) |
| 3296 | Sense-data are a false objectification of what is essentially subjective [Nagel] |
| Full Idea: The private object or sense datum view is an instance of the false objectification of what is essentially subjective. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.207) |
| 3295 | Inner v outer brings astonishment that we are a particular person [Nagel] |
| Full Idea: The problem of reconciling the objective and subjective points of view takes its purest form in a sense of incredulity that one should be anyone in particular. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.206) | |
| A reaction: Nice observation. This idea has always struck me forcibly, and seems to be one of those basic intuitions which motivates philosophy, and yet the subject has almost nothing to say about it. Of course you are you, or you wouldn't be amazed by it… |
| 3293 | If you assert that we have an ego, you can still ask if that future ego will be me [Nagel] |
| Full Idea: The metaphysical ego, if it is a continuing individual with its identity over time, is just one more thing about which the same problem can be raised - will that ego still be me? | |
| From: Thomas Nagel (Subjective and Objective [1979], p.200) | |
| A reaction: You can worry too much about some philosophical questions. If it is me now, and it has continuing individual identity over time, I'm not going to lose sleep over the possibility that it might nevertheless somehow cease to be me. I'm overrated. |
| 3292 | The most difficult problem of free will is saying what the problem is [Nagel] |
| Full Idea: The most difficult problem of free will is saying what the problem is. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.198) |
| 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? |
| 3294 | As far as possible we should become instruments to realise what is best from an eternal point of view [Nagel] |
| Full Idea: The right thing to do is to turn oneself as far as possible into an instrument for the realisation of what is best 'sub specie aeternitatis'. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.204) |