9 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!). |
| 17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
| Full Idea: Zermelo's paper sets out to show that the standard set-theoretic axioms (what he calls the 'constitutive axioms', thus the ZF axioms minus the axiom of infinity) have an unending sequence of different models, thus that they are non-categorical. | |
| From: report of Ernst Zermelo (On boundary numbers and domains of sets [1930]) by Michael Hallett - Introduction to Zermelo's 1930 paper p.1209 | |
| A reaction: Hallett says later that Zermelo is working with second-order set theory. The addition of an Axiom of Infinity seems to have aimed at addressing the problem, and the complexities of that were pursued by Gödel. |
| 13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
| Full Idea: Zermelo included Replacement in 1930, after it was noticed that the sequence of power sets was needed, and Replacement gave the ordinal form of the well-ordering theorem, and justification for transfinite recursion. | |
| From: report of Ernst Zermelo (On boundary numbers and domains of sets [1930]) by Penelope Maddy - Believing the Axioms I §1.8 | |
| A reaction: Maddy says that this axiom suits the 'limitation of size' theorists very well, but is not so good for the 'iterative conception'. |
| 17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
| Full Idea: Two opposite tendencies of thought, the idea of creative advance and of collection and completion (underlying the Kantian 'antinomies') find their symbolic representation and their symbolic reconciliation in the transfinite numbers based on well-ordering. | |
| From: Ernst Zermelo (On boundary numbers and domains of sets [1930], §5) | |
| A reaction: [a bit compressed] It is this sort of idea, from one of the greatest set-theorists, that leads philosophers to think that the philosophy of mathematics may offer solutions to metaphysical problems. As an outsider, I am sceptical. |
| 1457 | Morality requires a minimum commitment to the self [Rashdall] |
| Full Idea: A bare minimum of metaphysical belief about the self is found to be absolutely presupposed in the very idea of morality. | |
| From: Hastings Rashdall (Theory of Good and Evil [1907], II.III.I.4) | |
| A reaction: This may not be true of virtue theory, where we could have a whole creature which lacked any sense of personhood, but yet had clear virtues and vices in its social functioning. Even if choices are central to morality, that might not need a self. |
| 6674 | All moral judgements ultimately concern the value of ends [Rashdall] |
| Full Idea: All moral judgements are ultimately judgements as to the value of ends. | |
| From: Hastings Rashdall (Theory of Good and Evil [1907], VII.I) | |
| A reaction: I am increasingly struck by this, especially when observing that it is the great gap in Kant's theory. For some odd reason, he gives being rational the highest possible value. Why? Nietzsche is good on this. 'Eudaimonia' seems a good start, to me. |
| 6673 | Ideal Utilitarianism is teleological but non-hedonistic; the aim is an ideal end, which includes pleasure [Rashdall] |
| Full Idea: My view, called Ideal Utilitarianism, combines the utilitarian principle that Ethics must be teleological with a non-hedonistic view of ethical ends; actions are right or wrong as they produce an ideal end, which includes, but is not limited to, pleasure. | |
| From: Hastings Rashdall (Theory of Good and Evil [1907], VII.I) | |
| A reaction: I certainly think that if you are going to be a consequentialist, then it is ridiculous to limit the end to pleasure, as it is an 'open question' as to whether we judge pleasures or pains to be good or bad. I am fond of beauty, goodness and truth, myself. |
| 1458 | Conduct is only reasonable or unreasonable if the world is governed by reason [Rashdall] |
| Full Idea: Absolutely reasonable or unreasonable conduct could not exist in a world which was not itself the product of reason or governed by its dictates. | |
| From: Hastings Rashdall (Theory of Good and Evil [1907], II.III.I.4) |
| 1459 | Absolute moral ideals can't exist in human minds or material things, so their acceptance implies a greater Mind [Rashdall, by PG] |
| Full Idea: An absolute moral ideal cannot exist in material things, or in the minds of individual people, so belief in it requires belief in a Mind which contains the ideal and is its source. | |
| From: report of Hastings Rashdall (Theory of Good and Evil [1907], II.III.I.4) by PG - Db (ideas) |