6 ideas
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |
| 5126 | A carelessly thrown brick is condemned much more if it hits someone [Smith,A, by Harman] |
| Full Idea: Adam Smith wrote about the influence of fortune on moral judgements, giving nice examples. Someone carelessly throws a brick over a wall. His companion may complain even if no harm is done. But if the brick hits someone much greater condemnation ensues. | |
| From: report of Adam Smith (The Theory of Moral Sentiments [1759]) by Gilbert Harman - Moral Philosophy meets social psychology 10.7.1.2 | |
| A reaction: This appears to be the earliest observation of the phenomenon of moral luck, though Plato (Idea 269) endorsed the view that the luck of outcome should be taken into account in moral judgements. |
| 20991 | People prepare our dinner from their own self-interest, not from humanity [Smith,A] |
| Full Idea: It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest. We address ourselves, not to their humanity but to their self-love. | |
| From: Adam Smith (The Wealth of Nations [1776], p.26-7), quoted by Amartya Sen - The Idea of Justice 08 'Narrowing' | |
| A reaction: Sen passionately pleads that this not be taken out of context. It is about the motivation for the relationship of exchange, and not about morality in general, which also includes trust etc. The subsequent lines in Smith show this. |
| 20680 | Selfish profit-seeking increases collective wealth, so greed is good, and egoism is altruism [Smith,A, by Harari] |
| Full Idea: Smith's claim that the selfish human urge to increase private profits is the basis for collective wealth is one of the most revolutionary ideas in human history. …Greed is good …and egoism is altruism. | |
| From: report of Adam Smith (The Wealth of Nations [1776]) by Yuval Noah Harari - Sapiens: brief history of humankind 16 'Growing' | |
| A reaction: The central confrontation of political philosophy still seems to be Adam Smith v Karl Marx. Why can't there be altruistic non-greedy profit-seeking? Not 'I want profits' but 'we want profits'. Altruistic capitalists aim to create jobs. |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
| From: Herodotus (The Histories [c.435 BCE], 2.123.2) |