13 ideas
| 15946 | Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine] |
| Full Idea: Cantor's development of set theory began with his discovery of the progression 0, 1, ....∞, ∞+1, ∞+2, ..∞x2, ∞x3, ...∞^2, ..∞^3, ...∞^∞, ...∞^∞^∞..... | |
| From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite VIII.2 |
| 15911 | Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine] |
| Full Idea: Ordinal numbers are generated by two principles: each ordinal has an immediate successor, and each unending sequence has an ordinal number as its limit (that is, an ordinal that is next after such a sequence). | |
| From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite III.4 |
| 15119 | Aristotelian explanation by essence may need to draw on knowledge of other essences [Aristotle, by Koslicki] |
| Full Idea: From Aristotle's biology we learn that a successful scientific explanation of the necessary (but non-essential) features of one type of phenomenon (e.g. camels) my require appeal to facts about the essences of other types of phenomena (stomachs). | |
| From: report of Aristotle (The History of Animals [c.344 BCE]) by Kathrin Koslicki - Essence, Necessity and Explanation 13.4 |
| 7590 | Consequentialism emphasises value rather than obligation in morality [Scruton] |
| Full Idea: According to consequentialism, the fundamental concept of morality is not obligation (deontological ethics) but value (axiological ethics). | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'consequentialism') | |
| A reaction: These two views could come dramatically apart, in wartime, or in big ecological crises, or in a family breakup, or in religious disputes. Having identified the pair so clearly, why can we not aim for a civilised (virtuous) balance between the two? |
| 7589 | Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton] |
| Full Idea: Two distinct motives go by the name of altruism: the emotions of liking, love and friendship, making another's interest automatically mine; and the moral motive of respect or considerateness, where another's interests become reasons for me, but not mine. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'altruism') | |
| A reaction: The second one has a strongly Kantian flavour, with its notion of impersonal duty. Virtue theorists will aspire to achieve the first state rather than the second, because good actions are then actively desired, and give pleasure to the doer. |
| 7595 | The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton] |
| Full Idea: The idea of a right seems to be as basic as any other; we might even define justice in terms of it, as the disposition to accord to every person his rights. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'rights') | |
| A reaction: I am inclined to think that a set of fairly pure values (such as equality, kindness, sympathy, respect) must be in place before the idea of a right would occur to anyone. Aristotle has a powerful moral sense, but rights for slaves don't cross his mind. |
| 7588 | Allegiance is fundamental to the conservative view of society [Scruton] |
| Full Idea: Conservatives have made the concept of allegiance, conceived as a power, fundamental to their description of the experience of society | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'allegiance') | |
| A reaction: This provokes the famous slogan of "My country - right or wrong!" However, the issue here is not going to be decided by a consequentialist analysis, but by a view a of human nature. I think I would want to carefully prise allegiance apart from loyalty. |
| 7594 | Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton] |
| Full Idea: The paradox of democracy (emphasised by Rousseau) is that I am compelled by my belief in democracy to embrace conflicting - perhaps even contradictory - opinions. If I believe A, and the majority vote for B, I am committed to enacting them both. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'paradox of democracy') | |
| A reaction: The paradox would have to be resolved by qualifying what exactly one is committed to by being a democrat. I would say I am committed to the right of my opponents to enact a policy with which I disagree. |
| 7593 | Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG] |
| Full Idea: Liberalism believes (roughly) in the supremacy of the individual, who has freedom and natural rights; it focuses on human, not divine affairs; it claims rights and duties are universal; and it advocates tolerance in religion and morality. | |
| From: report of Roger Scruton (A Dictionary of Political Thought [1982], 'liberalism') by PG - Db (ideas) | |
| A reaction: I find it hard to disagree with these principles, but the upshot in practice is often an excessive commitment to freedom and tolerance, because people fail to realise the subtle long-term erosions of society that can result. |
| 7592 | For positivists law is a matter of form, for naturalists it is a matter of content [Scruton] |
| Full Idea: For the positivist, law is law by virtue of its form; for the naturalist, by virtue of its content. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'law') | |
| A reaction: Clearly a perverse and 'unnatural' social rule (backed by government and implied force) is a 'law' in some sense of the word. It is hard to see how you could gain social consensus for a law if it didn't appear in some way to be 'natural justice'. |
| 7587 | The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton] |
| Full Idea: The issue of abortion is intractable, partly because of the absence of any other case to which it can be assimilated. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'abortion') | |
| A reaction: This is the legalistic approach to the problem, which always looks for precedents and comparisons. All problems must hav solutions, though (mustn't they?). The problem, though, is not the value of the foetus, but the unique form of 'ownership'. |
| 23302 | Plants have far less life than animals, but more life than other corporeal entities [Aristotle] |
| Full Idea: The genus of plants, whilst it is devoid of life compared with an animal, is endowed with life as compared with other corporeal entities. In the sea there are certain objects which one would be at a loss to determine whether they be animal or vegetable. | |
| From: Aristotle (The History of Animals [c.344 BCE], 588b09) | |
| A reaction: It seems that Aristotle takes life to come in degrees, assessed by the amount of physical vitality observed. This seems to make lambs more alive than sheep, which isn't very plausible. This is part of his 'gradualist' view of nature. |
| 23301 | There is a gradual proceeding from the inanimate to animals, with no clear borderlines [Aristotle] |
| Full Idea: Nature proceeds little by little from things lifeless to animal life so that it is impossible to determine the exact line of demarcation, nor on which side an intermediate form should lie. ...In plants there is a continuous ascent towards the animal. | |
| From: Aristotle (The History of Animals [c.344 BCE], 588b04) | |
| A reaction: This in itself should have alerted medieval Christians to the problematic nature of the idea that animal species were divinely created. |