16 ideas
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| Full Idea: One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths). |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| Full Idea: Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1 | |
| A reaction: Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries. |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| Full Idea: In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2 | |
| A reaction: The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy. |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| Full Idea: Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3 | |
| A reaction: Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field. |
| 23814 | Every human yearns for an unattainable transcendent good [Weil] |
| Full Idea: There is a reality outside the world …outside any sphere that is accessible to human faculties. Corresponding to this reality, at the centre of the human heart, is the longing for an absolute good, which is always there and never appeased by this world. | |
| From: Simone Weil (Draft Statement of Human Obligations [1943], p.221) | |
| A reaction: I don't believe in any sort of transcendent reality, but I can identify with this. Even if you have a highly naturalistic view of what is valuable (see late Philippa Foot), there is this indeterminate yearning for that value. |
| 23824 | Where human needs are satisfied we find happiness, friendship and beauty [Weil] |
| Full Idea: Any place where the needs of human beings are satisfied can be recognised by the fact that there is a flowering of fraternity, joy, beauty, and happiness. | |
| From: Simone Weil (Draft Statement of Human Obligations [1943], p.230) | |
| A reaction: Weil writes a lengthy analysis of what she sees as the basic human needs, beyond the obvious food, water etc. An excellent place to start a line of political thought. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 23815 | We cannot equally respect what is unequal, so equal respect needs a shared ground [Weil] |
| Full Idea: It is impossible to feel equal respect for things that are in fact unequal unless the respect is given to something that is identical in all of them. Men are all unequal in all their relations with things of this world. | |
| From: Simone Weil (Draft Statement of Human Obligations [1943], p.223) | |
| A reaction: Weil votes for some link to transcendence in each of us, but I would prefer some more naturalistic proposal for what we all have in common. There are plenty of aspects which unite all human beings, which grounds this unconditional respect. |
| 23823 | Life needs risks to avoid sickly boredom [Weil] |
| Full Idea: The boredom produced by a complete absence of risk is a sickness of the human soul. | |
| From: Simone Weil (Draft Statement of Human Obligations [1943], p.229) | |
| A reaction: An unusual analysis of boredom. I think it is probably purposeful activity that we need, rather than actual risk, with all the stresses that involves. Risks are justified by their rewards. |
| 23822 | We all need to partipate in public tasks, and take some initiative [Weil] |
| Full Idea: The human soul has need of disciplined participation in a common task of public value, and it has need of personal initiative within this participation. | |
| From: Simone Weil (Draft Statement of Human Obligations [1943], p.229) | |
| A reaction: The intrusion of competitive capitalism into almost every area of modern life has more or less eliminated such activities. Only state employees now have such satisfactions, on the whole. I admire Weil's approach here. |
| 23817 | We need both equality (to attend to human needs) and hierarchy (as a scale of responsibilities) [Weil] |
| Full Idea: The human soul has need of equality and of hierarchy. Equality is the public recognition …of the principal that an equal degree of attention is due to the needs of all human beings. Hierarchy is the scale of responsibilities. | |
| From: Simone Weil (Draft Statement of Human Obligations [1943], p.228) | |
| A reaction: This is the conservative aspect of Weil's largely radical political thinking. Presumably what we respect in these people is their responsibilies, and not their mere rank. Idle members of the British House of Lords have no rank in this hierarchy. |
| 23819 | Deliberate public lying should be punished [Weil] |
| Full Idea: Every avoidable material falsehood publicly asserted should become a punishable offence. | |
| From: Simone Weil (Draft Statement of Human Obligations [1943], p.228) | |
| A reaction: Yes please! The early 21st century has become the time when truth lost all value in public life. Lying to the House of Commons in the UK required instant resignation 50 years ago. Now it is just a source of laughter. No freedom to lie! |
| 23818 | We have liberty in the space between nature and accepted authority [Weil] |
| Full Idea: Liberty is the power of choice within the latitude left between the direct constraint of natural forces and the authority accepted as legitimate. | |
| From: Simone Weil (Draft Statement of Human Obligations [1943], p.228) | |
| A reaction: Accepting legitimate authority is a nicely softened version of the social contract. We often find that the office and rank are accepted as legitimate, but then are unable to accept the appalling individual who holds the office. |
| 23820 | People need personal and collective property, and a social class lacking property is shameful [Weil] |
| Full Idea: The human soul has need of both personal property and collective property. …The existence of a social class defined by the lack of personal and collective property is as shameful as slavery. | |
| From: Simone Weil (Draft Statement of Human Obligations [1943], p.229) | |
| A reaction: Nice. Particularly the idea that we all need collective property, such as parks and beaches and public buildings. |
| 23821 | Crime should be punished, to bring the perpetrator freely back to morality [Weil] |
| Full Idea: The human soul needs punishment and honour. A committer of crime has become exiled from good, and needs to be reintegrated with it through suffering. This aims to bring the soul to recognise freely some day that is infliction was just. | |
| From: Simone Weil (Draft Statement of Human Obligations [1943], p.229) | |
| A reaction: The Scanlon contractualist approach to punishment - that the victim of it accepts its justice. Given her saintly character, Simone had a very tough view of this issue. |
| 23816 | Attention to a transcendent reality motivates a duty to foster the good of humanity [Weil] |
| Full Idea: Anyone whose attention and love are directed towards the reality outside the world recognises that he is bound by the permanent obligation to remedy …all the privations of soul and body which are liable to destroy or damage any human being whatsoever. | |
| From: Simone Weil (Draft Statement of Human Obligations [1943], p.225) | |
| A reaction: [abridged] An interesting attempt to articulate the religious motivation of morality. The Euthyphro question remains - of why this vision of a wholly good higher morality should motivate anyone, unless they already possess a desire for that good. |