24 ideas
| 13591 | Quantified modal logic collapses if essence is withdrawn [Quine] |
| Full Idea: The whole of quantified modal logic collapses if essence is withdrawn. | |
| From: Willard Quine (Intensions Revisited [1977], p.121) | |
| A reaction: Quine offers an interesting qualification to this crushing remark in Idea 13590. The point is that objects must retain their identity in modal contexts, as if I say 'John Kennedy might have been Richard Nixon'. What could that mean? |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 13590 | Essences can make sense in a particular context or enquiry, as the most basic predicates [Quine] |
| Full Idea: The notion of essence makes sense in context. Relative to a particular enquiry, some predicates may play a more basic role than others, or may apply more fixedly; and these may be treated as essential. | |
| From: Willard Quine (Intensions Revisited [1977], p.121) | |
| A reaction: Quine has got a bad press on essentialism, and on modal logic, but I take this point seriously. If you give something a fixed identity by means of essence in some context, you can then go ahead and apply possible world reasoning in that context. |
| 8483 | Necessity is relative to context; it is what is assumed in an inquiry [Quine] |
| Full Idea: The very notion of necessity makes sense to me only relative to context. Typically it is applied to what is assumed in an inquiry, as against what has yet to transpire. | |
| From: Willard Quine (Intensions Revisited [1977], p.121) | |
| A reaction: Lots of things are assumed by an inquiry without an assumption that they must be true. Quine is the greatest opponent of necessity in all of philosophy. Asserting necessities, though, is too much fun to give up. It would ruin philosophy. |
| 13589 | Possible worlds are a way to dramatise essentialism, and yet they presuppose essentialism [Quine] |
| Full Idea: Talk of possible worlds is a graphic way of waging the essentialist philosophy, but it is only that; it is not an explication. Essence is needed to identify an object from one possible world to another. | |
| From: Willard Quine (Intensions Revisited [1977], p.118) | |
| A reaction: He makes the proposal sound circular, but I take a commitment to essences to be prior to talk of possible worlds. Possible worlds are a tool for clarifying modalities, not for clarifying essential identities. |
| 13588 | A rigid designator (for all possible worlds) picks out an object by its essential traits [Quine] |
| Full Idea: A rigid designator differs from others in that it picks out its object by essential traits. It designates the object in all possible worlds in which it exists. | |
| From: Willard Quine (Intensions Revisited [1977], p.118) | |
| A reaction: This states the point more clearly than Kripke ever does, and I presume it is right. Thus when we say that we wish 'our' Hubert Humphrey had won the election, we can allow that his victory elation would change him a bit. Kripke is right. |
| 13592 | Beliefs can be ascribed to machines [Quine] |
| Full Idea: Beliefs have been ascribed to machines, in support of a mechanistic philosophy, and I share this attitude. | |
| From: Willard Quine (Intensions Revisited [1977], p.123) | |
| A reaction: [He cites Raymond Nelson] One suspects that this is Quine's latent behaviourism speaking. It strikes me as a crass misuse of 'belief' to ascribe it to a simple machine like a thermostat. |
| 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. |
| 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. |