24 ideas
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| Full Idea: Boolos's conception of plural logic is as a reinterpretation of second-order logic. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Oliver,A/Smiley,T - What are Sets and What are they For? n5 | |
| A reaction: Oliver and Smiley don't accept this view, and champion plural reference differently (as, I think, some kind of metalinguistic device?). |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| Full Idea: The metatheory of second-order logic is hopelessly set-theoretic, and the notion of second-order validity possesses many if not all of the epistemic debilities of the notion of set-theoretic truth. | |
| From: George Boolos (On Second-Order Logic [1975], p.45) | |
| A reaction: Epistemic problems arise when a logic is incomplete, because some of the so-called truths cannot be proved, and hence may be unreachable. This idea indicates Boolos's motivation for developing a theory of plural quantification. |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| Full Idea: One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts. | |
| From: George Boolos (On Second-Order Logic [1975], p.44) | |
| A reaction: My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction? |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| Full Idea: One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed. | |
| From: George Boolos (On Second-Order Logic [1975], p.46) | |
| A reaction: This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain. |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| Full Idea: A weak completeness theorem shows that a sentence is provable whenever it is valid; a strong theorem, that a sentence is provable from a set of sentences whenever it is a logical consequence of the set. | |
| From: George Boolos (On Second-Order Logic [1975], p.52) | |
| A reaction: So the weak version says |- φ → |= φ, and the strong versions says Γ |- φ → Γ |= φ. Presumably it is stronger if it can specify the source of the inference. |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| Full Idea: Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13 |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| Full Idea: The notions of infinity and countability can be characterized by second-order sentences, though not by first-order sentences (as compactness and Skolem-Löwenheim theorems show), .. as well as well-ordering, progression, ancestral and identity. | |
| From: George Boolos (On Second-Order Logic [1975], p.48) |
| 14979 | Being alone doesn't guarantee intrinsic properties; 'being alone' is itself extrinsic [Lewis, by Sider] |
| Full Idea: The property of 'being alone in the world' is an extrinsic property, even though it has had by an object that is alone in the world. | |
| From: report of David Lewis (Extrinsic Properties [1983]) by Theodore Sider - Writing the Book of the World 01.2 | |
| A reaction: I always choke on my cornflakes whenever anyone cites a true predicate as if it were a genuine property. This is a counterexample to Idea 14978. Sider offers another more elaborate example from Lewis. |
| 15454 | Extrinsic properties come in degrees, with 'brother' less extrinsic than 'sibling' [Lewis] |
| Full Idea: Properties may be more or less intrinsic; being a brother has more of an admixture of intrinsic structure than being a sibling does, yet both are extrinsic. | |
| From: David Lewis (Extrinsic Properties [1983], I) | |
| A reaction: I suppose the point is that a brother is intrinsically male - but then a sibling is intrinsically human. A totally extrinsic relation would be one between entities which shared virtually no categories of existence. |
| 15455 | Total intrinsic properties give us what a thing is [Lewis] |
| Full Idea: The way something is is given by the totality of its intrinsic properties. | |
| From: David Lewis (Extrinsic Properties [1983], I) | |
| A reaction: No. Some properties are intrinsic but trivial. The 'important' ones fix the identity (if the identity is indeed 'fixed'). |
| 18648 | Freedom to live according to our own conception of the good is the ultimate value [Nozick, by Kymlicka] |
| Full Idea: Nozick says that the freedom to lead our lives in accordance with our own conception of the good is the ultimate value, so important that it cannot be sacrificed for other social ideals (e.g. equality of opportunity). | |
| From: report of Robert Nozick (Anarchy,State, and Utopia [1974]) by Will Kymlicka - Contemporary Political Philosophy (1st edn) 4.2.b.ii | |
| A reaction: Clearly this ultimate value will not apply to children, so this view needs a sharp dislocation between children and adults. But some adults need a lot of looking after. Maybe we ALL need looking after (by one another)? |
| 20585 | If an experience machine gives you any experience you want, should you hook up for life? [Nozick] |
| Full Idea: Suppose there were an experience machine that would give you any experience you desired ...such as writing a great novel, or making a friend, or reading an interesting book. ...Should you plug into this machine for life? | |
| From: Robert Nozick (Anarchy,State, and Utopia [1974], 3 'Experience') | |
| A reaction: A classic though experiment which crystalises a major problem with hedonistic utilitarianism. My addition is a machine which maximises the pleasure of my family and friends, to save me the bother of doing it. |
| 18643 | A minimal state should protect, but a state forcing us to do more is unjustified [Nozick] |
| Full Idea: A minimal state, limited to the narrow functions of protection against force, theft, fraud, enforcement of contracts, and so on, is justified; any more extensive state will violate persons' rights not to be forced to do certain things, and is unjustified. | |
| From: Robert Nozick (Anarchy,State, and Utopia [1974], Pref) | |
| A reaction: This has some plausibility for a huge modern state, where we don't know one another, but it would be a ridiculous attitude in a traditional village. |
| 18642 | Individual rights are so strong that the state and its officials must be very limited in power [Nozick] |
| Full Idea: Individuals have rights, and there are things no person or group may do to them (without violating their rights). So strong and far-reaching are these rights that they raise the question of what, if anything, the state and its officials may do. | |
| From: Robert Nozick (Anarchy,State, and Utopia [1974], Pref) | |
| A reaction: This claim appears to be an axiom, but I'm not sure that the notion of 'rights' make any sense unless someone is granting the rights, where the someone is either a strong individual, or the community (perhaps represented by the state). |
| 18644 | States can't enforce mutual aid on citizens, or interfere for their own good [Nozick] |
| Full Idea: A state may not use its coercive apparatus for the purposes of getting some citizens to aid others, or in order to prohibit activities to people for their own good or protection. | |
| From: Robert Nozick (Anarchy,State, and Utopia [1974], Pref) | |
| A reaction: You certainly can't apply these principles to children, so becoming an 'adult' seems to be a very profound step in Nozick's account. At what age must we stop interfering with people for their own good. If the state is prohibited, are neighbours also? |
| 22661 | My Anarchy, State and Utopia neglected our formal social ties and concerns [Nozick on Nozick] |
| Full Idea: The political philosophy represented in Anarchy, State and Utopia ignored the importance of joint and official symbolic statement and expression of our social ties and concern, and hence (I have written) is inadequate. | |
| From: comment on Robert Nozick (Anarchy,State, and Utopia [1974], p.32) by Robert Nozick - The Nature of Rationality p.32 | |
| A reaction: In other words, it was far too individualistic, and neglected community, even though it has become the sacred text for libertarian individualism. Do any Nozick fans care about this recantation? |
| 18641 | If people hold things legitimately, just distribution is simply the result of free exchanges [Nozick, by Kymlicka] |
| Full Idea: If we assume that everyone is entitled to the goods they currently possess (their 'holdings'), then a just distribution is simply whatever distribution results from people's free exchanges. | |
| From: report of Robert Nozick (Anarchy,State, and Utopia [1974]) by Will Kymlicka - Contemporary Political Philosophy (1st edn) 4.1.b | |
| A reaction: If people's current 'legitimate' holdings are hugely unequal, it seems very unlikely that the ensuing exchanges will be 'free' in the way that Nozick envisages. |
| 20539 | Property is legitimate by initial acquisition, voluntary transfer, or rectification of injustice [Nozick, by Swift] |
| Full Idea: Nozick identified three ways in which people can acquire a legitimate property holding: initial acquisition, voluntary transfer, and rectification (of unjust transfers). | |
| From: report of Robert Nozick (Anarchy,State, and Utopia [1974]) by Adam Swift - Political Philosophy (3rd ed) 1 'Nozick' | |
| A reaction: I think it is a delusion to look for justice in the ownership of property. You can't claim justice for buying property if the money to do it was acquired unjustly. And what rights over those who live on the land come with the 'ownership'? |
| 18645 | Nozick assumes initial holdings include property rights, but we can challenge that [Kymlicka on Nozick] |
| Full Idea: Nozick assumes that the initial distribution of holdings includes full property-rights over them, ..but our preferred theory may not involve distributing such particular rights to particular people. ...The legitimacy of such rights is what is in question. | |
| From: comment on Robert Nozick (Anarchy,State, and Utopia [1974]) by Will Kymlicka - Contemporary Political Philosophy (1st edn) 4.1.c | |
| A reaction: [somewhat compressed] All of these political philosophies seem to have questionable values (such as freedom or equality) built into their initial assumptions. |
| 20521 | Can I come to own the sea, by mixing my private tomato juice with it? [Nozick] |
| Full Idea: If I own a can of tomato juice and spill it in the sea so that its molecules mingle evenly throughout the sea, do I thereby come to own the sea? | |
| From: Robert Nozick (Anarchy,State, and Utopia [1974], p.175) | |
| A reaction: This is a reductio of Locke's claim that I can own land by 'mixing' my labour with it. At first glance, mixing something with something would seem to have nothing to do with ownership. |
| 18646 | How did the private property get started? If violence was involved, we can redistribute it [Kymlicka on Nozick] |
| Full Idea: How did these natural resources, which were not initially owned by anyone, come to be part of someone's private property? ...The fact that the initial acquisition often involved force means there is no moral objection to redistributing existing wealth. | |
| From: comment on Robert Nozick (Anarchy,State, and Utopia [1974]) by Will Kymlicka - Contemporary Political Philosophy (1st edn) 4.2.b | |
| A reaction: [He cites G.A. Cphen 1988 for the second point] Put like this, Nozick's theory just looks like the sort of propaganda which is typically put out by the winners. Is there an implicit threat of violent resistance in his advocacy of individual rights? |
| 18647 | If property is only initially acquired by denying the rights of others, Nozick can't get started [Kymlicka on Nozick] |
| Full Idea: If there is no way that people can appropriate unowned resources for themselves without denying other people's claim to equal consideration, then Nozick's right of transfer never gets off the ground. | |
| From: comment on Robert Nozick (Anarchy,State, and Utopia [1974]) by Will Kymlicka - Contemporary Political Philosophy (1st edn) 4.2.b.i | |
| A reaction: The actual history of these things is too complex to judge. Early peoples desperately wanted a lord to rule over them, and their lord's ownership of the land implied the people's right to live there. See Anglo-Saxon poetry. |
| 21737 | Unowned things may be permanently acquired, if it doesn't worsen the position of other people [Nozick] |
| Full Idea: One may acquire a permanent bequeathable property right in a previously unowned thing, as long as the position of others no longer at liberty to use the thing is not thereby worsened. | |
| From: Robert Nozick (Anarchy,State, and Utopia [1974], p.178), quoted by G.A. Cohen - Are Freedom and Equality Compatible? 2 | |
| A reaction: Cohen attacks this vigorously. His main point is that Nozick has a very narrow view of what the acquisition should be compared with. There are many alternatives. Does being made unable to improve something 'worsen' a person's condition? |
| 21738 | Maybe land was originally collectively owned, rather than unowned? [Cohen,GA on Nozick] |
| Full Idea: Why should we not regard land as originally collectively owned rather than, as Nozick takes for granted, owned by no one? | |
| From: comment on Robert Nozick (Anarchy,State, and Utopia [1974], p.178) by G.A. Cohen - Are Freedom and Equality Compatible? 2 | |
| A reaction: Did native Americans and Australians collectively own the land? Lots of peoples, I suspect, don't privately own anything, because the very concept has never occured to them (and they have no legal system). |