29 ideas
| 10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
| Full Idea: It is often the case that the concern for rigor gets in the way of a true understanding of the phenomena to be explained. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
| A reaction: This is a counter to Timothy Williamson's love affair with rigour in philosophy. It strikes me as the big current question for analytical philosophy - of whether the intense pursuit of 'rigour' will actually deliver the wisdom we all seek. |
| 10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
| Full Idea: There is no stage at which we can take all the sets to have been generated, since the set of all those sets which have been generated at a given stage will itself give us something new. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
| Full Idea: We might combine the standard axioms of set theory with the standard axioms of mereology. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 17743 | De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki] |
| Full Idea: In 1846 De Morgan introduced the enormously influential notion of a possibly arbitrary and stipulated 'universe of discourse'. It replaced Boole's original - and metaphysically a bit suspect - universe of 'all things'. | |
| From: report of Augustus De Morgan (works [1846]) by Michal Walicki - Introduction to Mathematical Logic History D.1.1 | |
| A reaction: This not only brings formal logic under control, but also reflects normal talk, because there is always an explicit or implicit domain of discourse when we talk. Of virtually any conversation, you can say what it is 'about'. |
| 10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
| Full Idea: We are tempted to ask of second-order quantifiers 'what are you quantifying over?', or 'when you say "for some F" then what is the F?', but these questions already presuppose that the quantifiers are first-order. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005]) |
| 10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
| Full Idea: In doing semantics we normally assign some appropriate entity to each predicate, but this is largely for technical convenience. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
| Full Idea: Because of Dedekind's definition of reals by cuts, there is a bizarre modern doctrine that there are many 1's - the natural number 1, the rational number 1, the real number 1, and even the complex number 1. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
| A reaction: See Idea 10572. |
| 10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
| Full Idea: By what right can Dedekind suppose that there is a number corresponding to any pair of irrationals that constitute an irrational cut? | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
| Full Idea: What is the union of the singleton {0}, of zero, and the singleton {φ}, of the null set? Is it the one-element set {0}, or the two-element set {0, φ}? Unless the question of identity between 0 and φ is resolved, we cannot say. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
| Full Idea: Set-theoretic imperialists think that it must be possible to represent every mathematical object as a set. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
| Full Idea: Logicists traditionally claim that the theorems of mathematics can be derived by logical means from the relevant definitions of the terms, and that these theorems are epistemically innocent (knowable without Kantian intuition or empirical confirmation). | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
| Full Idea: It is natural to have a generative conception of abstracts (like the iterative conception of sets). The abstracts are formed at stages, with the abstracts formed at any given stage being the abstracts of those concepts of objects formed at prior stages. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
| A reaction: See 10567 for Fine's later modification. This may not guarantee 'levels', but it implies some sort of conceptual priority between abstract entities. |
| 10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
| Full Idea: Abstraction-theoretic imperialists think that it must be possible to represent every mathematical object as a Fregean abstract. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
| Full Idea: I propose a unified theory which is a version of ZF or ZFC with urelements, where the urelements are taken to be the abstracts. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
| Full Idea: Instead of viewing the abstracts (or sums) as being generated from objects, via the concepts from which they are defined, we can take them to be generated from conditions. The number of the universe ∞ is the number of self-identical objects. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
| A reaction: The point is that no particular object is now required to make the abstraction. |
| 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). |