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14234
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If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
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Full Idea:
A 'singularist', who refers to objects one at a time, must resort to the language of sets in order to replace plural reference to members ('Henry VIII's wives') by singular reference to a set ('the set of Henry VIII's wives').
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From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro)
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A reaction:
A simple and illuminating point about the motivation for plural reference. Null sets and singletons give me the creeps, so I would personally prefer to avoid set theory when dealing with ontology.
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14237
|
We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
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Full Idea:
Plurals earn their keep in set theory, to answer Skolem's remark that 'in order to treat of 'sets', we must begin with 'domains' that are constituted in a certain way'. We can speak in the plural of 'the objects', not a 'domain' of objects.
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From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro)
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A reaction:
[Skolem 1922:291 in van Heijenoort] Zermelo has said that the domain cannot be a set, because every set belongs to it.
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14246
|
If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
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Full Idea:
If mathematics was purely concerned with mathematical objects, there would be no room for applied mathematics.
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From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1)
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A reaction:
Love it! Of course, they are using 'objects' in the rather Fregean sense of genuine abstract entities. I don't see why fictionalism shouldn't allow maths to be wholly 'pure', although we have invented fictions which actually have application.
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14247
|
Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
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Full Idea:
Identifying numbers with sets may mean one of three quite different things: 1) the sets represent the numbers, or ii) they are the numbers, or iii) they replace the numbers.
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From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.2)
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A reaction:
Option one sounds the most plausible to me. I will take numbers to be patterns embedded in nature, and sets are one way of presenting them in shorthand form, in order to bring out what is repeated.
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16703
|
God could make a successive thing so that previous parts cease to exist [Albert of Saxony]
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Full Idea:
Something can be conceived of as successive simpliciter, with respect to both its substance and its state. For example, if Socrates were continually made and made again by the First Cause, as the Seine flow, so nothing of what preexists remains.
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From:
Albert of Saxony (On 'Physics' [1357], III.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.4
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A reaction:
This is precisely the problem that modern stage theory faces, of knowing how to connect the stages together.
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16699
|
Successive entities just need parts to succeed one another, without their existence [Albert of Saxony]
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Full Idea:
For existence to hold of completely successive entities it is not required that their parts exist, but that one part succeed another, as a future part succeeds a past part.
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From:
Albert of Saxony (On 'Physics' [1357], III.3 ad 2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.3
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A reaction:
A nice move, but it doesn't quite solve it. How can non-existent things 'succeed one another'? It is worrying for metaphysics that some things have entirely different concepts of persistence from other things.
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2748
|
A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]
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Full Idea:
Nozick says Gettier cases aren't knowledge because the proposition would be believed even if false. Proper justification must be more sensitive to the truth ("track the truth").
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From:
report of Robert Nozick (Philosophical Explanations [1981], 3.1) by Jonathan Dancy - Intro to Contemporary Epistemology 3.1
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A reaction:
This is a bad idea. I see a genuine tree in my garden and believe it is there, so I know it. That I might have believed it if I was in virtually reality, or observing a mirror, won't alter that.
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22662
|
In the instrumental view of rationality it only concerns means, and not ends [Nozick]
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Full Idea:
On the instrumental conception of rationality, it consists in the effective and efficient achievement of goals, ends, and desires. About the goals themselves it has little to say.
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From:
Robert Nozick (The Nature of Rationality [1993], p.64)
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A reaction:
[He quotes Russell 1954 p.viii as expressing this view] A long way from Greek logos, which obviously concerns the rational selection of right ends (for which, presumably, reasons can be given). In practice our ends may never be rational, of course.
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22667
|
Rationality needs some self-consciousness, to also evaluate how we acquired our reasons [Nozick]
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Full Idea:
Rationality involves some degree of self-consciousness. Not only reasons are evaluated, but also the processes by which information arrives, is stored, and recalled.
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From:
Robert Nozick (The Nature of Rationality [1993], p.74)
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A reaction:
I defend the idea that animals have a degree of rationality, because they can make sensible judgements, but I cannot deny this idea. Rationality comes in degrees, and second-level thought is a huge leap forward in degree.
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20585
|
If an experience machine gives you any experience you want, should you hook up for life? [Nozick]
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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?
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From:
Robert Nozick (Anarchy,State, and Utopia [1974], 3 'Experience')
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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.
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18643
|
A minimal state should protect, but a state forcing us to do more is unjustified [Nozick]
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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.
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|
From:
Robert Nozick (Anarchy,State, and Utopia [1974], Pref)
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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.
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18642
|
Individual rights are so strong that the state and its officials must be very limited in power [Nozick]
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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.
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|
From:
Robert Nozick (Anarchy,State, and Utopia [1974], Pref)
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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).
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18644
|
States can't enforce mutual aid on citizens, or interfere for their own good [Nozick]
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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.
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|
From:
Robert Nozick (Anarchy,State, and Utopia [1974], Pref)
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|
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?
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22661
|
My Anarchy, State and Utopia neglected our formal social ties and concerns [Nozick on Nozick]
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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.
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|
From:
comment on Robert Nozick (Anarchy,State, and Utopia [1974], p.32) by Robert Nozick - The Nature of Rationality p.32
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|
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?
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18641
|
If people hold things legitimately, just distribution is simply the result of free exchanges [Nozick, by Kymlicka]
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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.
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|
From:
report of Robert Nozick (Anarchy,State, and Utopia [1974]) by Will Kymlicka - Contemporary Political Philosophy (1st edn) 4.1.b
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|
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.
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20539
|
Property is legitimate by initial acquisition, voluntary transfer, or rectification of injustice [Nozick, by Swift]
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Full Idea:
Nozick identified three ways in which people can acquire a legitimate property holding: initial acquisition, voluntary transfer, and rectification (of unjust transfers).
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|
From:
report of Robert Nozick (Anarchy,State, and Utopia [1974]) by Adam Swift - Political Philosophy (3rd ed) 1 'Nozick'
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|
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'?
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18646
|
How did the private property get started? If violence was involved, we can redistribute it [Kymlicka on Nozick]
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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.
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|
From:
comment on Robert Nozick (Anarchy,State, and Utopia [1974]) by Will Kymlicka - Contemporary Political Philosophy (1st edn) 4.2.b
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|
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?
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21737
|
Unowned things may be permanently acquired, if it doesn't worsen the position of other people [Nozick]
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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.
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|
From:
Robert Nozick (Anarchy,State, and Utopia [1974], p.178), quoted by G.A. Cohen - Are Freedom and Equality Compatible? 2
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|
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?
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21738
|
Maybe land was originally collectively owned, rather than unowned? [Cohen,GA on Nozick]
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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
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|
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).
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