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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
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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
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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
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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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2854
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Prescriptivism says 'ought' without commitment to act is insincere, or weakly used [Hooker,B]
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Full Idea:
Prescriptivism holds that if you think one 'ought' to do a certain kind of act, and yet you are not committed to doing that act in the relevant circumstances, then you either spoke insincerely, or are using the word 'ought' in a weak sense.
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From:
Brad W. Hooker (Prescriptivism [1995], p.640)
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A reaction:
So that's an 'ought', but not a 'genuine ought', then? (No True Scotsman move). Someone ought to rescue that drowning child, but I can't be bothered.
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20883
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Modern utilitarians value knowledge, friendship, autonomy, and achievement, as well as pleasure [Hooker,B]
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Full Idea:
Most utilitarians now think that pleasure, even if construed widely, is not the only thing desirable in itself. ...Goods also include important knowledge, friendship, autonomy, achievement and so on.
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From:
Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 2)
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A reaction:
That pleasure is desired is empirically verifiable, which certainly motivated Bentham. A string of other desirables each needs to be justified - but how? What would be the value of a 'friendship' if neither party got pleasure from it?
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20885
|
Euthanasia is active or passive, and voluntary, non-voluntary or involuntary [Hooker,B]
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Full Idea:
Six types of euthanasia: 1) Active voluntary (knowing my wishes), 2) Active non-voluntary (not knowing my wishes), 3) Active involuntary (against my wishes), 4) Passive voluntary, 5) Passive non-voluntary, 6) Passive involuntary.
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From:
Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 5)
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A reaction:
'Active' is intervening, and 'passive' is not intervening. A helpful framework.
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20882
|
Euthanasia may not involve killing, so it is 'killing or not saving, out of concern for that person' [Hooker,B]
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Full Idea:
Passive euthanasia is arguably not killing, and the death involved is often painful, so let us take the term 'euthanasia' to mean 'either killing or passing up opportunities to save someone, out of concern for that person'.
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From:
Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 1)
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A reaction:
This sounds good, and easily settled, until you think concern for that person could have two different outcomes, depending on whether the criteria are those of the decider or of the patient. Think of religious decider and atheist patient, or vice versa.
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