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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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20014
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Actions include: the involuntary, the purposeful, the intentional, and the self-consciously autonomous [Wilson/Schpall]
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Full Idea:
There are different levels of action, including at least: unconscious and/or involuntary behaviour, purposeful or goal-directed activity, intentional action, and the autonomous acts or actions of self-consciously active human agents.
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From:
Wilson,G/Schpall,S (Action [2012], 1)
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A reaction:
The fourth class is obviously designed to distinguish us from the other animals. It immediately strikes me as very optimistic to distinguish four (at least) clear categories, but you have to start somewhere.
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20019
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Maybe bodily movements are not actions, but only part of an agent's action of moving [Wilson/Schpall]
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Full Idea:
Some say that the movement's of agent's body are never actions. It is only the agent's direct moving of, say, his leg that constitutes a physical action; the leg movement is merely caused by and/or incorporated as part of the act of moving.
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From:
Wilson,G/Schpall,S (Action [2012], 1.2)
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A reaction:
[they cite Jennifer Hornsby 1980] It seems normal to deny a twitch the accolade of an 'action', so I suppose that is right. Does the continual movement of my tongue count as action? Only if I bring it under control? Does it matter? Only in forensics.
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20021
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Is the action the arm movement, the whole causal process, or just the trying to do it? [Wilson/Schpall]
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Full Idea:
Some philosophers have favored the overt arm movement the agent performs, some favor the extended causal process he initiates, and some prefer the relevant event of trying that precedes and 'generates' the rest.
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From:
Wilson,G/Schpall,S (Action [2012], 1.2)
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A reaction:
[Davidson argues for the second, Hornsby for the third] There seems no way to settle this, and a compromise looks best. Mere movement won't do, and mere trying won't do, and whole processes get out of control.
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20022
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To be intentional, an action must succeed in the manner in which it was planned [Wilson/Schpall]
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Full Idea:
If someone fires a bullet to kill someone, misses, and dislodges hornets that sting him to death, this implies that an intentional action must include succeeding in a manner according to the original plan.
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From:
Wilson,G/Schpall,S (Action [2012], 2)
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A reaction:
[their example, compressed] This resembles Gettier's problem cases for knowledge. If the shooter deliberately and maliciously brought down the hornet's nest, that would be intentional murder. Sounds right.
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20023
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If someone believes they can control the lottery, and then wins, the relevant skill is missing [Wilson/Schpall]
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Full Idea:
If someone enters the lottery with the bizarre belief that they can control who wins, and then wins it, that suggest that intentional actions must not depend on sheer luck, but needs competent exercise of the relevant skill.
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From:
Wilson,G/Schpall,S (Action [2012], 2)
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A reaction:
A nice companion to Idea 20022, which show that a mere intention is not sufficient to motivate and explain an action.
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20025
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We might intend two ways to acting, knowing only one of them can succeed [Wilson/Schpall]
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Full Idea:
If an agent tries to do something by two different means, only one of which can succeed, then the behaviour is rational, even though one of them is an attempt to do an action which cannot succeed.
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From:
Wilson,G/Schpall,S (Action [2012], 2)
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A reaction:
[a concise account of a laborious account of an example from Bratman 1984, 1987] Bratman uses this to challenge the 'Simple View', that intention leads straightforwardly to action.
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20031
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On one model, an intention is belief-desire states, and intentional actions relate to beliefs and desires [Wilson/Schpall]
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Full Idea:
On the simple desire-belief model, an intention is a combination of desire-belief states, and an action is intentional in virtue of standing in the appropriate relation to these simpler terms.
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From:
Wilson,G/Schpall,S (Action [2012], 4)
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A reaction:
This is the traditional view found in Hume, and is probably endemic to folk psychology. They cite Bratman 1987 as the main opponent of the view.
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20028
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Groups may act for reasons held by none of the members, so maybe groups are agents [Wilson/Schpall]
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Full Idea:
Rational group action may involve a 'collectivising of reasons', with participants acting in ways that are not rationally recommended from the individual viewpoint. This suggests that groups can be rational, intentional agents.
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From:
Wilson,G/Schpall,S (Action [2012], 2)
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A reaction:
[Pettit 2003] is the source for this. Gilbert says individuals can have joint commitment; Pettit says the group can be an independent agent. The matter of shared intentions is interesting, but there is no need for the ontology to go berserk.
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20027
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If there are shared obligations and intentions, we may need a primitive notion of 'joint commitment' [Wilson/Schpall]
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Full Idea:
An account of mutual obligation to do something may require that we give up reductive individualist accounts of shared activity and posit a primitive notion of 'joint commitment'.
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From:
Wilson,G/Schpall,S (Action [2012], 2)
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A reaction:
[attributed to Margaret Gilbert 2000] If 'we' are trying to do something, that seems to give an externalist picture of intentions, rather like all the other externalisms floating around these days. I don't buy any of it, me.
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20018
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Strong Cognitivism implies a mode of 'practical' knowledge, not based on observation [Wilson/Schpall]
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Full Idea:
Strong Cognitivists say intentions/beliefs are not based on observation or evidence, and are causally reliable in leading to appropriate actions, so this is a mode of 'practical' knowledge that has not been derived from observation.
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From:
Wilson,G/Schpall,S (Action [2012], 1.1)
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A reaction:
[compressed - Stanford unnecessarily verbose!] I see no mention in this discussion of 'hoping' that your action will turn out OK. We are usually right to hope, but it would be foolish to say that when we reach for the salt we know we won't knock it over.
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