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All the ideas for 'Action', 'What is Cantor's Continuum Problem?' and 'Philosophy of Mind (Encylopedia III)'

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23 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
We perceive the objects of set theory, just as we perceive with our senses [Gödel]
     Full Idea: We have something like perception of the objects of set theory, shown by the axioms forcing themselves on us as being true. I don't see why we should have less confidence in this kind of perception (i.e. mathematical intuition) than in sense perception.
     From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.483), quoted by Michčle Friend - Introducing the Philosophy of Mathematics 2.4
     A reaction: A famous strong expression of realism about the existence of sets. It is remarkable how the ingredients of mathematics spread themselves before the mind like a landscape, inviting journeys - but I think that just shows how minds cope with abstractions.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
     Full Idea: Gödel proved the classical relative consistency of the axiom V = L (which implies the axiom of choice and the generalized continuum hypothesis). This established the full independence of the continuum hypothesis from the other axioms.
     From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Hilary Putnam - Mathematics without Foundations
     A reaction: Gödel initially wanted to make V = L an axiom, but the changed his mind. Maddy has lots to say on the subject.
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
Set-theory paradoxes are no worse than sense deception in physics [Gödel]
     Full Idea: The set-theoretical paradoxes are hardly any more troublesome for mathematics than deceptions of the senses are for physics.
     From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.271), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 03.4
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
     Full Idea: Gödel proved that the Continuum Hypothesis was not inconsistent with the axioms of set theory.
     From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15
If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
     Full Idea: Gödel proved that (if set theory is consistent) we cannot refute the continuum hypothesis, and Cohen proved that (if set theory is consistent) we cannot prove it either.
     From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by William D. Hart - The Evolution of Logic 10
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
     Full Idea: Evidently the 'given' underlying mathematics is closely related to the abstract elements contained in our empirical ideas.
     From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], Suppl)
     A reaction: Yes! The great modern mathematical platonist says something with which I can agree. He goes on to hint at a platonic view of the structure of the empirical world, but we'll let that pass.
16. Persons / F. Free Will / 2. Sources of Free Will
Freedom is produced by the activity of the mind, and is not intrinsically given [Hegel]
     Full Idea: Actual freedom is not something immediately existent in mindedness, but is something to be produced by the mind's own activity. It is thus as the producer of its freedom that we have to consider mindedness in philosophy.
     From: Georg W.F.Hegel (Philosophy of Mind (Encylopedia III) [1817], §382, Zusatz), quoted by Terry Pinkard - German Philosophy 1760-1860 11
     A reaction: Pinkard glosses this as an agent being free by being the centre of a group of social responsibilities. Hence I presume small children have no freedom. Presumably we could deprive citizens of all responsibility, and hence of metaphysical freedom.
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
Geist is distinct from nature, not as a substance, but because of its normativity [Hegel, by Pinkard]
     Full Idea: Hegel argued that it was the impossibility of a naturalistic account of normativity that distinguished Geist from nature, not Geist's being any kind of metaphysical substance.
     From: report of Georg W.F.Hegel (Philosophy of Mind (Encylopedia III) [1817]) by Terry Pinkard - German Philosophy 1760-1860 11
     A reaction: Hegel always seems to want to have his cake and eat it. Without a mental substance, how can Geist not be part of nature? What is Geist made of? Is his view functionalist? But that is usually naturalistic. Is normativity magic?
20. Action / A. Definition of Action / 1. Action Theory
Actions include: the involuntary, the purposeful, the intentional, and the self-consciously autonomous [Wilson/Schpall]
     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.
     From: Wilson,G/Schpall,S (Action [2012], 1)
     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.
20. Action / A. Definition of Action / 4. Action as Movement
Maybe bodily movements are not actions, but only part of an agent's action of moving [Wilson/Schpall]
     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.
     From: Wilson,G/Schpall,S (Action [2012], 1.2)
     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.
Is the action the arm movement, the whole causal process, or just the trying to do it? [Wilson/Schpall]
     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.
     From: Wilson,G/Schpall,S (Action [2012], 1.2)
     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.
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
To be intentional, an action must succeed in the manner in which it was planned [Wilson/Schpall]
     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.
     From: Wilson,G/Schpall,S (Action [2012], 2)
     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.
If someone believes they can control the lottery, and then wins, the relevant skill is missing [Wilson/Schpall]
     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.
     From: Wilson,G/Schpall,S (Action [2012], 2)
     A reaction: A nice companion to Idea 20022, which show that a mere intention is not sufficient to motivate and explain an action.
We might intend two ways to acting, knowing only one of them can succeed [Wilson/Schpall]
     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.
     From: Wilson,G/Schpall,S (Action [2012], 2)
     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.
20. Action / B. Preliminaries of Action / 1. Intention to Act / c. Reducing intentions
On one model, an intention is belief-desire states, and intentional actions relate to beliefs and desires [Wilson/Schpall]
     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.
     From: Wilson,G/Schpall,S (Action [2012], 4)
     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.
20. Action / B. Preliminaries of Action / 1. Intention to Act / d. Group intentions
Groups may act for reasons held by none of the members, so maybe groups are agents [Wilson/Schpall]
     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.
     From: Wilson,G/Schpall,S (Action [2012], 2)
     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.
If there are shared obligations and intentions, we may need a primitive notion of 'joint commitment' [Wilson/Schpall]
     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'.
     From: Wilson,G/Schpall,S (Action [2012], 2)
     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.
20. Action / C. Motives for Action / 2. Acting on Beliefs / b. Action cognitivism
Strong Cognitivism identifies an intention to act with a belief [Wilson/Schpall]
     Full Idea: A Strong Cognitivist is someone who identifies an intention with a certain pertinent belief about what she is doing or about to do.
     From: Wilson,G/Schpall,S (Action [2012], 1.1)
     A reaction: (Sarah Paul 2009 makes this distinction) The belief, if so, seems to be as much counterfactual as factual. Hope seems to come into it, which isn't exactly a belief.
Weak Cognitivism says intentions are only partly constituted by a belief [Wilson/Schpall]
     Full Idea: A Weak Cognitivist holds that intentions are partly constituted by, but are not identical with, relevant beliefs about the action. Grice (1971) said an intention is willing an action, combined with a belief that this will lead to the action.
     From: Wilson,G/Schpall,S (Action [2012], 1.1)
     A reaction: [compressed] I didn't find Strong Cognitivism appealing, but it seems hard to argue with some form of the weak version.
Strong Cognitivism implies a mode of 'practical' knowledge, not based on observation [Wilson/Schpall]
     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.
     From: Wilson,G/Schpall,S (Action [2012], 1.1)
     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.
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
Maybe the explanation of an action is in the reasons that make it intelligible to the agent [Wilson/Schpall]
     Full Idea: Some have maintained that we explain why an agent acted as he did when we explicate how the agent's normative reasons rendered the action intelligible in his eyes.
     From: Wilson,G/Schpall,S (Action [2012], Intro)
     A reaction: Modern psychology is moving against this, by showing how hidden biases can predominate over conscious reasons (as in Kahnemann's work). I would say this mode of explanation works better for highly educated people (but you can chuckle at that).
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Causalists allow purposive explanations, but then reduce the purpose to the action's cause [Wilson/Schpall]
     Full Idea: Most causalists allow that reason explanations are teleological, but say that such purposive explanations are analysable causally, where the primary reasons for the act are the guiding causes of the act.
     From: Wilson,G/Schpall,S (Action [2012], 3)
     A reaction: The authors observe that it is hard to adjudicate on this matter, and that the concept of the 'cause' of an action is unclear.
It is generally assumed that reason explanations are causal [Wilson/Schpall]
     Full Idea: The view that reason explanations are somehow causal explanations remains the dominant position.
     From: Wilson,G/Schpall,S (Action [2012], Intro)
     A reaction: I suspect that this is only because no philosopher has a better idea, and the whole issue is being slowly outflanked by psychology.