13 ideas
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 23218 | The brain has no responsibility for sensations, which occur in the heart [Aristotle] |
| Full Idea: And of course, the brain is not responsible for any of the sensations at all. The correct view is that the seat and source of sensation is the region of the heart. | |
| From: Aristotle (The Parts of Animals [c.345 BCE]), quoted by Matthew Cobb - The Idea of the Brain 1 | |
| A reaction: [Need a reference] Hippocrates's assertion a century earlier made no impression on the great man. I wish he had been a little more circumspect with his own view. |
| 22687 | Maybe literary assessment is evaluating the artist as a suitable friend [Gaut] |
| Full Idea: An approach in Hume (elaborated by Wayne Booth) holds that literary assessment is akin to an act of befriending, for one assesses the author of a work as a suitable friend. | |
| From: Berys Gaut (The Ethical Criticism of Art [1998], 'Some') | |
| A reaction: I like the idea that art exploits our normal range of social emotions and attitudes, so I think this has some truth, but some of the best artists are so out of my league as to not even be candidates for friendship. Dostoevsky? Webster? Caravaggio? |
| 22686 | Formalists say aesthetics concerns types of beauty, or unity, complexity and intensity [Gaut] |
| Full Idea: The formal objects which individuate the aesthetic attitude may be narrowly aesthetic, as beauty, and its subspecies, such as grace and elegance, or more broadly by other formalist criteria, such as Beardley's unity, complexity and intensity. | |
| From: Berys Gaut (The Ethical Criticism of Art [1998], 'Objections 1') | |
| A reaction: I'm not sure about unity or complexity, but intensity was endorsed by Henry James. Intensity doesn't sound very 'formal'. 'Beauty' doesn't seem the right word for the wonderful 'King Lear', or even for Jane Austen novels. |
| 22690 | 'Moralism' says all aesthetic merits are moral merits [Gaut] |
| Full Idea: The view that the only aesthetic merit of works are ethical ones is known as 'moralism'. | |
| From: Berys Gaut (The Ethical Criticism of Art [1998], n 1) | |
| A reaction: [He says this view was demolished by R.W.Beardsmore in 1971] Gaut contrasts this with his own carefully modulated 'ethicism'. Moralism predominated in the eighteenth century, but now looks clearly wrong (or naďve). |
| 22684 | Good ethics counts towards aesthetic merit, and bad ethics counts against it [Gaut] |
| Full Idea: I defend 'ethicism', which says that ethically admirable attitudes count toward the the aesthetic merit of a work, and ethically reprehensible attitudes count against its aesthetic merit. | |
| From: Berys Gaut (The Ethical Criticism of Art [1998], 'Ethicism') | |
| A reaction: He recognises that morally admirable works can explore unethical behaviour, and also that identifying the 'attitude' of a work is not simple. The ethics are not necessary. 'Triumph of the Will' is a classic test case. I disagree with Gaut. |
| 22689 | If we don't respond ethically in the way a work prescribes, that is an aesthetic failure [Gaut] |
| Full Idea: Our having reason not to respond in the way prescribed (because it is unethical) is a failure of the work …so that is an aesthetic failure, which is an aesthetic defect. | |
| From: Berys Gaut (The Ethical Criticism of Art [1998], 'Merited') | |
| A reaction: A key argument for Gaut's theory of 'ethicism' about literature. If 'Triumph of the Will' gets the right response from Nazi sympathisers, that is probably all aesthetic success. Jane Austen hasn't failed if she is rejected as bourgeois. |
| 22685 | Good art does not necessarily improve people (any more than good advice does) [Gaut] |
| Full Idea: Ethicism does not entail the causal thesis that good art ethically improves people, …any more than it follows that earnest ethical advice improves people. | |
| From: Berys Gaut (The Ethical Criticism of Art [1998], 'Ethicism') | |
| A reaction: How successful were sermons, in the great days of Christianity? It seems hard to disagree with Gaut's point. |