18 ideas
| 22701 | Jokes can sometimes be funny because they are offensive [Jacobson,D] |
| Full Idea: Sometimes it is exactly what is offensive about a joke that makes it funny. | |
| From: Daniel Jacobson (Ethical Criticism and the Vice of Moderation [2006], 'emotional') | |
| A reaction: Jacobson offers this in support of his immoralist view, that immoral literature can be aesthetically successful. It is uncomfortable to find yourself laughing at a joke of which you disapprove. |
| 10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
| Full Idea: Late nineteenth century mathematicians said that, although plus, minus and 0 could not be precisely defined, they could be partially 'implicitly defined' as a group. This nonsense was rejected by Frege and others, as expressed in Russell 1903. | |
| From: Wilfrid Hodges (Model Theory [2005], 2) | |
| A reaction: [compressed] This is helpful in understanding what is going on in Frege's 'Grundlagen'. I won't challenge Hodges's claim that such definitions are nonsense, but there is a case for understanding groups of concepts together. |
| 10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
| Full Idea: In first-order languages the completeness theorem tells us that T |= φ holds if and only if there is a proof of φ from T (T |- φ). Since the two symbols express the same relationship, theorist often just use |- (but only for first-order!). | |
| From: Wilfrid Hodges (Model Theory [2005], 3) | |
| A reaction: [actually no spaces in the symbols] If you are going to study this kind of theory of logic, the first thing you need to do is sort out these symbols, which isn't easy! |
| 10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
| Full Idea: If every structure which is a model of a set of sentences T is also a model of one of its sentences φ, then this is known as the model-theoretic consequence relation, and is written T |= φ. Not to be confused with |= meaning 'satisfies'. | |
| From: Wilfrid Hodges (Model Theory [2005], 3) | |
| A reaction: See also Idea 10474, which gives the other meaning of |=, as 'satisfies'. The symbol is ALSO used in propositional logical, to mean 'tautologically implies'! Sort your act out, logicians. |
| 10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
| Full Idea: The symbol in 'I |= S' reads that if the interpretation I (about word meaning) happens to make the sentence S state something true, then I 'is a model for' S, or I 'satisfies' S. | |
| From: Wilfrid Hodges (Model Theory [2005], 1) | |
| A reaction: Unfortunately this is not the only reading of the symbol |= [no space between | and =!], so care and familiarity are needed, but this is how to read it when dealing with models. See also Idea 10477. |
| 10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
| Full Idea: Model theory is the study of the interpretation of any language, formal or natural, by means of set-theoretic structures, with Tarski's truth definition as a paradigm. | |
| From: Wilfrid Hodges (Model Theory [2005], Intro) | |
| A reaction: My attention is caught by the fact that natural languages are included. Might we say that science is model theory for English? That sounds like Quine's persistent message. |
| 10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
| Full Idea: A 'structure' in model theory is an interpretation which explains what objects some expressions refer to, and what classes some quantifiers range over. | |
| From: Wilfrid Hodges (Model Theory [2005], 1) | |
| A reaction: He cites as examples 'first-order structures' used in mathematical model theory, and 'Kripke structures' used in model theory for modal logic. A structure is also called a 'universe'. |
| 10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
| Full Idea: The models in model-theory are structures, but there is also a common use of 'model' to mean a formal theory which describes and explains a phenomenon, or plans to build it. | |
| From: Wilfrid Hodges (Model Theory [2005], 5) | |
| A reaction: Hodges is not at all clear here, but the idea seems to be that model-theory offers a set of objects and rules, where the common usage offers a set of descriptions. Model-theory needs homomorphisms to connect models to things, |
| 10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
| Full Idea: First-order logic is hopeless for discriminating between one infinite cardinal and another. | |
| From: Wilfrid Hodges (Model Theory [2005], 4) | |
| A reaction: This seems rather significant, since mathematics largely relies on first-order logic for its metatheory. Personally I'm tempted to Ockham's Razor out all these super-infinities, but mathematicians seem to make use of them. |
| 22703 | We don't often respond to events in art as if they were real events [Jacobson,D] |
| Full Idea: We routinely do not respond to art as if we were as if we were real-life spectators of its events. | |
| From: Daniel Jacobson (Ethical Criticism and the Vice of Moderation [2006], 'rejection') | |
| A reaction: This strikes me as one of the basic facts about aesthetics, and especially of narrative art. People sometimes encounter terrible events on the street, only to find someone is making a film. |
| 22702 | Audiences can be too moral [Jacobson,D] |
| Full Idea: An audience can be overly moralistic. | |
| From: Daniel Jacobson (Ethical Criticism and the Vice of Moderation [2006], 'emotional') | |
| A reaction: People can be too moral in real life as well. Goody Two Shoes. |
| 22696 | 'Autonomism' says the morality is irrelevant to the aesthetics [Jacobson,D] |
| Full Idea: 'Autonomism' is the theory that the intrinsic moral merits and defects of an artwork are irrelevant to its aesthetic value. | |
| From: Daniel Jacobson (Ethical Criticism and the Vice of Moderation [2006], Intro) | |
| A reaction: This contrasts with 'moralism', which says the ethics is part of the aesthetics. Autonomism seems to be the modern academic label for art for art's sake. In nineteenth century novels the ethics are central; in modernist novels they seem to be irrelevant. |
| 22697 | Moral defects of art can be among its aesthetic virtues [Jacobson,D] |
| Full Idea: To put my claim most provocatively: the moral defects in a work of art can be among its aesthetic virtues. This claim has been called 'immoralism'. | |
| From: Daniel Jacobson (Ethical Criticism and the Vice of Moderation [2006], Intro) | |
| A reaction: To describe sympathetic descriptions of vile moral behaviour as 'defects' may be a misunderstanding. If a work sets out to promote wickedness, then its wickedness isn't a defect in the work. It could be a masterpiece of corruption. |
| 22700 | Immoral art encourages immoral emotions [Jacobson,D] |
| Full Idea: Humean moralism includes the view that immoral art prescribes unethical emotional responses. | |
| From: Daniel Jacobson (Ethical Criticism and the Vice of Moderation [2006], 'emotional') | |
| A reaction: [He cites Hume's 'On the Standard of Taste'] 'Prescribes' is tricky. Is a vivid description of wicked events, given without comment, a prescription? What if the commentary condemns, but the description entices? Trust the work itself, said Lawrence. |
| 22699 | Moderate moralism says moral qualities can sometimes also be aesthetic qualities [Jacobson,D] |
| Full Idea: Noël Carroll's moderate moralism maintains that some moral defects in artworks are aesthetic defects, and some moral virtues are aesthetic merits. | |
| From: Daniel Jacobson (Ethical Criticism and the Vice of Moderation [2006], 'How moderate') | |
| A reaction: I'm beginning to think that moralist critics are confusing morality and wisdom. We don't admire novels for hammering on about goodness. We admire their insight into characters and actions, of which the most interesting aspects happen to be moral. |
| 22698 | We can judge art ethically, or rate its ethical influence, or assess its quality via its ethics [Jacobson,D] |
| Full Idea: Ethical criticism includes 1) ethical judgements of art works, 2) assessment of an art work's role in moral education, or 3) bringing moral praise or censure to bear on the aesthetic evaluation. | |
| From: Daniel Jacobson (Ethical Criticism and the Vice of Moderation [2006], 'What is') | |
| A reaction: [a compressed summary of Jacobson. He cites Levinson 1998 and Carroll 2000 as examples of ethical criticism] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |