18 ideas
| 10017 | Truth in a model is more tractable than the general notion of truth [Hodes] |
| Full Idea: Truth in a model is interesting because it provides a transparent and mathematically tractable model - in the 'ordinary' rather than formal sense of the term 'model' - of the less tractable notion of truth. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: This is an important warning to those who wish to build their entire account of truth on Tarski's rigorously formal account of the term. Personally I think we should start by deciding whether 'true' can refer to the mental state of a dog. I say it can. |
| 10018 | Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes] |
| Full Idea: There is an enormous difference between the truth of sentences in the interpreted language of set theory and truth in some model for the disinterpreted skeleton of that language. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.132) | |
| A reaction: This is a warning to me, because I thought truth and semantics only entered theories at the stage of 'interpretation'. I must go back and get the hang of 'skeletal' truth, which sounds rather charming. [He refers to set theory, not to logic.] |
| 10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
| Full Idea: Brand higher-order logic as unintelligible if you will, but don't conflate it with set theory. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: [he gives Boolos 1975 as a further reference] This is simply a corrective, because the conflation of second-order logic with set theory is an idea floating around in the literature. |
| 10011 | Identity is a level one relation with a second-order definition [Hodes] |
| Full Idea: Identity should he considered a logical notion only because it is the tip of a second-order iceberg - a level 1 relation with a pure second-order definition. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) |
| 10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
| Full Idea: A model is created when a language is 'interpreted', by assigning non-logical terms to objects in a set, according to a 'true-in' relation, but we must bear in mind that this 'interpretation' does not associate anything like Fregean senses with terms. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: This seems like a key point (also made by Hofweber) that formal accounts of numbers, as required by logic, will not give an adequate account of the semantics of number-terms in natural languages. |
| 10027 | Mathematics is higher-order modal logic [Hodes] |
| Full Idea: I take the view that (agreeing with Aristotle) mathematics only requires the notion of a potential infinity, ...and that mathematics is higher-order modal logic. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) | |
| A reaction: Modern 'modal' accounts of mathematics I take to be heirs of 'if-thenism', which seems to have been Russell's development of Frege's original logicism. I'm beginning to think it is right. But what is the subject-matter of arithmetic? |
| 10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
| Full Idea: Arithmetic should be able to face boldly the dreadful chance that in the actual world there are only finitely many objects. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.148) | |
| A reaction: This seems to be a basic requirement for any account of arithmetic, but it was famously a difficulty for early logicism, evaded by making the existence of an infinity of objects into an axiom of the system. |
| 10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes] |
| Full Idea: The mathematical object-theorist says a number is an object that represents a cardinality quantifier, with the representation relation as the entire essence of the nature of such objects as cardinal numbers like 4. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) | |
| A reaction: [compressed] This a classic case of a theory beginning to look dubious once you spell it our precisely. The obvious thought is to make do with the numerical quantifiers, and dispense with the objects. Do other quantifiers need objects to support them? |
| 10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes] |
| Full Idea: The dogmatic Frege is more right than wrong in denying that numerical terms can stand for numerical quantifiers, for there cannot be a language in which object-quantifiers and objects are simultaneously viewed as level zero. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.142) | |
| A reaction: Subtle. We see why Frege goes on to say that numbers are level zero (i.e. they are objects). We are free, it seems, to rewrite sentences containing number terms to suit whatever logical form appeals. Numbers are just quantifiers? |
| 10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
| Full Idea: Talk about mirror images is a sort of fictional discourse. Statements 'about' such fictions are not made true or false by our whims; rather they 'encode' facts about the things reflected in mirrors. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.146) | |
| A reaction: Hodes's proposal for how we should view abstract objects (c.f. Frege and Dummett on 'the equator'). The facts involved are concrete, but Hodes is offering 'encoding fictionalism' as a linguistic account of such abstractions. He applies it to numbers. |
| 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 naïve). |
| 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. |
| 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. |
| 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. |