11 ideas
| 18189 | ZFC could contain a contradiction, and it can never prove its own consistency [MacLane] |
| Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC. | |
| From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30). |
| 12163 | Literary meaning emerges in comparisons, and tradition shows which comparisons are relevant [Scruton] |
| Full Idea: We must discover the meanings that emerge when works of literature are experience in relation to each other. ...The importance of tradition is that it denotes - ideally, at least - the class of relevant comparisons. | |
| From: Roger Scruton (Public Text and Common Reader [1982], p.27) | |
| A reaction: This is a nice attempt to explain why we all agree that a thorough education in an art is an essential prerequisite for good taste. Some people (e.g. among the young) seem to have natural good taste. How does that happen? |
| 12162 | In literature, word replacement changes literary meaning [Scruton] |
| Full Idea: In literary contexts semantically equivalent words cannot replace each other without loss of literary meaning. | |
| From: Roger Scruton (Public Text and Common Reader [1982], p.25) | |
| A reaction: The notion of 'literary meaning' is not a standard one, and is questionable whether 'meaning' is the right word, given that a shift in word in a poem is as much to do with sound as with connotations. |
| 12159 | Without intentions we can't perceive sculpture, but that is not the whole story [Scruton] |
| Full Idea: A person for whom it made no difference whether a sculpture was carved by wind and rain or by human hand would be unable to interpret or perceive sculptures - even though the interpretation of sculpture is not the reading of an intention. | |
| From: Roger Scruton (Public Text and Common Reader [1982], p.15) | |
| A reaction: Scruton compares it to the role of intention in language, where there is objective meaning, even though intention is basic to speech. |
| 12160 | In aesthetic interest, even what is true is treated as though it were not [Scruton] |
| Full Idea: In aesthetic interest, even what is true is treated as though it were not. | |
| From: Roger Scruton (Public Text and Common Reader [1982], p.18) | |
| A reaction: A nice aphorism. I always feel uncomfortable reading novels about real people, although the historical Macbeth doesn't bother me much. Novels are too close to reality. Macbeth didn't speak blank verse. |
| 12161 | We can be objective about conventions, but love of art is needed to understand its traditions [Scruton] |
| Full Idea: An historian can elucidate convention while having no feeling for the art that exploits it; whereas an understanding of tradition is reserved for those with the critical insight which comes from the love of art, both past and present. | |
| From: Roger Scruton (Public Text and Common Reader [1982], p.24) | |
| A reaction: This aesthetic observation is obviously close to Scruton's well-known conservatism in politics. I am doubtful whether the notion of 'tradition' can stand up to close examination, though we all know roughly what he means. |
| 6613 | The natural kinds are objects, processes and properties/relations [Ellis] |
| Full Idea: There are three hierarchies of natural kinds: objects or substances (substantive universals), events or processes (dynamic universals), and properties or relations (tropic universals). | |
| From: Brian Ellis (Katzav on limitations of dispositions [2005], 91) | |
| A reaction: Most interesting here is the identifying of natural kinds with universals, making universals into the families of nature. Universals are high-level sets of natural kinds. To grasp universals you must see patterns, and infer the underlying order. |
| 6616 | Least action is not a causal law, but a 'global law', describing a global essence [Ellis] |
| Full Idea: The principle of least action is not a causal law, but is what I call a 'global law', which describes the essence of the global kind, which every object in the universe necessarily instantiates. | |
| From: Brian Ellis (Katzav on limitations of dispositions [2005]) | |
| A reaction: As a fan of essentialism I find this persuasive. If I inherit part of my essence from being a mammal, I inherit other parts of my essence from being an object, and all objects would share that essence, so it would look like a 'law' for all objects. |
| 6615 | A species requires a genus, and its essence includes the essence of the genus [Ellis] |
| Full Idea: A specific universal can exist only if the generic universal of which it is a species exists, but generic universals don't depend on species; …the essence of any genus is included in its species, but not conversely. | |
| From: Brian Ellis (Katzav on limitations of dispositions [2005], 91) | |
| A reaction: Thus the species 'electron' would be part of the genus 'lepton', or 'human' part of 'mammal'. The point of all this is to show how individual items connect up with the rest of the universe, giving rise to universal laws, such as Least Action. |
| 6614 | A hierarchy of natural kinds is elaborate ontology, but needed to explain natural laws [Ellis] |
| Full Idea: The hierarchy of natural kinds proposed by essentialism may be more elaborate than is strictly required for purposes of ontology, but it is necessary to explain the necessity of the laws of nature, and the universal applicability of global principles. | |
| From: Brian Ellis (Katzav on limitations of dispositions [2005], 91) | |
| A reaction: I am all in favour of elaborating ontology in the name of best explanation. There seem, though, to be some remaining ontological questions at the point where the explanations of essentialism run out. |
| 6612 | Without general principles, we couldn't predict the behaviour of dispositional properties [Ellis] |
| Full Idea: It is objected to dispositionalism that without the principle of least action, or some general principle of equal power, the specific dispositional properties of things could tell us very little about how these things would be disposed to behave. | |
| From: Brian Ellis (Katzav on limitations of dispositions [2005], 90) | |
| A reaction: Ellis attempts to meet this criticism, by placing dispositional properties within a hierarchy of broader properties. There remains a nagging doubt about how essentialism can account for space, time, order, and the existence of essences. |