9 ideas
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong. | |
| From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1 |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory. | |
| From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2 | |
| A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this. |
| 18415 | The actual world is just the world you are in [Lewis, by Cappelen/Dever] |
| Full Idea: Lewis equates knowing which world is actual with knowing which world one is in. | |
| From: report of David Lewis (Attitudes De Dicto and De Se [1979]) by Cappelen,H/Dever,Josh - The Inessential Indexical 05.1 | |
| A reaction: [This view is not, of course, Actualism, but an alternative treatment of actuality, within a multitude of possibilities]. |
| 16392 | A content is a property, and believing it is self-ascribing that property [Lewis, by Recanati] |
| Full Idea: For Lewis, a belief mode is analysed by saying that to believe a content (analysed as a property) is for the subject of thought to 'self-ascribe' that property. | |
| From: report of David Lewis (Attitudes De Dicto and De Se [1979]) by François Recanati - Mental Files 18.3 | |
| A reaction: Lewis is weird. I would have thought you only self-ascribe the 'property' when you find yourself believing it. Lewis seems desperate to eliminate mental language. Belief can be a primitive concept without being primitive in ontology. |
| 18416 | Attitudes involve properties (not propositions), and belief is self-ascribing the properties [Lewis, by Solomon] |
| Full Idea: Lewis suggests that we take attitudes to have properties, rather than propositions, as contents. To stand in the belief relation to a property is to self-ascribe that property. | |
| From: report of David Lewis (Attitudes De Dicto and De Se [1979]) by Robert C. Solomon - Erotic Love as a Moral Virtue 05.1 | |
| A reaction: This is the sort of convoluted suggestion that Lewis has to come up with, in pursuit of his project of a wholly consistent metaphysics. Examine Lewis's account of properties before you judge this proposal! Self-ascribing is joining a set! |
| 16390 | Lewis's popular centred worlds approach gives an attitude an index of world, subject and time [Lewis, by Recanati] |
| Full Idea: Many philosophers now prefer Lewis's centred worlds framework for indexicals …It is two-dimensional, saying an attitude only has a truth-value when evaluated with respect to a contextual index, containing a subject and time, as well as a world. | |
| From: report of David Lewis (Attitudes De Dicto and De Se [1979]) by François Recanati - Mental Files 18.2 | |
| A reaction: [compressed; this is said to have largely ousted the older Kaplan-Perry view] You only begin to understand the possible worlds game when you see how many problems find proposed 'solutions' there. |
| 18418 | A theory of perspectival de se content gives truth conditions relative to an agent [Lewis, by Cappelen/Dever] |
| Full Idea: Lewis's theory of a perspectival 'de se' content ...delivers truth conditions not absolutely, but only relative to a choice of agent/center. | |
| From: report of David Lewis (Attitudes De Dicto and De Se [1979]) by Cappelen,H/Dever,Josh - The Inessential Indexical 05.7 | |
| A reaction: The proposal rests on a theory of 'centred' possible worlds, specifying the viewpoint of some agent within the whole system. It relies on accepting the idea that indexicals are special, which Cappelen and Dever reject. |
| 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. |