8 ideas
10855 | Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss] |
Full Idea: I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits ...which are permitted to increase without bound. | |
From: Carl Friedrich Gauss (Letter to Shumacher [1831]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.7 |
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. |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
Full Idea: Archelaus was the first person to say that the universe is boundless. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |