12 ideas
| 12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
| Full Idea: Not to the mathematician, but to the psychologist, belongs the task of explaining why ...we are averse to so-called contradictory systems in which the negative as well as the positive of certain propositions are valid. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.79) | |
| A reaction: Was the turning point of Graham Priest's life the day he read this sentence? I don't agree. I take the principle of non-contradiction to be a highly generalised observation of how the world works (and Russell agrees with me). |
| 12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
| Full Idea: A large part of the natural laws introduced by science treat only of the mutual relations between the results of counting and measuring. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.77) | |
| A reaction: His point, I take it, is that the higher reaches of numbers have lost touch with the original point of the system. I now see the whole issue as just depending on conventions about the agreed extension of the word 'number'. |
| 12454 | Intuitionists only accept denumerable sets [Brouwer] |
| Full Idea: The intuitionist recognises only the existence of denumerable sets. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: That takes you up to omega, but not beyond, presumably because it then loses sight of the original intuition of 'bare two-oneness' (Idea 12453). I sympathise, but the word 'number' has shifted its meaning a lot these days. |
| 12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
| Full Idea: Neo-intuitionism sees the falling apart of moments, reunited while remaining separated in time, as the fundamental phenomenon of human intellect, passing by abstracting to mathematical thinking, the intuition of bare two-oneness. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: [compressed] A famous and somewhat obscure idea. He goes on to say that this creates one and two, and all the finite ordinals. |
| 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. |
| 10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
| Full Idea: The concern of mathematical intuitionists was that the use of certain forms of inference generates, not contradiction, but unjustified assertions. | |
| From: report of Luitzen E.J. Brouwer (Intuitionism and Formalism [1912]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This seems to be the real origin of the verificationist idea in the theory of meaning. It is a hugely revolutionary idea - that ideas are not only ruled out of court by contradiction, but that there are other criteria which should also be met. |
| 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. |