4 ideas
10245 | One geometry cannot be more true than another [Poincaré] |
Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
9159 | You can't simply convert geometry into algebra, as some spatial content is lost [Burge] |
Full Idea: Although one can translate geometrical propositions into algebraic ones and produce equivalent models, the meaning of geometrical propositions seems to me to be thereby lost. Pure geometry involves spatial content, even if abstracted from physical space. | |
From: Tyler Burge (Frege on Apriority [2000], IV) | |
A reaction: This supports Frege's view (against Quine) that geometry won't easily fit into the programme of logicism. I agree with Burge. You would be focusing on the syntax of geometry, and leaving out the semantics. |
14286 | In nearby worlds where A is true, 'if A,B' is true or false if B is true or false [Stalnaker] |
Full Idea: Consider a possible world in which A is true and otherwise differs minimally from the actual world. 'If A, then B' is true (false) just in case B is true (false) in that possible world. | |
From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1 | |
A reaction: This is the first proposal to give a possible worlds semantics for conditional statements. Edgington observes that worlds which are nearby for me may not be nearby for you. |
14285 | A possible world is the ontological analogue of hypothetical beliefs [Stalnaker] |
Full Idea: A possible world is the ontological analogue of a stock of hypothetical beliefs. | |
From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1 | |
A reaction: Sounds neat and persuasive. What is the ontological analogue of a stock of hopes? Heaven! |