3 ideas
| 18758 | Validity is provable, but invalidity isn't, because the model is infinite [Church, by McGee] |
| Full Idea: Church showed that logic has a proof procedure, but no decision procedure. If an argument is invalid, there is a model with true premises and false conclusion, but the model will typically be infinite, so there is no way to display it concretely. | |
| From: report of Alonzo Church (A Note on the entscheidungsproblem [1936]) by Vann McGee - Logical Consequence 5 |
| 3449 | If parallelism is true, how does the mind know about the body? [Crease] |
| Full Idea: In parallelism, the idea that we have a body is like an astronaut hearing shouting on the moon, and reasoning that as this is impossible he must be simultaneously imagining shouting AND there is real shouting taking place! | |
| From: Jason Crease (works [2001]), quoted by PG - Db (ideas) | |
| A reaction: This seems to capture the absurdity of Leibniz's proposal. I experience what my brain is doing, but not because my brain is doing it. I would never know if God had made a slight error in setting His two 'clocks'; their accuracy is just a pious hope. |
| 8592 | Empty space is measurable in ways in which empty time necessarily is not [Bennett, by Shoemaker] |
| Full Idea: Because of the multidimensionality of space and unidimensionality of time, empty space is measurable in ways in which empty time necessarily is not. | |
| From: report of Jonathan Bennett (Kant's Analytic [1966], p.175) by Sydney Shoemaker - Time Without Change p.49 n4 | |
| A reaction: An interesting observation, which could have been used by Samuel Clarke in his attempts to prove absolute space to Leibniz. The point does not prove absolute space, of course, but it seems to make a difference. |