5 ideas
| 15102 | S4 says there must be some necessary truths (the actual ones, of which there is at least one) [Cameron] |
| Full Idea: S4 says there must be some necessary truths, because the actual necessary truths must be necessary. (It says if there are some actual necessary truths then that is so - but the S4 axiom is an actual necessary truth, if true). | |
| From: Ross P. Cameron (On the Source of Necessity [2010], 2) |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 15103 | Blackburn fails to show that the necessary cannot be grounded in the contingent [Cameron] |
| Full Idea: I conclude that Blackburn has not shown that any grounding of the necessary in the contingent (the Contingency Horn of his dilemma) is doomed to failure. | |
| From: Ross P. Cameron (On the Source of Necessity [2010], 2) | |
| A reaction: [You must read the article for details of Cameron's argument!] He goes on to also reject the Necessity Horn (that there is a regress if necessities must rely on necessities). |
| 6901 | Understanding is needed for imagination, just as much as the other way around [Betteridge] |
| Full Idea: Although it might be right to say that imagination is required in order to make reasoning and understanding possible, this also works the other way, as imagination cannot occur without some prior understanding. | |
| From: Alex Betteridge (talk [2005]), quoted by PG - Db (ideas) | |
| A reaction: This strikes me as a very illuminating remark, particularly for anyone who aspires to draw a simplified flowdiagram of the mind showing logical priority between its various parts. In fact, the parts are interdependent. Maybe imagination is understanding. |
| 15104 | The 'moving spotlight' theory makes one time privileged, while all times are on a par ontologically [Cameron] |
| Full Idea: What seems so wrong about the 'moving spotlight' theory is that here one time is privileged, but all the times are on a par ontologically. | |
| From: Ross P. Cameron (On the Source of Necessity [2010], 4) | |
| A reaction: The whole thing is baffling, but this looks like a good point. All our intuitions make presentism (there's only the present) look like a better theory than the moving spotlight (that the present is just 'special'). |