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) |
| 18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
| Full Idea: Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power. | |
| From: Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4 | |
| A reaction: Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects. |
| 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). |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 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'). |