5 ideas
| 10121 | Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal] |
| Full Idea: Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth. | |
| From: Blaise Pascal (works [1660]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: [Quoted in Auden and Kronenberger's Book of Aphorisms] Presumably we would now say that contradiction is a purely formal, syntactic notion, and not a semantic one. If you hit a contradiction, something has certainly gone wrong. |
| 9141 | Abstraction theories build mathematics out of second-order equivalence principles [Cook/Ebert] |
| Full Idea: A theory of abstraction is any account that reconstructs mathematical theories using second-order abstraction principles of the form: §xFx = §xGx iff E(F,G). We ignore first-order abstraction principles such as Frege's direction abstraction. | |
| From: R Cook / P Ebert (Notice of Fine's 'Limits of Abstraction' [2004], 1) | |
| A reaction: Presumably part of the neo-logicist programme, which also uses such principles. The function § (extension operator) 'provides objects corresponding to the argument concepts'. The aim is to build mathematics, rather than the concept of a 'rabbit'. |
| 15675 | We don't condemn people for being bad at reasoning [Finlayson] |
| Full Idea: We do not morally disapprove of people who are incompetent reasoners. | |
| From: James Gordon Finlayson (Habermas [2005], Ch.6:83) | |
| A reaction: Well, we don't morally disapprove simply of their lack of reasoning ability, but we may morally disapprove of their actions, which have arisen entirely from the disability. |
| 15674 | One can universalise good advice, but that doesn't make it an obligation [Finlayson] |
| Full Idea: 'Early to bed and early to rise' is a universalizable maxim, but, though it might be good advice, there is obviously no such obligation. | |
| From: James Gordon Finlayson (Habermas [2005], Ch.6:83) | |
| A reaction: I take it that Kant's rule won't distinguish moral guidance from prudential guidance. Unfair, I think. I may be a lark, but when I universalise this maxim I see that it can't be willed as a universal rule, because we should tolerate the owls. |
| 15662 | The 'culture industry' is an advertisement for the way things are [Finlayson] |
| Full Idea: Critical theory said that culture unwittingly played the role of an advertisement for the way things are. Horkheimer and Adorno referred to this phenomenon as the 'culture industry'. | |
| From: James Gordon Finlayson (Habermas [2005], Ch.1:04) | |
| A reaction: An interesting perspective. However, absolutely everything is an advertisement for what it offers. I think this is especially true of moral (and immoral) actions. |