10 ideas
| 18119 | Mathematics is a mental activity which does not use language [Brouwer, by Bostock] |
| Full Idea: Brouwer made the rather extraordinary claim that mathematics is a mental activity which uses no language. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: Since I take language to have far less of a role in thought than is commonly believed, I don't think this idea is absurd. I would say that we don't use language much when we are talking! |
| 18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
| Full Idea: Brouwer regards as somehow 'wicked' the idea that mathematics can be applied to a non-mental subject matter, the physical world, and that it might develop in response to the needs which that application reveals. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: The idea is that mathematics only concerns creations of the human mind. It presumably has no more application than, say, noughts-and-crosses. |
| 13768 | Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington] |
| Full Idea: If your interest in logic is confined to applications to mathematics or other a priori matters, it is fine for validity to preserve certainty, ..but if you use conditionals when arguing about contingent matters, then great caution will be required. | |
| From: Dorothy Edgington (Conditionals [2001], 17.2.1) |
| 13770 | There are many different conditional mental states, and different conditional speech acts [Edgington] |
| Full Idea: As well as conditional beliefs, there are conditional desires, hopes, fears etc. As well as conditional statements, there are conditional commands, questions, offers, promises, bets etc. | |
| From: Dorothy Edgington (Conditionals [2001], 17.3.4) |
| 13764 | Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington] |
| Full Idea: Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? Are they non-truth-functional, like 'because' or 'before'? Do the values of A and B, in some cases, leave open the value of 'If A,B'? | |
| From: Dorothy Edgington (Conditionals [2001], 17.1) | |
| A reaction: I would say they are not truth-functional, because the 'if' asserts some further dependency relation that goes beyond the truth or falsity of A and B. Logical ifs, causal ifs, psychological ifs... The material conditional ⊃ is truth-functional. |
| 13765 | 'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington] |
| Full Idea: If it were possible to have A true, B false, and If A,B true, it would be unsafe to infer B from A and If A,B: modus ponens would thus be invalid. Hence 'If A,B' must entail ¬(A & ¬B). | |
| From: Dorothy Edgington (Conditionals [2001], 17.1) | |
| A reaction: This is a firm defence of part of the truth-functional view of conditionals, and seems unassailable. The other parts of the truth table are open to question, though, if A is false, or they are both true. |
| 5122 | Maybe consequentialism is a critique of ordinary morality, rather than describing it [Harman] |
| Full Idea: Consequentialism may be put forward not as an attempt to capture intuitive folk morality but rather as a critique of ordinary tuitions. | |
| From: Gilbert Harman (Moral Philosophy meets social psychology [1999], 10.1) | |
| A reaction: It is certainly true that most people are concerned with why an action was performed, and (after initial anger) are prepared to forgive an unintended disaster. We have no moral objections to earthquakes, which have bad consequences. |
| 5123 | Maybe there is no such thing as character, and the virtues and vices said to accompany it [Harman] |
| Full Idea: It may be the case that there is no such thing as character, no ordinary character traits of the sort people think there are, none of the usual moral virtues and vices. | |
| From: Gilbert Harman (Moral Philosophy meets social psychology [1999], 10.1) | |
| A reaction: This would be a devastating fact for virtue theory, if it were true. I don't believe it. He thinks patterns of behaviour result from circumstances, but we give accurate and detailed pictures of people's characters (esp. in novels). |
| 5124 | If a person's two acts of timidity have different explanations, they are not one character trait [Harman] |
| Full Idea: If Herbert is disposed to not speak in history class (but not other subjects), and explanation of this is different from his avoidance of roller coaster rides, then these two dispositions are not special cases of a single character trait. | |
| From: Gilbert Harman (Moral Philosophy meets social psychology [1999], 10.2) | |
| A reaction: A basic Harman argument for denying the existence of character (and hence of virtues). I just say that character traits are more complex than his caricature of them. If I keep imagining disaster and humiliation for myself, that is a character trait. |
| 5125 | Virtue ethics might involve judgements about the virtues of actions, rather than character [Harman] |
| Full Idea: There are variants of virtue ethics that do not require character traits in the ordinary sense. For example, moral thinking might be explicated by appeal to judgements about whether particular actions are just or courageous or whatever. | |
| From: Gilbert Harman (Moral Philosophy meets social psychology [1999], 10.7.1.1) | |
| A reaction: A very interesting proposal (from Judith Jarvis Thomson). This would flatly reject Aristotle, and one presumes that the judgement about the virtue of the action would largely be a matter of pondering cultural conventions (or, perhaps, consequences). |