10 ideas
| 8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
| Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3 | |
| A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
| A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
| 10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
| Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
| From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
| A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
| 3534 | To be is to have causal powers [Alexander,S] |
| Full Idea: To be is to have causal powers. | |
| From: Samuel Alexander (works [1927], §4), quoted by Jaegwon Kim - Nonreductivist troubles with ment.causation | |
| A reaction: This is sometimes called Alexander's Principle. It is first found in Plato, and is popular with physicalists, but there are problem cases... A thing needs to exist in order to have causal powers. To exist is more than to be perceived. |
| 3398 | Epiphenomenalism makes the mind totally pointless [Alexander,S] |
| Full Idea: Epiphenomenalism supposes something to exist in nature which has nothing to do and no purpose to serve. | |
| From: Samuel Alexander (works [1927]), quoted by Jaegwon Kim - Philosophy of Mind p.129 | |
| A reaction: An objection, but not, I think, a strong one. The fact, for example, that sweat is shiny is the result of good evolutionary reasons, but I cannot think of any purpose which it serves. All events which are purposeful are likely to have side-effects. |
| 20180 | A happy and joyous life must largely be a quiet life [Russell] |
| Full Idea: A happy life must to a great extent be a quiet life, for it is only in an atmosphere of quiet that true joy can live. | |
| From: Bertrand Russell (The Conquest of Happiness [1930], 4) | |
| A reaction: Most people's image of happiness is absorption in an interesting task, or relaxing in good company. The idea that happiness is wild excitement exists, but is a minority view. |
| 20177 | Boredom always involves not being fully occupied [Russell] |
| Full Idea: It is one of the essentials of boredom that one's faculties must not be fully occupied. | |
| From: Bertrand Russell (The Conquest of Happiness [1930], 4) | |
| A reaction: He gives running for your life as an example of non-boredom. I suspect that this is only the sort of boredom that troubled Russell, and not the sort of profound boredom that led the actor George Sanders to suicide (according to his last note). |
| 20179 | Happiness involves enduring boredom, and the young should be taught this [Russell] |
| Full Idea: A certain power of enduring boredom is essential to a happy life, and is one of the things that ought to be taught to the young. | |
| From: Bertrand Russell (The Conquest of Happiness [1930], 4) | |
| A reaction: As an example he suggests that Wordsworth would never have written 'The Prelude' is he had never been bored when young. Which suggests that Russell doesn't really get boredom, seeing it merely as a stimulus to work. |
| 20176 | Boredom is an increasingly strong motivating power [Russell] |
| Full Idea: Boredom has been, I believe, one of the great motive powers throughout the historical epoch, and is so at the present day more than ever. | |
| From: Bertrand Russell (The Conquest of Happiness [1930], 4) | |
| A reaction: Most of his essay tells us how to avoid boredom, rather than how it motivates. |
| 20178 | Life is now more interesting, but boredom is more frightening [Russell] |
| Full Idea: We are less bored than our ancestors were, but we are more afraid of boredom | |
| From: Bertrand Russell (The Conquest of Happiness [1930], 4) | |
| A reaction: I get the impression that the invention of the powerful mobile phone has largely banished boredom from human life, except when you are obliged to switch it off. The fear of boredom may hence be even greater now. |