6 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? |
| 3979 | The Turing Machine is the best idea yet about how the mind works [Fodor on Turing] |
| Full Idea: Alan Turing had (in his theory of the 'Turing Machine') what I suppose is the best thought about how the mind works that anyone has had so far. | |
| From: comment on Alan Turing (Computing Machinery and Intelligence [1950]) by Jerry A. Fodor - Jerry A. Fodor on himself p.296 | |
| A reaction: I am not convinced, because I don't think rationality is possible without consciousness. The brain may bypass the representations used by a computer. |
| 5321 | In 50 years computers will successfully imitate humans with a 70% success rate [Turing] |
| Full Idea: In about fifty years' time it will be possible to program computers to play the imitation game so well that an average interrogator will not have more than 70% chance of making the right identification after five minutes of questioning. | |
| From: Alan Turing (Computing Machinery and Intelligence [1950], p.57), quoted by Robert Kirk - Mind and Body §5.9 | |
| A reaction: This is the famous prophecy called 'The Turing Test'. The current state (2004) seems to be that the figure of 70% is very near, but no one sees much prospect of advancing much further in the next 100 years. Dennett sees jokes as a big problem. |
| 19739 | The maxim for suicide is committed to the value of life, and is thus contradictory [Kant] |
| Full Idea: If my maxim is to shorten my life if its continuance threatens more evil than pleasure ...it is seen that a system of nature by whose law the feeling intended to further life should actually destroy life would contradict itself, and could not subsist. | |
| From: Immanuel Kant (Lectures on Ethics [1780], 422:53) | |
| A reaction: [compressed] I take it this means that a potential suicide is assessing what is best for life, and is therefore implicitly committed to life. Not persuasive! Should we not terminate the life of a mass murderer in mid-crime? |