3 ideas
| 8714 | Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true [Field,H] |
| Full Idea: The fictionalist can say that the sense in which '2+2=4' is true is pretty much the same as the sense in which 'Oliver Twist lived in London' is true. They are true 'according to a well-known story', or 'according to standard mathematics'. | |
| From: Hartry Field (Realism, Mathematics and Modality [1989], 1.1.1), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 6.3 | |
| A reaction: The roots of this idea are in Carnap. Fictionalism strikes me as brilliant, but poisonous in large doses. Novels can aspire to artistic truth, or to documentary truth. We invent a fiction, and nudge it slowly towards reality. |
| 3193 | Turing showed that logical rules can be specified computationally and mechanically [Turing, by Rey] |
| Full Idea: Turing showed that any formal process can be specified computationally, and captured by a Turing Machine. Hence logical rules (and arithmetic) could be obeyed not by someone representing and following them, but by causal organisation of the brain. | |
| From: report of Alan Turing (works [1935]) by Georges Rey - Contemporary Philosophy of Mind 8.2 | |
| A reaction: It is questionable whether logic is an entirely formal process, if it involves truth. You would need an entirely formal notion of truth for that. But a brain can do whatever a flow diagram can do. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |