5 ideas
| 15045 | The big issue since the eighteenth century has been: what is Reason? Its effect, limits and dangers? [Foucault] |
| Full Idea: I think the central issue of philosophy and critical thought since the eighteenth century has always been, still is, and will, I hope, remain the question: What is this Reason that we use? What are its historical effects? What are its limits and dangers? | |
| From: Michel Foucault (Space, Knowledge and Power (interview) [1982], p.358) | |
| A reaction: One can hardly deny the fairness of the question, but I hope that won't prevent us from trying to be rational. Maybe logicians do a better job of clarifying reason than the political and historical speculations of Foucault? |
| 18200 | Very large sets should be studied in an 'if-then' spirit [Putnam] |
| Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example), should today be investigated in an 'if-then' spirit. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.347), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Quine says the large sets should be regarded as 'uninterpreted'. |
| 18199 | Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam] |
| Full Idea: We may say that indispensability is a pretty strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.346), quoted by Penelope Maddy - Naturalism in Mathematics II.2 |
| 8857 | We must quantify over numbers for science; but that commits us to their existence [Putnam] |
| Full Idea: Quantification over mathematical entities is indispensable for science..., therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.57), quoted by Stephen Yablo - Apriority and Existence | |
| A reaction: I'm not surprised that Hartry Field launched his Fictionalist view of mathematics in response to such a counterintuitive claim. I take it we use numbers to slice up reality the way we use latitude to slice up the globe. No commitment to lines! |
| 7803 | Modal logic began with translation difficulties for 'If...then' [Lewis,CI, by Girle] |
| Full Idea: C.I.Lewis began his groundbreaking work in modal logic because he was concerned about the unreliability of the material conditional as a translation of 'If ... then' conditionals. | |
| From: report of C.I. Lewis (Symbolic Logic (with Langford) [1932]) by Rod Girle - Modal Logics and Philosophy 12.3 | |
| A reaction: Compare 'if this is square then it has four corners' with 'if it rains then our afternoon is ruined'. Different modalities seem to be involved. We even find that 'a square has four corners' will be materially implied if it rains! |