8 ideas
| 19053 | Logic would be more natural if negation only referred to predicates [Dummett] |
| Full Idea: A better proposal for a formal logic closer to natural language would be one that had a negation-operator only for (simple) predicates. | |
| From: Michael Dummett (Presupposition [1960], p.27) | |
| A reaction: Dummett observes that classical formal logic was never intended to be close to natural language. Term logic does have that aim, but the meta-question is whether that end is desirable, and why. |
| 19052 | Natural language 'not' doesn't apply to sentences [Dummett] |
| Full Idea: Natural language does not possess a sentential negation-operator. | |
| From: Michael Dummett (Presupposition [1960], p.27) | |
| A reaction: This is a criticism of Strawson, who criticises logic for not following natural language, but does it himself with negation. In the question of how language and logic connect, this idea seems important. Term Logic aims to get closer to natural language. |
| 13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
| Full Idea: Von Neumann's decision was to start with the ordinals and to treat cardinals as a special sort of ordinal. | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by William D. Hart - The Evolution of Logic 3 | |
| A reaction: [see Hart 73-74 for an explication of this] |
| 12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
| Full Idea: In Von Neumann's definition an ordinal is a transitive set in which all of the elements are transitive. | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Alain Badiou - Briefings on Existence 11 |
| 18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
| Full Idea: For Von Neumann the successor of n is n U {n} (rather than Zermelo's successor, which is {n}). | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n8 |
| 18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
| Full Idea: Von Neumann's version of the natural numbers is in fact preferred because it carries over directly to the transfinite ordinals. | |
| From: comment on John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n9 |
| 15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
| Full Idea: Each Von Neumann ordinal number is the set of its predecessors. ...He had shown how to introduce ordinal numbers as sets, making it possible to use them without leaving the domain of sets. | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Shaughan Lavine - Understanding the Infinite V.3 |
| 3102 | Why don't we experience or remember going to sleep at night? [Magee] |
| Full Idea: As a child it was incomprehensible to me that I did not experience going to sleep, and never remembered it. When my sister said 'Nobody remembers that', I just thought 'How does she know?' | |
| From: Bryan Magee (Confessions of a Philosopher [1997], Ch.I) | |
| A reaction: This is actually evidence for something - that we do not have some sort of personal identity which is separate from consciousness, so that "I am conscious" would literally mean that an item has a property, which it can lose. |