11 ideas
| 14767 | The demonstrations of the metaphysicians are all moonshine [Peirce] |
| Full Idea: The demonstrations of the metaphysicians are all moonshine. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.2) |
| 14764 | I am saturated with the spirit of physical science [Peirce] |
| Full Idea: I am saturated, through and through, with the spirit of the physical sciences. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.1) |
| 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 |
| 14768 | Infallibility in science is just a joke [Peirce] |
| Full Idea: Infallibility in scientific matters seems to me irresistibly comical. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.3) |
| 14765 | Association of ideas is the best philosophical idea of the prescientific age [Peirce] |
| Full Idea: The doctrine of the association of ideas is, to my thinking, the finest piece of philosophical work of the prescientific ages. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.2) |
| 14766 | Duns Scotus offers perhaps the best logic and metaphysics for modern physical science [Peirce] |
| Full Idea: The works of Duns Scotus have strongly influenced me. …His logic and metaphysics, torn away from its medievalism, …will go far toward supplying the philosophy which is best to harmonize with physical science. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.2) |
| 7006 | Observing irrelevant items supports both 'all x are y' and 'all x are non-y', revealing its absurdity [Schofield,J] |
| Full Idea: Although Hempel's raven paradox produces an absurdity of irrelevant observations, we can ignore it because (unlike good observations) observing a white handbag supports the contradictions of 'ravens are black' and 'ravens are non-black'. | |
| From: Jonathan Schofield (talk [2005]), quoted by PG - Db (ideas) | |
| A reaction: The idea of 'eliminating it from our enquiries' cannot be totally irrational (e.g. in detective work), but it is only seriously sensible in a restricted domain (such as a country house) |