5 ideas
| 10835 | True sentences says the appropriate descriptive thing on the appropriate demonstrative occasion [Austin,JL] |
| Full Idea: A sentence is said to be true when the historic state of affairs to which it is correlated by the demonstrative conventions (the one to which it 'refers') is of a type with which the sentence used in making it is correlated by the descriptive conventions. | |
| From: J.L. Austin (Truth [1950], §3) | |
| A reaction: This is correspondence by convention rather than correspondence by mapping. Personally I prefer some sort of mapping account, despite all the difficulty and vagueness of specifying what maps onto what. |
| 10836 | Correspondence theorists shouldn't think that a country has just one accurate map [Austin,JL] |
| Full Idea: Correspondence theorists too often talk as one would who held that every map is either accurate or inaccurate; that every country can have but one accurate map. | |
| From: J.L. Austin (Truth [1950], n 24) | |
| A reaction: A well-made point, for those who intuitively hang on to correspondence as not only good common sense, but also some sort of salvation for a realist view of the world which might give us certainty in epistemology. |
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong. | |
| From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1 |
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal. | |
| From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'. |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory. | |
| From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2 | |
| A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this. |