display all the ideas for this combination of texts
3 ideas
| 10676 | The Axiom of Choice is a non-logical principle of set-theory [Hossack] |
| Full Idea: The Axiom of Choice seems better treated as a non-logical principle of set-theory. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4 n8) | |
| A reaction: This reinforces the idea that set theory is not part of logic (and so pure logicism had better not depend on set theory). |
| 10686 | The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack] |
| Full Idea: We cannot explicitly define one-one correspondence from the sets to the ordinals (because there is no explicit well-ordering of R). Nevertheless, the Axiom of Choice guarantees that a one-one correspondence does exist, even if we cannot define it. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) |
| 10687 | Maybe we reduce sets to ordinals, rather than the other way round [Hossack] |
| Full Idea: We might reduce sets to ordinal numbers, thereby reversing the standard set-theoretical reduction of ordinals to sets. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) | |
| A reaction: He has demonstrated that there are as many ordinals as there are sets. |