19 ideas
| 8996 | If if time is money then if time is not money then time is money then if if if time is not money... [Quine] |
| 8995 | Definition by words is determinate but relative; fixing contexts could make it absolute [Quine] |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| 10064 | Quine quickly dismisses If-thenism [Quine, by Musgrave] |
| 20296 | Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey] |
| 8998 | Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine] |
| 8999 | Logic isn't conventional, because logic is needed to infer logic from conventions [Quine] |
| 9000 | If a convention cannot be communicated until after its adoption, what is its role? [Quine] |
| 8994 | If analytic geometry identifies figures with arithmetical relations, logicism can include geometry [Quine] |
| 8997 | There are four different possible conventional accounts of geometry [Quine] |
| 8993 | If mathematics follows from definitions, then it is conventional, and part of logic [Quine] |
| 15788 | Syntax and semantics are indeterminate, and modern 'semantics' is a bogus subject [Quine, by Lycan] |