17 ideas
| 10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 8942 | Lukasiewicz's L3 logic has three truth-values, T, F and I (for 'indeterminate') [Lukasiewicz, by Fisher] |
| 10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
| 10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
| 10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
| 10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
| 10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
| 10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| 10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
| 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
| 6303 | Sets are positions in patterns [Resnik] |
| 6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
| 6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
| 6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |