23 ideas
| 291 | Don't assume that wisdom is the automatic consequence of old age [Plato] |
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| 8492 | Relations are functions with two arguments [Frege] |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
| 6303 | Sets are positions in patterns [Resnik] |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [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] |
| 8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
| 18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
| 4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
| 8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
| 9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
| 10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
| 8488 | A concept is a function whose value is always a truth-value [Frege] |
| 9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
| 4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
| 293 | Being unafraid (perhaps through ignorance) and being brave are two different things [Plato] |
| 8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |