35 ideas
| 16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
| 11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
| 16878 | We must be clear about every premise and every law used in a proof [Frege] |
| 16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
| 16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
| 16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
| 16865 | 'Theorems' are both proved, and used in proofs [Frege] |
| 16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
| 16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
| 16871 | A truth can be an axiom in one system and not in another [Frege] |
| 16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
| 16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
| 16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
| 4444 | One moderate nominalist view says that properties and relations exist, but they are particulars [Armstrong] |
| 4445 | If properties and relations are particulars, there is still the problem of how to classify and group them [Armstrong] |
| 4448 | Should we decide which universals exist a priori (through words), or a posteriori (through science)? [Armstrong] |
| 4446 | It is claimed that some universals are not exemplified by any particular, so must exist separately [Armstrong] |
| 4440 | 'Resemblance Nominalism' finds that in practice the construction of resemblance classes is hard [Armstrong] |
| 4439 | 'Resemblance Nominalism' says properties are resemblances between classes of particulars [Armstrong] |
| 4431 | 'Predicate Nominalism' says that a 'universal' property is just a predicate applied to lots of things [Armstrong] |
| 4433 | Concept and predicate nominalism miss out some predicates, and may be viciously regressive [Armstrong] |
| 4432 | 'Concept Nominalism' says a 'universal' property is just a mental concept applied to lots of things [Armstrong] |
| 4436 | 'Class Nominalism' may explain properties if we stick to 'natural' sets, and ignore random ones [Armstrong] |
| 4434 | 'Class Nominalism' says that properties or kinds are merely membership of a set (e.g. of white things) [Armstrong] |
| 4435 | 'Class Nominalism' cannot explain co-extensive properties, or sets with random members [Armstrong] |
| 4437 | 'Mereological Nominalism' sees whiteness as a huge white object consisting of all the white things [Armstrong] |
| 4438 | 'Mereological Nominalism' may work for whiteness, but it doesn't seem to work for squareness [Armstrong] |
| 9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
| 16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
| 16875 | We use signs to mark receptacles for complex senses [Frege] |
| 16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
| 16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
| 16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
| 16874 | The parts of a thought map onto the parts of a sentence [Frege] |
| 15998 | Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard] |