33 ideas
16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
21704 | 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B] |
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] |
21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
19369 | Lull's combinatorial art would articulate all the basic concepts, then show how they combine [Lull, by Arthur,R] |
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] |
21727 | Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B] |
21719 | Extensionalism means what is true of a function is true of coextensive functions [Linsky,B] |
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] |
16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
16871 | A truth can be an axiom in one system and not in another [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] |
21723 | The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B] |
21721 | Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B] |
21703 | Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B] |
21714 | The ramified theory subdivides each type, according to the range of the variables [Linsky,B] |
21713 | Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B] |
21715 | For those who abandon logicism, standard set theory is a rival option [Linsky,B] |
21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |
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] |
19371 | Nine principles of God: goodness, greatness, eternity, power, wisdom, will, virtue, truth and glory [Lull, by Arthur,R] |