31 ideas
8952 | We reach 'reflective equilibrium' when intuitions and theory completely align [Fisher] |
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] |
16519 | No one can conceive of a possible substance, apart from those which God has created [Arnauld] |
8943 | Three-valued logic says excluded middle and non-contradition are not tautologies [Fisher] |
8945 | Fuzzy logic has many truth values, ranging in fractions from 0 to 1 [Fisher] |
16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
8951 | Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism [Fisher] |
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] |
8950 | Logic formalizes how we should reason, but it shouldn't determine whether we are realists [Fisher] |
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] |
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] |
8946 | We could make our intuitions about heaps precise with a million-valued logic [Fisher] |
9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
8944 | Vagueness can involve components (like baldness), or not (like boredom) [Fisher] |
8941 | We can't explain 'possibility' in terms of 'possible' worlds [Fisher] |
8947 | If all truths are implied by a falsehood, then not-p might imply both q and not-q [Fisher] |
8949 | In relevance logic, conditionals help information to flow from antecedent to consequent [Fisher] |
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] |