32 ideas
| 19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
| 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] |
| 19067 | A successful proof requires recognition of truth at every step [Dummett] |
| 19060 | Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett] |
| 11066 | Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna] |
| 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] |
| 19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
| 16865 | 'Theorems' are both proved, and used in proofs [Frege] |
| 19063 | Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett] |
| 19059 | In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett] |
| 19062 | Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett] |
| 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] |
| 19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett] |
| 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] |
| 13128 | 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins] |
| 9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
| 19061 | An explanation is often a deduction, but that may well beg the question [Dummett] |
| 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] |
| 19064 | Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett] |
| 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] |