35 ideas
18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
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] |
18789 | Intuitionist logic looks best as natural deduction [Mares] |
18790 | Intuitionism as natural deduction has no rule for negation [Mares] |
18787 | Three-valued logic is useful for a theory of presupposition [Mares] |
16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
18793 | Material implication (and classical logic) considers nothing but truth values for implications [Mares] |
18784 | In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares] |
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] |
18780 | Standard disjunction and negation force us to accept the principle of bivalence [Mares] |
18786 | Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares] |
18782 | The connectives are studied either through model theory or through proof theory [Mares] |
16865 | 'Theorems' are both proved, and used in proofs [Frege] |
18783 | Many-valued logics lack a natural deduction system [Mares] |
18792 | Situation semantics for logics: not possible worlds, but information in situations [Mares] |
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] |
18785 | Consistency is semantic, but non-contradiction is syntactic [Mares] |
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] |
18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
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] |
18791 | In 'situation semantics' our main concepts are abstracted from situations [Mares] |
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] |
467 | A virtue is a combination of intelligence, strength and luck [Ion] |