22 ideas
10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
10001 | An adjective contributes semantically to a noun phrase [Hofweber] |
10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |
10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
10003 | Why is arithmetic hard to learn, but then becomes easy? [Hofweber] |
10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |
10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |
10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
10004 | Our minds are at their best when reasoning about objects [Hofweber] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |