17 ideas
13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski] |
10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
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] |
13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski] |
13336 | A language containing its own semantics is inconsistent - but we can use a second language [Tarski] |
10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |
10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
13745 | Supervenience is not a dependence relation, on the lines of causal, mereological or semantic dependence [Kim] |
13746 | Supervenience is just a 'surface' relation of pattern covariation, which still needs deeper explanation [Kim] |