19 ideas
10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
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] |
11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
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] |
17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
18087 | If x changes by less and less, it must approach a limit [Dedekind] |
10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |