13 ideas
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] |
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] |
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] |
10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
8921 | Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman] |
8922 | Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman] |
12167 | Reference without predication is the characteristic of expression [Scruton] |
12166 | If music refers to love, it contains no predication, so it is expression, not language [Scruton] |
12168 | Music is not representational, since thoughts about a subject are never essential to it [Scruton] |