17 ideas
10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
10152 | Set theory and logic are fairy tales, but still worth studying [Tarski] |
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] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
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] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
10151 | I am a deeply convinced nominalist [Tarski] |