20 ideas
9766 | Study vagueness first by its logic, then by its truth-conditions, and then its metaphysics [Fine,K] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
9775 | Excluded Middle, and classical logic, may fail for vague predicates [Fine,K] |
9771 | Logic holding between indefinite sentences is the core of all language [Fine,K] |
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] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
13672 | All the axioms for mathematics presuppose set theory [Neumann] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
9768 | Vagueness is semantic, a deficiency of meaning [Fine,K] |
9776 | A thing might be vaguely vague, giving us higher-order vagueness [Fine,K] |
9767 | A vague sentence is only true for all ways of making it completely precise [Fine,K] |
9770 | Logical connectives cease to be truth-functional if vagueness is treated with three values [Fine,K] |
9772 | Meaning is both actual (determining instances) and potential (possibility of greater precision) [Fine,K] |
9773 | With the super-truth approach, the classical connectives continue to work [Fine,K] |
9774 | Borderline cases must be under our control, as capable of greater precision [Fine,K] |
9769 | Vagueness can be in predicates, names or quantifiers [Fine,K] |