27 ideas
| 19115 | You can 'rebut' an argument's conclusion, or 'undercut' its premises [Antonelli] |
| 19119 | We infer that other objects are like some exceptional object, if they share some of its properties [Antonelli] |
| 19111 | Reasoning may be defeated by new premises, or by finding out more about the given ones [Antonelli] |
| 19114 | Should we accept Floating Conclusions, derived from two arguments in conflict? [Antonelli] |
| 19113 | Weakest Link Principle: prefer the argument whose weakest link is the stronger [Antonelli] |
| 19116 | Non-monotonic core: Reflexivity, Cut, Cautious Monotonicity, Left Logical Equivalence, Right Weakening [Antonelli] |
| 19117 | We can rank a formula by the level of surprise if it were to hold [Antonelli] |
| 19118 | People don't actually use classical logic, but may actually use non-monotonic logic [Antonelli] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 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] |
| 19110 | In classical logic the relation |= has Monotony built into its definition [Antonelli] |
| 19112 | Cautious Monotony ignores proved additions; Rational Monotony fails if the addition's negation is proved [Antonelli] |
| 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] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 2705 | How can intuitionists distinguish universal convictions from local cultural ones? [Hare] |
| 2712 | You can't use intuitions to decide which intuitions you should cultivate [Hare] |
| 2706 | Emotivists mistakenly think all disagreements are about facts, and so there are no moral reasons [Hare] |
| 2709 | Prescriptivism sees 'ought' statements as imperatives which are universalisable [Hare] |
| 2704 | If morality is just a natural or intuitive description, that leads to relativism [Hare] |
| 2703 | Descriptivism say ethical meaning is just truth-conditions; prescriptivism adds an evaluation [Hare] |
| 2707 | If there can be contradictory prescriptions, then reasoning must be involved [Hare] |
| 2708 | An 'ought' statement implies universal application [Hare] |
| 2711 | Prescriptivism implies a commitment, but descriptivism doesn't [Hare] |
| 2710 | Moral judgements must invoke some sort of principle [Hare] |