21 ideas
| 10304 | Very few things in set theory remain valid in intuitionist mathematics [Bernays] |
| 14775 | Numbers are just names devised for counting [Peirce] |
| 10303 | Restricted Platonism is just an ideal projection of a domain of thought [Bernays] |
| 14776 | That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce] |
| 10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
| 14770 | Reasoning is based on statistical induction, so it can't achieve certainty or precision [Peirce] |
| 14774 | Innate truths are very uncertain and full of error, so they certainly have exceptions [Peirce] |
| 14772 | If we decide an idea is inspired, we still can't be sure we have got the idea right [Peirce] |
| 14773 | A truth is hard for us to understand if it rests on nothing but inspiration [Peirce] |
| 14771 | Only reason can establish whether some deliverance of revelation really is inspired [Peirce] |
| 14769 | Only imagination can connect phenomena together in a rational way [Peirce] |
| 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] |
| 2708 | An 'ought' statement implies universal application [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] |
| 2711 | Prescriptivism implies a commitment, but descriptivism doesn't [Hare] |
| 2709 | Prescriptivism sees 'ought' statements as imperatives which are universalisable [Hare] |
| 2710 | Moral judgements must invoke some sort of principle [Hare] |