17 ideas
| 9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
| 9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
| 9965 | There couldn't just be one number, such as 17 [Jubien] |
| 14775 | Numbers are just names devised for counting [Peirce] |
| 9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
| 9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
| 9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
| 9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
| 14776 | That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce] |
| 9969 | The empty set is the purest abstract object [Jubien] |
| 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] |
| 14773 | A truth is hard for us to understand if it rests on nothing but inspiration [Peirce] |
| 14772 | If we decide an idea is inspired, we still can't be sure we have got the idea right [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] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |