15 ideas
17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
14775 | Numbers are just names devised for counting [Peirce] |
17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
14776 | That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce] |
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] |
19399 | Prime matter is nothing when it is at rest [Leibniz] |