14 ideas
10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
13342 | Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap] |
13251 | Each person is free to build their own logic, just by specifying a syntax [Carnap] |
10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
14775 | Numbers are just names devised for counting [Peirce] |
10885 | Computer proofs don't provide explanations [Horsten] |
10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
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] |