36 ideas
| 24032 | Clever scholars can obscure things which are obvious even to peasants [Descartes] |
| 24033 | Most scholastic disputes concern words, where agreeing on meanings would settle them [Descartes] |
| 24024 | The secret of the method is to recognise which thing in a series is the simplest [Descartes] |
| 24018 | One truth leads us to another [Descartes] |
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| 13416 | Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C] |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| 24035 | Unity is something shared by many things, so in that respect they are equals [Descartes] |
| 24036 | I can only see the proportion of two to three if there is a common measure - their unity [Descartes] |
| 24029 | Among the simples are the graspable negations, such as rest and instants [Descartes] |
| 24030 | 3+4=7 is necessary because we cannot conceive of seven without including three and four [Descartes] |
| 24019 | If we accept mere probabilities as true we undermine our existing knowledge [Descartes] |
| 24020 | We all see intuitively that we exist, where intuition is attentive, clear and distinct rational understanding [Descartes] |
| 24031 | When Socrates doubts, he know he doubts, and that truth is possible [Descartes] |
| 24025 | Clear and distinct truths must be known all at once (unlike deductions) [Descartes] |
| 24022 | Our souls possess divine seeds of knowledge, which can bear spontaneous fruit [Descartes] |
| 24034 | If someone had only seen the basic colours, they could deduce the others from resemblance [Descartes] |
| 24021 | The method starts with clear intuitions, followed by a process of deduction [Descartes] |
| 24027 | Nerves and movement originate in the brain, where imagination moves them [Descartes] |
| 24026 | Our four knowledge faculties are intelligence, imagination, the senses, and memory [Descartes] |
| 24028 | The force by which we know things is spiritual, and quite distinct from the body [Descartes] |
| 24023 | All the sciences searching for order and measure are related to mathematics [Descartes] |