58 ideas
| 13786 | Wisdom is called 'beautiful', because it performs fine works [Plato] |
| 13780 | Good people are no different from wise ones [Plato] |
| 7740 | There exists a realm, beyond objects and ideas, of non-spatio-temporal thoughts [Frege, by Weiner] |
| 13778 | A dialectician is someone who knows how to ask and to answer questions [Plato] |
| 19466 | The word 'true' seems to be unique and indefinable [Frege] |
| 13776 | Truths say of what is that it is, falsehoods say of what is that it is not [Plato] |
| 19465 | There cannot be complete correspondence, because ideas and reality are quite different [Frege] |
| 19468 | The property of truth in 'It is true that I smell violets' adds nothing to 'I smell violets' [Frege] |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 13777 | A name is a sort of tool [Plato] |
| 13790 | A name-giver might misname something, then force other names to conform to it [Plato] |
| 13791 | Things must be known before they are named, so it can't be the names that give us knowledge [Plato] |
| 13789 | Anyone who knows a thing's name also knows the thing [Plato] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| 18182 | The extension of concepts is not important to me [Maddy] |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 19470 | Thoughts in the 'third realm' cannot be sensed, and do not need an owner to exist [Frege] |
| 2063 | How can beauty have identity if it changes? [Plato] |
| 19471 | A fact is a thought that is true [Frege] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 13775 | We only succeed in cutting if we use appropriate tools, not if we approach it randomly [Plato] |
| 9877 | Late Frege saw his non-actual objective objects as exclusively thoughts and senses [Frege, by Dummett] |
| 13787 | Doesn't each thing have an essence, just as it has other qualities? [Plato] |
| 13774 | Things don't have every attribute, and essence isn't private, so each thing has an essence [Plato] |
| 13772 | Is the being or essence of each thing private to each person? [Plato] |
| 13788 | If we made a perfect duplicate of Cratylus, there would be two Cratyluses [Plato] |
| 13792 | There can't be any knowledge if things are constantly changing [Plato] |
| 13781 | Soul causes the body to live, and gives it power to breathe and to be revitalized [Plato] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 19469 | We grasp thoughts (thinking), decide they are true (judgement), and manifest the judgement (assertion) [Frege] |
| 8162 | Thoughts have their own realm of reality - 'sense' (as opposed to the realm of 'reference') [Frege, by Dummett] |
| 9818 | A thought is distinguished from other things by a capacity to be true or false [Frege, by Dummett] |
| 16379 | Thoughts about myself are understood one way to me, and another when communicated [Frege] |
| 19467 | A 'thought' is something for which the question of truth can arise; thoughts are senses of sentences [Frege] |
| 19472 | A sentence is only a thought if it is complete, and has a time-specification [Frege] |
| 13785 | 'Arete' signifies lack of complexity and a free-flowing soul [Plato] |
| 13779 | The natural offspring of a lion is called a 'lion' (but what about the offspring of a king?) [Plato] |
| 13783 | Even the gods love play [Plato] |