41 ideas
| 17651 | Without words or other symbols, we have no world [Goodman] |
| 18776 | Contextual definitions eliminate descriptions from contexts [Linsky,B] |
| 17652 | Truth is irrelevant if no statements are involved [Goodman] |
| 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] |
| 18774 | Definite descriptions, unlike proper names, have a logical structure [Linsky,B] |
| 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] |
| 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] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [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] |
| 17656 | Being primitive or prior always depends on a constructional system [Goodman] |
| 17661 | We don't recognise patterns - we invent them [Goodman] |
| 17659 | Reality is largely a matter of habit [Goodman] |
| 17657 | We build our world, and ignore anything that won't fit [Goodman] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 17654 | A world can be full of variety or not, depending on how we sort it [Goodman] |
| 17653 | Things can only be judged the 'same' by citing some respect of sameness [Goodman] |
| 17660 | Discovery is often just finding a fit, like a jigsaw puzzle [Goodman] |
| 17658 | Users of digital thermometers recognise no temperatures in the gaps [Goodman] |
| 17650 | We lack frames of reference to transform physics, biology and psychology into one another [Goodman] |
| 17655 | Grue and green won't be in the same world, as that would block induction entirely [Goodman] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 17649 | If the world is one it has many aspects, and if there are many worlds they will collect into one [Goodman] |