35 ideas
| 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] |
| 7306 | If the only property of a name was its reference, we couldn't explain bearerless names [Miller,A] |
| 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] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 7322 | Constitutive scepticism is about facts, and epistemological scepticism about our ability to know them [Miller,A] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 7325 | Dispositions say what we will do, not what we ought to do, so can't explain normativity [Miller,A] |
| 7324 | Explain meaning by propositional attitudes, or vice versa, or together? [Miller,A] |
| 7323 | If truth is deflationary, sentence truth-conditions just need good declarative syntax [Miller,A] |
| 7315 | 'Jones is a married bachelor' does not have the logical form of a contradiction [Miller,A] |
| 7328 | The principle of charity is holistic, saying we must hold most of someone's system of beliefs to be true [Miller,A] |
| 7329 | Maybe we should interpret speakers as intelligible, rather than speaking truth [Miller,A] |
| 7333 | The Frege-Geach problem is that I can discuss the wrongness of murder without disapproval [Miller,A] |