48 ideas
| 20320 | Truth is what unites, and the profound truths create a community [Jaspers] |
| 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] |
| 8195 | Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 18190 | Completed infinities resulted from giving foundations to calculus [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] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [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] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic 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] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [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] |
| 8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
| 8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
| 8192 | I no longer think what a statement about the past says is just what can justify it [Dummett] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 20323 | Freedom needs knowledge, the possibility of arbitrariness, and law [Jaspers] |
| 20322 | I am aware that freedom is possible, and the freedom is not in theory, but in seeking freedom [Jaspers] |
| 8193 | Verification is not an individual but a collective activity [Dummett] |
| 8189 | Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett] |
| 8191 | The truth-conditions theory must get agreement on a conception of truth [Dummett] |
| 20324 | My freedom increases as I broaden my vision of possiblities and motives [Jaspers] |
| 20321 | The struggle for Existenz is between people who are equals, and are utterly honest [Jaspers] |
| 20318 | My helplessness in philosophising reveals my being, and begins its upsurge [Jaspers] |
| 20325 | Once we grasp freedom 'from' things, then freedom 'for' things becomes urgent [Jaspers] |
| 20315 | 'Existenz' is the potential being, which I could have, and ought to have [Jaspers] |
| 20317 | Mundane existence is general, falling under universals, but Existens is unique to individuals [Jaspers] |
| 20319 | We want the correct grasp on being that is neither solipsism nor absorption in the crowd [Jaspers] |
| 20316 | Every decision I make moves towards or away from fulfilled Existenz [Jaspers] |
| 8197 | Maybe past (which affects us) and future (which we can affect) are both real [Dummett] |
| 8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |