37 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] |
| 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] |
| 23634 | Accepting the existence of anything presupposes the notion of existence [Reid] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 23635 | Truths are self-evident to sensible persons who understand them clearly without prejudice [Reid] |
| 7631 | Sensation is not committed to any external object, but perception is [Reid] |
| 23637 | Primary qualities are the object of mathematics [Reid] |
| 23638 | Secondary qualities conjure up, and are confused with, the sensations which produce them [Reid] |
| 23639 | It is unclear whether a toothache is in the mind or in the tooth, but the word has a single meaning [Reid] |
| 6492 | Reid is seen as the main direct realist of the eighteenth century [Reid, by Robinson,H] |
| 23641 | People dislike believing without evidence, and try to avoid it [Reid] |
| 23642 | If non-rational evidence reaches us, it is reason which then makes use of it [Reid] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 23640 | Only mature minds can distinguish the qualities of a body [Reid] |
| 16709 | Some people return to scholastic mysterious qualities, disguising them as 'forces' [Leibniz] |