40 ideas
| 15163 | The interest of quantified modal logic is its metaphysical necessity and essentialism [Soames] |
| 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] |
| 15158 | Indefinite descriptions are quantificational in subject position, but not in predicate position [Soames] |
| 15157 | Recognising the definite description 'the man' as a quantifier phrase, not a singular term, is a real insight [Soames] |
| 15156 | The universal and existential quantifiers were chosen to suit mathematics [Soames] |
| 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] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 15162 | We understand metaphysical necessity intuitively, from ordinary life [Soames] |
| 15161 | There are more metaphysically than logically necessary truths [Soames] |
| 9312 | Consciousness is reductively explained either by how it represents, or how it is represented [Kriegel/Williford] |
| 9313 | Experiences can be represented consciously or unconsciously, so representation won't explain consciousness [Kriegel/Williford] |
| 9315 | Red tomato experiences are conscious if the state represents the tomato and itself [Kriegel/Williford] |
| 9316 | How is self-representation possible, does it produce a regress, and is experience like that? [Kriegel/Williford] |
| 9314 | Unfortunately, higher-order representations could involve error [Kriegel/Williford] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 15152 | To study meaning, study truth conditions, on the basis of syntax, and representation by the parts [Soames] |
| 15153 | Tarski's account of truth-conditions is too weak to determine meanings [Soames] |
| 15154 | We should use cognitive states to explain representational propositions, not vice versa [Soames] |