84 ideas
| 23948 | Wisdom needs both thought and passion, with each reflecting on the other [Solomon] |
| 23942 | Philosophy is creating an intellectual conceptual structure for life [Solomon] |
| 23945 | Reason is actually passions, guided by perspicacious reflection [Solomon] |
| 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] |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| 10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [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] |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| 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] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [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] |
| 23957 | We often trust our intuitions as rational, despite their lack of reflection [Solomon] |
| 23943 | Distinguishing reason from passion is based on an archaic 'faculty' theory [Solomon] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 23952 | I say bodily chemistry and its sensations have nothing to do with emotions [Solomon] |
| 23954 | Emotions are judgements about ourselves, and our place in the world [Solomon] |
| 23960 | Emotions are defined by their objects [Solomon] |
| 23961 | The heart of an emotion is its judgement of values and morality [Solomon] |
| 23965 | Emotions can be analysed under fifteen headings [Solomon] |
| 23959 | Some emotions are externally directed, others internally [Solomon] |
| 23936 | It is only our passions which give our lives meaning [Solomon] |
| 23963 | Which emotions we feel depends on our sense of our own powers [Solomon] |
| 23946 | The passions are subjective, concerning what is important to me, rather than facts [Solomon] |
| 23940 | Emotions are strategies for maximising our sense of dignity and self-esteem [Solomon] |
| 23949 | Passions exist as emotions, moods and desires, which all generate meaning [Solomon] |
| 23956 | The Myth of the Passions says they are irrational, uncontrolled and damaging [Solomon] |
| 23953 | Feeling is a superficial aspect of emotion, and may be indeterminate, or even absent [Solomon] |
| 23964 | There are no 'basic' emotions, only socially prevalent ones [Solomon] |
| 23937 | It is reason which needs the anchorage of passions, rather than vice versa [Solomon] |
| 23947 | Dividing ourselves into confrontational reason and passion destroys our harmonious whole [Solomon] |
| 23958 | The supposed irrationality of our emotions is often tactless or faulty expression of them [Solomon] |
| 23944 | Emotions are our life force, and the source of most of our values [Solomon] |
| 23962 | Lovers adopt the interests of their beloved, rather than just valuing them [Solomon] |
| 23941 | 'Absurdity' is just the result of our wrong choices in life [Solomon] |
| 23955 | Ideologies are mythologies which guide our actions [Solomon] |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |