112 ideas
| 14227 | We could refer to tables as 'xs that are arranged tablewise' [Inwagen] |
| 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] |
| 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] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [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] |
| 8972 | What in the real world could ground the distinction between the sets {A,{A,B}} and {B,{A,B}}? [Inwagen] |
| 10662 | Mereology is 'nihilistic' (just atoms) or 'universal' (no restrictions on what is 'whole') [Inwagen, by Varzi] |
| 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] |
| 17587 | The 'Law' of Excluded Middle needs all propositions to be definitely true or definitely false [Inwagen] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 17558 | Variables are just like pronouns; syntactic explanations get muddled over dummy letters [Inwagen] |
| 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] |
| 17583 | There are no heaps [Inwagen] |
| 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] |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| 18182 | The extension of concepts is not important to me [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] |
| 17578 | I reject talk of 'stuff', and treat it in terms of particles [Inwagen] |
| 17582 | Singular terms can be vague, because they can contain predicates, which can be vague [Inwagen] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 17556 | Material objects are in space and time, move, have a surface and mass, and are made of some stuff [Inwagen] |
| 8264 | Maybe table-shaped particles exist, but not tables [Inwagen, by Lowe] |
| 17565 | Nihilism says composition between single things is impossible [Inwagen] |
| 14228 | If there are no tables, but tables are things arranged tablewise, the denial of tables is a contradiction [Liggins on Inwagen] |
| 14468 | Actions by artefacts and natural bodies are disguised cooperations, so we don't need them [Inwagen] |
| 17571 | Every physical thing is either a living organism or a simple [Inwagen] |
| 17562 | The statue and lump seem to share parts, but the statue is not part of the lump [Inwagen] |
| 17574 | If you knead clay you make an infinite series of objects, but they are rearrangements, not creations [Inwagen] |
| 17531 | I assume matter is particulate, made up of 'simples' [Inwagen] |
| 17560 | If contact causes composition, do two colliding balls briefly make one object? [Inwagen] |
| 17561 | If bricks compose a house, that is at least one thing, but it might be many things [Inwagen] |
| 17566 | I think parthood involves causation, and not just a reasonably stable spatial relationship [Inwagen] |
| 14230 | We can deny whole objects but accept parts, by referring to them as plurals within things [Inwagen, by Liggins] |
| 17557 | Special Composition Question: when is a thing part of something? [Inwagen] |
| 17564 | The essence of a star includes the released binding energy which keeps it from collapse [Inwagen] |
| 17575 | The persistence of artifacts always covertly involves intelligent beings [Inwagen] |
| 17577 | When an electron 'leaps' to another orbit, is the new one the same electron? [Inwagen] |
| 17589 | If you reject transitivity of vague identity, there is no Ship of Theseus problem [Inwagen] |
| 17588 | We should talk of the transitivity of 'identity', and of 'definite identity' [Inwagen] |
| 17572 | Actuality proves possibility, but that doesn't explain how it is possible [Inwagen] |
| 17579 | Counterparts reduce counterfactual identity to problems about similarity relations [Inwagen] |
| 17590 | A merely possible object clearly isn't there, so that is a defective notion [Inwagen] |
| 17591 | Merely possible objects must be consistent properties, or haecceities [Inwagen] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 6981 | Determinism clashes with free will, as the past determines action, and is beyond our control [Inwagen, by Jackson] |
| 7404 | Nations are not obliged to help one-another, but are obliged not to harm one another [Grotius, by Tuck] |
| 7101 | Virtue theory needs an external standard to judge behaviour and character [Inwagen, by Statman] |
| 7402 | Everyone has a right of self-preservation, and harming others is usually unjustifiable [Grotius, by Tuck] |
| 21938 | Democracy needs respect for individuality, but the 'community of friends' implies strict equality [Grotius] |
| 19845 | A person is free to renounce their state, as long as it is not a moment of crisis [Grotius, by Rousseau] |
| 22133 | Grotius and Pufendorf based natural law on real (rather than idealised) humanity [Grotius, by Ford,JD] |
| 7406 | A natural right of self-preservation is balanced by a natural law to avoid unnecessary harm [Grotius, by Tuck] |
| 7403 | Grotius ignored elaborate natural law theories, preferring a basic right of self-preservation [Grotius, by Tuck] |
| 23585 | It is permissible in a just cause to capture a place in neutral territory [Grotius] |
| 17563 | The strong force pulls, but also pushes apart if nucleons get too close together [Inwagen] |
| 17559 | Is one atom a piece of gold, or is a sizable group of atoms required? [Inwagen] |
| 17586 | At the lower level, life trails off into mere molecular interaction [Inwagen] |
| 17570 | The chemical reactions in a human life involve about sixteen elements [Inwagen] |
| 17585 | Life is vague at both ends, but could it be totally vague? [Inwagen] |
| 17568 | A tumour may spread a sort of life, but it is not a life, or an organism [Inwagen] |
| 17581 | Being part of an organism's life is a matter of degree, and vague [Inwagen] |
| 17567 | A flame is like a life, but not nearly so well individuated [Inwagen] |
| 17576 | If God were to 'reassemble' my atoms of ten years ago, the result would certainly not be me [Inwagen] |
| 17584 | Some events are only borderline cases of lives [Inwagen] |
| 17569 | Unlike waves, lives are 'jealous'; it is almost impossible for them to overlap [Inwagen] |
| 17580 | One's mental and other life is centred on the brain, unlike any other part of the body [Inwagen] |
| 6892 | Moral principles have some validity without a God commanding obedience [Grotius, by Mautner] |
| 17573 | There is no reason to think that mere existence is a valuable thing [Inwagen] |