113 ideas
| 6979 | Serious metaphysics cares about entailment between sentences [Jackson] |
| 6980 | Conceptual analysis studies whether one story is made true by another story [Jackson] |
| 6983 | Intuitions about possibilities are basic to conceptual analysis [Jackson] |
| 14707 | Conceptual analysis is needed to establish that metaphysical reductions respect original meanings [Jackson, by Schroeter] |
| 7005 | Something can only have a place in a preferred account of things if it is entailed by the account [Jackson] |
| 6994 | Truth supervenes on being [Jackson] |
| 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] |
| 14352 | '¬', '&', and 'v' are truth functions: the truth of the compound is fixed by the truth of the components [Jackson] |
| 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] |
| 6984 | Smooth reductions preserve high-level laws in the lower level [Jackson] |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| 6978 | Baldness is just hair distribution, but the former is indeterminate, unlike the latter [Jackson] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 6993 | Redness is a property, but only as a presentation to normal humans [Jackson] |
| 8499 | Nominalists cannot translate 'red resembles pink more than blue' into particulars [Jackson] |
| 8500 | Colour resemblance isn't just resemblance between things; 'colour' must be mentioned [Jackson] |
| 14633 | How do we tell a table's being contingently plastic from its being essentially plastic? [Jackson] |
| 14635 | An x is essentially F if it is F in every possible world in which it appears [Jackson] |
| 14632 | Quine may have conflated de re and de dicto essentialism, but there is a real epistemological problem [Jackson] |
| 6987 | We should not multiply senses of necessity beyond necessity [Jackson] |
| 14360 | Possible worlds for subjunctives (and dispositions), and no-truth for indicatives? [Jackson] |
| 14288 | 'If A,B' affirms that A⊃B, and also that this wouldn't change if A were certain [Jackson, by Edgington] |
| 13769 | Conditionals are truth-functional, but should only be asserted when they are confident [Jackson, by Edgington] |
| 13858 | The truth-functional account of conditionals is right, if the antecedent is really acceptable [Jackson, by Edgington] |
| 14289 | There are some assertable conditionals one would reject if one learned the antecedent [Jackson, by Edgington] |
| 14353 | Modus ponens requires that A→B is F when A is T and B is F [Jackson] |
| 14354 | When A and B have the same truth value, A→B is true, because A→A is a logical truth [Jackson] |
| 14355 | (A&B)→A is a logical truth, even if antecedent false and consequent true, so it is T if A is F and B is T [Jackson] |
| 14358 | In the possible worlds account of conditionals, modus ponens and modus tollens are validated [Jackson] |
| 14359 | Only assertions have truth-values, and conditionals are not proper assertions [Jackson] |
| 14357 | Possible worlds account, unlike A⊃B, says nothing about when A is false [Jackson] |
| 14356 | We can't insist that A is relevant to B, as conditionals can express lack of relevance [Jackson] |
| 14631 | How can you show the necessity of an a posteriori necessity, if it might turn out to be false? [Jackson] |
| 6988 | Mathematical sentences are a problem in a possible-worlds framework [Jackson] |
| 6975 | Possible worlds could be concrete, abstract, universals, sentences, or properties [Jackson] |
| 6982 | Long arithmetic calculations show the a priori can be fallible [Jackson] |
| 6991 | We examine objects to determine colour; we do not introspect [Jackson] |
| 4894 | I say Mary does not have new knowledge, but knows an old fact in a new way [Perry on Jackson] |
| 4895 | Is it unfair that physicalist knowledge can be written down, but dualist knowledge can't be [Perry on Jackson] |
| 4886 | Mary knows all the physical facts of seeing red, but experiencing it is new knowledge [Jackson] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 6976 | In physicalism, the psychological depends on the physical, not the other way around [Jackson] |
| 6986 | Is the dependence of the psychological on the physical a priori or a posteriori? [Jackson] |
| 6992 | If different states can fulfil the same role, the converse must also be possible [Jackson] |
| 7880 | If a blind persons suddenly sees a kestrel, that doesn't make visual and theoretical kestrels different [Papineau on Jackson] |
| 7378 | No one bothers to imagine what it would really be like to have ALL the physical information [Dennett on Jackson] |
| 7377 | Mary learns when she sees colour, so her complete physical information had missed something [Jackson] |
| 6996 | Folk psychology covers input, internal role, and output [Jackson] |
| 6977 | Egocentric or de se content seems to be irreducibly so [Jackson] |
| 6990 | Keep distinct the essential properties of water, and application conditions for the word 'water' [Jackson] |
| 6985 | Analysis is finding necessary and sufficient conditions by studying possible cases [Jackson] |
| 6995 | Successful predication supervenes on nature [Jackson] |
| 6989 | I can understand "He has a beard", without identifying 'he', and hence the truth conditions [Jackson] |
| 6998 | Folk morality does not clearly distinguish between doing and allowing [Jackson] |
| 6997 | Moral functionalism says moral terms get their meaning from their role in folk morality [Jackson] |
| 7000 | Which are prior - thin concepts like right, good, ought; or thick concepts like kindness, equity etc.? [Jackson] |
| 6999 | It is hard to justify the huge difference in our judgements of abortion and infanticide [Jackson] |