48 ideas
| 2956 | There is nothing so obvious that a philosopher cannot be found to deny it [Lockwood] |
| 2963 | There may only be necessary and sufficient conditions (and counterfactuals) because we intervene in the world [Lockwood] |
| 2958 | No one has ever succeeded in producing an acceptable non-trivial analysis of anything [Lockwood] |
| 2959 | If something is described in two different ways, is that two facts, or one fact presented in two ways? [Lockwood] |
| 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] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 18190 | Completed infinities resulted from giving foundations to calculus [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] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [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] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic 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] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| 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] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 2969 | How does a direct realist distinguish a building from Buckingham Palace? [Lockwood] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 3570 | Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M] |
| 2970 | Dogs seem to have beliefs, and beliefs require concepts [Lockwood] |
| 2961 | Empiricism is a theory of meaning as well as of knowledge [Lockwood] |
| 2960 | Commonsense realism must account for the similarity of genuine perceptions and known illusions [Lockwood] |
| 2748 | A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J] |
| 2952 | A 1988 estimate gave the brain 3 x 10-to-the-14 synaptic junctions [Lockwood] |
| 2964 | How come unconscious states also cause behaviour? [Lockwood] |
| 2951 | Could there be unconscious beliefs and desires? [Lockwood] |
| 2953 | Fish may operate by blindsight [Lockwood] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 2967 | We might even learn some fundamental physics from introspection [Lockwood] |
| 2966 | Can phenomenal qualities exist unsensed? [Lockwood] |
| 2955 | If mental events occur in time, then relativity says they are in space [Lockwood] |
| 2950 | Only logical positivists ever believed behaviourism [Lockwood] |
| 2954 | Identity theory likes the identity of lightning and electrical discharges [Lockwood] |
| 2971 | Perhaps logical positivism showed that there is no dividing line between science and metaphysics [Lockwood] |
| 2962 | Maybe causation is a form of rational explanation, not an observation or a state of mind [Lockwood] |
| 2949 | We have the confused idea that time is a process of change [Lockwood] |