37 ideas
| 8868 | Objective truth arises from interpersonal communication [Davidson] |
| 8877 | We can't attain a coherent system by lopping off any beliefs that won't fit [Sosa] |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 8884 | The phenomenal concept of an eleven-dot pattern does not include the concept of eleven [Sosa] |
| 8878 | It is acceptable to say a supermarket door 'knows' someone is approaching [Sosa] |
| 8867 | A belief requires understanding the distinctions of true-and-false, and appearance-and-reality [Davidson] |
| 8880 | In reducing arithmetic to self-evident logic, logicism is in sympathy with rationalism [Sosa] |
| 8881 | Most of our knowledge has insufficient sensory support [Sosa] |
| 8882 | Perception may involve thin indexical concepts, or thicker perceptual concepts [Sosa] |
| 8883 | Do beliefs only become foundationally justified if we fully attend to features of our experience? [Sosa] |
| 8885 | Some features of a thought are known directly, but others must be inferred [Sosa] |
| 8876 | Much propositional knowledge cannot be formulated, as in recognising a face [Sosa] |
| 8879 | Fully comprehensive beliefs may not be knowledge [Sosa] |
| 10347 | Objectivity is intersubjectivity [Davidson] |
| 8866 | If we know other minds through behaviour, but not our own, we should assume they aren't like me [Davidson] |
| 10346 | Knowing other minds rests on knowing both one's own mind and the external world [Davidson, by Dummett] |
| 8870 | Content of thought is established through communication, so knowledge needs other minds [Davidson] |
| 8869 | The principle of charity attributes largely consistent logic and largely true beliefs to speakers [Davidson] |