17 ideas
| 9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
| 9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
| 18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
| 9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
| 18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
| 9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
| 9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
| 18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
| 9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
| 9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
| 18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
| 17555 | 'One' can mean undivided and not a multitude, or it can add measurement, giving number [Aquinas] |
| 18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
| 18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
| 18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
| 18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
| 18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |