25 ideas
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
8443 | Mereological essentialism says an entity must have exactly those parts [Sosa] |
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] |
8442 | What law would explain causation in the case of causing a table to come into existence? [Sosa] |
8445 | The necessitated is not always a result or consequence of the necessitator [Sosa] |
8444 | Where is the necessary causation in the three people being tall making everybody tall? [Sosa] |