30 ideas
17729 | Examining concepts can recover information obtained through the senses [Jenkins] |
17740 | Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins] |
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] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
10290 | Second-order variables also range over properties, sets, relations or functions [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] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
17730 | Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
17719 | Arithmetic concepts are indispensable because they accurately map the world [Jenkins] |
17717 | Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins] |
17724 | It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins] |
17727 | We can learn about the world by studying the grounding of our concepts [Jenkins] |
17720 | There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG] |
17728 | The concepts we have to use for categorising are ones which map the real world well [Jenkins] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
17726 | Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins] |
17734 | It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins] |
17723 | Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins] |
17739 | The physical effect of world on brain explains the concepts we possess [Jenkins] |
17718 | Grounded concepts are trustworthy maps of the world [Jenkins] |
17731 | Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins] |
17732 | Success semantics explains representation in terms of success in action [Jenkins] |
19216 | Propositions (such as 'that dog is barking') only exist if their items exist [Williamson] |
17725 | 'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins] |