28 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] |
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] |
17518 | Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers] |
17516 | If counting needs a sortal, what of things which fall under two sortals? [Ayers] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
17520 | Events do not have natural boundaries, and we have to set them [Ayers] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
17519 | To express borderline cases of objects, you need the concept of an 'object' [Ayers] |
17510 | Speakers need the very general category of a thing, if they are to think about it [Ayers] |
17522 | We use sortals to classify physical objects by the nature and origin of their unity [Ayers] |
17515 | Seeing caterpillar and moth as the same needs continuity, not identity of sortal concepts [Ayers] |
17511 | Recognising continuity is separate from sortals, and must precede their use [Ayers] |
17517 | Could the same matter have more than one form or principle of unity? [Ayers] |
17513 | If there are two objects, then 'that marble, man-shaped object' is ambiguous [Ayers] |
17523 | Sortals basically apply to individuals [Ayers] |
17521 | You can't have the concept of a 'stage' if you lack the concept of an object [Ayers] |
17514 | Temporal 'parts' cannot be separated or rearranged [Ayers] |
17509 | Some say a 'covering concept' completes identity; others place the concept in the reference [Ayers] |
17512 | If diachronic identities need covering concepts, why not synchronic identities too? [Ayers] |
15666 | To understand language is to know how to use it to reach shared understandings [Habermas] |