36 ideas
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
13258 | The 'aggregative' objections says mereology gets existence and location of objects wrong [Koslicki] |
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] |
13288 | Consequence is truth-preserving, either despite substitutions, or in all interpretations [Koslicki] |
14506 | 'Roses are red; therefore, roses are colored' seems truth-preserving, but not valid in a system [Koslicki] |
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] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
14505 | Some questions concern mathematical entities, rather than whole structures [Koslicki] |
15201 | That Queen Anne is dead is a 'general fact', not a fact about Queen Anne [Prior,AN] |
13289 | Structures have positions, constituent types and number, and some invariable parts [Koslicki] |
14501 | 'Categorical' properties exist in the actual world, and 'hypothetical' properties in other worlds [Koslicki] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
14495 | I aim to put the notion of structure or form back into the concepts of part, whole and object [Koslicki] |
13264 | If a whole is just a structure, a dinner party wouldn't need the guests to turn up [Koslicki] |
14497 | The clay is just a part of the statue (its matter); the rest consists of its form or structure [Koslicki] |
13280 | Statue and clay differ in modal and temporal properties, and in constitution [Koslicki] |
14496 | Structure or form are right at the centre of modern rigorous modes of enquiry [Koslicki] |
13279 | There are at least six versions of constitution being identity [Koslicki] |
14498 | For three-dimensionalist parthood must be a three-place relation, including times [Koslicki] |
13283 | The parts may be the same type as the whole, like a building made of buildings [Koslicki] |
13266 | Wholes in modern mereology are intended to replace sets, so they closely resemble them [Koslicki] |
14500 | Wholes are entities distinct from their parts, and have different properties [Koslicki] |
13281 | Wholes are not just their parts; a whole is an entity distinct from the proper parts [Koslicki] |
14504 | The Kripke/Putnam approach to natural kind terms seems to give them excessive stability [Koslicki] |
13285 | Natural kinds support inductive inferences, from previous samples to the next one [Koslicki] |
13287 | Concepts for species are either intrinsic structure, or relations like breeding or ancestry [Koslicki] |
13284 | Should vernacular classifications ever be counted as natural kind terms? [Koslicki] |
13286 | There are apparently no scientific laws concerning biological species [Koslicki] |
22899 | 'Thank goodness that's over' is not like 'thank goodness that happened on Friday' [Prior,AN] |