39 ideas
| 13030 | Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen] |
| 13032 | Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen] |
| 13033 | Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen] |
| 13037 | Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen] |
| 13038 | Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen] |
| 13034 | Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen] |
| 13039 | Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen] |
| 13036 | Choice: ∀A ∃R (R well-orders A) [Kunen] |
| 15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |
| 13029 | Set Existence: ∃x (x = x) [Kunen] |
| 13031 | Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen] |
| 13040 | Constructibility: V = L (all sets are constructible) [Kunen] |
| 13258 | The 'aggregative' objections says mereology gets existence and location of objects wrong [Koslicki] |
| 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] |
| 15712 | 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan] |
| 15711 | The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan] |
| 15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
| 15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
| 14505 | Some questions concern mathematical entities, rather than whole structures [Koslicki] |
| 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] |
| 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] |
| 15713 | The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan] |
| 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] |