18 ideas
20771 | Six parts: dialectic, rhetoric, ethics, politics, physics, theology [Cleanthes, by Diog. Laertius] |
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] |
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] |
20752 | For man, being is not what he is, but what he is going to be [Ortega y Gassett] |
18465 | An 'equivalence' relation is one which is reflexive, symmetric and transitive [Kunen] |
6028 | Bodies interact with other bodies, and cuts cause pain, and shame causes blushing, so the soul is a body [Cleanthes, by Nemesius] |
20831 | The soul suffers when the body hurts, creates redness from shame, and pallor from fear [Cleanthes] |
20756 | Instead of having a nature, man only has a history [Ortega y Gassett] |
5993 | The ascending scale of living creatures requires a perfect being [Cleanthes, by Tieleman] |