20 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] |
13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
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] |
13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey] |
13334 | Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey] |
13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
22328 | I just confront the evidence, and let it act on me [Ramsey] |
22325 | A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey] |
16711 | Heretics should be eradicated like wolves [Aquinas] |