23 ideas
22820 | Early Romantics sought a plurality of systems, in a quest for freedom [Hösle] |
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] |
18465 | An 'equivalence' relation is one which is reflexive, symmetric and transitive [Kunen] |
22189 | Why abandon a theory if you don't have a better one? [Gorham] |
22190 | If a theory is more informative it is less probable [Gorham] |
22195 | Structural Realists must show the mathematics is both crucial and separate [Gorham] |
22192 | Is Newton simpler with universal simultaneity, or Einstein simpler without absolute time? [Gorham] |
22194 | Structural Realism says mathematical structures persist after theory rejection [Gorham] |
22197 | Theories aren't just for organising present experience if they concern the past or future [Gorham] |
22196 | For most scientists their concepts are not just useful, but are meant to be true and accurate [Gorham] |
22193 | Consilience makes the component sciences more likely [Gorham] |
22819 | In the 18th century history came to be seen as progressive, rather than cyclical [Hösle] |
22198 | Aristotelian physics has circular celestial motion and linear earthly motion [Gorham] |