40 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] |
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] |
7771 | We need 'events' to explain adverbs, which are adjectival predicates of events [Davidson, by Lycan] |
8860 | Language-learning is not good enough evidence for the existence of events [Yablo on Davidson] |
15002 | If the best theory of adverbs refers to events, then our ontology should include events [Davidson, by Sider] |
2730 | Because 'gold is malleable' is necessary does not mean that it is analytic [Audi,R] |
2715 | Beliefs are based on perception, memory, introspection or reason [Audi,R] |
2735 | Could you have a single belief on its own? [Audi,R] |
2736 | We can make certain of what we know, so knowing does not entail certainty [Audi,R] |
2721 | If you gradually remove a book's sensory properties, what is left at the end? [Audi,R] |
2722 | Sense-data theory is indirect realism, but phenomenalism is direct irrealism [Audi,R] |
2728 | The concepts needed for a priori thought may come from experience [Audi,R] |
2727 | Red and green being exclusive colours seems to be rationally graspable but not analytic [Audi,R] |
2716 | To see something as a field, I obviously need the concept of a field [Audi,R] |
2717 | How could I see a field and believe nothing regarding it? [Audi,R] |
2719 | Sense data imply representative realism, possibly only representing primary qualities [Audi,R] |
2720 | Sense-data (and the rival 'adverbial' theory) are to explain illusions and hallucinations [Audi,R] |
2718 | Perception is first simple, then objectual (with concepts) and then propositional [Audi,R] |
2741 | The principles of justification have to be a priori [Audi,R] |
2729 | Virtually all rationalists assert that we can have knowledge of synthetic a priori truths [Audi,R] |
2725 | To remember something is to know it [Audi,R] |
2724 | I might remember someone I can't recall or image, by recognising them on meeting [Audi,R] |
2731 | Justification is either unanchored (infinite or circular), or anchored (in knowledge or non-knowledge) [Audi,R] |
2739 | Internalism about justification implies that there is a right to believe something [Audi,R] |
2732 | Maths may be consistent with observations, but not coherent [Audi,R] |
2733 | It is very hard to show how much coherence is needed for justification [Audi,R] |
2734 | A consistent madman could have a very coherent belief system [Audi,R] |
2738 | Consistent accurate prediction looks like knowledge without justified belief [Audi,R] |
2740 | A reliability theory of knowledge seems to involve truth as correspondence [Audi,R] |
2737 | 'Reliable' is a very imprecise term, and may even mean 'justified' [Audi,R] |
2726 | We can be ignorant about ourselves, for example, our desires and motives [Audi,R] |