32 ideas
14782 | Philosophy is an experimental science, resting on common experience [Peirce] |
14787 | Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce] |
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] |
21495 | Theoretical and practical politics are both concerned with the best lives for individuals [Russell] |
14783 | Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce] |
14788 | Mathematics is close to logic, but is even more abstract [Peirce] |
14786 | Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce] |
14789 | Experience is indeed our only source of knowledge, provided we include inner experience [Peirce] |
14785 | The world is one of experience, but experiences are always located among our ideas [Peirce] |
14784 | Ethics is the science of aims [Peirce] |
21517 | Individuals need creativity, reverence for others, and self-respect [Russell] |
21523 | We would not want UK affairs to be settled by a world parliament [Russell] |
21522 | Democracy is inadequate without a great deal of devolution [Russell] |
21521 | Anarchy does not maximise liberty [Russell] |
21528 | Groups should be autonomous, with a neutral authority as arbitrator [Russell] |
21527 | On every new question the majority is always wrong at first [Russell] |
21526 | Unfortunately ordinary voters can't detect insincerity [Russell] |
21525 | When the state is the only employer, there is no refuge from the prejudices of other people [Russell] |
21518 | Men unite in pursuit of material things, and idealise greed as part of group loyalty [Russell] |
21519 | We need security and liberty, and then encouragement of creativity [Russell] |
21524 | The right to own land gives a legal right to a permanent income [Russell] |
21520 | That our heaven is a dull place reflects the misery of excessive work in life [Russell] |