47 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] |
8195 | Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett] |
8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
8192 | I no longer think what a statement about the past says is just what can justify it [Dummett] |
8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |
8193 | Verification is not an individual but a collective activity [Dummett] |
8189 | Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett] |
8191 | The truth-conditions theory must get agreement on a conception of truth [Dummett] |
7222 | It is a crime for someone with a violent disposition to get drunk [Mill] |
7214 | Ethics rests on utility, which is the permanent progressive interests of people [Mill] |
7212 | Individuals have sovereignty over their own bodies and minds [Mill] |
7210 | The will of the people is that of the largest or most active part of the people [Mill] |
7227 | It is evil to give a government any more power than is necessary [Mill] |
7228 | Individuals often do things better than governments [Mill] |
7230 | Aim for the maximum dissemination of power consistent with efficiency [Mill] |
20515 | Maximise happiness by an area of strict privacy, and an area of utilitarian interventions [Mill, by Wolff,J] |
7229 | People who transact their own business will also have the initiative to control their government [Mill] |
7211 | Prevention of harm to others is the only justification for exercising power over people [Mill] |
7231 | The worth of a State, in the long run, is the worth of the individuals composing it [Mill] |
7217 | The main argument for freedom is that interference with it is usually misguided [Mill] |
7213 | Liberty arises at the point where people can freely and equally discuss things [Mill] |
20517 | Utilitarianism values liberty, but guides us on which ones we should have or not have [Mill, by Wolff,J] |
20516 | Mill defends freedom as increasing happiness, but maybe it is an intrinsic good [Wolff,J on Mill] |
7215 | True freedom is pursuing our own good, while not impeding others [Mill] |
7218 | Individuals are not accountable for actions which only concern themselves [Mill] |
7221 | Blocking entry to an unsafe bridge does not infringe liberty, since no one wants unsafe bridges [Mill] |
7223 | Pimping and running a gambling-house are on the border between toleration and restraint [Mill] |
7220 | Restraint for its own sake is an evil [Mill] |
7219 | Society can punish actions which it believes to be prejudicial to others [Mill] |
7226 | Benefits performed by individuals, not by government, help also to educate them [Mill] |
7224 | We need individual opinions and conduct, and State education is a means to prevent that [Mill] |
7225 | It is a crime to create a being who lacks the ordinary chances of a desirable existence [Mill] |
8197 | Maybe past (which affects us) and future (which we can affect) are both real [Dummett] |
8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |
7216 | The ethics of the Gospel has been supplemented by barbarous Old Testament values [Mill] |