53 ideas
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| 13044 | Infinity: There is at least one limit level [Potter] |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| 6248 | Reason is too slow and doubtful to guide all actions, which need external and moral senses [Hutcheson] |
| 7222 | It is a crime for someone with a violent disposition to get drunk [Mill] |
| 6238 | We approve of actions by a superior moral sense [Hutcheson] |
| 6239 | We dislike a traitor, even if they give us great benefit [Hutcheson] |
| 6240 | The moral sense is not an innate idea, but an ability to approve or disapprove in a disinterested way [Hutcheson] |
| 6242 | We cannot choose our moral feelings, otherwise bribery could affect them [Hutcheson] |
| 6247 | Everyone feels uneasy when seeing others in pain, unless the others are evil [Hutcheson] |
| 6244 | Human nature seems incapable of universal malice, except what results from self-love [Hutcheson] |
| 6243 | As death approaches, why do we still care about family, friends or country? [Hutcheson] |
| 6246 | My action is not made good by a good effect, if I did not foresee and intend it [Hutcheson] |
| 6241 | Contempt of danger is just madness if it is not in some worthy cause [Hutcheson] |
| 6245 | That action is best, which procures the greatest happiness for the greatest number [Hutcheson] |
| 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] |
| 6251 | The loss of perfect rights causes misery, but the loss of imperfect rights reduces social good [Hutcheson] |
| 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] |
| 6250 | We say God is good if we think everything he does aims at the happiness of his creatures [Hutcheson] |
| 6249 | If goodness is constituted by God's will, it is a tautology to say God's will is good [Hutcheson] |
| 7216 | The ethics of the Gospel has been supplemented by barbarous Old Testament values [Mill] |