59 ideas
| 8093 | Seek wisdom rather than truth; it is easier [Joubert] |
| 8095 | We must think with our entire body and soul [Joubert] |
| 8107 | The love of certainty holds us back in metaphysics [Joubert] |
| 8099 | The truths of reason instruct, but they do not illuminate [Joubert] |
| 8098 | Truth consists of having the same idea about something that God has [Joubert] |
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 8101 | To know is to see inside oneself [Joubert] |
| 8094 | The imagination has made more discoveries than the eye [Joubert] |
| 8103 | A thought is as real as a cannon ball [Joubert] |
| 8100 | Where does the bird's idea of a nest come from? [Joubert] |
| 7222 | It is a crime for someone with a violent disposition to get drunk [Mill] |
| 8096 | He gives his body up to pleasure, but not his soul [Joubert] |
| 8104 | What will you think of pleasures when you no longer enjoy them? [Joubert] |
| 8097 | Virtue is hard if we are scorned; we need support [Joubert] |
| 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] |
| 8106 | In raising a child we must think of his old age [Joubert] |
| 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] |
| 8105 | We can't exactly conceive virtue without the idea of God [Joubert] |
| 8102 | We cannot speak against Christianity without anger, or speak for it without love [Joubert] |
| 7216 | The ethics of the Gospel has been supplemented by barbarous Old Testament values [Mill] |