79 ideas
| 19767 | Reason leads to prudent selfishness, which overrules natural compassion [Rousseau] |
| 9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
| 5745 | Quine says quantified modal logic creates nonsense, bad ontology, and false essentialism [Melia on Quine] |
| 21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
| 10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro] |
| 18208 | We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead] |
| 8789 | Various strategies try to deal with the ontological commitments of second-order logic [Hale/Wright on Quine] |
| 8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
| 9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
| 21707 | Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B] |
| 10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
| 18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
| 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
| 10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
| 8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
| 10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
| 10093 | The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman] |
| 8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
| 10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
| 8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
| 8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
| 16966 | Philosophers tend to distinguish broad 'being' from narrower 'existence' - but I reject that [Quine] |
| 16965 | All we have of general existence is what existential quantifiers express [Quine] |
| 16963 | Existence is implied by the quantifiers, not by the constants [Quine] |
| 16964 | Theories are committed to objects of which some of its predicates must be true [Quine] |
| 4216 | Express a theory in first-order predicate logic; its ontology is the types of bound variable needed for truth [Quine, by Lowe] |
| 18966 | Ontological commitment of theories only arise if they are classically quantified [Quine] |
| 14490 | You can be implicitly committed to something without quantifying over it [Thomasson on Quine] |
| 16961 | In formal terms, a category is the range of some style of variables [Quine] |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| 19757 | No one would bother to reason, and try to know things, without a desire for enjoyment [Rousseau] |
| 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
| 19760 | General ideas are purely intellectual; imagining them is immediately particular [Rousseau] |
| 19759 | Only words can introduce general ideas into the mind [Rousseau] |
| 21725 | The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B] |
| 23474 | A judgement is a complex entity, of mind and various objects [Russell/Whitehead] |
| 23455 | The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead] |
| 23480 | The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead] |
| 18275 | Only the act of judging completes the meaning of a statement [Russell/Whitehead] |
| 19758 | Language may aid thinking, but powerful thought was needed to produce language [Rousseau] |
| 23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
| 19773 | Without love, what use is beauty? [Rousseau] |
| 19769 | Rational morality is OK for brainy people, but ordinary life can't rely on that [Rousseau] |
| 19752 | If we should not mistreat humans, it is mainly because of sentience, not rationality [Rousseau] |
| 19768 | The better Golden Rule is 'do good for yourself without harming others' [Rousseau] |
| 19766 | The fact that we weep (e.g. in theatres) shows that we are naturally compassionate [Rousseau] |
| 19756 | Humans are less distinguished from other animals by understanding, than by being free agents [Rousseau] |
| 19755 | Most human ills are self-inflicted; the simple, solitary, regular natural life is good [Rousseau] |
| 19762 | Is language a pre-requisite for society, or might it emerge afterwards? [Rousseau] |
| 19763 | I doubt whether a savage person ever complains of life, or considers suicide [Rousseau] |
| 19778 | Leisure led to envy, inequality, vice and revenge, which we now see in savages [Rousseau] |
| 19779 | Primitive man was very gentle [Rousseau] |
| 19751 | Our two starting principles are concern for self-interest, and compassion for others [Rousseau] |
| 19765 | Savages avoid evil because they are calm, and never think of it (not because they know goodness) [Rousseau] |
| 19771 | Savage men quietly pursue desires, without the havoc of modern frenzied imagination [Rousseau] |
| 19774 | A savage can steal fruit or a home, but there is no means of achieving obedience [Rousseau] |
| 19772 | In a state of nature people are much more equal; it is society which increases inequalities [Rousseau] |
| 19789 | It is against nature for children to rule old men, fools to rule the wise, and the rich to hog resources [Rousseau] |
| 19787 | People accept the right to be commanded, because they themselves wish to command [Rousseau] |
| 19780 | We seem to have made individual progress since savagery, but actually the species has decayed [Rousseau] |
| 19747 | Revolutionaries usually confuse liberty with total freedom, and end up with heavier chains [Rousseau] |
| 19748 | Plebiscites are bad, because they exclude the leaders from crucial decisions [Rousseau] |
| 19749 | In a direct democracy, only the leaders should be able to propose new laws [Rousseau] |
| 19784 | Enslaved peoples often boast of their condition, calling it a state of 'peace' [Rousseau] |
| 19785 | If the child of a slave woman is born a slave, then a man is not born a man [Rousseau] |
| 19775 | People must be made dependent before they can be enslaved [Rousseau] |
| 19746 | Like rich food, liberty can ruin people who are too weak to cope with it [Rousseau] |
| 19786 | Three stages of the state produce inequalities of wealth, power, and enslavement [Rousseau] |
| 19788 | The pleasure of wealth and power is largely seeing others deprived of them [Rousseau] |
| 19777 | Persuading other people that some land was 'owned' was the beginning of society [Rousseau] |
| 19782 | What else could property arise from, but the labour people add to it? [Rousseau] |
| 19781 | Land cultivation led to a general right of ownership, administered justly [Rousseau] |
| 19754 | If we have a natural right to property, what exactly does 'belonging to' mean? [Rousseau] |
| 19750 | Writers just propose natural law as the likely useful agreements among people [Rousseau] |
| 19770 | Primitive people simply redressed the evil caused by violence, without thought of punishing [Rousseau] |
| 19783 | A state of war remains after a conquest, if the losers don't accept the winners [Rousseau] |
| 19753 | Both men and animals are sentient, which should give the latter the right not to be mistreated [Rousseau] |
| 19761 | Men started with too few particular names, but later had too few natural kind names [Rousseau] |
| 19776 | Small uninterrupted causes can have big effects [Rousseau] |