65 ideas
19767 | Reason leads to prudent selfishness, which overrules natural compassion [Rousseau] |
9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
10261 | The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro] |
18218 | Hilbert explains geometry, by non-numerical facts about space [Field,H] |
9623 | Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H] |
18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
19757 | No one would bother to reason, and try to know things, without a desire for enjoyment [Rousseau] |
18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
19760 | General ideas are purely intellectual; imagining them is immediately particular [Rousseau] |
19759 | Only words can introduce general ideas into the mind [Rousseau] |
19758 | Language may aid thinking, but powerful thought was needed to produce language [Rousseau] |
9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
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] |
5996 | Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA] |
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] |
19775 | People must be made dependent before they can be enslaved [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] |
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] |
18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
18220 | Both philosophy and physics now make substantivalism more attractive [Field,H] |
18219 | Relational space is problematic if you take the idea of a field seriously [Field,H] |
19776 | Small uninterrupted causes can have big effects [Rousseau] |