171 ideas
| 7396 | Hobbes created English-language philosophy [Hobbes, by Tuck] |
| 17240 | Definitions are the first step in philosophy [Hobbes] |
| 6211 | Laughter is a sudden glory in realising the infirmity of others, or our own formerly [Hobbes] |
| 8014 | Resolve a complex into simple elements, then reconstruct the complex by using them [Hobbes, by MacIntyre] |
| 17237 | Definitions of things that are caused must express their manner of generation [Hobbes] |
| 17239 | Definition is resolution of names into successive genera, and finally the difference [Hobbes] |
| 17241 | A defined name should not appear in the definition [Hobbes] |
| 17242 | 'Petitio principii' is reusing the idea to be defined, in disguised words [Hobbes] |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| 17245 | A part of a part is a part of a whole [Hobbes] |
| 10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 17258 | If we just say one, one, one, one, we don't know where we have got to [Hobbes] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| 18182 | The extension of concepts is not important to me [Maddy] |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 16789 | Only supernatural means could annihilate anything once it had being [Hobbes] |
| 17253 | Change is nothing but movement [Hobbes] |
| 7559 | Every part of the universe is body, and non-body is not part of it [Hobbes] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 16670 | Accidents are just modes of thinking about bodies [Hobbes] |
| 16621 | Accidents are not parts of bodies (like blood in a cloth); they have accidents as things have a size [Hobbes] |
| 16734 | The complete power of an event is just the aggregate of the qualities that produced it [Hobbes] |
| 17247 | The only generalities or universals are names or signs [Hobbes] |
| 14960 | Bodies are independent of thought, and coincide with part of space [Hobbes] |
| 17250 | If you separate the two places of one thing, you will also separate the thing [Hobbes] |
| 17249 | If you separated two things in the same place, you would also separate the places [Hobbes] |
| 17248 | If a whole body is moved, its parts must move with it [Hobbes] |
| 16620 | A chair is wood, and its shape is the form; it isn't 'compounded' of the matter and form [Hobbes] |
| 16790 | A body is always the same, whether the parts are together or dispersed [Hobbes] |
| 17244 | To make a whole, parts needn't be put together, but can be united in the mind [Hobbes] |
| 17233 | Particulars contain universal things [Hobbes] |
| 17246 | Some accidental features are permanent, unless the object perishes [Hobbes] |
| 17251 | The feature which picks out or names a thing is usually called its 'essence' [Hobbes] |
| 16622 | Essence is just an artificial word from logic, giving a way of thinking about substances [Hobbes] |
| 17257 | It is the same river if it has the same source, no matter what flows in it [Hobbes] |
| 12853 | Some individuate the ship by unity of matter, and others by unity of form [Hobbes] |
| 17256 | If a new ship were made of the discarded planks, would two ships be numerically the same? [Hobbes] |
| 16794 | As an infant, Socrates was not the same body, but he was the same human being [Hobbes] |
| 17255 | Two bodies differ when (at some time) you can say something of one you can't say of the other [Hobbes] |
| 6215 | 'Contingent' means that the cause is unperceived, not that there is no cause [Hobbes] |
| 16582 | We can imagine a point swelling and contracting - but not how this could be done [Hobbes] |
| 16638 | The qualities of the world are mere appearances; reality is the motions which cause them [Hobbes] |
| 2356 | Appearance and reality can be separated by mirrors and echoes [Hobbes] |
| 16688 | Evidence is conception, which is imagination, which proceeds from the senses [Hobbes] |
| 7405 | Experience can't prove universal truths [Hobbes] |
| 2357 | Dreams must be false because they seem absurd, but dreams don't see waking as absurd [Hobbes] |
| 17238 | Science aims to show causes and generation of things [Hobbes] |
| 17260 | Imagination is just weakened sensation [Hobbes] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 19373 | A 'conatus' is an initial motion, experienced by us as desire or aversion [Hobbes, by Arthur,R] |
| 2385 | If a man suddenly develops an intention of doing something, the cause is out of his control, not in his will [Hobbes] |
| 2358 | Freedom is absence of opposition to action; the idea of 'free will' is absurd [Hobbes] |
| 2384 | Those actions that follow immediately the last appetite are voluntary [Hobbes] |
| 6213 | A man cannot will to will, or will to will to will, so the idea of a voluntary will is absurd [Hobbes] |
| 6214 | Liberty and necessity are consistent, as when water freely flows, by necessity [Hobbes] |
| 6208 | Conceptions and apparitions are just motion in some internal substance of the head [Hobbes] |
| 2948 | Sensation is merely internal motion of the sentient being [Hobbes] |
| 23987 | The 'simple passions' are appetite, desire, love, aversion, hate, joy, and grief [Hobbes, by Goldie] |
| 17261 | Apart from pleasure and pain, the only emotions are appetite and aversion [Hobbes] |
| 17236 | Words are not for communication, but as marks for remembering what we have learned [Hobbes] |
| 2362 | The will is just the last appetite before action [Hobbes] |
| 7408 | It is an error that reason should control the passions, which give right guidance on their own [Hobbes, by Tuck] |
| 2363 | Reason is usually general, but deliberation is of particulars [Hobbes] |
| 7407 | Good and evil are what please us; goodness and badness the powers causing them [Hobbes] |
| 2360 | 'Good' is just what we desire, and 'Evil' what we hate [Hobbes] |
| 7410 | Self-preservation is basic, and people judge differently about that, implying ethical relativism [Hobbes, by Tuck] |
| 2368 | Men's natural desires are no sin, and neither are their actions, until law makes it so [Hobbes] |
| 6209 | There is no absolute good, for even the goodness of God is goodness to us [Hobbes] |
| 2359 | Desire and love are the same, but in the desire the object is absent, and in love it is present [Hobbes] |
| 2370 | All voluntary acts aim at some good for the doer [Hobbes] |
| 7409 | Hobbes shifted from talk of 'the good' to talk of 'rights' [Hobbes, by Tuck] |
| 23529 | Conduct is not isolated from its effect on the moral code [Hart,HLA] |
| 6210 | Life has no end (not even happiness), because we have desires, which presuppose a further end [Hobbes] |
| 8015 | Hobbes wants a contract to found morality, but shared values are needed to make a contract [MacIntyre on Hobbes] |
| 2371 | A contract is a mutual transfer of rights [Hobbes] |
| 2372 | The person who performs first in a contract is said to 'merit' the return, and is owed it [Hobbes] |
| 5337 | For Hobbes the Golden Rule concerns not doing things, whereas Jesus encourages active love [Hobbes, by Flanagan] |
| 2374 | In the violent state of nature, the merest suspicion is enough to justify breaking a contract [Hobbes] |
| 2375 | Suspicion will not destroy a contract, if there is a common power to enforce it [Hobbes] |
| 8016 | Fear of sanctions is the only motive for acceptance of authority that Hobbes can think of [MacIntyre on Hobbes] |
| 2377 | No one who admitted to not keeping contracts could ever be accepted as a citizen [Hobbes] |
| 2379 | If there is a good reason for breaking a contract, the same reason should have stopped the making of it [Hobbes] |
| 2373 | The first performer in a contract is handing himself over to an enemy [Hobbes] |
| 2382 | Someone who keeps all his contracts when others are breaking them is making himself a prey to others [Hobbes] |
| 2383 | Virtues are a means to peaceful, sociable and comfortable living [Hobbes] |
| 2376 | Injustice is the failure to keep a contract, and justice is the constant will to give what is owed [Hobbes] |
| 2367 | In time of war the life of man is solitary, poor, nasty, brutish and short [Hobbes] |
| 19764 | Hobbes attributed to savages the passions which arise in a law-bound society [Hobbes, by Rousseau] |
| 20566 | Hobbes says the people voluntarily give up their sovereignty, in a contract with a ruler [Hobbes, by Oksala] |
| 23530 | The great danger of democracy is that the oppression of the minority becomes unobjectionable [Hart,HLA] |
| 23522 | In an organised society all actions have some effect on other people [Hart,HLA] |
| 23528 | The value of liberty allows freedom of action, even if that distresses other people [Hart,HLA] |
| 2366 | There is not enough difference between people for one to claim more benefit than another [Hobbes] |
| 20485 | Hobbes says people are roughly equal; Locke says there is no right to impose inequality [Hobbes, by Wolff,J] |
| 21004 | Hart (against Bentham) says human rights are what motivate legal rights [Hart,HLA, by Sen] |
| 2369 | If we seek peace and defend ourselves, we must compromise on our rights [Hobbes] |
| 23523 | The principle of legality requires crimes to be precisely defined in advance of any action [Hart,HLA] |
| 23524 | Some private moral issues are no concern of the law [Hart,HLA] |
| 23521 | Do morals influence law? Is morality an aspect of law? Can law be morally criticised? [Hart,HLA] |
| 23525 | Is the enforcement of morality morally justifiable? [Hart,HLA] |
| 23526 | Modern law still suppresses practices seen as immoral, and yet harmless [Hart,HLA] |
| 20932 | Positive law needs secondary 'rules of recognition' for their correct application [Hart,HLA, by Zimmermann,J] |
| 20484 | We should obey the laws of nature, provided other people are also obeying them [Hobbes, by Wolff,J] |
| 7573 | The legal positivism of Hobbes said law is just formal or procedural [Hobbes, by Jolley] |
| 20931 | Hart replaced positivism with the democratic requirement of the people's acceptance [Hart,HLA, by Zimmermann,J] |
| 2380 | Punishment should only be for reform or deterrence [Hobbes] |
| 23527 | Moral wickedness of an offence is always relevant to the degree of punishment [Hart,HLA] |
| 23609 | I act justly if I follow my Prince in an apparently unjust war, and refusing to fight would be injustice [Hobbes] |
| 2361 | If fear of unknown powers is legal it is religion, if it is illegal it is superstition [Hobbes] |
| 6212 | Lust involves pleasure, and also the sense of power in pleasing others [Hobbes] |
| 16600 | Prime matter is body considered with mere size and extension, and potential [Hobbes] |
| 17252 | Acting on a body is either creating or destroying a property in it [Hobbes] |
| 17254 | An effect needs a sufficient and necessary cause [Hobbes] |
| 2364 | Causation is only observation of similar events following each other, with nothing visible in between [Hobbes] |
| 17235 | A cause is the complete sum of the features which necessitate the effect [Hobbes] |
| 17234 | Motion is losing one place and acquiring another [Hobbes] |
| 17259 | 'Force' is the quantity of movement imposed on something [Hobbes] |
| 17243 | Past times can't exist anywhere, apart from in our memories [Hobbes] |
| 7411 | The attributes of God just show our inability to conceive his nature [Hobbes] |
| 2365 | Religion is built on ignorance and misinterpretation of what is unknown or frightening [Hobbes] |
| 2378 | Belief in an afterlife is based on poorly founded gossip [Hobbes] |