159 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] |
5692 | Introspection is not perception, because there are no extra qualities apart from the mental events themselves [Rosenthal] |
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] |
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] |
8016 | Fear of sanctions is the only motive for acceptance of authority that Hobbes can think of [MacIntyre on Hobbes] |
2375 | Suspicion will not destroy a contract, if there is a common power to enforce it [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] |
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] |
2369 | If we seek peace and defend ourselves, we must compromise on our rights [Hobbes] |
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] |
2380 | Punishment should only be for reform or deterrence [Hobbes] |
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] |