149 ideas
7396 | Hobbes created English-language philosophy [Hobbes, by Tuck] |
13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
13477 | The problems are the monuments of philosophy [Hart,WD] |
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] |
13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
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] |
13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
17245 | A part of a part is a part of a whole [Hobbes] |
13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
9117 | The smallest heap has four objects: three on the bottom, one on the top [Hart,WD, by Sorensen] |
13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
17258 | If we just say one, one, one, one, we don't know where we have got to [Hobbes] |
13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
16789 | Only supernatural means could annihilate anything once it had being [Hobbes] |
17253 | Change is nothing but movement [Hobbes] |
13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
7559 | Every part of the universe is body, and non-body is not part of it [Hobbes] |
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] |
13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
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] |
19373 | A 'conatus' is an initial motion, experienced by us as desire or aversion [Hobbes, by Arthur,R] |
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] |
2385 | If a man suddenly develops an intention of doing something, the cause is out of his control, not in his will [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] |
13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
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] |
22745 | Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus] |
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] |
5883 | Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero] |
2378 | Belief in an afterlife is based on poorly founded gossip [Hobbes] |