146 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] |
10073 | There cannot be a set theory which is complete [Smith,P] |
17245 | A part of a part is a part of a whole [Hobbes] |
10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
10605 | Two functions are the same if they have the same extension [Smith,P] |
10075 | A 'partial function' maps only some elements to another set [Smith,P] |
10074 | A 'total function' maps every element to one element in another set [Smith,P] |
10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
10613 | No nice theory can define truth for its own language [Smith,P] |
10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
17258 | If we just say one, one, one, one, we don't know where we have got to [Hobbes] |
10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
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] |
10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
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] |
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] |
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] |
20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |
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] |