154 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] |
9535 | 'Contradictory' propositions always differ in truth-value [Lemmon] |
9508 | The sign |- may be read as 'therefore' [Lemmon] |
9511 | We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon] |
9510 | That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon] |
9512 | We write the 'negation' of P (not-P) as ¬ [Lemmon] |
9513 | We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P) [Lemmon] |
9514 | If A and B are 'interderivable' from one another we may write A -||- B [Lemmon] |
9509 | That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon] |
9516 | A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon] |
9517 | The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon] |
9519 | A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon] |
9529 | A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon] |
9531 | 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon] |
9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon] |
9530 | A wff is 'contingent' if produces at least one T and at least one F [Lemmon] |
9532 | 'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon] |
9533 | A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon] |
9528 | A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon] |
9518 | A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon] |
9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
9393 | A: we may assume any proposition at any stage [Lemmon] |
9399 | ∧E: Given A∧B, we may derive either A or B separately [Lemmon] |
9398 | ∧I: Given A and B, we may derive A∧B [Lemmon] |
9397 | CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon] |
9394 | MPP: Given A and A→B, we may derive B [Lemmon] |
9402 | RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon] |
9395 | MTT: Given ¬B and A→B, we derive ¬A [Lemmon] |
9400 | ∨I: Given either A or B separately, we may derive A∨B [Lemmon] |
9401 | ∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon] |
9521 | 'Modus tollendo ponens' (MTP) says ¬P, P ∨ Q |- Q [Lemmon] |
9522 | 'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon] |
9525 | We can change conditionals into negated conjunctions with P→Q -||- ¬(P ∧ ¬Q) [Lemmon] |
9524 | We can change conditionals into disjunctions with P→Q -||- ¬P ∨ Q [Lemmon] |
9523 | De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon] |
9527 | The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon] |
9526 | We can change conjunctions into negated conditionals with P→Q -||- ¬(P → ¬Q) [Lemmon] |
9537 | Truth-tables are good for showing invalidity [Lemmon] |
9538 | A truth-table test is entirely mechanical, but this won't work for more complex logic [Lemmon] |
9536 | If any of the nine rules of propositional logic are applied to tautologies, the result is a tautology [Lemmon] |
9539 | Propositional logic is complete, since all of its tautologous sequents are derivable [Lemmon] |
13909 | Write '(∀x)(...)' to mean 'take any x: then...', and '(∃x)(...)' to mean 'there is an x such that....' [Lemmon] |
13902 | 'Gm' says m has property G, and 'Pmn' says m has relation P to n [Lemmon] |
13911 | The 'symbols' are bracket, connective, term, variable, predicate letter, reverse-E [Lemmon] |
13910 | Our notation uses 'predicate-letters' (for 'properties'), 'variables', 'proper names', 'connectives' and 'quantifiers' [Lemmon] |
13904 | Universal Elimination (UE) lets us infer that an object has F, from all things having F [Lemmon] |
13906 | With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro [Lemmon] |
13908 | UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon] |
13901 | Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon] |
13903 | Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon] |
13905 | If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon] |
13900 | 'Some Frenchmen are generous' is rendered by (∃x)(Fx→Gx), and not with the conditional → [Lemmon] |
17245 | A part of a part is a part of a whole [Hobbes] |
9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
17258 | If we just say one, one, one, one, we don't know where we have got to [Hobbes] |
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] |
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] |
604 | Knowledge is mind and knowing 'cohabiting' [Lycophron, by Aristotle] |
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] |
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] |