95 ideas
| 22733 | Epicurus accepted God in his popular works, but not in his writings on nature [Epicurus, by Sext.Empiricus] |
| 13291 | Slavery to philosophy brings true freedom [Epicurus] |
| 22758 | Philosophy aims at a happy life, through argument and discussion [Epicurus] |
| 14523 | We should come to philosophy free from any taint of culture [Epicurus] |
| 22240 | The aim of medicine is removal of sickness, and philosophy similarly removes our affections [Epicurus] |
| 1484 | We should say nothing of the whole if our contact is with the parts [Epicurus, by Plutarch] |
| 2670 | Epicurus despises and laughs at the whole of dialectic [Epicurus, by Cicero] |
| 10073 | There cannot be a set theory which is complete [Smith,P] |
| 10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
| 21668 | Epicurus rejected excluded middle, because accepting it for events is fatalistic [Epicurus, by Cicero] |
| 21676 | Epicureans say disjunctions can be true whiile the disjuncts are not true [Epicurus, by Cicero] |
| 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] |
| 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] |
| 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] |
| 10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
| 10079 | A 'bijective' function has one-to-one correspondence in both directions [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] |
| 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] |
| 10618 | All numbers are related to zero by the ancestral of the successor relation [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] |
| 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] |
| 10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
| 10852 | Robinson Arithmetic (Q) is not negation complete [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] |
| 10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
| 1823 | We can't seek for things if we have no idea of them [Epicurus, by Diog. Laertius] |
| 1824 | To name something, you must already have an idea of what it is [Epicurus, by Diog. Laertius] |
| 5949 | Epicurus says colours are relative to the eye, not intrinsic to bodies [Epicurus, by Plutarch] |
| 1821 | Sensations cannot be judged, because similar sensations have equal value, and different ones have nothing in common [Epicurus, by Diog. Laertius] |
| 1820 | The criteria of truth are senses, preconceptions and passions [Epicurus, by Diog. Laertius] |
| 1822 | Reason can't judge senses, as it is based on them [Epicurus, by Diog. Laertius] |
| 4549 | Epicurus denied knowledge in order to retain morality or hedonism as the highest values [Nietzsche on Epicurus] |
| 2668 | Epicurus says if one of a man's senses ever lies, none of his senses should ever be believed [Epicurus, by Cicero] |
| 1482 | If two people disagree over taste, who is right? [Epicurus, by Plutarch] |
| 1483 | Bath water is too hot for some, too cold for others [Epicurus, by Plutarch] |
| 1487 | When entering a dark room it is colourless, but colour gradually appears [Epicurus] |
| 14526 | The rational soul is in the chest, and the non-rational soul is spread through the body [Epicurus] |
| 6035 | Soul is made of four stuffs, giving warmth, rest, motion and perception [Epicurus, by Aetius] |
| 6018 | Epicurus was the first to see the free will problem, and he was a libertarian [Epicurus, by Long/Sedley] |
| 20922 | Epicurus showed that the swerve can give free motion in the atoms [Epicurus, by Diogenes of Oen.] |
| 14516 | There is no necessity to live with necessity [Epicurus] |
| 1909 | How can pleasure or judgement occur in a heap of atoms? [Sext.Empiricus on Epicurus] |
| 7814 | It was Epicurus who made the question of the will's freedom central to ethics [Epicurus, by Grayling] |
| 22410 | Maybe the unthinkable is a moral category, and considering some options is dishonourable or absurd [Williams,B] |
| 3562 | Fine things are worthless if they give no pleasure [Epicurus] |
| 1840 | Pleasure is the chief good because it is the most natural, especially for animals [Epicurus, by Diog. Laertius] |
| 22408 | Consequentialism assumes that situations can be compared [Williams,B] |
| 22411 | For a consequentialist massacring 7 million must be better than massacring 7 million and one [Williams,B] |
| 1839 | Pains of the soul are worse than pains of the body, because it feels the past and future [Epicurus, by Diog. Laertius] |
| 1842 | Pleasures only differ in their duration and the part of the body affected [Epicurus] |
| 3557 | The end for Epicurus is static pleasure [Epicurus, by Annas] |
| 1845 | Justice has no independent existence, but arises entirely from keeping contracts [Epicurus] |
| 1841 | We choose virtue because of pleasure, not for its own sake [Epicurus, by Diog. Laertius] |
| 1829 | A wise man would be happy even under torture [Epicurus, by Diog. Laertius] |
| 1843 | Friendship is by far the most important ingredient of a complete and happy life [Epicurus] |
| 22409 | We don't have a duty to ensure that others do their duty [Williams,B] |
| 22407 | Utilitarianism cannot make any serious sense of integrity [Williams,B] |
| 1831 | Wise men should partake of life even if they go blind [Epicurus, by Diog. Laertius] |
| 12044 | Only Epicurus denied purpose in nature, for the whole world, or for its parts [Epicurus, by Annas] |
| 20907 | Democritus says atoms have size and shape, and Epicurus added weight [Epicurus, by Ps-Plutarch] |
| 21669 | Atoms don't swerve by being struck, because they move in parallel, so the swerve is uncaused [Cicero on Epicurus] |
| 21680 | What causes atomic swerves? Do they draw lots? What decides the size or number of swerves? [Cicero on Epicurus] |
| 14525 | Stoics say time is incorporeal and self-sufficient; Epicurus says it is a property of properties of things [Epicurus] |
| 2637 | For Epicureans gods are made of atoms, and are not eternal [Epicurus, by Cicero] |
| 2633 | Epicurus saw that gods must exist, because nature has imprinted them on human minds [Epicurus, by Cicero] |
| 2639 | Some say Epicurus only pretended to believe in the gods, so as not to offend Athenians [Epicurus, by Cicero] |
| 14527 | If god answered prayers we would be destroyed, because we pray for others to suffer [Epicurus] |