68 ideas
23350 | A wise philosophers uses reason to cautiously judge each aspect of living [Epictetus] |
23355 | The task of philosophy is to establish standards, as occurs with weights and measures [Epictetus] |
23367 | Even pointing a finger should only be done for a reason [Epictetus] |
21394 | Philosophy is knowing each logos, how they fit together, and what follows from them [Epictetus] |
20876 | Philosophy investigates the causes of disagreements, and seeks a standard for settling them [Epictetus] |
23344 | Reason itself must be compounded from some of our impressions [Epictetus] |
23343 | Because reason performs all analysis, we should analyse reason - but how? [Epictetus] |
10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
10857 | Set theory made a closer study of infinity possible [Clegg] |
10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
10871 | Axiom of Existence: there exists at least one set [Clegg] |
10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
17807 | To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
17806 | It is untenable that mathematics is general physical truths, because it needs infinity [Curry] |
17808 | Saying mathematics is logic is merely replacing one undefined term by another [Curry] |
23359 | We can't believe apparent falsehoods, or deny apparent truths [Epictetus] |
23356 | Self-evidence is most obvious when people who deny a proposition still have to use it [Epictetus] |
23329 | We make progress when we improve and naturalise our choices, asserting their freedom [Epictetus] |
23342 | Freedom is acting by choice, with no constraint possible [Epictetus] |
23330 | Freedom is making all things happen by choice, without constraint [Epictetus] |
23332 | Zeus gave me a nature which is free (like himself) from all compulsion [Epictetus] |
23331 | Not even Zeus can control what I choose [Epictetus] |
23338 | You can fetter my leg, but not even Zeus can control my power of choice [Epictetus] |
20875 | If we could foresee the future, we should collaborate with disease and death [Epictetus] |
23347 | If I know I am fated to be ill, I should want to be ill [Epictetus] |
23325 | Epictetus developed a notion of will as the source of our responsibility [Epictetus, by Frede,M] |
20873 | Tragedies are versified sufferings of people impressed by externals [Epictetus] |
23364 | Homer wrote to show that the most blessed men can be ruined by poor judgement [Epictetus] |
23340 | We consist of animal bodies and god-like reason [Epictetus] |
23366 | We see nature's will in the ways all people are the same [Epictetus] |
23358 | Every species produces exceptional beings, and we must just accept their nature [Epictetus] |
23339 | I will die as becomes a person returning what he does not own [Epictetus] |
23345 | Don't be frightened of pain or death; only be frightened of fearing them [Epictetus] |
23357 | Knowledge of what is good leads to love; only the wise, who distinguish good from evil, can love [Epictetus] |
23363 | The evil for everything is what is contrary to its nature [Epictetus] |
23328 | The essences of good and evil are in dispositions to choose [Epictetus] |
23362 | All human ills result from failure to apply preconceptions to particular cases [Epictetus] |
23353 | We have a natural sense of honour [Epictetus] |
23354 | If someone harms themselves in harming me, then I harm myself by returning the harm [Epictetus] |
23324 | In the Discourses choice [prohairesis] defines our character and behaviour [Epictetus, by Frede,M] |
4022 | Epictetus says we should console others for misfortune, but not be moved by pity [Epictetus, by Taylor,C] |
23365 | If someone is weeping, you should sympathise and help, but not share his suffering [Epictetus] |
23361 | Health is only a good when it is used well [Epictetus] |
23346 | A person is as naturally a part of a city as a foot is part of the body [Epictetus] |
23351 | We are citizens of the universe, and principal parts of it [Epictetus] |
20874 | A citizen is committed to ignore private advantage, and seek communal good [Epictetus] |
23352 | A citizen should only consider what is good for the whole society [Epictetus] |
22604 | Punishing a criminal for moral ignorance is the same as punishing someone for being blind [Epictetus] |
23368 | Perhaps we should persuade culprits that their punishment is just? [Epictetus] |
23349 | Asses are born to carry human burdens, not as ends in themselves [Epictetus] |
23341 | God created humans as spectators and interpreters of God's works [Epictetus] |
23348 | Both god and the good bring benefits, so their true nature seems to be the same [Epictetus] |
23360 | Each of the four elements in you is entirely scattered after death [Epictetus] |