67 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] |
21394 | Philosophy is knowing each logos, how they fit together, and what follows from them [Epictetus] |
23367 | Even pointing a finger should only be done for a reason [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] |
17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
17765 | Propositional language can only relate statements as the same or as different [Walicki] |
17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
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] |
23330 | Freedom is making all things happen by choice, without constraint [Epictetus] |
23342 | Freedom is acting by choice, with no constraint possible [Epictetus] |
23329 | We make progress when we improve and naturalise our choices, asserting their freedom [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] |
23352 | A citizen should only consider what is good for the whole society [Epictetus] |
20874 | A citizen is committed to ignore private advantage, and seek communal good [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] |