74 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] |
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| 9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
| 10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
| 7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
| 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
| 14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
| 17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
| 10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
| 14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
| 18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
| 18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| 18087 | If x changes by less and less, it must approach a limit [Dedekind] |
| 13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
| 18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
| 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
| 14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
| 8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| 3425 | Reduction has been defined as deriving one theory from another by logic and maths [Nagel,E, by Kim] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 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] |
| 9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
| 9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
| 9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
| 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] |