103 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] |
18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
17824 | The master science is physical objects divided into sets [Maddy] |
8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
18182 | The extension of concepts is not important to me [Maddy] |
18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
10718 | A natural number is a property of sets [Maddy, by Oliver] |
18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
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] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
23329 | We make progress when we improve and naturalise our choices, asserting their freedom [Epictetus] |
23330 | Freedom is making all things happen by choice, without constraint [Epictetus] |
23342 | Freedom is acting by choice, with no constraint possible [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] |
23366 | We see nature's will in the ways all people are the same [Epictetus] |
23340 | We consist of animal bodies and god-like reason [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] |
6004 | The cardinal virtues are theoretical (based on knowledge), and others are 'non-theoretical' [Hecato, by Dorandi] |
23365 | If someone is weeping, you should sympathise and help, but not share his suffering [Epictetus] |
4022 | Epictetus says we should console others for misfortune, but not be moved by pity [Epictetus, by Taylor,C] |
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] |