87 ideas
13773 | For the truth you need Prodicus's fifty-drachma course, not his one-drachma course [Socrates] |
7421 | A philosopher is one who cares about what other people care about [Socrates, by Foucault] |
1649 | Socrates opened philosophy to all, but Plato confined moral enquiry to a tiny elite [Vlastos on Socrates] |
5842 | Philosophical discussion involves dividing subject-matter into categories [Socrates, by Xenophon] |
648 | Socrates began the quest for something universal with his definitions, but he didn't make them separate [Socrates, by Aristotle] |
164 | It is legitimate to play the devil's advocate [Socrates] |
1647 | In Socratic dialogue you must say what you believe, so unasserted premises are not debated [Vlastos on Socrates] |
115 | Socrates was pleased if his mistakes were proved wrong [Socrates] |
22099 | The method of Socrates shows the student is discovering the truth within himself [Socrates, by Carlisle] |
5844 | Socrates always proceeded in argument by general agreement at each stage [Socrates, by Xenophon] |
11389 | Socrates sought essences, which are the basis of formal logic [Socrates, by Aristotle] |
639 | Socrates developed definitions as the basis of syllogisms, and also inductive arguments [Socrates, by Aristotle] |
9065 | S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P) [Keefe/Smith] |
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] |
18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [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] |
18196 | An 'inaccessible' cardinal cannot be reached by union sets or power 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] |
18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
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] |
18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
9064 | Objects such as a cloud or Mount Everest seem to have fuzzy boundaries in nature [Keefe/Smith] |
9044 | If someone is borderline tall, no further information is likely to resolve the question [Keefe/Smith] |
9048 | The simplest approach, that vagueness is just ignorance, retains classical logic and semantics [Keefe/Smith] |
9055 | The epistemic view of vagueness must explain why we don't know the predicate boundary [Keefe/Smith] |
9049 | Supervaluationism keeps true-or-false where precision can be produced, but not otherwise [Keefe/Smith] |
9056 | Vague statements lack truth value if attempts to make them precise fail [Keefe/Smith] |
9058 | Some of the principles of classical logic still fail with supervaluationism [Keefe/Smith] |
9059 | The semantics of supervaluation (e.g. disjunction and quantification) is not classical [Keefe/Smith] |
9060 | Supervaluation misunderstands vagueness, treating it as a failure to make things precise [Keefe/Smith] |
9050 | A third truth-value at borderlines might be 'indeterminate', or a value somewhere between 0 and 1 [Keefe/Smith] |
9061 | People can't be placed in a precise order according to how 'nice' they are [Keefe/Smith] |
9062 | If truth-values for vagueness range from 0 to 1, there must be someone who is 'completely tall' [Keefe/Smith] |
9063 | How do we decide if my coat is red to degree 0.322 or 0.321? [Keefe/Smith] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
1652 | Socrates did not consider universals or definitions as having separate existence, but Plato made Forms of them [Socrates, by Aristotle] |
9045 | Vague predicates involve uncertain properties, uncertain objects, and paradoxes of gradual change [Keefe/Smith] |
9047 | Many vague predicates are multi-dimensional; 'big' involves height and volume; heaps include arrangement [Keefe/Smith] |
9053 | If there is a precise borderline area, that is not a case of vagueness [Keefe/Smith] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
1650 | For Socrates our soul, though hard to define, is our self [Vlastos on Socrates] |
23252 | Socrates first proposed that we are run by mind or reason [Socrates, by Frede,M] |
195 | No one willingly commits an evil or base act [Socrates] |
1653 | Socrates did not accept the tripartite soul (which permits akrasia) [Vlastos on Socrates] |
5843 | People do what they think they should do, and only ever do what they think they should do [Socrates, by Xenophon] |
5253 | Socrates was shocked by the idea of akrasia, but observation shows that it happens [Aristotle on Socrates] |
199 | The common belief is that people can know the best without acting on it [Socrates] |
5839 | For Socrates, wisdom and prudence were the same thing [Socrates, by Xenophon] |
5867 | For Socrates, virtues are forms of knowledge, so knowing justice produces justice [Socrates, by Aristotle] |
5069 | Socrates was the first to base ethics upon reason, and use reason to explain it [Taylor,R on Socrates] |
5836 | All human virtues are increased by study and practice [Socrates, by Xenophon] |
5840 | The wise perform good actions, and people fail to be good without wisdom [Socrates, by Xenophon] |
185 | Socrates despised good looks [Socrates, by Plato] |
5070 | Socrates conservatively assumed that Athenian conventions were natural and true [Taylor,R on Socrates] |
5838 | A well-made dung basket is fine, and a badly-made gold shield is base, because of function [Socrates, by Xenophon] |
5837 | Things are both good and fine by the same standard [Socrates, by Xenophon] |
3017 | The only good is knowledge, and the only evil is ignorance [Socrates, by Diog. Laertius] |
1646 | Socrates was the first to put 'eudaimonia' at the centre of ethics [Socrates, by Vlastos] |
1663 | By 'areté' Socrates means just what we mean by moral virtue [Vlastos on Socrates] |
4323 | Socrates is torn between intellectual virtue, which is united and teachable, and natural virtue, which isn't [PG on Socrates] |
8003 | Socrates agrees that virtue is teachable, but then denies that there are teachers [Socrates, by MacIntyre] |
126 | We should ask what sort of people we want to be [Socrates] |
4111 | Socrates believed that basically there is only one virtue, the power of right judgement [Socrates, by Williams,B] |
7808 | Socrates made the civic values of justice and friendship paramount [Socrates, by Grayling] |
23907 | Courage is scientific knowledge [Socrates, by Aristotle] |
7585 | Socrates emphasises that the knower is an existing individual, with existence his main task [Socrates, by Kierkegaard] |
5841 | Obedience to the law gives the best life, and success in war [Socrates, by Xenophon] |
1661 | Socrates was the first to grasp that a cruelty is not justified by another cruelty [Vlastos on Socrates] |
5846 | A lover using force is a villain, but a seducer is much worse, because he corrupts character [Socrates, by Xenophon] |
1657 | Socrates holds that right reason entails virtue, and this must also apply to the gods [Vlastos on Socrates] |
1662 | A new concept of God as unswerving goodness emerges from Socrates' commitment to virtue [Vlastos on Socrates] |