77 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] |
8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
639 | Socrates developed definitions as the basis of syllogisms, and also inductive arguments [Socrates, by Aristotle] |
13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
10676 | The Axiom of Choice is a non-logical principle of set-theory [Hossack] |
10686 | The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack] |
10687 | Maybe we reduce sets to ordinals, rather than the other way round [Hossack] |
10677 | Extensional mereology needs two definitions and two axioms [Hossack] |
10671 | Plural definite descriptions pick out the largest class of things that fit the description [Hossack] |
10666 | Plural reference will refer to complex facts without postulating complex things [Hossack] |
10669 | Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack] |
10675 | A plural comprehension principle says there are some things one of which meets some condition [Hossack] |
10673 | Plural language can discuss without inconsistency things that are not members of themselves [Hossack] |
6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
10680 | The theory of the transfinite needs the ordinal numbers [Hossack] |
10684 | I take the real numbers to be just lengths [Hossack] |
9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
10674 | A plural language gives a single comprehensive induction axiom for arithmetic [Hossack] |
1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
10681 | In arithmetic singularists need sets as the instantiator of numeric properties [Hossack] |
10685 | Set theory is the science of infinity [Hossack] |
10668 | We are committed to a 'group' of children, if they are sitting in a circle [Hossack] |
1652 | Socrates did not consider universals or definitions as having separate existence, but Plato made Forms of them [Socrates, by Aristotle] |
10664 | Complex particulars are either masses, or composites, or sets [Hossack] |
10678 | The relation of composition is indispensable to the part-whole relation for individuals [Hossack] |
10682 | The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack] |
10665 | Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack] |
1650 | For Socrates our soul, though hard to define, is our self [Vlastos on Socrates] |
10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
23252 | Socrates first proposed that we are run by mind or reason [Socrates, by Frede,M] |
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] |
1653 | Socrates did not accept the tripartite soul (which permits akrasia) [Vlastos on Socrates] |
195 | No one willingly commits an evil or base act [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] |
10683 | We could ignore space, and just talk of the shape of matter [Hossack] |
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] |