66 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] |
15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
1652 | Socrates did not consider universals or definitions as having separate existence, but Plato made Forms of them [Socrates, by Aristotle] |
15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
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] |