37 ideas
23250 | Desired responsible actions result either from rational or from irrational desire [Aristotle] |
5847 | It is the role of dialectic to survey syllogisms [Aristotle] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
5862 | A single counterexample is enough to prove that a truth is not necessary [Aristotle] |
5854 | Nobody fears a disease which nobody has yet caught [Aristotle] |
5849 | Rhetoric is a political offshoot of dialectic and ethics [Aristotle] |
5851 | Pentathletes look the most beautiful, because they combine speed and strength [Aristotle] |
5858 | Men are physically prime at thirty-five, and mentally prime at forty-nine [Aristotle] |
5855 | We all feel universal right and wrong, independent of any community or contracts [Aristotle] |
22410 | Maybe the unthinkable is a moral category, and considering some options is dishonourable or absurd [Williams,B] |
22408 | Consequentialism assumes that situations can be compared [Williams,B] |
22411 | For a consequentialist massacring 7 million must be better than massacring 7 million and one [Williams,B] |
5850 | Happiness is composed of a catalogue of internal and external benefits [Aristotle] |
5856 | Self-interest is a relative good, but nobility an absolute good [Aristotle] |
5853 | The best virtues are the most useful to others [Aristotle] |
5848 | All good things can be misused, except virtue [Aristotle] |
5857 | The young feel pity from philanthropy, but the old from self-concern [Aristotle] |
5859 | Rich people are mindlessly happy [Aristotle] |
22409 | We don't have a duty to ensure that others do their duty [Williams,B] |
22407 | Utilitarianism cannot make any serious sense of integrity [Williams,B] |
5852 | The four constitutions are democracy (freedom), oligarchy (wealth), aristocracy (custom), tyranny (security) [Aristotle] |
1660 | It is noble to avenge oneself on one's enemies, and not come to terms with them [Aristotle] |
5861 | People assume events cause what follows them [Aristotle] |