31 ideas
22338 | An unexamined life can be virtuous [Murdoch] |
22337 | Philosophy must keep returning to the beginning [Murdoch] |
23563 | Philosophy moves continually between elaborate theories and the obvious facts [Murdoch] |
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] |
22341 | Literature is the most important aspect of culture, because it teaches understanding of living [Murdoch] |
22347 | Appreciating beauty in art or nature opens up the good life, by restricting selfishness [Murdoch] |
22339 | Love is a central concept in morals [Murdoch] |
22348 | Ordinary human love is good evidence of transcendent goodness [Murdoch] |
22343 | If I attend properly I will have no choices [Murdoch] |
22349 | Art trains us in the love of virtue [Murdoch] |
22340 | It is hard to learn goodness from others, because their virtues are part of their personal history [Murdoch] |
22350 | Only trivial virtues can be possessed on their own [Murdoch] |
22346 | Moral reflection and experience gradually reveals unity in the moral world [Murdoch] |
22342 | Kantian existentialists care greatly for reasons for action, whereas Surrealists care nothing [Murdoch] |
22351 | Only a philosopher might think choices create values [Murdoch] |
20751 | As a young girl assumes her status as feminine, she acts in a more fragile immobile way [Young,IM] |
22345 | Moral philosophy needs a central concept with all the traditional attributes of God [Murdoch] |