25 ideas
| 4424 | A warlike philosopher challenges problems to single combat [Nietzsche] |
| 21829 | Philosophy aims to understand how things (broadly understood) hang together (broadly understood) [Sellars] |
| 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] |
| 6550 | Reduction requires that an object's properties consist of its constituents' properties and relations [Sellars] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 2886 | The distinction between egoistic and non-egoistic acts is absurd [Nietzsche] |
| 4426 | A bad result distorts one's judgement about the virtue of what one has done [Nietzsche] |
| 4425 | The overcoming of pity I count among the noble virtues [Nietzsche] |
| 20132 | To become what you are you must have no self-awareness [Nietzsche] |
| 20144 | Eternal recurrence is the highest attainable affirmation [Nietzsche] |
| 2889 | One repays a teacher badly if one remains only a pupil [Nietzsche] |
| 2887 | I am not an atheist because of reasoning or evidence, but because of instinct [Nietzsche] |