28 ideas
| 2922 | All intelligent Romans were Epicureans [Nietzsche] |
| 23520 | Truth has had to be fought for, and normal life must be sacrificed to achieve it [Nietzsche] |
| 2914 | One must never ask whether truth is useful [Nietzsche] |
| 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] |
| 23217 | All of our happiness and misery arises entirely from the brain [Hippocrates] |
| 2921 | Philosophy grasps the limits of human reason, and values are beyond it [Nietzsche] |
| 20138 | Christianity is at war with the higher type of man, and excommunicates his basic instincts [Nietzsche] |
| 20375 | Virtues must be highly personal; if not, it is merely respect for a concept [Nietzsche] |
| 2915 | Each person should devise his own virtues and categorical imperative [Nietzsche] |
| 2920 | A God who cures us of a head cold at the right moment is a total absurdity [Nietzsche] |
| 2917 | Christianity is a revolt of things crawling on the ground against elevated things [Nietzsche] |
| 2918 | The story in Genesis is the story of God's fear of science [Nietzsche] |
| 2919 | 'Faith' means not wanting to know what is true [Nietzsche] |
| 2916 | The great lie of immortality destroys rationality and natural instinct [Nietzsche] |