34 ideas
| 6947 | Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce] |
| 6937 | Reason aims to discover the unknown by thinking about the known [Peirce] |
| 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] |
| 21492 | Realism is basic to the scientific method [Peirce] |
| 6949 | If someone doubted reality, they would not actually feel dissatisfaction [Peirce] |
| 6940 | The feeling of belief shows a habit which will determine our actions [Peirce] |
| 6941 | We are entirely satisfied with a firm belief, even if it is false [Peirce] |
| 6942 | We want true beliefs, but obviously we think our beliefs are true [Peirce] |
| 6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 6598 | We need our beliefs to be determined by some external inhuman permanency [Peirce] |
| 6944 | Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce] |
| 6948 | Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce] |
| 6945 | Once doubt ceases, there is no point in continuing to argue [Peirce] |
| 5122 | Maybe consequentialism is a critique of ordinary morality, rather than describing it [Harman] |
| 5123 | Maybe there is no such thing as character, and the virtues and vices said to accompany it [Harman] |
| 5124 | If a person's two acts of timidity have different explanations, they are not one character trait [Harman] |
| 5125 | Virtue ethics might involve judgements about the virtues of actions, rather than character [Harman] |
| 6939 | What is true of one piece of copper is true of another (unlike brass) [Peirce] |
| 6938 | Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce] |
| 6946 | If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce] |