28 ideas
| 19336 | Wisdom involves the desire to achieve perfection [Leibniz] |
| 19463 | Induction assumes some uniformity in nature, or that in some respects the future is like the past [Ayer] |
| 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] |
| 7696 | Leibniz first asked 'why is there something rather than nothing?' [Leibniz, by Jacquette] |
| 19341 | There must be a straining towards existence in the essence of all possible things [Leibniz] |
| 19428 | Because something does exist, there must be a drive in possible things towards existence [Leibniz] |
| 5047 | The world is physically necessary, as its contrary would imply imperfection or moral absurdity [Leibniz] |
| 19461 | Knowing I exist reveals nothing at all about my nature [Ayer] |
| 19459 | To say 'I am not thinking' must be false, but it might have been true, so it isn't self-contradictory [Ayer] |
| 19460 | 'I know I exist' has no counterevidence, so it may be meaningless [Ayer] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 19464 | We only discard a hypothesis after one failure if it appears likely to keep on failing [Ayer] |
| 19462 | Induction passes from particular facts to other particulars, or to general laws, non-deductively [Ayer] |
| 19343 | We follow the practical rule which always seeks maximum effect for minimum cost [Leibniz] |
| 19429 | The principle of determination in things obtains the greatest effect with the least effort [Leibniz] |