33 ideas
| 7578 | I conceived it my task to create difficulties everywhere [Kierkegaard] |
| 22047 | Wherever there is painless contradiction there is also comedy [Kierkegaard] |
| 22092 | Kierkegaard's truth draws on authenticity, fidelity and honesty [Kierkegaard, by Carlisle] |
| 15999 | Pure truth is for infinite beings only; I prefer endless striving for truth [Kierkegaard] |
| 20313 | The highest truth we can get is uncertainty held fast by an inward passion [Kierkegaard] |
| 3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
| 3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
| 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] |
| 22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
| 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] |
| 20742 | The real subject is ethical, not cognitive [Kierkegaard] |
| 7579 | While big metaphysics is complete without ethics, personal philosophy emphasises ethics [Kierkegaard] |
| 7581 | Speculative philosophy loses the individual in a vast vision of humanity [Kierkegaard] |
| 20314 | People want to lose themselves in movements and history, instead of being individuals [Kierkegaard] |
| 7582 | Becoming what one is is a huge difficulty, because we strongly aspire to be something else [Kierkegaard] |
| 7586 | God does not think or exist; God creates, and is eternal [Kierkegaard] |
| 20312 | God cannot be demonstrated objectively, because God is a subject, only existing inwardly [Kierkegaard] |
| 7580 | Pantheism destroys the distinction between good and evil [Kierkegaard] |
| 7583 | Faith is the highest passion in the sphere of human subjectivity [Kierkegaard] |
| 7584 | Without risk there is no faith [Kierkegaard] |