29 ideas
| 22087 | Philosophy fails to articulate the continual becoming of existence [Kierkegaard, by Carlisle] |
| 5651 | Traditional views of truth are tautologies, and truth is empty without a subject [Kierkegaard, by Scruton] |
| 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] |
| 11993 | Jones may cease to exist without some simple property, but that doesn't make it essential [Kung] |
| 11997 | A property may belong essentially to one thing and contingently to another [Kung] |
| 11992 | Aristotelian essences underlie a thing's existence, explain it, and must belong to it [Kung] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 11995 | Some peripheral properties are explained by essential ones, but don't themselves explain properties [Kung] |
| 11996 | Some non-essential properties may explain more than essential-but-peripheral ones do [Kung] |
| 22090 | For me time stands still, and I with it [Kierkegaard, by Carlisle] |
| 9305 | The plebeians bore others; only the nobility bore themselves [Kierkegaard] |
| 5650 | Reason is just abstractions, so our essence needs a subjective 'leap of faith' [Kierkegaard, by Scruton] |
| 22095 | There are aesthetic, ethical and religious subjectivity [Kierkegaard, by Carlisle] |
| 20747 | What matters is not right choice, but energy, earnestness and pathos in the choosing [Kierkegaard] |
| 22091 | Kierkegaard prioritises the inward individual, rather than community [Kierkegaard, by Carlisle] |
| 22088 | Faith is like a dancer's leap, going up to God, but also back to earth [Kierkegaard, by Carlisle] |