29 ideas
| 20768 | Like spiderswebs, dialectical arguments are clever but useless [Ariston, by Diog. Laertius] |
| 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] |
| 12790 | Generalisations must be invariant to explain anything [Leuridan] |
| 12789 | Biological functions are explained by disposition, or by causal role [Leuridan] |
| 14388 | Mechanisms must produce macro-level regularities, but that needs micro-level regularities [Leuridan] |
| 14386 | Mechanisms are ontologically dependent on regularities [Leuridan] |
| 12787 | Mechanisms can't explain on their own, as their models rest on pragmatic regularities [Leuridan] |
| 14384 | We can show that regularities and pragmatic laws are more basic than mechanisms [Leuridan] |
| 14389 | There is nothing wrong with an infinite regress of mechanisms and regularities [Leuridan] |
| 3049 | The chief good is indifference to what lies midway between virtue and vice [Ariston, by Diog. Laertius] |
| 3549 | Ariston says rules are useless for the virtuous and the non-virtuous [Ariston, by Annas] |
| 14387 | Rather than dispositions, functions may be the element that brought a thing into existence [Leuridan] |
| 14382 | Pragmatic laws allow prediction and explanation, to the extent that reality is stable [Leuridan] |
| 14385 | Strict regularities are rarely discovered in life sciences [Leuridan] |
| 14383 | A 'law of nature' is just a regularity, not some entity that causes the regularity [Leuridan] |