28 ideas
| 6601 | Science rules the globe because of colonising power, not inherent rationality [Feyerabend] |
| 10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
| 10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
| 10811 | The null set plays the role of last resort, for class abstracts and for existence [Lewis] |
| 10812 | The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis] |
| 10813 | What on earth is the relationship between a singleton and an element? [Lewis] |
| 10814 | Are all singletons exact intrinsic duplicates? [Lewis] |
| 10806 | Megethology is the result of adding plural quantification to mereology [Lewis] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 10816 | We can use mereology to simulate quantification over relations [Lewis] |
| 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] |
| 10808 | Mathematics is generalisations about singleton functions [Lewis] |
| 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] |
| 10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
| 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] |
| 10810 | I say that absolutely any things can have a mereological fusion [Lewis] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 2561 | For Feyerabend the meaning of a term depends on a whole theory [Feyerabend, by Rorty] |