24 ideas
15842 | An ad hominem refutation is reasonable, if it uses the opponent's assumptions [Harte,V] |
15841 | Mereology began as a nominalist revolt against the commitments of set theory [Harte,V] |
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] |
15858 | Traditionally, the four elements are just what persists through change [Harte,V] |
15848 | Mereology treats constitution as a criterion of identity, as shown in the axiom of extensionality [Harte,V] |
15837 | What exactly is a 'sum', and what exactly is 'composition'? [Harte,V] |
15838 | The problem with the term 'sum' is that it is singular [Harte,V] |
15839 | If something is 'more than' the sum of its parts, is the extra thing another part, or not? [Harte,V] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
17960 | Eternalism says all times are equally real, and future and past objects and properties are real [Merricks] |
17961 | Growing block has a subjective present and a growing edge - but these could come apart [Merricks, by PG] |