274 ;;Quote: transitive counting is measuring the cardinality of a set by counting; one-to-one correspondence

274+;;Quote: intransitive counting is repeating number words in right order, as in counting sheep

275 ;;Quote: less-than over natural numbers should be recursive so we can compare numbers and count them

275 ;;Quote: QuineWV defines the numbers as any progression; but also need transitive counting

278 ;;Quote: there are many ways to define numbers as sets; each defines relations differently; so number is not a particular set

281 ;;Quote: number words function like quantification operators; if numbers exist then so should quantifiers

281+;;Quote: FregeG defined number as an equivalence class, but numbers are neither predicates nor adjectives

284 ;;Quote: consistent set theories do not include the class of all classes with 17 members; this avoids the paradoxes

286 ;;Quote: identity statements are senseless outside of a consistent context for individuating things

286+;;Quote: while FregeG felt numbers needed a reference, it does not make sense to identify '3' with '[[[0]]]'; their contexts differ

291 ;;Quote: a sequence of number words is just that, a sequence with certain properties; not distinct from numbers

291+;;Quote: arithmetic concerns the abstract structure of progression, and not particular objects--the numbers

293 ;;Quote: the value of a particular expression is the position of a number within a sequence and the corresponding rules for counting and cardinality

293 ;;Quote: numbers have a recursive 'less-than' relation because numeric notation is generated recursively