structure for 'Mathematics'    |     alphabetical list of themes    |     expand these ideas

### 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

#### [procedure for finding the size of a group of things]

32 ideas
 17861 Two men do not make one thing, as well as themselves [Aristotle]
 646 When we count, are we adding, or naming numbers? [Aristotle]
 19584 Whoever first counted to two must have seen the possibility of infinite counting [Novalis]
 14775 Numbers are just names devised for counting [Peirce]
 9824 In counting we see the human ability to relate, correspond and represent [Dedekind]
 14424 Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell]
 14120 Counting explains none of the real problems about the foundations of arithmetic [Russell]
 17424 Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha]
 17425 To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha]
 9898 We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf]
 17903 Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf]
 4045 Children may have three innate principles which enable them to learn to count [Goldman]
 17447 Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
 17818 How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau]
 17822 Nothing is 'intrinsically' numbered [Yourgrau]
 16014 It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan]
 17812 Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]
 3907 Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton]
 17448 In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
 17456 Counting is the assignment of successively larger cardinal numbers to collections [Heck]
 17455 Is counting basically mindless, and independent of the cardinality involved? [Heck]
 10712 If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
 7466 Mesopotamian numbers applied to specific things, and then became abstract [Watson]
 15912 Counting results in well-ordering, and well-ordering makes counting possible [Lavine]
 17694 Some non-count nouns can be used for counting, as in 'several wines' or 'fewer cheeses' [Laycock]
 17695 Some apparent non-count words can take plural forms, such as 'snows' or 'waters' [Laycock]
 23460 To count, we must distinguish things, and have a series with successors in it [Morris,M]
 23451 Counting needs to distinguish things, and also needs the concept of a successor in a series [Morris,M]
 23452 Discriminating things for counting implies concepts of identity and distinctness [Morris,M]
 17439 There is no deep reason why we count carrots but not asparagus [Koslicki]
 17433 We can still count squares, even if they overlap [Koslicki]
 17462 A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt]