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

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

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