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] |
17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
15916 | Frege's one-to-one correspondence replaces well-ordering, because infinities can't be counted [Lavine on Frege] |
17437 | Non-arbitrary division means that what falls under the concept cannot be divided into more of the same [Koslicki on Frege] |
17438 | Our concepts decide what is countable, as in seeing the leaves of the tree, or the foliage [Koslicki on Frege] |
17428 | Frege says counting is determining what number belongs to a given concept [Koslicki on Frege] |
17446 | Counting rests on one-one correspondence, of numerals to objects [Frege] |
9582 | Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege] |
17444 | Husserl said counting is more basic than Frege's one-one correspondence [Heck on Husserl] |
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] |
12154 | Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting [Perry on Geach] |
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] |
9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
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] |
17518 | Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers] |
17516 | If counting needs a sortal, what of things which fall under two sortals? [Ayers] |
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 [Heck on Parsons,C] |
17529 | Maybe the concept needed under which things coincide must also yield a principle of counting [Wiggins] |
17530 | The sortal needed for identities may not always be sufficient to support counting [Wiggins] |
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] |
13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
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] |
17450 | Understanding 'just as many' needn't involve grasping one-one correspondence [Heck] |
17451 | We can know 'just as many' without the concepts of equinumerosity or numbers [Heck] |
17455 | Is counting basically mindless, and independent of the cardinality involved? [Heck] |
17456 | Counting is the assignment of successively larger cardinal numbers to collections [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] |
17439 | There is no deep reason why we count carrots but not asparagus [Koslicki] |
17427 | Frege's 'isolation' could be absence of overlap, or drawing conceptual boundaries [Koslicki] |
17433 | We can still count squares, even if they overlap [Koslicki] |
17434 | We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki] |
17462 | A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt] |