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

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts

[grouping by concept for counting]

12 ideas
Frege's 'isolation' could be absence of overlap, or drawing conceptual boundaries [Frege, by Koslicki]
Non-arbitrary division means that what falls under the concept cannot be divided into more of the same [Frege, by Koslicki]
Our concepts decide what is countable, as in seeing the leaves of the tree, or the foliage [Frege, by Koslicki]
A concept creating a unit must isolate and unify what falls under it [Frege]
Frege says counting is determining what number belongs to a given concept [Frege, by Koslicki]
Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry]
Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers]
If counting needs a sortal, what of things which fall under two sortals? [Ayers]
Maybe the concept needed under which things coincide must also yield a principle of counting [Wiggins]
The sortal needed for identities may not always be sufficient to support counting [Wiggins]
Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C]
We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki]