Ideas from 'Isolation and Non-arbitrary Division' by Kathrin Koslicki [1997], by Theme Structure

[found in 'Synthese' (ed/tr -) [- ,]].

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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units

17435

Objects do not naturally form countable units

			Full Idea: Objects do not by themselves naturally fall into countable units.
			From: Kathrin Koslicki (Isolation and Non-arbitrary Division [1997], 2.2)
			A reaction: Hm. This seems to be modern Fregean orthodoxy. Why did the institution of counting ever get started if the things in the world didn't demand counting? Even birds are aware of the number of eggs in their nest (because they miss a stolen one).

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

17439

There is no deep reason why we count carrots but not asparagus

			Full Idea: Why do speakers of English count carrots but not asparagus? There is no 'deep' reason.
			From: Kathrin Koslicki (Isolation and Non-arbitrary Division [1997])
			A reaction: Koslick is offering this to defend the Fregean conceptual view of counting, but what seems to matter is what is countable, and not whether we happen to count it. You don't need to know what carrots are to count them. Cooks count asparagus.

17433

We can still count squares, even if they overlap

			Full Idea: The fact that there is overlap does not seem to inhibit our ability to count squares.
			From: Kathrin Koslicki (Isolation and Non-arbitrary Division [1997], 2.2)
			A reaction: She has a diagram of three squares overlapping slightly at their corners. Contrary to Frege, these seems to depend on a subliminal concept of the square that doesn't depend on language.

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

17434

We struggle to count branches and waves because our concepts lack clear boundaries

			Full Idea: The reason we have a hard time counting the branches and the waves is because our concepts 'branches on the tree' and 'waves on the ocean' do not determine sufficiently precise boundaries: the concepts do not draw a clear invisible line around each thing.
			From: Kathrin Koslicki (Isolation and Non-arbitrary Division [1997], 2.2)
			A reaction: This is the 'isolation' referred to in Frege.

7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff

17436

We talk of snow as what stays the same, when it is a heap or drift or expanse

			Full Idea: Talk of snow concerns what stays the same when some snow changes, as it might be, from a heap of snow to a drift, to an expanse.
			From: Kathrin Koslicki (Isolation and Non-arbitrary Division [1997], 2.2)
			A reaction: The whiteness also stays the same, but isn't stuff.