Combining Texts

All the ideas for 'works', 'Isolation and Non-arbitrary Division' and 'On the Natural Faculties'

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7 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Objects do not naturally form countable units [Koslicki]
     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
We can still count squares, even if they overlap [Koslicki]
     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.
There is no deep reason why we count carrots but not asparagus [Koslicki]
     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.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki]
     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.
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
     Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
     From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
     A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
We talk of snow as what stays the same, when it is a heap or drift or expanse [Koslicki]
     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.
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
We just use the word 'faculty' when we don't know the psychological cause [Galen]
     Full Idea: So long as we are ignorant of the true essence of the cause which is operating, we call it a 'faculty'.
     From: Galen (On the Natural Faculties [c.170], I.iv), quoted by Dominik Perler - Intro to The Faculties: a History 2
     A reaction: This is probably the view of most modern neuroscientists. I want to defend the idea that we need the concept of a faculty in philosophy, even if the psychologists and neuroscientists say it is too vague for their purposes.