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18. Thought / E. Abstraction / 3. Abstracta by Ignoring

[creating abstractions by ignoring some features]

22 ideas
Mathematicians study quantity and continuity, and remove the perceptible features of things [Aristotle]
Mathematicians suppose inseparable aspects to be separable, and study them in isolation [Aristotle]
Mathematicians study what is conceptually separable, and doesn't lead to error [Aristotle]
Mathematical objects abstract both from perceived matter, and from particular substance [Aquinas]
We can just think of an apple's colour, because the apple is not part of the colour's nature [Aquinas]
Abstracting either treats something as separate, or thinks of it separately [Aquinas]
Numbers and shapes are abstracted by ignoring their sensible qualities [Aquinas]
Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind ,by Dummett]
We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind]
The modern account of real numbers detaches a ratio from its geometrical origins [Frege]
Frege himself abstracts away from tone and color [Yablo on Frege]
If we abstract 'from' two cats, the units are not black or white, or cats [Tait on Frege]
Disregarding properties of two cats still leaves different objects, but what is now the difference? [Frege]
How do you find the right level of inattention; you eliminate too many or too few characteristics [Frege]
'Abstractionism' is acquiring a concept by picking out one experience amongst a group [Geach]
The Way of Abstraction says an incomplete description of a concrete entity is the complete abstraction [Lewis]
Maths deals with quantities of physical significance, ignoring irrelevant features [Geroch]
Abstractions come before the mind by concentrating on a part of what is presented [Campbell,K]
We can apprehend structures by focusing on or ignoring features of patterns [Shapiro]
We can focus on relations between objects (like baseballers), ignoring their other features [Shapiro]
A structure is an abstraction, focussing on relationships, and ignoring other features [Shapiro]
We can abstract to a dependent entity by blocking out features of its bearer [Koslicki]