9792 | Mathematicians study quantity and continuity, and remove the perceptible features of things [Aristotle] |
9077 | Mathematicians suppose inseparable aspects to be separable, and study them in isolation [Aristotle] |
9788 | Mathematicians study what is conceptually separable, and doesn't lead to error [Aristotle] |
9094 | Mathematical objects abstract both from perceived matter, and from particular substance [Aquinas] |
10504 | Abstracting either treats something as separate, or thinks of it separately [Aquinas] |
10505 | We can just think of an apple's colour, because the apple is not part of the colour's nature [Aquinas] |
10507 | Numbers and shapes are abstracted by ignoring their sensible qualities [Aquinas] |
9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
9890 | The modern account of real numbers detaches a ratio from its geometrical origins [Frege] |
10803 | Frege himself abstracts away from tone and color [Yablo on Frege] |
9988 | If we abstract 'from' two cats, the units are not black or white, or cats [Tait on Frege] |
9579 | Disregarding properties of two cats still leaves different objects, but what is now the difference? [Frege] |
9587 | How do you find the right level of inattention; you eliminate too many or too few characteristics [Frege] |
8770 | 'Abstractionism' is acquiring a concept by picking out one experience amongst a group [Geach] |
8904 | The Way of Abstraction says an incomplete description of a concrete entity is the complete abstraction [Lewis] |
9567 | Maths deals with quantities of physical significance, ignoring irrelevant features [Geroch] |
8512 | Abstractions come before the mind by concentrating on a part of what is presented [Campbell,K] |
10217 | We can apprehend structures by focusing on or ignoring features of patterns [Shapiro] |
9554 | We can focus on relations between objects (like baseballers), ignoring their other features [Shapiro] |
9626 | A structure is an abstraction, focussing on relationships, and ignoring other features [Shapiro] |
17316 | We can abstract to a dependent entity by blocking out features of its bearer [Koslicki] |