Aristotle on Mathematics - Dictionary of Arguments
Thiel I 23 ff
Mathematics/Tradition/Thiel: Aristotle, Kant and Plato accept an object, an area of mathematics. More important to them is the question of how the human behaves in relation to this object.
Differentiation invent/discover/Plato: Euthydemos: geometers, arithmetic artists and astronomers are like hunters, they are exploring what is already there.
AristotleVsPlato: he had joined the Kratylos and Heraclitus inasmuch as there could be no science of the sensible after him, since everything was in flux. Thus, objects cannot even be defined.
Plato: There are always many of the same kind of the mathematical objects, while the idea is always only one.
Thiel: one may think of the four-time appearance of the isosceles triangle in the square.
Aristotle's Plato: denies an existence of the mathematical objects independent of the bodies. They exist on or in objects and can be isolated by abstraction. Mathematical objects are not themselves concrete, real objects. But they also have no "separated being". Each number is always only number of something._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Philosophie und Mathematik Darmstadt 1995