@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 29 Mar 2024}, author = {Frege,Gottlob}, subject = {Abstraction}, note = {Stuhlmann-Laeisz II 49 Definition abstraction/Frege/St: abstraction is a process to identify each other in the various elements of a region, e.g. same color, same size, same shape. New objects are gained by abstraction of the partial identity. ((s) Such objects which are only about numerical equality or color identity are individuated.) If A is such an abstraction, then there is by definition a (base) object a, so that the following is true: A is the F of a. --- Thiel I 131 Abstraction/Mathematics/Frege/Thiel: abstraction is a purely logical process, an operation with statements, the logical character of which is revealed by the change from the structure of the complicated initial statement to the structure of the new statement. Frege understood this first. Tere are statements not only about numbers, but also about sets, functions, concepts, situations, meaning and truth value of a statement, about structures. I 133 Numbers/digits/number names/names/mathematics/Thiel: the philosophical punch line of the transition from general statements via digits to arithmetic statements is that although we have introduced the speech about numbers in addition to the speech about digits, it is still a form of speech, a facon de parler, whose possibility does not depend on the fact that there are still abstract objects beyond the concrete digits, which we call "numbers". >Numerals. I 134 We also had no reason to conceive the digits as "names" of numbers, so that 4, IV, and |||| would denote the same number four, as it was assumed in the traditional philosophy of numbers. >Numbers.}, note = { F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F II G. Frege Funktion, Begriff, Bedeutung Göttingen 1994 F IV G. Frege Logische Untersuchungen Göttingen 1993 SL I R. Stuhlmann Laeisz Philosophische Logik Paderborn 2002 Stuhlmann II R. Stuhlmann-Laeisz Freges Logische Untersuchungen Darmstadt 1995 T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=197831} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=197831} }