@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 29 Mar 2024}, author = {Wittgenstein,Ludwig}, subject = {Numbers}, note = {II 32 Number/Wittgenstein: not a concept, but a logical form. II 283 Numbers/cardinal/Wittgenstein: that there are infinitely many cardinals, is a rule that one sets up. II 343 Number/Frege/WittgensteinVsFrege: a number is a property of a property. - Problem: E.g. for blue-eyed men in the room. - Then the five would be a property of a property - to be a blue-eyed man in the room - e.g. to express that Hans and Paul are two, they would then have a property in common, which not exactly belongs to the other. - ((s) each would have the property to be different from the other.) - Solution/Frege: the property of being Hans or Paul. II 344 Number/Wittgenstein: are not merely signs. - One can have two items of the form three, but only one number. - ((s) WittgensteinVsFormalism). >Formalism. II 360 Number/Definition/WittgensteinVsRussell: numerical equality is a prerequisite for a clear correspondence. - Therefore, Russell's definition of the number is useless. - ((s) Because it is circular reasoning if you want to define number via illustration). II 361 Definition/Wittgenstein: instead of a definition of "number" we must figure out the rules of usage. >Rules, >Use. II 415 Number/Russell/Wittgenstein: has claimed, 3 is a property that is common to all triads. - ((s) Frege: classes of classes - does Frege not mean objects with classes (instead of properties)?). II 416 Definition number/WittgensteinVsRussell: the number is an attribute of a function which defines a class, not a property of the extension. - E.g. Extension: it would be a tautology to say, ABC is three. - In contrast, meaingful: to say, in this room are three people. >Functions, >Extensions, >Sets. --- IV 93 Definition number/numbers/Wittgenstein/Tractatus: 6,021 - the number is the exponent of an operation. - - - Waismann I 66 Def Natural numbers/Wittgenstein: those to which induction can be applied in proofs.}, note = { W II L. Wittgenstein Wittgenstein’s Lectures 1930-32, from the notes of John King and Desmond Lee, Oxford 1980 German Edition: Vorlesungen 1930-35 Frankfurt 1989 W III L. Wittgenstein The Blue and Brown Books (BB), Oxford 1958 German Edition: Das Blaue Buch - Eine Philosophische Betrachtung Frankfurt 1984 W IV L. Wittgenstein Tractatus Logico-Philosophicus (TLP), 1922, C.K. Ogden (trans.), London: Routledge & Kegan Paul. Originally published as “Logisch-Philosophische Abhandlung”, in Annalen der Naturphilosophische, XIV (3/4), 1921. German Edition: Tractatus logico-philosophicus Frankfurt/M 1960 Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=286687} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=286687} }