Philosophy Lexicon of Arguments

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I 219
Not all abstract objects are properties: numbers, classes, functions, geometric shapes, ideas, possibilities - give up or re-trace abstract objects - can be distinguished by the faithful use of "-ness" from concrete objects.
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II 26
Numbers: quantification is objectification, numeric name - diagonals: are irrational, scope: is transcendental.
Measure: measuring scale: multidigit general term, puts physical objects in relation to pure numbers - counting: measuring a class.
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II 28
Numbers/Ontology: Numbers are merely "facon de parler" - higher classes needed to replace numbers - otherwise only physical objects.
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IX 54
Numbers/Frege/Quine: like predecessors (ancestor): Definition predecessor/Frege: the common elements of all classes for which the initial condition was fulfilled: "y e z" and the seclusion condition: which resulted in "a" "z 0 e z]} - Problem: the successor relation could also lead to things that are not >numbers - Numbers/Quine: we will mainly use them as a measure of multiplicities (that is how Frege had defined them) - a hasx elements"- the scheme goes back to Frege: a has 0 elements a = L. - s has SA°x elements Ey(y e a n _{y} has x elements.
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IX 59
Numbers/Zermelo: (1908) takes L as 0, then {x} as S°x for each x. (i.e. "{x}" always one more than x! - {x} successor of x! - as numbers we then receive L, {L}, {{L}} .. etc.
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IX 59~
Numbers/Von Neumann (1923) regards every natural number as the class of the previous numbers: 0 becomes L again, - but successor S°x does not become {x}, but x U {x}. (Combined with) - 1: as in Zermelo: equal {L} - but 2: {0,1} or {L,{L}}. - 3: {0,1,2} or {L,{L},{L,{L,{L}}} - for von Neuman this says that a has x elements, that a ~ x. (Number, equipotent) - that’s just the "a ~ {y: y < x}" from chapter 11, because for von Neumann is x = {y: y.

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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.

Q I
W.V.O. Quine
Wort und Gegenstand Stuttgart 1980

Q II
W.V.O. Quine
Theorien und Dinge Frankfurt 1985

Q III
W.V.O. Quine
Grundzüge der Logik Frankfurt 1978

Q IX
W.V.O. Quine
Mengenlehre und ihre Logik Wiesbaden 1967

Q V
W.V.O. Quine
Die Wurzeln der Referenz Frankfurt 1989

Q VI
W.V.O. Quine
Unterwegs zur Wahrheit Paderborn 1995

Q VII
W.V.O. Quine
From a logical point of view Cambridge, Mass. 1953

Q VIII
W.V.O. Quine
Bezeichnung und Referenz
In
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982

Q X
W.V.O. Quine
Philosophie der Logik Bamberg 2005

Q XII
W.V.O. Quine
Ontologische Relativität Frankfurt 2003


> Counter arguments against Quine
> Counter arguments in relation to Numbers



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Ed. Martin Schulz, access date 2017-06-24