# Philosophy Dictionary of Arguments

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Propositional function: open sentence E.g. "Something is green", "x is green" - neither true nor false. A propositional function has an argument position (variable) in which an expression can be inserted. Only after inserting we can decide whether the then complete sentence is true or false.

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Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

Author Concept Summary/Quotes Sources

W.V.O. Quine on Propositional Functions - Dictionary of Arguments

IX 178
Propositional Function/Principia Mathematica/Theoretical Terms/Russell: name for attributes and relations - "f", "y"... as variables - i.e. that x has the attribute f, that x is to y in the relation y, etc. "fx",y(x,y)", etc. - ^x: to abstract propositional function from statements he just inserted variables with an accent circonflexe into the argument positions - E.g. the attribute to love: "^x loves y" E.g. to be loved: "x loves ^y" (active/passive, without classes!) (>lambda notation/(s) Third Way between Russell and Quinean classes) - Analog in class abstraction: "{x: x loves y}", "{y: x loves y}" - E.g. relation of loving: "{: x loves y}" or "{: x loves}". Abstraction: Problem: in wider contexts sometimes you have no clues as to whether a variable ^x should be understood as if it caused an abstraction of a short or a longer clause - Solution/Russell: Context Definition - statement function must not occur as a value of bound variables that are used to describe it - it must always have too high an order to be a value for such variables - characteristic back and forth between sign and object: the propositional function receives its order from the abstracting expression, and the order of the variables is the order of the values.
>Variables/Quine, >Attributes/Quine
IX 185
Propositional Function/Attribute/Predicate/Theoretical Terms/QuineVsRussell: overlooked the following difference and its analogues:
a) "propositional functions": as attributes (or intensional relations) and
b) "proposition functions": as expressions, i.e. predicates (and open statements: E.g. "x is mortal") - accordingly:
a) attributes
b) open statements - solution/Quine: allow an expression of higher order to refer straight away to an attribute or a relation of lower order.

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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. 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.

Quine I
W.V.O. Quine
Word and Object, Cambridge/MA 1960
German Edition:
Wort und Gegenstand Stuttgart 1980

Quine II
W.V.O. Quine
Theories and Things, Cambridge/MA 1986
German Edition:
Theorien und Dinge Frankfurt 1985

Quine III
W.V.O. Quine
Methods of Logic, 4th edition Cambridge/MA 1982
German Edition:
Grundzüge der Logik Frankfurt 1978

Quine V
W.V.O. Quine
The Roots of Reference, La Salle/Illinois 1974
German Edition:
Die Wurzeln der Referenz Frankfurt 1989

Quine VI
W.V.O. Quine
Pursuit of Truth, Cambridge/MA 1992
German Edition:

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

Quine VII (a)
W. V. A. Quine
On what there is
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (b)
W. V. A. Quine
Two dogmas of empiricism
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (c)
W. V. A. Quine
The problem of meaning in linguistics
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (d)
W. V. A. Quine
Identity, ostension and hypostasis
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (e)
W. V. A. Quine
New foundations for mathematical logic
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (f)
W. V. A. Quine
Logic and the reification of universals
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (g)
W. V. A. Quine
Notes on the theory of reference
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (h)
W. V. A. Quine
Reference and modality
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (i)
W. V. A. Quine
Meaning and existential inference
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VIII
W.V.O. Quine
Designation and Existence, in: The Journal of Philosophy 36 (1939)
German Edition:
Bezeichnung und Referenz
In
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982

Quine IX
W.V.O. Quine
Set Theory and its Logic, Cambridge/MA 1963
German Edition:
Mengenlehre und ihre Logik Wiesbaden 1967

Quine X
W.V.O. Quine
The Philosophy of Logic, Cambridge/MA 1970, 1986
German Edition:
Philosophie der Logik Bamberg 2005

Quine XII
W.V.O. Quine
Ontological Relativity and Other Essays, New York 1969
German Edition:
Ontologische Relativität Frankfurt 2003

Quine XIII
Willard Van Orman Quine
Quiddities Cambridge/London 1987

> Counter arguments against Quine

Ed. Martin Schulz, access date 2022-05-20