Philosophy Lexicon 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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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.
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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.

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


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Ed. Martin Schulz, access date 2017-05-25