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.

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.

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Books on Amazon
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.
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.

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.

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

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

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

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

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

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

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

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

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

W.V.O. Quine
Ontologische Relativität Frankfurt 2003

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Ed. Martin Schulz, access date 2017-11-22