Economics Dictionary of ArgumentsHome
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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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W.V.O. Quine on Propositional Functions - Dictionary of Arguments
IX 178 Propositional Function/Principia Mathematica(1)/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. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press._____________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: Unterwegs zur Wahrheit Paderborn 1995 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 |
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> Counter arguments against Quine
> Counter arguments in relation to Propositional Functions
