Philosophy Lexicon of Arguments

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II 83 f
Function: generality, law. - Any number of x-range is assigned to a number of the y-range - A function is not a variable! (An elliptic function is not an elliptic variable). Function: is unsaturated.
II 87
Functional Characters: unsaturated - in connection with numerals: saturated.
Argument: every time a number >value of the function
Caution: It has become common to read the equation "y = f (x)": "y is a function of x". This contains two errors:
1) If the equal sign is translated by the copula.
2) the function with its value is mistaken for an argument. These errors gave rise to the opinion that the function was a number.
V 93
Functions of numbers are fundamentally different (because they are unsaturated).
Logic/Grammar: E.g. "Peter plays with Agnes": in the logic both Peter and Agnes can be declared subjects.
V 93
Argument/Function: E.g. "(3) to the power of 2": argument expression: "3"
Function expression: "(...) to the power of 2".
E.g. "3 + 2" argument expressions: "2" and "3" - function expression: "+".
E.g. "Peter is asleep" - argument expression: "Peter" - function expression: "is asleep".
E.g. "Everybody loves Agnes" argument expression "loves Agnes" function expression: "everybody"
Function expressions: "+", (..) to the power of"! - verb (sometimes also argument expression)
second order function expression: "everybody", "nobody".
Function expressions:
1st order E.g. "is asleep"
2nd order E.g. "everybody", "nobody".

G. Frege
Die Grundlagen der Arithmetik Stuttgart 1987

G. Frege
Funktion, Begriff, Bedeutung Göttingen 1994

G. Frege
Logische Untersuchungen Göttingen 1993

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Ed. Martin Schulz, access date 2017-05-26