Lexicon of Arguments

 

II 83 f
Function: a function has generality; it is a law. Any number of an x-range is assigned to a number of the y-range. A function is not a variable (also: an elliptic function is not an elliptic variable). Function: a function is unsaturated.
>Generality, >unsaturated, >Generalization.
II 87
Functional characters: functional characters are unsaturated. However, in connection with numerals they are 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.
>Equations, >Numbers.
- - -
Husted 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.
>Subject, >Predicate.
V 93
Argument/function: E.g. "(3) to the power of 2". The argument expression is: "3". The function expression is: "(...) to the power of 2".
E.g. "3 + 2". The argument expressions is: "2" and "3". The function expression is: "+".
E.g. "Peter is asleep". The argument expression is: "Peter". The function expression is: "is asleep".
E.g. "Everybody loves Agnes". The argument expression is: "loves Agnes". The function expression is: "everybody".
Function expressions: "+", (...) to the power of"! The verb (sometimes also the argument expression) is a second order function expression: "everybody", "nobody".
Function expressions:
1st order E.g. "is asleep"
2nd order E.g. "everybody", "nobody".