Philosophy Lexicon of Arguments

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Bertrand Russell

Function/Russell/Gödel: Axiom: that functions can only occur "through their values", i.e. they are extensional.
I 58
Function/Russell: presupposes values, but values do not presuppose a function - ((s) In order for 16 to be a square number, there must be a natural number 16 first, etc.)
I 69
Function/Principia Mathematica/Russell: no object, since ambiguous - "values ​​of j z^" are assigned to the j and not to the z.
I 72
Def a-functions/Principia Mathematica/Russell: functions that make sense for a given argument a - ((s) E.g. reversal of function: for example, y = x² can give the value y = 4 for x = 2). - A-function: now we can conversely search for functions that give the value 4 E.g. root of - 16, 2² and any number of others - E.g. "A satisfies all functions that belong to the selection in question": we replace a by a variable and get an A-function. However, and according to the circle fault principle, it may not be an element of this selection, since it refers to the totality of this selection - the selection consists of all those functions that satisfy f(jz^) - then the function is (j). ({f(jz^)) implies jx} where x is the argument - such that there are other a-functions for any possible selection of a-functions that are outside of the selection - ((s)> "all he said").
I 107
Derived function/notation/Principia Mathematica/Russell: (derived from a predicative function).
"f{z^(q,z)}" - defined as follows: if a function f(y ! z^) is given, our derived function must be: "there is a predicative function, which is formally equivalent to j z^ and satisfies f" - always extensional.
I 119
Function/Truth/Principia Mathematica/Russell: a function that is always true, can still be false for the argument (ix)( j x) - if this object does not exist.
I 119
Function/Waverley/identity/equivalence/Principia Mathematica/Russell: the functions x = Scott and x = author of Waverley are formally equivalent - but not identical, because George IV did not want to know if Scott = Scott.
I 144
Varying function/variable function/variability/Principia Mathematica/Russell: old: only transition from E.g. "Socrates is mortal" to "Socrates is wise" (from f ! x to f ! y) (sic) - new: (Second Edition): now the transition to "Plato is mortal" is also possible - (from j ! a to y ! a) - "notation: Greek letters: stand for individuals, Latin ones for predicates -> E.g. "Napoleon had all the properties of a great emperor" - Function as variable.

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.

B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986

B. Russell
Das ABC der Relativitätstheorie Frankfurt 1989

B. Russell
Probleme der Philosophie Frankfurt 1967

B. Russell
Die Philosophie des logischen Atomismus
Eigennamen, U. Wolf (Hg), Frankfurt 1993

B. Russell
Wahrheit und Falschheit
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996

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Ed. Martin Schulz, access date 2018-05-20