## Philosophy Lexicon of Arguments | |||

Author | Item | Excerpt | Meta data |
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Russell, Bertrand Books on Amazon: Bertrand Russell |
Functions | I XII / XIII 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. |
R I B. Russell/A.N. Whitehead Principia Mathematica Frankfurt 1986 R II B. Russell Das ABC der Relativitätstheorie Frankfurt 1989 R IV B. Russell Probleme der Philosophie Frankfurt 1967 R VI B. Russell Die Philosophie des logischen Atomismus InEigennamen, U. Wolf (Hg), Frankfurt 1993 R VII B. Russell Wahrheit und Falschheit InWahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996 |

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Ed. Martin Schulz, access date 2017-03-29