Economics Dictionary of ArgumentsHome
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| Functions: I. A function in mathematics is a relation between a set of inputs and a set of outputs, where each input is related to exactly one output. The set of inputs is called the domain of the function. Functions can be represented by formulas, graphs, or tables. For example, the function f(x) = x^2 is represented by the formula y = x^2, which takes any number as input and returns its square as output. The graph of this function is a parabola.
II. In psychology, functions refer to the various mental processes and behaviors that enable individuals to adapt and interact effectively with their environment. These include cognitive functions like perception, memory, and reasoning, as well as emotional and social functions like regulating emotions, forming relationships, and making decisions._____________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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Bertrand Russell on Functions - Dictionary of Arguments
I XII / XIII Function/Russell/Gödel: Axiom: functions can only occur "through their values", i.e. they are extensional. >Extensionality, >Extension. 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(1)/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) > "Everythingl 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. 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. |
Russell I B. Russell/A.N. Whitehead Principia Mathematica Frankfurt 1986 Russell II B. Russell The ABC of Relativity, London 1958, 1969 German Edition: Das ABC der Relativitätstheorie Frankfurt 1989 Russell IV B. Russell The Problems of Philosophy, Oxford 1912 German Edition: Probleme der Philosophie Frankfurt 1967 Russell VI B. Russell "The Philosophy of Logical Atomism", in: B. Russell, Logic and KNowledge, ed. R. Ch. Marsh, London 1956, pp. 200-202 German Edition: Die Philosophie des logischen Atomismus In Eigennamen, U. Wolf (Hg), Frankfurt 1993 Russell VII B. Russell On the Nature of Truth and Falsehood, in: B. Russell, The Problems of Philosophy, Oxford 1912 - Dt. "Wahrheit und Falschheit" In Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996 |
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