Lexicon of Arguments

Philosophical and Scientific Issues in Dispute
 
[german]


Complaints - Corrections

Table
Concepts
Versus
Sc. Camps
Theses I
Theses II

Concept/Author*  

What is wrong?
Page
Other metadata
Translation
Excerpt or content
Other

Correction: Year / Place / Page
/ /

Correction:
(max 500 charact.)

Your username*
or User-ID

Email address*

The complaint
will not be published.

 
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.

Found an error? Use our Complaint Form. Perhaps someone forgot to close a bracket? A page number is wrong?
Help us to improve our lexicon.
However, if you are of a different opinion, as regards the validity of the argument, post your own argument beside the contested one.
The correction will be sent to the contributor of the original entry to get his opinion about.