Lexicon of Arguments

Philosophical and Scientific Issues in Dispute
 
[german]


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Theses I
Theses II

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Prior I 163
Identity/Russell: "a=a" "the a is the a" is false if there is no a or if there are multiple a - Def self-identity/Russell: nevertheless Russell’s Law "x = x" is part of his system - "For any φ if x φs, then φs x" - if we define individual existence as Lesniewkian self-identity, then it comes out at a class which must be regarded as a class of one and which can be predicted from some, but not from all classes.
>Element relation/Lesniewski, >Unit set.
- - -
Russell I 58
Identity/Principia Mathematica(1)/Russell: no judgment! E.g. we do not judge that Socrates = Socrates. In a way, we judge an ambiguous case of propositional function (propositional function) "A is A".
>Propositional function.
ad I 111f
Containment/Identity/Element relations/Equal sign/Epsilon/Principia Mathematica/(s): therefore containment must not be the same as identity, otherwise from the right
i'x = i'x
follows the wrong
i'x ε i'x
i.e., a class may not be identical with its (perhaps only) element.
>Element relation, >Equal sign.

1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press.

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