Lexicon of Arguments

Philosophical and Scientific Issues in Dispute
 
[german]


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Concepts
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Sc. Camps
Theses I
Theses II

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I XX
Constructivist attitude/Constructivism/Russell/Gödel: was abandoned in the first edition, since the reducibility axiom for higher types makes it necessary that basic predicates of an infinitely high type exist - of constructivism only remains:
1) Classes as facon de parler
2) The definition of ~, v, etc. as valid for propositions that contain quantifiers
3) Gradual construction of functions of orders higher than 1 (superfluous of course, because of the reducibility-axiom)
4) Interpretation of definitions as mere typographical shortcuts.
GoedelVs: because of reducibility axiom: there always exist real objects in the form of basic predicates corresponding to each defined symbol.
>Reducibility axiom, >Classes, >Logical connectives, >Quantifiers, >Proposition.
>
I XX
Constructivist attitude/Constructivism/Principia Mathematica(1)/Gödel: is taken in again in the second edition and the reducibility axiom is dropped. - It is determined that all basic predicates belong to the lowest type.


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

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