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Full Idea
Russell's theory of types meant that features common to different levels of the hierarchy became uncapturable (since any attempt to capture them would involve a predicate which disobeyed the hierarchy restrictions).
Gist of Idea
Type theory cannot identify features across levels (because such predicates break the rules)
Source
comment on Bertrand Russell (The Theory of Logical Types [1910]) by Michael Morris - Guidebook to Wittgenstein's Tractatus 2H
Book Ref
Morris,Michael: 'Guidebook to Wittgenstein's Tractatus' [Routledge 2008], p.112
A Reaction
I'm not clear whether this is the main reason why type theory was abandoned. Ramsey was an important critic.
| 23457 | Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell] |
| 21556 | Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey] |
| 21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
| 21567 | 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell] |
| 21568 | A one-variable function is only 'predicative' if it is one order above its arguments [Russell] |