Full Idea
Predicativism has it that a mathematical object (such as a set of numbers) cannot be defined by quantifying over a collection that includes that same mathematical object. To do so would be a violation of the vicious circle principle.
Gist of Idea
Predicativism says mathematical definitions must not include the thing being defined
Source
Leon Horsten (The Tarskian Turn [2011], 07.7)
Book Reference
Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.100
A Reaction
In other words, when you define an object you are obliged to predicate something new, and not just recycle the stuff you already have.