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Full Idea
Some authors (Poincaré and Russell, for example) were disposed to reject properties that are not definable, or are definable only impredicatively.
Clarification
'Impredicative' definitions tend towards circularity
Gist of Idea
Some reject formal properties if they are not defined, or defined impredicatively
Source
Stewart Shapiro (Foundations without Foundationalism [1991], 7.1)
Book Ref
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.174
A Reaction
I take Quine to be the culmination of this line of thought, with his general rejection of 'attributes' in logic and in metaphysics.