Another opinion concerning Richard's paradox relates to mathematical predicativism.
These included intuitionism, formalism, and predicativism.
Hence predicativism would reject this definition.
More recently, predicativism has been studied by Solomon Feferman, who has used proof theory to explore the relationship between predicative and impredicative systems.
Although Richard's solution to the paradox did not gain favor with mathematicians, predicativism is an important part of the study of the foundations of mathematics.
An early proponent of predicativism was Hermann Weyl, who showed it is possible to develop a large part of real analysis using only predicative methods ( Weyl 1918 ).
In fact Kruskal's tree theorem ( or its finite form ) is undecidable in a much stronger system codifying the principles acceptable based on a philosophy of mathematics called predicativism.
In fact Kruskal's tree theorem ( or its finite form ) is undecidable in a much stronger system codifying the principles acceptable on basis of a philosophy of mathematics called predicativism.
Predicativism was first studied in detail by Hermann Weyl in " Das Kontinuum ", wherein he showed that much of elementary real analysis can be conducted in a predicative manner starting with only the natural numbers.
The rejection of impredicatively defined mathematical objects ( while accepting the natural numbers as classically understood ) leads to the position in the philosophy of mathematics known as predicativism, advocated by Henri Poincar?and Hermann Weyl in his " Das Kontinuum ".
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