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Natural Logicism is a new species of logicism. It is based on Gentzenian rules of natural deduction, including ones governing logico-mathematical expressions that Gentzen himself did not treat. Natural Logicism could be developed for any branch of mathematics. The aim would be to determine how much of its foundation is ‘logical’, or analytic; and in what sense the objects dealt with might be logical objects. Here the focus is on Natural Logicism for the numbers.