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10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
Full Idea: The axiom of Peano which states that no two numbers have the same successor requires the Axiom of Infinity for its proof. | |
From: Alan Musgrave (Logicism Revisited [1977], §4 n) | |
A reaction: [He refers to Russell 1919:131-2] The Axiom of Infinity is controversial and non-logical. |