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Full Idea
Mill does not give us a clue as to how to understand the number zero, he limits our mathematical knowledge to the limits of our experience, ..and induction can only give you probability, but that presupposes arithmetical laws.
Gist of Idea
Empirical theories of arithmetic ignore zero, limit our maths, and need probability to get started
Source
comment on John Stuart Mill (System of Logic [1843]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations)
Book Ref
Scruton,Roger: 'A Short History of Modern Philosophy' [ARK 1985], p.244
A Reaction
This summarises Frege's criticisms of Mill's empirical account of maths. I like 'maths is the science of patterns', in which case zero is just a late-introduced trick (it is hardly a Platonic Form!), and induction is the wrong account to give.