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2. Reason / D. Definition / 9. Recursive Definition

[specify one item, and a rule to produce more of them]

2 ideas
Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter]
     Full Idea: Dedkind gave a rigorous proof of the principle of definition by recursion, permitting recursive definitions of addition and multiplication, and hence proofs of the familiar arithmetical laws.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 13 'Deriv'
Recursive definition defines each instance from a previous instance [Mautner]
     Full Idea: An example of a recursive definition is 'y is an ancestor of x' is defined as 'y is a parent of x, or y is a parent of an ancestor of x'.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], 'definition')
     A reaction: From this example I guess that 'ancestor' means 'friend'. Or have I misunderstood? I think we need to define 'grand-parent' as well, and then offer the definition of 'ancestor' with the words 'and so on...'. Essentially, it is mathematical induction.