22289 | 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' |
9958 | 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. |