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Full Idea
Any relation will yield a new relation, called the 'ancestral', which is the iterated relation which leads up to it, as when 'x is the parent of y' can lead us to the relation 'x is an ancestor of y'
Gist of Idea
'Ancestral' relations are derived by iterating back from a given relation
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §79) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2
Book Ref
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.36
A Reaction
This idea is one of Frege's notable discoveries. The ancestral seems to be a generalisation of a given relation.
Related Idea
Idea 15562 Causation is a general relation derived from instances of causal dependence [Lewis]
10032 | 'Ancestral' relations are derived by iterating back from a given relation [Frege, by George/Velleman] |
12056 | An ancestral relation is either direct or transitively indirect [Wiggins] |
10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
22284 | 'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers [Potter] |