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Single Idea 10617

[from 'Intro to Gödel's Theorems' by Peter Smith, in 8. Modes of Existence / A. Relations / 4. Formal Relations / c. Ancestral relation ]

Full Idea

The 'ancestral' of a relation is that relation which holds when there is an indefinitely long chain of things having the initial relation.

Gist of Idea

The 'ancestral' of a relation is a new relation which creates a long chain of the original relation

Source

Peter Smith (Intro to Gödel's Theorems [2007], 23.5)

Book Reference

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.209


A Reaction

The standard example is spotting the relation 'ancestor' from the receding relation 'parent'. This is a sort of abstraction derived from a relation which is not equivalent (parenthood being transitive but not reflexive). The idea originated with Frege.