Non-wellfounded mereology

Short description: Philosophical study of circular or otherwise recursive relationships lacking inductive order

In philosophy, specifically metaphysics, mereology is the study of parthood relationships. In mathematics and formal logic, wellfoundedness prohibits [math]\displaystyle{ \cdots\lt x\lt \cdots\lt x\lt \cdots }[/math] for any x.

Thus non-wellfounded mereology treats topologically circular, cyclical, repetitive, or other eventual self-containment.

More formally, non-wellfounded partial orders may exhibit [math]\displaystyle{ \cdots\lt x\lt \cdots\lt x\lt \cdots }[/math] for some x whereas well-founded orders prohibit that.

See also

• Aczel's anti-foundation axiom
• Peter Aczel
• John Barwise
• Steve Awodey
• Dana Scott

External links

• Non-wellfounded Set Theory entry by Lawrence S. Moss in the Stanford Encyclopedia of Philosophy, 2017-01-05