Fundamentality and Ontological Well-foundedness

Tuesday 2 December 2014, 12:30-14:00
IP Lunchtime Seminar: Room 246, Senate House, London, WC1

Fundamentality and Ontological Well-foundedness
Tuomas Tahko (Helsinki)

Fundamentality is often characterized in terms of well-foundedness, a set-theoretical notion associated with the axiom of foundation. Well-foundedness can be defined for parthood or some other order. It states that every nonempty subset of a given domain has a minimal element. Well-foundedness rules out infinite descent and the minimal element may be considered fundamental. This paper expands the applicability of the notion of well-foundedness by introducing an ontological version of it: an order is said to be ontologically well-founded if there is an analogous, ‘ontologically minimal’ element. The idea of ontological well-foundedness will be examined and it emerges that it may be compatible with some versions of metaphysical infinitism, such as so called 'boring infinite descent', whereby the same structure repeats infinitely.

Admission Free. All welcome.