Two Conceptions of Fundamentality

Two Conceptions of Fundamentality

This article aims to show that fundamentality is construed differently in the two most prominent strategies of analysis we find in physical science and engineering today: (1) atomistic, reductive analysis and (2) Systems analysis. Correspondingly, atomism is the conception according to which the simplest (smallest) indivisible entity of a certain kind is most fundamental; while systemism, as wi...

Two Conceptions of Sustainability

Mathis Wackernagel and William Rees describe the ‘ecological footprint’ (i.e. the ecological capacity, measured in hectares of biologically productive land, needed to supply a given person’s consumption of natural resources and absorb their waste) as a conception of environmental sustainability, and have accumulated significant data to measure the footprints of nations, cities and even individu...

Two Conceptions of Relevance

Two Conceptions of Experience

T HE canonical text relating experience to knowledge for the philosophers of the High Middle Ages was Aristotle’s Metaphysics A.1. The very first remarks in First Philosophy describe how humans, after repeated exposure to the world, come to have art and then science through experience: hominibus autem scientia et ars per experientiam evenit (9812–3: ‚pobaÐnei d âpist mh kaÈ tèxnh di€ t ̈j âmpeir...

Fundamentality of Ridge Functions

For a given integer d, 1 ≤ d ≤ n − 1, let Ω be a subset of the set of all d × n real matrices. Define the subspace M(Ω) = span{g(Ax) : A ∈ Ω, g ∈ C(IR, IR)} . We give necessary and sufficient conditions on Ω so that M(Ω) is dense in C(IR, IR) in the topology of uniform convergence on compact subsets. This generalizes work of Vostrecov and Kreines. We also consider some related problems. §