The Method of Abstraction

Abstract

A method is proposed for phenomenological or conceptual analysis, based on making explicit the level of abstraction of discourse. The result formalises an approach that is traditional in science, but has hitherto found little application in philosophy. The constituents of the method are ‘observables’ collected together and moderated by predicates restraining their ‘behaviour’. The resulting collection of sets of observables is called a ‘gradient of abstractions’ and it formalises the minimum consistency conditions that the chosen abstractions must satisfy.
Two useful kinds of gradient of abstraction – disjoint and nested – are identified. The case is made that in any discrete (as distinct from analogue) domain of discourse a complex phenomenon may be explicated in terms of simple approximations organised together in a gradient of abstractions. Thus the method replaces, for discrete disciplines, the differential and integral calculus, which form the basis for understanding the complex analogue phenomena of science and engineering.
The method is demonstrated on the Turing test, the concept of agenthood, the definition of emergence and the notion of artificial life, and its place in philosophy is considered. It is hoped that our treatment will promote the use of the method in certain areas of the humanities and especially in philosophy.

Keywords: Abstraction, Level of abstraction, Gradient of Abstraction, Levelism, Observable, Stance