Towards a theory of emergence for the physical sciences

Abstract

I begin to develop a framework for emergence in the physical sciences. Namely, I propose to explicate ontological emergence in terms of the notion of 'novel reference', and of an account of interpretation as a map from theory to world. I then construe ontological emergence as the "failure of the interpretation to mesh" with an appropriate linkage map between theories. Ontological emergence can obtain between theories that have the same extension but different intensions, and between theories that have both different extensions and intensions. I illustrate the framework in three examples: the emergence of spontaneous magnetisation in a ferromagnet, the emergence of masslessness, and the emergence of space, in specific models of physics. The account explains why ontological emergence is independent of reduction: namely, because emergence is primarily concerned with adequate interpretation, while the sense of reduction that is relevant here is concerned with inter-theoretic relations between uninterpreted theories.

The heuristic function of duality

“…Our question is whether the successor theory, T S , which one constructs from a duality between models could be 'bigger' than its models: what we would like the outcome of such a construction to be is a more general and precise theory, which comprises the models as special cases, or as approximations to, specific physical situations-so, they are approximate representations of the theory. It is not hard to suggest how this may happen, and I will illustrate this in one of the examples from De Haro (2018).…”

“…The specific structure,M = {S, X}, is given by the particular S ∈ Sp(2, R) matrix chosen for the model, together with the choice of reference state X, out of which the set of models is generated. In De Haro (2018) it was argued that one can reconstruct a common core theory from a set of models Eq. (5.3).…”

“…I will discuss the Rickles' views in Section 6.2, and Coffey's in Section 4.2 (cf. alsoDe Haro (2018: §3.4.1)). However, I here anticipate that a philosophical analysis of the heuristic function of dualities does not yet exist in the literature: and so, this paper aims to fill that gap.…”

“…351-363). For the notion of approximation which I use, see DeHaro (2018).16 I am assuming that there is no novelty in the interpretation of the top theory, relative to the basic theory (for an account of ontological and epistemic novelty and the associated notions of emergence, see DeHaro (2018)). For I take a procedure that helps develop a new interpretation of a theory to be part of a heuristic function as well.…”

“…This possibility of a 'loss', when going from T t to T b , is of course the counterpart of emergence, in the reverse direction. See DeHaro (2018).…”