Lewis's Principle of Recombination: Reply to Efird and Stoneham

Abstract

According to Lewis's modal realism, all ways the world could be are represented by possible worlds, and all possible worlds represent some way the world could be. That there are just the right possible worlds to represent all and only the ways the world could be is to be guaranteed by the principle of recombination. Lewis sketches the principle (put roughly: anything can co‐exist with anything else), but does not spell out a precise version that generates just the right possibilities. David Efird and Tom Stoneham have offered a principle that aims to do just that. In this paper, we argue that Efird's and Stoneham's principle of recombination is not successful – it fails to generate the right possibilities – but we also suggest ways that their account might be improved to solve the problem we raise. We also argue against Efird's and Stoneham's claim that the correct principle of recombination demonstrates the possibility of nothing concrete – it is true that their principle of recombination has models consistent with the existence of an empty world, but we only get the possibility of nothing if mereologically null individuals are possible. The Lewisian should only think mereologically null individuals are possible if he or she has some independent reason for believing in the possibility of an empty world, so the principle of recombination provides no new evidence for that possibility. We draw some morals from this for the correct way to formulate the principle of recombination.

On the Lewisian Principle of Recombination and Quidditism

“…Consequently, contemporary researchers lack consensus on how to properly formulate Lewisian PR. Some recent commentaries on Lewis's works (Darby & Watson 2010, Efird & Stoneham 2008 include sophisticated characterisations of PR meant to address issues affecting Lewis's original formulation. In this paper, however, I am not interested in deciding the best way of characterising Lewisian PR.…”

The Close Possibility of Time Travel

“…Humeans usually accept a liberal principle of recombination. There is a debate about how best to cash out such a recombinatorial principle [224][225][226][227]. This paper takes it to be the claim that, for any fundamentalia, it is possible for there to be any number of duplicates of those fundamentalia (where zero is a number), standing to one another in any perfectly natural relation (where 'possible' picks out some species of broad possibility, which may vary to yield a variety of different strengths of recombinatorial principle).…”

A formal framework for the study of the notion of undefined particle number in quantum mechanics

“…The development of a quantum mereology is still an open problem, and the formal framework presented here is a concrete step in this direction. In particular, the formal approach to quantum features of our system is not present in previous mereological discussions (as for example, in [1,85,86]).…”