Humean revisions to the best system account of lawhood - Hughes, Mike (2020)
Metaphysical theories of lawhood may be grouped broadly into three groups: those that deny the mind-independent existence of laws of nature, those that assert both their mind-independent existence and their existence independent of the physical world, and finally those that assert their mind-independent existence, but deny their existence independent of the physical world. Of the last type of theory is Lewis’s best system account (BSA) of lawhood. This theory states that laws are supervenient on the Humean mosaic of each world, and are those sets of propositions that best summarise the regularities in nature. ‘Best’ in this context means optimal in terms of strength and simplicity, and in the case of indeterministic worlds, fit. The BSA in its Humean formulation after Lewis suffers from many problems. The first of these is the problem of undermining futures, where the BSA-determined chance functions appearing in indeterministic laws may be inconsistent with other possible worlds that should in theory have exactly the same laws. The second problem is the zero-fit problem, where worlds with infinite sequences of chance events would have as equally good fit as an infinite number of other worlds, and thus all worlds would have zero fit according to traditional notions of statistical fit measured as the similarity between two sequences of chance events. The third problem is the problem of non-locality, where quantum mechanics suggests some predicates apply to spatially non-contiguous entities, thus implying the apparent falsehood of the foundational principle in Lewis’s version of the BSA of Humeanism. Finally, Armstrong’s problem, where the simplicity-strength trade-off is language dependent, with some languages allowing for expressions that are simpler than an equivalent translation in some other language due to differing vocabulary. Solutions will be provided to each of these problems in turn. The solution to the problem of undermining and to Armstrong’s problem both relies on a background assumption of modal realism (in the case of the solution to the problem of undermining, modal realism in the strongest sense of each world being as concrete as the actual world, rather than logical constructions). Briefly, in the case of the problem of undermining, the proposed solution involves applying the algorithm to identify the best systematization over the Humean mosaic representing a multiverse of possible worlds, rather than a single world. This multiverse is shown to be constructible without circularity, and would necessarily comprise all but the most extreme cases of undermining worlds. For Armstrong’s problem, it is shown how an objective set of predicates may be defined. These predicates are identified as those containing the least amount of contingent information. This concept of contingent information is given formal mathematical expression using analogous reasoning to the concept of Shannon information or entropy as used in communication theory and statistical mechanics. The solutions presented for the zero-fit problem and the problem of non-locality are rather more straightforward. In the case of the zero-fit problem, an alternative measure of fit is presented. This alternative measure, known to statisticians as -square, is shown to give a non-zero measure over both finite and infinite probability spaces. The solution to the problem of non-locality is to first dismiss it as irrelevant, since the non-local predicates are supervenient, and not part of the fundamental ontology of the Humean mosaic. This response in itself is not original. What is original however is the speculation that such non-local properties could not in fact be fundamental if the solution to Armstrong’s problem mentioned above is accepted, since such non-local predicates would contain more contingent information than extensionally equivalent combinations of local predicates. Proponents of theories of lawhood that assert both the mind-independence of laws and their independence of the physical world often do so premised on the failure of those that attempt a physically supervenient account of lawhood. In conclusion therefore, resolution of these four outstanding problems with the leading supervenient theory of lawhood makes some progress towards resolution of this age-old problem in metaphysics of what laws of nature are.