Sometimes one finds inspiration in reading old articles, as it happened to me when I read Larry Sklar’s “Comments on Malament”, from the PSA 1984, Vol 2, 106-110. In this short paper, Sklar takes consistency constraints that arise in spacetimes with closed timelike curves (CTCs) to indicate that the principled distinction–a “distinction at the very root of the notion of physical possibility and necessity” (108)–between initial conditions and laws breaks down:
“If there is, relative to the proposition we now countenance as the laws of nature […], a lawlike constraint on ‘initial conditions’, if, that is, some specifications of the world ‘at a time’ are impossible since they are lawlike incompossible with themselves, what solid distinction is left between laws of nature and ‘mere matter of fact initial conditions’?” (108)
Well taken. According to Sklar, there have been, of course, previous reasons to doubt such a distinction: (i) the Humean view of laws as mere summaries of particular facts discourages such principled a gap, and (ii) the “existence of such more-than-mere-fact mere facts like the parallelism of likely entropic increase for branch systems” (ibid.) can be thought to have the same consequence. Translated into the terms of the recent debate, one might well debate whether the past hypothesis–the assumption that there was an early state of the universe with rather low entropy–is indeed an initial condition (as it is on the face of it), or more akin to laws of nature. But even if the past hypothesis were a law, it’s not a dynamical law. So perhaps there is still a principled distinction to be had between dynamical laws and their initial conditions?
Be this as it may, it (and other things Sklar says in this article) led me to ponder modality–a longtime hobby horse of mine. I would like to argue that even if the distinction between laws and initial conditions breaks down, there is still a clear notion of possibility and necessity relative to a theory (about the world). Consider the semantic view of theories. Here, we could say that a proposition is necessary just in case it is true in all models of the theory and possible (or contingent) just in case it is true in some models.
Thus, given a theory, modality is completely unproblematic. (Conversely, starting out from considerations of what is possible or necessary, one may arrive at a semantic characterization of a theory). Modal considerations become completely unfettered and loose beyond the framing confines of a theory. Thus, talk of whether the laws “could have been different” is meaningless unless it is embedded in a “higher-order” or more encompassing theory. If correct, this view entails that there is no such thing as possible or necessary “simpliciter”.
As an example, consider the structure of spacetime. Within special relativity (SR), the spacetime structure is necessarily Minkowskian, but relative to general relativity (GR), which contains the models of SR, but also many more, it is only contingently Minkowskian. Within SR, it simply makes no sense to ask whether the spacetime geometry could have been different, while of course in GR it does.
Of course, this view must offer a rigorous characterization of the models of a theory, or of the worlds that are possible according to it. For instance, more needs to be said what exactly the models of SR are; is it just Minkowski spacetime, or are there many models, i.e. all those physical situations compatible with SR such as the one where the birthday cake is pink and Obama is re-elected for a second term (assuming these scenarios are possible in a world without gravity, which they may well not be).
Any thoughts are welcome!