In What is a Law of Nature? (1983) David Armstrong promotes a theory of laws according to which laws of nature are contingent relations of necessitation between universals. The metaphysics Armstrong develops uses deterministic causal laws as paradigmatic cases of laws, but he thinks his metaphysics explicates other sorts of laws too, including probabilistic laws, like that of the half-life of radium being 1602 years. Bas van Fraassen (1987) gives seven arguments for why Armstrong's theory of laws is incapable of explicating probabilistic laws. The main thrust of the arguments is that Armstrong's metaphysical apparatus serves to drive up the initial probability values stated by probabilistic laws. Armstrong replies to van Fraassen in his (1988) and (1997) by appealing to limiting relative frequencies. Remarkably little has since been written about Armstrong's theory of probabilistic laws and I wish to revive interest in the debate here by assessing Armstrong's response. I will argue that his response fails because the principle of instantiation puts the limiting relative frequencies that he requires out of reach.

A Liar sentence is a sentence that, paradoxically, we cannot evaluate for truth in accordance with classical logic and semantics without arriving at a contradiction. For example, consider L

If we assume that L is true, then given that what L says is ‘L is false,’ it follows that L is false. On the other hand, if we assume that L is false, then given that what L says is ‘L is false,’ it follows that L is true. Thus, L is an example of a Liar sentence.

Several philosophers have proposed that the Liar paradox, and related paradoxes, can be solved by accepting the contradictions that these paradoxes seem to imply (including Priest 2006, Rescher and Brandom 1980). The theory that there are true contradictions is known as ‘dialetheism’ and we may call this the ‘dialethic solution.’ One standard response to the dialethic solution to the Liar paradox and related paradoxes has been to attempt to develop new ‘revenge’ versions of the paradoxes that are not subject to the dialethic solution (e.g. Parsons 1990, Restall 2007, Shapiro 2007).

In an insightful and provocative paper, Jessica Rett (2006) claims that attempts to locate the (non-indexical, non-demonstrative) semantic contributions of context in syntax run into problems respecting compositionality. This is an especially biting problem for hidden indexical theorists such as Stanley (2000, 2002) who deploy hidden variables to provide a compositional theory of semantic interpretation. Fortunately for the hidden indexical theorists, her attack fails, albeit in interesting and subtle ways.

The following paper is divided into four sections. Section I presents a skeletal version of Rett's argument. Those already familiar with Rett (2006) can skip ahead without shame. Section II offers a defense to the hidden indexical theorists.

I-theories of bare demonstratives take the semantic referent of a demonstrative to be determined by an inner state of the utterer. These states are typically taken to be states that constitute having certain referential intentions. E-theories take the referent to be determined by factors external to the utterer. These are typically taken to be criteria like salience, conversational relevance and the like. The issue has recently flared up again in an exchange between Gauker (2008), who defends an E-theory, and Åkerman (2009; 2010), who defends an I-theory.