This paper argues, based on Lewis’ claim that communication is a coordination game (Lewis in Minnesota studies in the philosophy of science, University of Minnesota Press, Minneapolis, pp 3–35, 1975), that we can account for the communicative function of demonstratives without assuming that they semantically refer. The appeal of such a game theoretical version of the case for non-referentialism is that the communicative role of demonstratives can be accounted for without entering the cul de sac of trying to construct conventions of ever-increasing complexity. Instead communication via demonstratives is explained with reference to the general, non-domain specific ability of human beings to solve games of coordination. Furthermore, there is empirical support for such a view. Judgments concerning demonstrative reference have been shown to be sensitive to judgments concerning common ground (Clark et al. in J Verb Learn Verb Behav 22:245–258, 1983), which is exactly what the non-referentialist account would predict. The game theoretical account also allows for an intuitively plausible, non-referentialist treatment of Speaks’ ‘trumping argument’ (Speaks in Philos Stud 174:709–734, 2017), as well as the Carnap/Agnew puzzle (Kaplan in Syntax Semant 9:221–43, 1970).

In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets, or, in other words, to have a specific probability of having a given set-theoretic property.

Although Benjamin Schnieder’s theory of the “ordinary conception” of properties successfully handles paradoxical properties—particularly, the property of non-self-instantiation—it fails to account for ordinary, non-pathological cases. The theory allows the inference of ‘a has the property of being F’ only given F(a) and the prior assertibility of ‘the property of being F can exist’. While this allows us to block an inference to a contradiction, it also blocks all of the non-pathological instances of the inference from ‘a is F’ to ‘a has the property of being F’. It thereby fails both as a theory of the ordinary conception and as a replacement of the ordinary notion, assuming the latter is defective.

Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover at most one mathematical universe. Indispensability arguments may thus lose their central role in the debate about mathematical ontology.

The problem of dream skepticism – i.e., the problem of what can justify one’s belief that they are not dreaming – is one of the most famous problems in philosophy. I propose a way of responding to the problem which is available if one subscribes to the theory that the sensory experiences that we have in dreams consist of images (as opposed to false percepts). The response exploits a particular feature of imagination, viz., that it is not possible to simultaneously have two separate imagistic experiences in the same modality.