David Sanson

Al-Taftāzānī introduces the Liar Paradox, in a commentary on al-Rāzī, in a short passage that is part of a polemic against the ethical rationalism of the Muʿtazila. In this essay, we consider his remarks and their place in the history of the Liar Paradox in Arabic Logic. In the passage, al-Taftāzānī introduces Liar Cycles into the tradition, gives the paradox a puzzling name—the fallacy of the “irrational root” —which became standard, and suggests a connection between the paradox and what it tells us about truth and falsehood, and arguments for divine voluntarism and what they tell us about the nature of goodness and badness. On this last point, we also discuss a passage from al-Rāzī, which suggests similar connections.

The authors consider a recurring objection to fictional realism, the view that fictional characters are objects. The authors call this the counting objection. Russell presses a version of the objection against Meinong’s view. Everett presses a version of the objection against contemporary fictional realist views, as do Nolan and Sandgren. As the authors see it, the objection assumes that the fictional realist must provide criteria of identity for fictional characters, so its force depends on the plausibility of that assumption. Rather than coming up with such criteria, a fictional realist might argue that the demand is misplaced.

Possible worlds are maximal possibilities. But what kind of thing is a maximal possibility? Not a maximal individual: there are maximal possibilities that are not maximal individuals, because each maximal individual could have any one of several maximal properties. And not a maximal property: there are maximal possibilities that are not maximal properties, because each maximal property could be had by any one of many possible maximal individuals. So if you like your worlds concrete, you should say that they are maximal facts, and if you like your worlds abstract, you should say that they are maximal propositions.

If reality is temporary, then reality changes, and if reality changes, the past has explanatory work to do, and it cannot do that work unless it is no longer real. This tells against the Moving Now Theory, the Growing Block Theory, and any form of Presentism that attempts to understand the past in terms of the present, including Tensed Properties Presentism and Tensed Facts Presentism. It tells in favor of a form Presentism that allows us to appeal to unreal past facts. I suggest that Priorian Presentism, conjoined with a certain way of understanding the role played by tense operators, is one such view.

We want to say both that Sherlock Holmes does not exist, and that he is a fictional character. But how can we say these things without committing ourselves to the existence of Sherlock Holmes? Here I develop and defend a non-commital paraphrase of quantification over fictional characters, modeled on the non-commital paraphrase Kit Fine provides for quantification over possibilia. I also develop and defend the view that names for fictional characters are weakly non-referring, in Nathan Salmon’s sense, and so provide us with a non-commital means to express singular propositions. The resulting position allows us to reap the benefits of Fictional Realism without paying the associated ontological cost.

We describe the earliest occurrences of the Liar Paradox in the Arabic tradition. e early Mutakallimūn claim the Liar Sentence is both true and false; they also associate the Liar with problems concerning plural subjects, which is somewhat puzzling. Abharī (1200-1265) ascribes an unsatisfiable truth condition to the Liar Sentence—as he puts it, its being true is the conjunction of its being true and false—and so concludes that the sentence is not true. Tūsī (1201-1274) argues that self-referential sentences, like the Liar, are not truth-apt, and defends this claim by appealing to a correspondence theory of truth. Translations of the texts are provided as an appendix.

The possibility of Junk is the possibility that something exists and everything is a proper part. Just as we might imagine that there are no simples—that everything has a proper part, all the way down—we might imagine that there are no caps—that everything is a proper part, all the way up. It is not obvious that this apparent possibility can be accommodated within a Lewisian modal framework. For Lewis, every possibility involves the existence of a possible world, and a possible world is just is a maximal sum, and so a cap. But the Lewisian can accommodate Junk, if she wishes, by allowing parts of possible worlds to represent complete possibilities.