In this paper, I raise some interconnected concerns for Paul Horwich’s minimal theory of truth, framed by these three questions: How should the minimal theory be formulated? How does the minimal theory address the liar paradox? What is the explanatory role of the concept of truth? I conclude that we cannot be linguistic or conceptual deflationists about truth.

Patrick Grim has put forward a set theoretical argument purporting to prove that omniscience is an inconsistent concept and a model theoretical argument for the claim that we cannot even consistently define omniscience. The former relies on the fact that the class of all truths seems to be an inconsistent multiplicity (or a proper class, a class that is not a set); the latter is based on the difficulty of quantifying over classes that are not sets. We first address the (...) set theoretical argument and make explicit some ways in which it depends on mathematical Platonism. Then we sketch a non Platonistic account of inconsistent multiplicities, based on the notion of indefinite extensibility, and show how Grim’s set theoretical argument could fail to be conclusive in such a context. Finally, we confront Grim’s model theoretical argument suggesting a way to define a being as omniscient without quantifying over any inconsistent multiplicity. (shrink)

Although recent evidence is somewhat ambiguous, if not confusing, Patrick Grim still seems to believe that his Cantorian argument against omniscienceis sound. According to this argument, it follows by Cantor’s power set theorem that there can be no set of all truths. Hence, assuming that omniscience presupposes precisely such a set, there can be no omniscient being. Reconsidering this argument, however, guided in particular by Alvin Plantinga’s critique thereof, I find it far from convincing. Not only does it have an (...) enormously untoward side effect, but it is self-referentially incoherent as well. (shrink)

Patrick Grim advances arguments meant to show that the doctrine of divine omniscience—the classical doctrine according to which God knows all truths—is false. In particular, we here have in mind to focus on two such arguments: the set theoretic argument and the semantic argument. These arguments due to Grim run parallel to, respectively, familiar paradoxes in set theory and naive truth theory. It is beyond the purview of this article to adjudicate whether or not these are successful arguments against the (...) classical doctrine of omniscience. What we are here interested in is a way in which these arguments can be generalized. In particular, we show how generalizations of those arguments can target, explicitly, alternatives to the classical doctrine of omniscience, including what we here call 'restricted omniscience' and 'open future open theism'. As a corollary, considerations of Grim-style arguments do not support these alternatives to the classical doctrine of omniscience over the classical doctrine. We conclude that what is paradoxical is not the classical doctrine of omniscience just as such; rather, what is paradoxical is a core commitment shared by the classical doctrine and its more modest alternatives, namely, the thesis that God is a perfectly logical reasoner. (shrink)

The divine attributes of omniscience and omnipotence have faced objections to their very consistency. Such objections rely on reasoning parallel to semantic paradoxes such as the Liar or to set-theoretic paradoxes like Russell's paradox. With the advent of paraconsistent logics, dialetheism—the view that some contradictions are true—became a major player in the search for a solution to such paradoxes. This paper explores whether dialetheism, armed with the tools of paraconsistent logics, has the resources to respond to the objections levelled against (...) the divine attributes. (shrink)

A survey of logical problems for the concept of omniscience.

Among the most telling atheistic arguments are those to the effect that the existence of any being that meets standard divine specifications is impossible – that there not only is not but could not be any such being.