Guilherme Araújo Cardoso

In this paper, our main goal is to present a new account for contradictions and impossible truths. It is loosely based on both Austin’s account of truth and the Logic of Impossible Truths (LIT), a formal semantics designed to address incomplete, inconsistent, and non-normal sets of sentences. Our main thesis is that some truths are impossible (in the sense that they accurately classify impossible situations), but no impossibility is real, no impossible truth is about real situations. We divide the paper into four sections. In section 1, we motivate the Riddle of Impossible Truths as a general observation based on paradoxes, counterpossibles and impossible fictions. In section 2, we present our account of impossible truths, drawing on LIT and Austin’s views on truth and propositions. Section 3 is dedicated to reflecting on the artifactual nature of impossible situations. We also argue, based on Knuuttila’s ideas about models, that impossible situations serve as epistemic tools. Finally, in section 4, we conclude the paper with some thoughts on future directions for research.

Openness is a distinctive feature in the episodes of joint attention. In such an episode, everything is in the open, nothing is hidden (PEACOCKE, 2005, p. 298). But what is this metaphorical description supposed to grasp? On the common knowledge approach, openness is characterized by an infinite list of iterated perceptual knowledge attributions. This approach overloads the cognitive costs of joint attention. On the relational approach, openness is a primitive notion; the phenomenon results from the fusion of perceptions between the agents, a singular experience of co-percipience that explains joint attention for free. This paper aims to argue for an intermediate approach to explain openness. We offer here an account of openness in terms of non-wellfounded situations. We shall argue that it not only fully characterizes mutual awareness in a finite adequate way but that it also preserves the low cognitive burden of the co-presence situation.

In this paper, we discuss a family of arguments that show the inconsistency of the concept of omniscience, which is one of the central attributes of the theistic God. We introduce three member of this family: Grim’s Divine Liar Paradox, Milne’s Paradox and our own Divine Curry. They can be seen as theological counterparts of well-known semantic paradoxes. We argue that the very simple dialetheist response to these paradoxes doesn’t work well and then introduce our own response based on a framework that we call Logic of Impossible Truths. LIT is a non-dialetheist paraconsistent logic designed to represent divine ominiscience and to preserve the transparency of the truth predicate and which semantics rests on the concept of situation. Since some rules of classical logic are not valid in LIT, we are in a position to block the derivation of the paradoxes. Thus, LIT offers a way out of the dilemma of accepting that there are true contradictions or giving up the idea that there is an all-powerful, omniscient and perfectly good being.

In this paper we intend to outline an introduction to Situation Theory as an approach to the liar paradoxes. This idea was first presented by the work of Barwise and Etchemendy ). First we introduce the paradoxes in their most appealing and important versions. Second we show that non-classical approaches on the problem usually get puzzled by the revenge problem on one side and loss of expressive power on the other side. Last, we present Situation Theory and try to show how it is capable of solving the old paradoxes and blocking revenge. The price we pay on this view is universality, since it would allow a new revenge situated liar. We don’t intend to address the problem of universality here, but we try at least to motivate the reader to make sense of this theory.

In this paper, I intend to offer a non-dialetheist semantics for a modal treatment of both negation and conditional that represents the Transparency of Truth. I shall argue that to evaluate paradoxical self-referential sentences (extensional and hyper-intensional ones) we need to consider inconsistent situations, even if we are evaluating these sentences in a consistent situation. This is a good point pro paraconsistency but does not force us into Dialetheism. I offer here a paracomplete paraconsistent logical consequence (LIT—The Logic of Impossible Truths) based on structures that preserve intuitions behind non-vacuism about counterpossibles, and non-dialetheism about semantic paradoxes. One of the main important results in this framework is that worlds are impossible (inconsistent) fictional situations. This result mirrors inside my framework the indefinite extensibility of situations and truth, what I take to be one of the main lessons we should learn from paradoxes.