In this paper, we develop a duality for the varieties of a Łukasiewicz n + 1-valued modal System. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory...) are then derived and we propose some ideas for future research.

According to the zombie conceivability argument, phenomenal zombies are conceivable, and hence possible, and hence physicalism is false. Critics of the conceivability argument have responded by denying either that zombies are conceivable or that they are possible. Much of the controversy hinges on how to establish and understand what is conceivable, what is possible, and the link between the two—matters that are at least as obscure and controversial as whether consciousness is physical. Because of this, the debate over physicalism is (...) unlikely to be resolved by thinking about zombies—or at least, zombies as discussed by philosophers to date.



In this paper, I explore an alternative strategy against the zombie conceivability argument. I accept the possibility of zombies and ask whether that possibility is accessible (in the sense of ‘accessible’ used in possible world semantics) to our world. It turns out that the question of whether zombie worlds are accessible to our world is equivalent to the question of whether physicalism is true. By assuming that zombie worlds are accessible to our world, supporters of the zombie conceivability argument beg the question against physicalists. I will then consider what happens if a supporter of the zombie conceivability argument should insist that zombie worlds are accessible to our world. I will argue that the same ingredients used in the zombie conceivability argument—whatever they might be—can be used to construct an argument to the opposite conclusion. If that is correct, we reach a stalemate between physicalism and property dualism: while the possibility of some zombies entails property dualism, the possibility of other creatures entails physicalism. Since these two possibilities are inconsistent, one of them is not genuine. To resolve this stalemate, we need more than thought experiments. (shrink)

Summary This paper is intended to discuss the problems occurring in the relation between the notion of truth and the question of self-reference. To do this, we shall review Tarski's (T) convention and its related terminology. We shall clarify the relation between truth and extension in order to lead into the question of semantic paradoxes appearing in the theoretical models concerned with truth. Subsequently, we shall review the logical system which develops in the reformulation of the modal proposal of the (...) (T) convention. In closing, we shall critically examine Kripke's interpretation from the proposals made by Tarski. (shrink)