The two-dimensional modal logic of Davies and Humberstone [3] is an important aid to our understanding the relationship between actuality, necessity and a priori knowability. I show how a cut-free hypersequent calculus for 2D modal logic not only captures the logic precisely, but may be used to address issues in the epistemology and metaphysics of our modal concepts. I will explain how the use of our concepts motivates the inference rules of the sequent calculus, and then show that the completeness (...) of the calculus for Davies–Humberstone models explains why those concepts have the structure described by those models. The result is yet another application of the completeness theorem. (shrink)

In this paper we present tableau methods for two-dimensional modal logics. Although models for such logics are well known, proof systems remain rather unexplored as most of their developments have been purely axiomatic. The logics herein considered contain first-order quantifiers with identity, and all the formulas in the language are doubly-indexed in the proof systems, with the upper indices intuitively representing the actual or reference worlds, and the lower indices representing worlds of evaluation—first and second dimensions, respectively. The tableaux modulate (...) over different notions of validity such as local, general, and diagonal, besides being general enough for several two-dimensional logics proposed in the literature. We also motivate the introduction of a new operator into two-dimensional languages and explore some of the philosophical questions raised by it concerning the relations there are between actuality, necessity, and the a priori, that seem to undermine traditional intuitive interpretations of two-dimensional operators. (shrink)

This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two (...) arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics. (shrink)

Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I also describe (...) some properties of the logic that are interesting from a philosophical perspective, and apply it to the so-called nesting problem. (shrink)

‘A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science.’ This paper is an attempt to follow Russell’s advice by using a puzzle about the contingent a priori to test and explore certain theories of reference and modality. No one could claim that (...) the puzzle is of any great philosophical importance by itself, but to understand it, one has to get clear about certain aspects of the theory of reference; and to solve it, one has to think a little more deeply than one is perhaps accustomed about what it means to say that a statement is contingent or necessary. (shrink)

‘A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science.’ This paper is an attempt to follow Russell’s advice by using a puzzle about the contingent a priori to test and explore certain theories of reference and modality. No one could claim that (...) the puzzle is of any great philosophical importance by itself, but to understand it, one has to get clear about certain aspects of the theory of reference; and to solve it, one has to think a little more deeply than one is perhaps accustomed about what it means to say that a statement is contingent or necessary. (shrink)

The book is an extended study of the problem of consciousness. After setting up the problem, I argue that reductive explanation of consciousness is impossible , and that if one takes consciousness seriously, one has to go beyond a strict materialist framework. In the second half of the book, I move toward a positive theory of consciousness with fundamental laws linking the physical and the experiential in a systematic way. Finally, I use the ideas and arguments developed earlier to defend (...) a form of strong artificial intelligence and to analyze some problems in the foundations of quantum mechanics. (shrink)

Frank Jackson champions the cause of conceptual analysis as central to philosophical inquiry. In recent years conceptual analysis has been undervalued and widely misunderstood, suggests Jackson. He argues that such analysis is mistakenly clouded in mystery, preventing a whole range of important questions from being productively addressed. He anchors his argument in discussions of specific philosophical issues, starting with the metaphysical doctrine of physicalism and moving on, via free will, meaning, personal identity, motion, and change, to ethics and the philosophy (...) of color. In this way the book not only offers a methodological program for philosophy, but also casts new light on some much-debated problems and their interrelations. (shrink)