We provide a description and informal analysis of the commonalities in moral discourse concerning issues in the field of information and communications technology, present a logic model (DEAL) of this type of moral discourse that makes use of recent research in deontic, epistemic, and action logic, and indicate – drawing upon recent research in computer implementations of modal logic – how information systems may be developed that implement the proposed formalization.

ABSTRACT This paper reports on an empirical performance analysis of four modal theorem provers on benchmark suites of randomly generated formulae. The theorem provers tested are the Davis-Putnam-based procedure KSAT, the tableaux-based system KRZIS, the sequent-based Logics Workbench, and a translation approach combined with the first-order theorem prover SPASS. Our benchmark suites are sets of multi-modal formulae in a certain normal form randomly generated according to the scheme of Giunchiglia and Sebastiani [GS 96a, GS 96b]. We (...) investigate the quality of the random modal formulae and show that the scheme has some shortcomings, which may lead to mistaken conclusions. We propose improvements to the evaluation method and show that the translation approach provides a viable alternative to the other approaches. (shrink)

An automatic theorem prover for a proof system in the style of dual tableaux for the relational logic associated with modal logic K has been introduced. Although there are many well-known implementations of provers for modal logic, as far as we know, it is the first implementation of a specific relational prover for a standard modal logic. There are two main contributions in this paper. First, the implementation of new rules, called (k1) and (k2), which substitute (...) the classical relational rules for composition and negation of composition in order to guarantee not only that every proof tree is finite but also to decrease the number of applied rules in dual tableaux. Second, the implementation of an order of application of the rules which ensures that the proof tree obtained is unique.As a consequence, we have implemented a decision procedure for modal logic K. Moreover, this work would be the basis for successive extensions of this logic, such as T, B and S4. (shrink)

This paper is the second in a series of three papers. All three papers deal with interpretability logics and related matters. In the first paper a construction method was exposed to obtain models of these logics. Using this method, we obtained some completeness results, some already known, and some new. In this paper, we will set the construction method to work to obtain more results. First, the modal completeness of the logic ILM is proved using the construction method. This (...) is not a new result, but by using our new proof we can obtain new results. Among these new results are some admissible rules for ILM and GL. Moreover, the new proof will be used to classify all the essentially Δ1 and also all the essentially Σ1 formulas of ILM. Closely related to essentially Σ1 sentences are the so-called self provers. A self-prover is a formula φ which implies its own provability, that is φ → □φ. Each formula φ will generate a self prover φ ^ □φ. We will use the construction method to characterize those sentences of GL that generate a self prover that is trivial in the sense that it is Σ1. (shrink)

In previous work we gave an approach, based on labelled natural deduction, for formalizing proof systems for a large class of propositional modal logics that includes K, D, T, B, S4, S4.2, KD45, and S5. Here we extend this approach to quantified modal logics, providing formalizations for logics with varying, increasing, decreasing, or constant domains. The result is modular with respect to both properties of the accessibility relation in the Kripke frame and the way domains of individuals change (...) between worlds. Our approach has a modular metatheory too; soundness, completeness and normalization are proved uniformly for every logic in our class. Finally, our work leads to a simple implementation of a modal logic theorem prover in a standard logical framework. (shrink)

This paper presents a recent formalization of a Henkin-style completeness proof for the propositional modal logic S5 using the Lean theorem prover. The proof formalized is close to that of Hughes and Cresswell, but the system, based on a different choice of axioms, is better described as a Mendelson system augmented with axiom schemes for K, T, S4, and B, and the necessitation rule as a rule of inference. The language has the false and implication as the only primitive (...) logical connectives and necessity as the only primitive modal operator. The full source code is available online and has been typechecked with Lean 3.4.2. (shrink)

THINKER is an automated natural deduction first-order theorem proving program. This paper reports on how it was adapted so as to prove theorems in modal logic. The method employed is an indirect semantic method, obtained by considering the semantic conditions involved in being a valid argument in these modal logics. The method is extended from propositional modal logic to predicate modal logic, and issues concerning the domain of quantification and existence in a world's domain are discussed. (...) Finally, we look at the very interesting issues involved with adding identity to the theorem prover in the realm of modal predicate logic. Various alternatives are discussed. (shrink)

Our computational metaphysics group describes its use of automated reasoning tools to study Leibniz’s theory of concepts. We start with a reconstruction of Leibniz’s theory within the theory of abstract objects (henceforth ‘object theory’). Leibniz’s theory of concepts, under this reconstruction, has a non-modal algebra of concepts, a concept-containment theory of truth, and a modal metaphysics of complete individual concepts. We show how the object-theoretic reconstruction of these components of Leibniz’s theory can be represented for investigation by means (...) of automated theorem provers and finite model builders. The fundamental theorem of Leibniz’s theory is derived using these tools. (shrink)

Classical logic has proved inadequate in various areas of computer science, artificial intelligence, mathematics, philosopy and linguistics. This is an introduction to extensions of first-order logic, based on the principle that many-sorted logic (MSL) provides a unifying framework in which to place, for example, second-order logic, type theory, modal and dynamic logics and MSL itself. The aim is two fold: only one theorem-prover is needed; proofs of the metaproperties of the different existing calculi can be avoided by borrowing them (...) from MSL. To make the book accessible to readers from different disciplines, whilst maintaining precision, the author has supplied detailed step-by-step proofs, avoiding difficult arguments, and continually motivating the material with examples. Consequently this can be used as a reference, for self-teaching or for first-year graduate courses. (shrink)

Our computational metaphysics group describes its use of automated reasoning tools to study Leibniz’s theory of concepts. We start with a reconstruction of Leibniz’s theory within the theory of abstract objects (henceforth ‘object theory’). Leibniz’s theory of concepts, under this reconstruction, has a non-modal algebra of concepts, a concept-containment theory of truth, and a modal metaphysics of complete individual concepts. We show how the object-theoretic reconstruction of these components of Leibniz’s theory can be represented for investigation by means (...) of automated theorem provers and finite model builders. The fundamental theorem of Leibniz’s theory is derived using these tools. (shrink)

The subject of Labelled Non-Classical Logics is the development and investigation of a framework for the modular and uniform presentation and implementation of non-classical logics, in particular modal and relevance logics. Logics are presented as labelled deduction systems, which are proved to be sound and complete with respect to the corresponding Kripke-style semantics. We investigate the proof theory of our systems, and show them to possess structural properties such as normalization and the subformula property, which we exploit not only (...) to establish advantages and limitations of our approach with respect to related ones, but also to give, by means of a substructural analysis, a new proof-theoretic method for investigating decidability and complexity of (some of) the logics we consider. All of our deduction systems have been implemented in the generic theorem prover Isabelle, thus providing a simple and natural environment for interactive proof development. Labelled Non-Classical Logics is essential reading for researchers and practitioners interested in the theory and applications of non-classical logics. (shrink)

\ is a 7000 line Prolog parser/theorem-prover for logical categorial grammar. In such logical categorial grammar syntax is universal and grammar is reduced to logic: an expression is grammatical if and only if an associated logical statement is a theorem of a fixed calculus. Since the syntactic component is invariant, being the logic of the calculus, logical categorial grammar is purely lexicalist and a particular language model is defined by just a lexical dictionary. The foundational logic of continuity was established (...) by Lambek while a corresponding extension including also logic of discontinuity was established by Morrill and Valentín :167–192, 2010). \ implements a logic including as primitive connectives the continuous and discontinuous connectives of the displacement calculus, additives, 1st order quantifiers, normal modalities, bracket modalities, and universal and existential subexponentials. In this paper we review the rules of inference for these primitive connectives and their linguistic applications, and we survey the principles of Andreoli’s focusing, and of a generalisation of van Benthem’s count-invariance, on the basis of which \ is implemented. (shrink)

A growing number of applications of automated reasoning exhibitsthe necessity of flexible deduction systems. A deduction system should beable to execute inference rules which are appropriate to the given problem.One way to achieve this behavior is the integration of different calculi. Thisled to so called hybrid reasoning [22, 1, 10, 20] which means the integrationof a general purpose foreground reasoner with a specialized background reasoner. A typical task of a background reasoner is to perform special purposeinference rules according to a (...) built-in theory. The aim of this paper is togo a step further, i.e. to treat the background reasoner as a hybrid systemitself. The paper formulates sufficient criteria for the construction of complete calculi which enable reasoning under hybrid theories combined fromsub-theories. For this purpose we use a generic approach described in [20].This more detailed view on built-in theories is not covered by the knowngeneral approaches [1, 3, 6, 20] for building in theories into theorem provers.The approach is demonstrated by its application to the target calculi of thealgebraic translation [9] of multi-modal and extended multi-modal [7] logicto first-order logic. (shrink)

ABSTRACT Real-time graphical interval logic is a modal logic for reasoning about time in which the basic modality is the interval. The logic differs from other logics in that it has a natural intuitive graphical representation that resembles the timing diagrams drawn by system designers. We have developed an automted deduction system for the logic, which includes a theorem prover and a user interface. The theorem prover checks the validity of proofs in the logic and produces counterexamples to invalid (...) proofs. The user interface includes a graphical editor that enables the user to create graphical formulas on a workstation display, and a database and proof manager that tracks proof dependencies and allows graphical formulas to be stored and retrieved. In this paper we describe the logic, the automated deduction system, and an application to robotics. (shrink)

The purpose of this study is to propose new similarity measures namely rough variational coefficient similarity measure under the rough neutrosophic environment. The weighted rough variational coefficient similarity measure has been also defined. The weighted rough variational coefficient similarity measures between the rough ideal alternative and each alternative are xxxxx calculated to find the best alternative. The ranking order of all the alternatives can be determined by using the numerical values of similarity measures. Finally, an illustrative example has been provided (...) to show the effectiveness and validity of the proposed approach. Comparisons of decision results of existing rough similarity measures have been provided. (shrink)

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation operators and the (...) pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)

It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If there were nothing otherwise “uniquely metaphysically (...) significant” about metaphysical necessity, then paradigmatic metaphysical necessities would be necessary in one sense of “necessary”, not necessary in another, and that would be it. The question of whether they were necessary simpliciter would be like the question of whether the Parallel Postulate is true simpliciter – understood as a pure mathematical conjecture, rather than as a hypothesis about physical spacetime. In a sense, the latter question has no objective answer. In this article, I argue that paradigmatic questions of modal metaphysics are like the Parallel Postulate question. I then discuss the deflationary ramifications of this argument. I conclude with an alternative conception of the space of possibility. According to this conception, there is no objective boundary between possibility and impossibility. Along the way, I sketch an analogy between modal metaphysics and set theory. (shrink)

I critically examine the claim that modal collapse arguments against the traditional doctrine of divine simplicity (DDS) are in general fallacious. In a recent paper, Christopher Tomaszewski alleges that modal collapse arguments against DDS are invalid, owing to illicit substitutions of nonrigid singular terms into intensional contexts. I show that this is not, in general, the case. I show, further, that where existing modal collapse arguments are vulnerable to this charge the arguments can be repaired without any (...) apparent dialectical impropriety. I conclude that the genuine debate over modal collapse and divine simplicity and modal collapse is substantially a controversy over the metaphysics of divine action, and that this constitutes a fruitful direction in which to take future discussions of the subject. (shrink)

In this paper I shall present some of the results I have obtained on modal theories which contain quantifiers for propositions. The paper is in two parts: in the first part I consider theories whose non-quantificational part is S5; in the second part I consider theories whose non-quantificational part is weaker than or not contained in S5. Unless otherwise stated, each theory has the same language L. This consists of a countable set V of propositional variables pl, pa, ... (...) , the operators v (or), ~ (not) and □ (necessarily), the universal quantifier (p), p a propositional variable, and brackets ( and ). The formulas of L are then defined in the usual way. (shrink)

We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x (...) ⊧ ⍯φ iff Vy(y ≠ x → y ⊧ φ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in ℒ $_{c}$ . Strong completeness of the normal ℒ $_{c}$ logics is proved with respect to models in which all worlds are named. Every ℒ $_{c}$ -logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from ℒ to ℒ $_{c}$ are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched. (shrink)

We consider structural completeness in modal logics. The main result is the necessary and sufficient condition for modal logics over K4 to be hereditarily structurally complete: a modal logic λ is hereditarily structurally complete $\operatorname{iff} \lambda$ is not included in any logic from the list of twenty special tabular logics. Hence there are exactly twenty maximal structurally incomplete modal logics above K4 and they are all tabular.

This volume contains eighteen papers, three with new postscripts, that were written over the past 35 years. Five of the papers have not been previously published. Together they provide a comprehensive account of modal reality—the realm of possible worlds—from a Humean perspective, with excursions into neighboring topics in metaphysics. Part 1 sketches an account of reality as a whole, both the mathematical and the modal, defending a form of plenitudinous realism: every consistent proposition is true of some portion (...) of reality. Part 2 presents and defends a realist theory of concrete possible worlds with an absolute ontological distinction between the actual and the merely possible. Part 3 presents and defends a Humean account of modal plenitude, formulating and endorsing principles of recombination, of plenitude of possible structures, and of plenitude of alien contents. Part 4 applies the Humean account to truthmaking, mereology, spacetime, and quantities. I argue that holding fast to Humean strictures leads to views that differ in radical ways from those put forth by contemporary metaphysicians. (shrink)

I propose that we approach the epistemology of modality by putting modal metaphysics first and, specifically, by investigating the metaphysics of essence. Following a prominent Neo-Aristotelian view, I hold that metaphysical necessity depends on the nature of things, namely their essences. I further clarify that essences are core properties having distinctive superexplanatory powers. In the case of natural kinds, which is my focus in the paper, superexplanatoriness is due to the fact that the essence of a kind is what (...) causes all the many properties and behaviors that are typically shared by all the instances of the kind. Accordingly, we know what is necessarily true of kinds by knowing what is essential to them in the sense of actually playing such causal-explanatory roles. Modal reasoning aimed at discovering metaphysical necessity thus proceeds via essentialist deduction: we move from essentialist truths to reach necessary truths. (shrink)

This collection highlights the new trend away from rationalism and toward empiricism in the epistemology of modality. Accordingly, the book represents a wide range of positions on the empirical sources of modal knowledge. Readers will find an introduction that surveys the field and provides a brief overview of the work, which progresses from empirically-sensitive rationalist accounts to fully empiricist accounts of modal knowledge. Early chapters focus on challenges to rationalist theories, essence-based approaches to modal knowledge, and the (...) prospects for naturalizing modal epistemology. The middle chapters present positive accounts that reject rationalism, but which stop short of advocating exclusive appeal to empirical sources of modal knowledge. The final chapters mark a transition toward exclusive reliance on empirical sources of modal knowledge. They explore ways of making similarity-based, analogical, inductive, and abductive arguments for modal claims based on empirical information. Modal epistemology is coming into its own as a field, and this book has the potential to anchor a new research agenda. (shrink)

We reply to various arguments by Otavio Bueno and Edward Zalta (‘Object Theory and Modal Meinongianism’) against Modal Meinongianism, including that it presupposes, but cannot maintain, a unique denotation for names of fictional characters, and that it is not generalizable to higher-order objects. We individuate the crucial difference between Modal Meinongianism and Object Theory in the former’s resorting to an apparatus of worlds, possible and impossible, for the representational purposes for which the latter resorts to a distinction (...) between two kinds of predication, exemplification and encoding. We show that encoding has fewer forerunners in the history of philosophy than Bueno and Zalta want, and that there’s a reason why the notion has been found baffling by some. (shrink)

The function of a trait token is usually defined in terms of some properties of other (past, present, future) tokens of the same trait type. I argue that this strategy is problematic, as trait types are (at least partly) individuated by their functional properties, which would lead to circularity. In order to avoid this problem, I suggest a way to define the function of a trait token in terms of the properties of the very same trait token. To able to (...) allow for the possibility of malfunctioning, some of these properties need to be modal ones: a function of a trait is to do F just in case its doing F would contribute to the inclusive fitness of the organism whose trait it is. Function attributions have modal force. Finally, I explore whether and how this theory of biological function could be modified to cover artifact function. (shrink)

What does ‘Smith knows that it might be raining’ mean? Expressivism here faces a challenge, as its basic forms entail a pernicious type of transparency, according to which ‘Smith knows that it might be raining’ is equivalent to ‘it is consistent with everything that Smith knows that it is raining’ or ‘Smith doesn’t know that it isn’t raining’. Pernicious transparency has direct counterexamples and undermines vanilla principles of epistemic logic, such as that knowledge entails true belief and that something can (...) be true without one knowing it might be. I re-frame the challenge in precise terms and propose a novel expressivist formal semantics that meets it by exploiting (i) the topic-sensitivity and fragmentation of knowledge and belief states and (ii) the apparent context-sensitivity of epistemic modality. The resulting form of assertibility semantics advances the state of the art for state-based bilateral semantics by combining attitude reports with context-sensitive modal claims, while evading various objectionable features. In appendices, I compare the proposed system to Beddor and Goldstein’s ‘safety semantics’ and discuss its analysis of a modal Gettier case due to Moss. (shrink)

Discrimination is a central epistemic capacity but typically, theories of discrimination only use discrimination as a vehicle for analyzing knowledge. This paper aims at developing a self-contained theory of discrimination. Internalist theories of discrimination fail since there is no compelling correlation between discriminatory capacities and experiences. Moreover, statistical reliabilist theories are also flawed. Only a modal theory of discrimination is promising. Versions of sensitivity and adherence that take particular alternatives into account provide necessary and sufficient conditions on discrimination. Safety (...) in contrast is not sufficient for discrimination as there are cases of safety that are clearly instances of discrimination failure. The developed account of discrimination between objects will be extended to discrimination between kinds and between types. (shrink)

According to the simple modal account of essence, an object has a property essentially just in case it has it in every world in which it exists. As many have observed, the simple modal account is implausible for a number of reasons. This has led to various proposals for strengthening the account, for example, by adding a restriction to the intrinsic or sparse properties. I argue, however, that these amendments to the simple modal account themselves fail. Drawing (...) on lessons from these failures, I propose a new version of a modal account, inspired by Ruth Barcan Marcus's defense of the coherence of quantified modal logic, according to which an object has a property essentially just in case (i) it has it in every world in which it exists, (ii) the property is discriminating (or non-trivial), and (iii) the property is qualitative. The resulting account of essence does not face any of the standard objections other accounts face, and I defend it from other potential objections. (shrink)

We outline a neo-Meinongian framework labeled as Modal Meinongian Metaphysics (MMM) to account for the ontology and semantics of fictional discourse. Several competing accounts of fictional objects are originated by the fact that our talking of them mirrors incoherent intuitions: mainstream theories of fiction privilege some such intuitions, but are forced to account for others via complicated paraphrases of the relevant sentences. An ideal theory should resort to as few paraphrases as possible. In Sect. 1, we make this explicit (...) via two methodological principles, called the Minimal Revision and the Acceptability Constraint. In Sect. 2, we introduce the standard distinction between internal and external fictional discourse. In Sects. 3–5, we discuss the approaches of (traditional) Meinongianism, Fictionalism, and Realism—and their main troubles. In Sect. 6 we propose our MMM approach. This is based upon (1) a modal semantics including impossible worlds (Subsect. 6.1); (2) a qualified Comprehension Principle for objects (Subsect. 6.2); (3) a notion of existence-entailment for properties (Subsect. 6.3). In Sect. 7 we present a formal semantics for MMM based upon a representation operator. And in Sect. 8 we have a look at how MMM solves the problems of the three aforementioned theories. (shrink)

The present paper attempts to provide an exact truthmaker semantical analysis of modalized propositions. According to the present proposal, an exact truthmaker for “Necessarily _P_” is a state that bans every exact truthmaker for “Not _P_”, and an exact truthmaker for “Possibly _P_” is a state that allows an exact truthmaker for _P_. Based on this proposal, a formal semantics will be developed; and the soundness and completeness results for a well-known family of the systems of normal modal propositional (...) logic will be established. It shall be seen that the present analysis offers an exactification of the standard Kripke semantics in the sense that it analyzes the accessibility relation between possible worlds in terms of the banning and allowing relations between the constituent states, and thereby gives an account of “truth at a possible world” in terms of exact truthmaking. (shrink)

We introduce the subject of modal model theory, where one studies a mathematical structure within a class of similar structures under an extension concept that gives rise to mathematically natural notions of possibility and necessity. A statement φ is possible in a structure (written φ) if φ is true in some extension of that structure, and φ is necessary (written φ) if it is true in all extensions of the structure. A principal case for us will be the class (...) Mod(T) of all models of a given theory T—all graphs, all groups, all fields, or what have you—considered under the substructure relation. In this article, we aim to develop the resulting modal model theory. The class of all graphs is a particularly insightful case illustrating the remarkable power of the modal vocabulary, for the modal language of graph theory can express connectedness, k-colorability, finiteness, countability, size continuum, size ℵ1, ℵ2, ℵω, ℶω, first ℶ-fixed point, first ℶ-hyper-fixed point, and much more. A graph obeys the maximality principle φ(a)→φ(a) with parameters if and only if it satisfies the theory of the countable random graph, and it satisfies the maximality principle for sentences if and only if it is universal for finite graphs. (shrink)

The paper gives a physicist's view on the framework of branching space-time, 385--434). Branching models are constructed from physical state assignments. The models are then employed to give a formal semantics for the modal operators ``possibly'' and ``necessarily'' and for the counterfactual conditional. The resulting formal language can be used to analyze quantum correlation experiments. As an application sketch, Stapp's premises LOC1 and LOC2 from his purported proof of non-locality, 300--304) are analyzed.

The paper studies many-dimensional modal logics corresponding to products of Kripke frames. It proves results on axiomatisability, the finite model property and decidability for product logics, by applying a rather elaborated modal logic technique: p-morphisms, the finite depth method, normal forms, filtrations. Applications to first order predicate logics are considered too. The introduction and the conclusion contain a discussion of many related results and open problems in the area.

Actualists of a certain stripe—dispositionalists—hold that metaphysical modality is grounded in the powers of actual things. Roughly: p is possible iff something has, or some things have, the power to bring it about that p. Extant critiques of dispositionalism focus on its material adequacy, and question whether there are enough powers to account for all the possibilities we intuitively want to countenance. For instance, it seems possible that none of the actual contingent particulars ever existed, but it is impossible to (...) explain this by appealing to the powers of some actual thing or things to bring it about. I argue instead that dispositionalism, in the simple form championed by its proponents, is formally inadequate. Dispositionalists interpret the modal operators as simple existential claims about powers, but if we interpret the operators that way, the resulting system of modal logic is too weak to capture metaphysical modality. I argue that we can modify the standard dispositionalist interpretations of the operators to secure formal adequacy, but at the cost of accepting that not all modality is grounded in powers. This, I shall suggest, is not a bad thing—the resulting theory still has powers at its core and has certain attractive features, in addition to formal adequacy, that the standard theory lacks. (shrink)

The philosophy of necessity and possibility has flourished in the last half-century, but much less attention has been paid to the question of how we know what can be the case and what must be the case. Many friends of modal metaphysics and many enemies of modal metaphysics have agreed that while empirical discoveries can tell us what is the case, they cannot shed much light on what must be the case or on what non-actual possibilities there are. (...) In this paper, in contrast, I discuss and defend naturalistic approaches to discovering the facts about necessity and possibility. After some remarks about what methodological naturalism in philosophy might amount to, I argue that naturalistic method in modal investigations may not need to be particularly revisionary of much of what is currently being done in modal investigation. I then discuss a number of respects in which a naturalistic orientation in modal investigation may improve on our current epistemic situation. (shrink)

forthcoming in R. Cameron, B. Hale and A. Hoffmann (ed.s), The Logic, Epistemology and Metaphysics of Modality, Oxford University Press. Presents a concept-grounding account of modal knowledge.

This text aims to convey some of the interest and charm of modal logic, and to put a reader new to the subject in a position to have an informed opinion as to its applicability to each of several areas of philosophical concern in which the merits of a modal approach' have been controversial. he main focus, for these purposes, is on normal modal logics, though some attention is given to the non-normal side of the picture.