Deontic necessity modals (e.g. 'have to', 'ought to', 'must', 'need to', 'should', etc.) seem to vary in how they interact with negation. According to some accounts, what forces modals like 'ought' and 'should' to outscope negation is their polarity sensitivity -- modals that scope over negation do so because they are positive polarity items. But there is a conflict between this account and a widely assumed theory of if-clauses, namely the restrictor analysis. In particular, the conflict arises (...) for constructions containing a bound pronoun in the if-clause. This note spells out the core conflict. (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)

I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the (...) following results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds. (shrink)

We use imperatives to refute a naïve analysis of update potentials (force-operators attaching to sentences), arguing for a dynamic analysis of imperative force as restrictable, directed, and embeddable. We propose a dynamic, non-modal analysis of conditional imperatives, as a counterpoint to static, modal analyses. Our analysis retains Kratzer's analysis of if-clauses as restrictors of some operator, but avoids typing it as a generalized quantifier over worlds (against her), instead as a dynamic force operator. Arguments for a restrictor treatment (but against (...) a quantificational treatment) are mustered, and we propose a novel analysis of update on conditional imperatives (and an independently motivated revision of the standard ordering-semantics for root modals that makes use of it). Finally, we argue that imperative force is embeddable under an operation much like dynamic conjunction. (shrink)

How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model-theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness (or: determinacy) operator. We will show (...) how epistemicists, supervaluationists, and theorists of metaphysical vagueness like Barnes and Williams (2010) can interpret the framework.  We will also present a complete axiomatization of the logic we recommend to both epistemicists and local supervaluationists. . (shrink)

Modal Meinongianism is a form of Meinongianism whose main supporters are Graham Priest and Francesco Berto. The main idea of modal Meinongianism is to restrict the logical deviance of Meinongian non-existent objects to impossible worlds and thus prevent it from “contaminating” the actual world: the round square is round and not round, but not in the actual world, only in an impossible world. In the actual world, supposedly, no contradiction is true. I will show that Priest’s semantics, as originally formulated (...) in Towards Non-being, tell us something different. According to certain models, there are true contradictions in the actual world. Berto and Priest have noticed this unexpected consequence and have suggested a solution, but I will show that their solution is highly questionable. In the last section of this paper, I will introduce a new and simpler version of modal Meinongianism that avoids the problem. (shrink)

The subject of my article is the principle of characterization – the most controversial principle of Meinong’s Theory of Objects. The aim of this text is twofold. First of all, I would like to show that Russell’s well-known objection to Meinong’s Theory of Objects can be reformulated against a new modal interpretation of Meinongianism that is presented mostly by Graham Priest. Secondly, I would like to propose a strategy which gives uncontroversial restriction to the principle of characterization and which allows (...) to avoid Russell’s argument. The strategy is based on the distinction between object- and metalanguage, and it applies to modal Meinongianism as well as to other so-called Meinongian theories. (shrink)

Philosophers have always taken an interest not only in what is actually the case, but in what is necessarily the case and what could possibly be the case. These are questions of modality. Epistemologists of modality enquire into how we can know what is necessary and what is possible. This dissertation concerns the meta-epistemology of modality. It engages with the rules that govern construction and evaluation of theories in the epistemology of modality, by using modal empiricism – a form of (...) modal epistemology – as a running example. In particular, I investigate the assumption that it is important to be able to meet the integration challenge. Meeting the integration challenge is a source of serious difficulty for many approaches, but modal empiricism is supposed to do well in this respect. But I argue that once we have a better grasp of what the integration challenge is, it is not obvious that it presents no problem for modal empiricism. Moreover, even if modal empiricism could be said to be in a relatively good position with respect to integration, it comes at the cost of a forced choice between far-reaching partial modal scepticism and non-uniformism about the epistemology of modality. Non-uniformism is the view that more than one modal epistemology will be correct. While non-uniformism might not in itself be unpalatable, it must be defined and defended in a way which squares with the modal empiricist’s other commitment. I explore two ways of doing so, both involving a revised idea of the integration challenge and its role for the epistemology of modality. One involves a bifurcation of the integration challenge, and the other a restriction of the integration challenge’s relevance. Both ways are interesting, but neither is, as it turns out, a walk in the park. (shrink)

What is our epistemic access to metaphysical modality? Timothy Williamson suggests that the epistemology of counterfactuals will provide the answer. This paper challenges Williamson's account and argues that certain elements of the epistemology of counterfactuals that he discusses, namely so called background knowledge and constitutive facts, are already saturated with modal content which his account fails to explain. Williamson's account will first be outlined and the role of background knowledge and constitutive facts analysed. Their key role is to restrict our (...) imagination to rule out irrelevant counterfactual suppositions. However, background knowledge turns out to be problematic in cases where we are dealing with metaphysically possible counterfactual suppositions that violate the actual laws of physics. As we will see, unless Williamson assumes that background knowledge corresponds with the actual, true laws of physics and that these laws are metaphysically necessary, it will be difficult to address this problem. Furthermore, Williamson's account fails to accommodate the distinction between conceivable yet metaphysically impossible scenarios, and conceivable and metaphysically possible scenarios. This is because background knowledge and constitutive facts are based strictly on our knowledge of the actual world. Williamson does attempt to address this concern with regard to metaphysical necessities – as they hold across all possible worlds – but we will see that even in this case the explanation is questionable. These problems, it will be suggested, cannot be addressed in a counterfactual account of the epistemology of modality. The paper finishes with an analysis of Williamson's possible rejoinders and some discussion about the prospects of an alternative account of modal epistemology. (shrink)

The COVID-19 pandemic might be regarded as an example of a risky situation that demands proper action and decision-making in the absence of full information. It is noticeable, however, that scientists have divided into two camps concerning the best way of dealing with the very situation. Some of them have relied on mathematical models and typically proposed restrictive measures, while the others opted for the evidence-based approach and typically recommended more relaxed measures. I argue in this paper that practical possibilities (...) (or impossibilities) have been considerably neglected in those debates and current decisionmaking, especially by the proponents of mathematical epidemiology. (shrink)

Relative to any reasonable frame, satisfiability of modal quantificational formulae in which “= ” is the sole predicate is undecidable; but if we restrict attention to satisfiability in structures with the expanding domain property, satisfiability relative to the familiar frames (K, K4, T, S4, B, S5) is decidable. Furthermore, relative to any reasonable frame, satisfiability for modal quantificational formulae with a single monadic predicate is undecidable ; this improves the result of Kripke concerning formulae with two monadic predicates.

Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of “probabilistic” semantics are often motivated by their ability to explain intuitions about inferences involving “likely” and “probably”—intuitions that Angelika Kratzer’s canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely thought to (...) undercut this motivation: they present a world-ordering semantics that yields essentially the same logic as probabilistic semantics. In this paper, I argue that the challenge remains: defenders of world-ordering semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood. Holliday & Icard’s semantics yields an adequate logic only if models are restricted to Noetherian pre-orders. But I argue that the Noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities. As a result, probabilistic semantics remains the better explanation of the data. (shrink)

Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal scope. I (...) prove soundness and completeness theorems with respect to Hodes’ semantics, as well as semantics with fewer restrictions on the accessibility relation. (shrink)

On what I call absolutist essentialism about modality (AE), the metaphysical necessities are the propositions that are true in virtue of the essence (i.e. Aristotelian, absolute essence) of some entities. Other kinds of necessity can then be defined by restriction – e.g. the conceptual necessities are the propositions that are true in virtue of the essence of conceptual entities specifically. As an account of metaphysical modality and some other kinds (e.g. logical, conceptual), AE may have important virtues. However, when it (...) comes to accounting for further important kinds, like natural or normative necessity, it faces a challenge. Three main options have been defended: treat those kinds as further restricted forms of metaphysical necessity; define them as conditional forms of metaphysical necessity; treat them as primitive kinds. -/- In this paper, I propose a new option, which combines the main idea of AE (reducing necessities to essences) with an idea which has been developed largely independently: that of relative essence. On the proposed view, those kinds (e.g. natural necessity) that cannot be grounded in the essences (i.e. absolute essences) of the relevant entities (e.g. natural entities) may be grounded in their relative essences instead. Thus, I propose a generalized, or extended, version of AE, which I call relativized essentialism about modality (RE). In particular, RE offers prospects for a general framework for kinds of modality which is flexible enough to cover a large range of kinds (both absolute and relative ones) while remaining parsimonious and unified. (shrink)

⦿ In my dissertation I introduce, motivate and take the first steps in the implementation of, the project of naturalising modal metaphysics: the transformation of the field into a chapter of the philosophy of science rather than speculative, autonomous metaphysics. -/- ⦿ In the introduction, I explain the concept of naturalisation that I apply throughout the dissertation, which I argue to be an improvement on Ladyman and Ross' proposal for naturalised metaphysics. I also object to Williamson's proposal that modal metaphysics (...) --- or some view in the area --- is already a quasi-scientific discipline. -/- ⦿ Recently, some philosophers have argued that the notion of metaphysical modality is as ill defined as to be of little theoretical utility. In the second chapter I intend to contribute to such skepticism. First, I observe that each of the proposed marks of the concept, except for factivity, is highly controversial; thus, its logical structure is deeply obscure. With the failure of the "first principles" approach, I examine the paradigmatic intended applications of the concept, and argue that each makes it a device for a very specific and controversial project: a device, therefore, for which a naturalist will find no use for. I conclude that there is no well-defined or theoretically useful notion of objective necessity other than logical or physical necessity, and I suggest that naturalising modal metaphysics can provide more stable methodological foundations. -/- ⦿ In the third chapter I answer a possible objection against the in-principle viability of the project: that the concept of metaphysical modality cannot be understood through the philosophical analysis of any scientific theory, since metaphysical necessity "transcends'' natural necessity, and science only deals with the latter. I argue that the most important arguments for this transcendence thesis fail or face problems that, as of today, remain unsolved. -/- ⦿ Call the idea that science doesn't need modality, "demodalism''. Demodalism is a first step in a naturalistic argument for modal antirealism. In the fourth chapter I examine six versions of demodalism to explain why a family of formalisms, that I call "spaces of possibility'', are (i) used in a quasi-ubiquitous way in mathematised sciences (I provide examples from theoretical computer science to microeconomics), (ii) scientifically interpreted in modal terms, and (iii) used for at least six important tasks: (1) defining laws and theories; (2) defining important concepts from different sciences (I give several examples); (3) making essential classifications; (4) providing different types of explanations; (5) providing the connection between theory and statistics, and (6) understanding the transition between a theory and its successor (as is the case with quantisation). -/- ⦿ In fifth chapter I propose and defend a naturalised modal ontology. This is a realism about modal structure: my realism about constraints. The modal structure of a system are the relationships between its possible states and between its possible states and those of other systems. It is given by the plurality of restrictions to which said system is subject. A constraint is a factor that explains the impossibility of a class of states; I explain this concept further. First, I defend my point of view by rejecting some of its main rivals: constructive empiricism, Humean conventionalism, and wave function realism, as they fail to make sense of quantum chaos. This is because the field requires the notion of objective modal structure, and the mentioned views have trouble explaining the modal facts of quantum dynamics. Then, I argue that constraint realism supersedes these views in the context of Bohm's standard theory and mechanics, and underpins the study of quantum chaos. Finally, I consider and reject two possible problems for my point of view. -/- ⦿ A central concern of modal metaphysicians has been to understand the logical system that best characterises necessity. In the sixth chapter I intend to recover the logical project applied to my naturalistic modal metaphysics. Scientists and philosophers of science accept different degrees of physical necessity, ranging from purely mathematically necessary facts that restrict physical behaviour, to kinetic principles, to particular dynamical constraints. I argue that this motivates a multimodal approach to modal logic, and that the time dependence of dynamics motivates a logic of historical necessity. I propose multimodal propositional (classical) logics for Bohmian mechanics and the Everettian theory of many divergent worlds, and I close with a criticism of Williamson's approach to the logic of state spaces of dynamic systems. (shrink)

It is often argued that inferential role semantics (IRS) entails semantic holism as long as theorists fail to answer the question about which inferences, among the many, are meaning-constitutive. Since analyticity, as truth in virtue of meaning, is a widely dismissed notion in indicating which inferences determine meaning, it seems that holism follows. Semantic holism is often understood as facing problems with the stability of content and many usual explanations of communication. Thus, we should choose between giving up IRS, to (...) avoid these holistic entailments, and defending holism against this charge, to rescue IRS. I try to pursue the second goal by analyzing certain patterns of counterfactual reasoning. Wilfrid Sellars and Robert Brandom claim that, to defend IRS, content-constitutive inferences are those counterfactually robust. While it is difficult to assess the goodness of such a view, it nonetheless entails that counterfactually non-robust inferences (which I call “modally ruled out inferences”) are not content-constitutive. If this is true, and if we take certain remarks about the grasp of concepts on board, there is a way to restrict the scope of the holism entailed by IRS to the extent of reshaping problems with the stability of content. (shrink)

The thought experiment is a seemingly indispensable tool in the armchair philosopher’s toolbox. One wonders, for example, how philosophers could come to think that justified true belief isn’t knowledge, that reference isn’t determined by an expression’s associated description, or that moral responsibility doesn’t require the ability to do otherwise, without the use of thought experiments. But even if thought experiments play an integral role in philosophical methodology, their legitimacy is at least initially puzzling: one would think that significant knowledge of (...) the world requires extensive empirical investigation. But since thought experiments are done from the armchair, how can they tell us about the world? -/- A standard account of the nature and utility of thought experiments provides an answer to this question, and in a way that fits naturally with a standard picture of the nature of the facts philosophers investigate: Philosophers are about the business of investigating the essences of things and kinds. But a thing’s essential and accidental properties are modal properties. Thus, one can discern a thing’s essence by discovering its modal profile. But if so, then thought experiments are naturally suited as tools for the armchair philosopher. For thought experiments shed light on modal facts. Therefore, since philosophers investigate essences, facts about essence are modal facts, and the thought experiment is one of the few tools they have for discerning such facts, thought experiments play a legitimate and indispensable role in philosophical methodology. In my dissertation, I argue that the standard account of the nature and utility of thought experiments is inadequate, and sketch a more promising account. -/- First, I argue that our knowledge of possibility is restricted to the relatively humdrum. And if so, then since the standard account ties the utility of thought experiments to our knowledge of possibility, too many thought experiments will be ruled out as useless, which raises serious concerns about the significance, and perhaps even the legitimacy, of armchair philosophy. Thus, there is pressure for armchair philosophers to reject the standard account. -/- Second, I sketch an alternative picture of the nature of facts philosophers investigate – one that’s more fine-grained than the standard modal-profile picture. Relatedly, I sketch a correspondingly fine-grained semantics for claims about such facts. This alternative picture underwrites the legitimacy of a hitherto underappreciated sort of thought experiment, which I call the non-modal thought experiment. Such thought experiments shed light on facts about the world that are more fine-grained than what can be discerned by merely examining their modal profiles. I argue that non-modal thought experiments often succeed at just the points where the more familiar modal thought experiments fail, and thus that the two are naturally suited to complement one another in the philosopher’s practice. -/- Finally, I exploit the points mentioned above to sketch an account of the variety and utility of thought experiments that’s much more nuanced than that of the standard account. I then illustrate some of its virtues by indicating its ability to account for a wide range of epistemically forceful thought experiments – both humdrum and exotic –, and by demonstrating how it can be used to make progress in debates that have reached a stalemate due to conflicting modal intuitions. -/- . (shrink)

In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop several extensions of (...) \SQEMA\ where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension \SSQEMA\ we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon's monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versions of \SSQEMA\ which guarantee canonicity, too. (shrink)

A central idea in Ruth Millikan’s biosemantics is that a representation’s content is restricted to conditions required for the normal success of actions that it has as its function to guide. This paper raises and responds to a problem for this idea. The problem is that the success requirement seems to block us from saying that epistemic modal judgments represent our epistemic circumstances. For the normal success of actions guided by these judgments seems to depend on what is actually (...) the case, not on whether or to what extent various possibilities were supported by our evidence. In response, I argue, first, that actions guided by epistemic modal judgments have as their function to implement strategies for handling epistemic circumstances, second, that the successful performance of this function requires that aspects of these circumstances obtain, and, third, that biosemantics can thus understand epistemic modal judgments as representing these aspects. The recognition of such strategic contents introduces complications; I further argue that these are benign. (shrink)

In this paper, we axiomatize the deontic logic in Fusco 2015, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the restrictions (...) Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to ‘lift’ a Kripke frame for a one- dimensional modal logic into two dimensions. (shrink)

In this paper I would like to offer a new framework for hypothetical reasoning, with the goal of predicting what scenarios we consider when we interpret a conditional or causal claim (such as a sentence containing the word ‘because‘). The idea is that when we interpret a conditional or causal claim, we identify a part of the world to change and imagine changing that. Sentences are about parts of the world: when we interpret a conditional antecedent or because clause, we (...) allow the part of the world it is about to vary. -/- My main evidence for this approach is that it gives just the right range of hypothetical scenarios to account for how we interpret both conditionals and causal claims. Some approaches (such as Stalnaker and Lewis’s semantics of conditionals based on similarity, and Kratzer’s premise semantics) consider too few scenarios, while others (such as Fine’s truthmaker semantics of conditionals) consider too many. The present approach inhabits a Goldilocks zone between these extremes: not too restrictive, not too permissive, but just right. (shrink)

Necessitism is the controversial thesis that necessarily everything is necessarily something, namely that everything, everywhere, necessarily exists. What is controversial about necessitism is that, at its core, it claims that things could not have failed to exist, while we have a pre-theoretical intuition that not everything necessarily exists. Contingentism, in accordance with common sense, denies necessitism: it claims that some things could have failed to exist. Timothy Williamson is a necessitist and claims that David Lewis is a necessitist too. The (...) paper argues that, granted the assumptions that lead to interpret the Lewisian as a necessitist, she can preserve contingentist intuitions, by genuinely agreeing with the folk that existence is contingent. This is not just the uncontroversial claim that the Lewisian, as a result of the prevalence of restricted quantification in counterpart theoretic regimentations of natural language, can agree with the folk while disagreeing with them in the metaphysical room. Rather, this is the claim that it is in the metaphysical room that the Lewisian can endorse the intuitions lying behind contingentism. (shrink)

Future Logic is an original, and wide-ranging treatise of formal logic. It deals with deduction and induction, of categorical and conditional propositions, involving the natural, temporal, extensional, and logical modalities. Traditional and Modern logic have covered in detail only formal deduction from actual categoricals, or from logical conditionals (conjunctives, hypotheticals, and disjunctives). Deduction from modal categoricals has also been considered, though very vaguely and roughly; whereas deduction from natural, temporal and extensional forms of conditioning has been all but totally ignored. (...) As for induction, apart from the elucidation of adductive processes (the scientific method), almost no formal work has been done. This is the first work ever to strictly formalize the inductive processes of generalization and particularization, through the novel methods of factorial analysis, factor selection and formula revision. This is the first work ever to develop a formal logic of the natural, temporal and extensional types of conditioning (as distinct from logical conditioning), including their production from modal categorical premises. Future Logic contains a great many other new discoveries, organized into a unified, consistent and empirical system, with precise definitions of the various categories and types of modality (including logical modality), and full awareness of the epistemological and ontological issues involved. Though strictly formal, it uses ordinary language, wherever symbols can be avoided. Among its other contributions: a full list of the valid modal syllogisms (which is more restrictive than previous lists); the main formalities of the logic of change (which introduces a dynamic instead of merely static approach to classification); the first formal definitions of the modal types of causality; a new theory of class logic, free of the Russell Paradox; as well as a critical review of modern metalogic. But it is impossible to list briefly all the innovations in logical science — and therefore, epistemology and ontology — this book presents; it has to be read for its scope to be appreciated. (shrink)

This paper offers a unified, quantificational treatment of incomplete descriptions like ‘the table’. An incomplete quantified expression like ‘every bottle’ (as in “Every bottle is empty”) can feature in true utterances despite the fact that the world contains nonempty bottles. Positing a contextual restriction on the bottles being talked about is a straightforward solution. It is argued that the same strategy can be extended to incomplete definite descriptions across the board. ncorporating the contextual restrictions into semantics involves meeting a complex (...) array of desiderata, yet the apparently simpler pragmatic alternative faces severe problems and is therefore a nonstarter. (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)

According to the Principle of Sufficient Reason (‘PSR’), every fact has an explanation for why it obtains. If the PSR is true, there must be a sufficient reason for why God chose to create our world. But a sufficient reason for God’s choice plausibly necessitates that choice. It thus seems that God could not have done otherwise, and that our world exists necessarily. We therefore appear forced to pick between the PSR, and the contingency of creation and divine choice. I (...) show that a third option remains open, and thus that it is possible to preserve the contingency of creation and divine choice even while endorsing the PSR. My solution depends on the coherence of a restricted modal realism. On this modal realism, there is more than one possible morally optimal created world, and for each such world there is an existing possibility in which God creates that world. (shrink)

This paper presents a puzzle involving embedded attitude reports. We resolve the puzzle by arguing that attitude verbs take restricted readings: in some environments the denotation of attitude verbs can be restricted by a given proposition. For example, when these verbs are embedded in the consequent of a conditional, they can be restricted by the proposition expressed by the conditional’s antecedent. We formulate and motivate two conditions on the availability of verb restrictions: a constraint that ties the (...) content of restrictions to the “dynamic effects” of sentential connectives and a constraint that limits the availability of restriction effects to present tense verbs with first-person subjects. However, we also present some cases that make trouble for these conditions, and outline some possible ways of modifying the view to account for the recalcitrant data. We conclude with a brief discussion of some of the connections between our semantics for attitude verbs and issues concerning epistemic modals and theories of knowledge. (shrink)

Many philosophers have been attracted to a restricted version of the principle of indifference in the case of self-locating belief. Roughly speaking, this principle states that, within any given possible world, one should be indifferent between different hypotheses concerning who one is within that possible world, so long as those hypotheses are compatible with one’s evidence. My first goal is to defend a more precise version of this principle. After responding to several existing criticisms of such a principle, I (...) argue that existing formulations of the principle are crucially ambiguous, and I go on to defend a particular disambiguation of the principle. According to the disambiguation I defend, how we should apply this restricted principle of indifference sensitively depends on our background metaphysical beliefs. My second goal is to apply this disambiguated principle to classical skeptical problems in epistemology. In particular, I argue that Eternalism threatens to lead us to external world skepticism, and Modal Realism threatens to lead us to inductive skepticism. (shrink)

We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such (...) points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan. (shrink)

Among philosophers working on modality, there is a common assumption that there is a strong connection between temporal possibility and counterfactual possibility. For example, Sydney Shoemaker 1998, 69 70) writes: It seems to me a general feature of our thought about possibility that how we think that something could have differed from how it in fact is [is] closely related to how we think that the way something is at one time could differ from the way that same thing is (...) at a different time. In possible worlds jargon, the ways one and the same thing of a given sort can differ across worlds correspond to the ways one and the same thing of that sort can differ at different times in the same world. Could I have been a plumber or an accountant instead of a philosopher? The answer seems to be yes -- and this goes with the fact that we acknowledge the possibility of a scenario in which someone who was exactly as I was at some point in my life undergoes a series of changes resulting in his eventually being a plumber or an accountant. In a footnote, he acknowledges that this connection between counterfactual and temporal possibility needs to be qualified in response to an objection by Randy Clarke: «The property of being the child of someone who has visited Paris is not one that one can have and then lose; but it is one that one can have in the actual world and not have in some other possible world.» (1998, 75n.9) Therefore, he restricts the inference from temporal to counterfactual possibility and vice versa to «non historical properties.». (shrink)

When it comes to evaluating reductive hypotheses in metaphysics, supervenience arguments are the tools of the trade. Jaegwon Kim and Frank Jackson have argued, respectively, that strong and global supervenience are sufficient for reduction, and others have argued that supervenience theses stand in need of the kind of explanation that reductive hypotheses are particularly suited to provide. Simon Blackburn's arguments about what he claims are the specifically problematic features of the supervenience of the moral on the natural have also been (...) influential. But most discussions of these arguments have proceeded under the strong and restrictive assumptions of the S5 modal logic. In this paper we aim to remedy that defect, by illustrating in an accessible way what happens to these arguments under relaxed assumptions and why. The occasion is recent work by Ralph Wedgwood, who seeks to defend non-reductive accounts of moral and mental properties together with strong supervenience, but to evade both the arguments of Kim and Jackson and the explanatory challenge by accepting only the weaker, B, modal logic. In addition to drawing general lessons about what happens to supervenience arguments under relaxed assumptions, our goal is therefore to shed some light on both the virtues and costs of Wedgwood's proposal. (shrink)

We bring together two ideas that are widely accepted in the literature: (i) conditionals with modal consequents are systematically ambiguous between a reading on which the if-clause restricts the modal, and a reading on which the if-clause introduces an epistemic supposition and the modal is unrestricted; (ii) ‘will’ is a modal. Together, (i) and (ii) imply that ‘will’-conditionals are systematically ambiguous between a reading as restricted historical claims, and one as unrestricted historical claims made under a supposition. We argue (...) that this prediction is correct and that the existence of the relevant ambiguity has far-reaching repercussions for several important debates concerning conditionals. (shrink)

This paper analyzes a non-temporal interpretation of the adverb sempre “always” in European Portuguese and Italian, in which the adverb expresses persistence of the truth of a proposition over time and displays specific contextual constraints (TP-sempre). Despite an overlap in the contexts in which TP-sempre may occur in both languages, we provide data showing that its distribution is not exactly the same in European Portuguese and Italian. In view of these data, we propose that TP-sempre is a modal operator of (...) confirmation in both languages, but that it is more restricted in Italian in that it has a plan presupposition only in this language. (shrink)

The idea that the epistemology of modality is in some sense a priori is a popular one, but it has turned out to be difficult to precisify in a way that does not expose it to decisive counterexamples. The most common precisifications follow Kripke’s suggestion that cases of necessary a posteriori truth that can be known a priori to be necessary if true ‘may give a clue to a general characterization of a posteriori knowledge of necessary truths’. The idea is (...) that whether it is contingent whether p can be known a priori for at least some broad range of sentences ‘p’. Recently, Al Casullo and Jens Kipper have discussed restrictions of such principles to atomic sentences. We show that decisive counterexamples even to such dramatically restricted Kripke-style principles can be constructed using minimal logical resources. We then consider further restrictions, and show that the counterexamples to the original principles can be turned into counterexamples to the further restricted principles. We conclude that, if there are any true restrictions of Kripke-style principles, then they are so weak as to be of little epistemological interest. (shrink)

In identifying intrinsic molecular chance and extrinsic adaptive pressures as the only causally relevant factors in the process of evolution, the theoretical perspective of the Modern Synthesis had a major impact on the perceived tenability of an ontology of dispositional properties. However, since the late 1970s, an increasing number of evolutionary biologists have challenged the descriptive and explanatory adequacy of this “chance alone, extrinsic only” understanding of evolutionary change. Because morphological studies of homology, convergence, and teratology have revealed a space (...) of possible forms and phylogenetic trajectories that is considerably more restricted than expected, evo-devo has focused on the causal contribution of intrinsic developmental processes to the course of evolution. Evo-devo’s investigation into the developmental structure of the modality of morphology – including both the possibility and impossibility of organismal form – has led to the utilisation of a number of dispositional concepts that emphasise the tendency of the evolutionary process to change along certain routes. In this sense, and in contrast to the perspective of the Modern Synthesis, evo-devo can be described as a “science of dispositions.” This chapter discusses the recent philosophical literature on dispositional properties in evo-devo, exploring debates about both the metaphysical and epistemological aspects of the central dispositional concepts utilised in contemporary evo-devo and addressing the epistemological question of how dispositional properties challenge existing explanatory models in evolutionary biology. (shrink)

According to EJ Lowe, diachronic necessity and synchronic necessity are logically independent. Diachronic possibility concerns what could happen to an object over time and therefore concerns future possibilities for that object given its past history. Synchronic possibility concerns what is possible for an object in the present or at a past present moment. These are logically independent, given certain assumptions. While it may true that because I am 38, it is impossible diachronically for me to be 30 (at least once (...) we restrict the degree of relevant possibility), it is possible, given that at some point in the past, I may have been conceived slightly earlier than I was, that I am now 37. Likewise, it is possible diachronically for me to be somewhere other than where I am, but given that one object cannot be in different places at the same time, it is impossible for me now to be somewhere other than where I am, and this is true at each past point in my history too. There are, then, two axis upon which to distinguish what is and is not possible: tensed possibilities and possibilities of degree, which include nomic, metaphysical, and logical necessities, among others. I examine the interactions between these possibilities and I come to the conclusion that logical necessity is not in fact logical necessity simpliciter. Whether something is logically necessary depends upon tensed possibilities. I argue that while synchronic logical necessity entails diachronic logical necessity, the reverse entailment does not hold. I explore the consequences of this for certain philosophical debates in semantics including the concept of rigid designation, and descriptive names. (shrink)

In this paper, I argue that an adequate meta-semantic framework capable of accommodating the range of projects currently identified as projects in conceptual engineering must be sensitive to the fact that concepts (and hence projects relating to them) fall into distinct kinds. Concepts can vary, I will argue, with respect to their direction of determination, their modal range, and their temporal range. Acknowledging such variations yields a preliminary taxonomy of concepts and generates a meta-semantic framework that allows us both to (...) accommodate the full range of cases and to identify a proper subset of concepts for special ameliorative consideration. Ignoring such variations, in contrast, leads to a restricted meta-semantic framework that accommodates only a subset of the particular projects while generating implausible accounts of others. (shrink)

The Forrest-Armstrong argument, as reconfigured by David Lewis, is a reductio against an unrestricted principle of recombination. There is a gap in the argument which Lewis thought could be bridged by an appeal to recombination. After presenting the argument, I show that no plausible principle of recombination can bridge the gap. But other plausible principles of plenitude can bridge the gap, both principles of plenitude for world contents and principles of plenitude for world structures. I conclude that the Forrest-Armstrong argument, (...) when fortified in one of these ways, demands that unrestricted recombination be rejected. The appropriate restriction comes from a consideration of what world structures are possible. I argue that, although there are too many worlds to form a set, for any world, the individuals at that world do form a set. To defend it I invoke a principle of Limitation of Size together with an iterative conception of structure. (shrink)

Visual imagery is a form of sensory imagination, involving subjective experiences typically described as similar to perception, but which occur in the absence of corresponding external stimuli. We used the Activation Likelihood Estimation algorithm (ALE) to identify regions consistently activated by visual imagery across 40 neuroimaging studies, the first such meta-analysis. We also employed a recently developed multi-modal parcellation of the human brain to attribute stereotactic co-ordinates to one of 180 anatomical regions, the first time this approach has been combined (...) with the ALE algorithm. We identified a total 634 foci, based on measurements from 464 participants. Our overall comparison identified activation in the superior parietal lobule, particularly in the left hemisphere, consistent with the proposed ‘top-down’ role for this brain region in imagery. Inferior premotor areas and the inferior frontal sulcus were reliably activated, a finding consistent with the prominent semantic demands made by many visual imagery tasks. We observed bilateral activation in several areas associated with the integration of eye movements and visual information, including the supplementary and cingulate eye fields (SCEFs) and the frontal eye fields (FEFs), suggesting that enactive processes are important in visual imagery. V1 was typically activated during visual imagery, even when participants have their eyes closed, consistent with influential depictive theories of visual imagery. Temporal lobe activation was restricted to area PH and regions of the fusiform gyrus, adjacent to the fusiform face complex (FFC). These results provide a secure foundation for future work to characterise in greater detail the functional contributions of specific areas to visual imagery. (shrink)

This essay proposes a reductive account of robust macro-regularities. On the view proposed, regularities can earn their elite scientific status by featuring in good summaries of restricted regions in the space of physical possibilities: our “modal neighborhoods.” I argue that this view vindicates “nomic foundationalism”, while doing justice to the practice of invoking physically contingent generalizations in higher-level explanations. Moreover, the view suggests an explanation for the particular significance of robust macro-regularities: we rely on summaries of our modal neighborhoods (...) when reasoning hypothetically about “agentially accessible” possibilities. (shrink)

Mereological universalists, according to whom every plurality of entities has a fusion, usually claim that most quantifications are restricted to ordinary entities. However, there is no evidence that our usual quantifications over ordinary objects are restricted. In this article I explore an alternative way of reconciling Mereological Universalism with our usual quantifications. I resort to a modest form of ontological expansionism and to the so-called interpretational modalities. Quantifications over ordinary objects are the initial stages of the expansion. From (...) these initial stages, expansions can proceed upwards (fusions of entities in the domain of quantification are added), downwards (parts of entities in the domain are added), and sidewards (entities which are mereologically disjoint from the entities in the domain are added). These expansions are driven by a variety of epistemic and pragmatic reasons and raise different kinds of problems. At each stage, a modalized version of Mereological Universalism is true. By contrast, only at some especially rich stages, standard, non-modalized Mereological Universalism is true as well. Among these especially rich stages, there is a final, metaphysically pre-eminent stage of mereological plenitude. In the last part of the article I discuss some problems and limitations of expansionism. (shrink)

We examine a prominent naturalistic line on the method of cases, exemplified by Timothy Williamson and Edouard Machery: MoC is given a fallibilist and non-exceptionalist treatment, accommodating moderate modal skepticism. But Gettier cases are in dispute: Williamson takes them to induce substantive philosophical knowledge; Machery claims that the ambitious use of MoC should be abandoned entirely. We defend an intermediate position. We offer an internal critique of Macherian pessimism about Gettier cases. Most crucially, we argue that Gettier cases needn’t exhibit (...) ‘disturbing characteristics’ that Machery posits to explain why philosophical cases induce dubious judgments. It follows, we show, that Machery’s central argument for the effective abandonment of MoC is undermined. Nevertheless, we engineer a restricted variant of the argument—in harmony with Williamsonian ideology–that survives our critique, potentially limiting philosophy’s scope for establishing especially ambitious modal theses, despite traditional MoC’s utility being partially preserved. (shrink)

Carnap's theory of descriptions was restricted in two ways. First, the descriptive conditions had to be non-modal. Second, only primitive predicates or the identity predicate could be used to predicate something of the descriptum . The motivating reasons for these two restrictions that can be found in the literature will be critically discussed. Both restrictions can be relaxed, but Carnap's theory can still be blamed for not dealing adequately with improper descriptions.

This paper focuses on the Enkratic principle of rationality, according to which rationality requires that if an agent sincerely and with conviction believes she ought to X, then X-ing is a goal in her plan. We analyze the logical structure of Enkrasia and its implications for deontic logic. To do so, we elaborate on the distinction between basic and derived oughts, and provide a multi-modal neighborhood logic with three characteristic operators: a non-normal operator for basic oughts, a non-normal operator for (...) goals in plans, and a normal operator for derived oughts. We prove two completeness theorems for the resulting logic, and provide a dynamic extension of the logic by means of product updates. We illustrate how this setting informs deontic logic by considering issues related to the filtering of inconsistent oughts, the restricted validity of deontic closure, and the stability of oughts and goals under dynamics. (shrink)

Organisations are computing systems. The university’s sports centre is a computing system for managing sports teams and facilities. The tenure committee is a computing system for assigning tenure status. Despite an increasing number of publications in group ontology, the computational nature of organisations has not been recognised. The present paper is the first in this debate to propose a theory of organisations as groups structured for computing. I begin by describing the current situation in group ontology and by spelling out (...) the thesis in more detail. I then present the example of a sports centre to illustrate why one might intuitively think of organisations as computing systems. To substantiate the thesis, I introduce Piccinini’s restrictive analysis of physical computation. As I show, organisations meet all criteria for being computing systems. Organisations are structured groups with the function of manipulating medium-independent vehicles according to rules. Furthermore, I argue for the modal claim that this is a necessary feature of organisations. Having sketched the computational account of organisations, I compare it to other proposals in the literature. (shrink)

Chancy modus ponens is the following inference scheme: ‘probably φ’, ‘if φ, then ψ’, therefore, ‘probably ψ’. I argue that Chancy modus ponens is invalid in general. I further argue that the invalidity of Chancy modus ponens sheds new light on the alleged counterexample to modus ponens presented by McGee. I close by observing that, although Chancy modus ponens is invalid in general, we can recover a restricted sense in which this scheme of inference is valid.

The early modern period was the natural historical habitat of the Principle of Sufficient Reason, i.e., the demand that everything must have a cause, or reason. It is in this period that the principle was explicitly articulated and named, and throughout the period we find numerous formulations and variants of the PSR and its closely related ‘ex nihilo nihil fit’ principle, which the early moderns inherited from medieval philosophy. Contemporary discussions of these principles were not restricted to philosophy. “Nothing (...) will come of nothing; speak again” old King Lear tells his daughter Cordelia at the beginning of Shakespeare’s celebrated tragedy, and in early modern science, conservation principles were the order of the day. Within philosophy, Malebranche stipulates that there cannot be an effect without a cause, and Berkeley motivates his idealism by an appeal to ‘ex nihilo nihil fit.’ Were we to try to provide an exhaustive survey the various formulations of the PSR in this period – including the weaker ones – we would be writing an encyclopedia. In fact, one wonders whether any early modern thinker was willing to accept a wholesale rejection of the PSR, i.e., a view which states that no fact requires an explanation. Moreover, the view that many – perhaps most – facts require an explanation seems to be tacitly assumed even by us today, in both our theoretical and colloquial discourse. For these reasons, this chapter will focus on two early modern philosophers who advocated very strong (i.e., virtually exceptionless) versions of the PSR: Benedict de Spinoza and G.W. Leibniz. Following a brief overview of Descartes’s restricted endorsement of the PSR, I will turn to discuss the central features of the PSR in the writings of Spinoza (§2) and those of Leibniz (§3). In the cases of each of these philosophers, we will examine carefully: (i) their main statements of the PSR, (ii) the scope they assign to the principle (i.e., what requires an explanation and what counts as an explanation), (iii) the modal strength they assign to the principle, (iv) the main implications they draw from the principle, (v) exceptions to the principle, and, finally, (vi) the justification of the principle. In §4, we will study a principle, complementing the PSR, namely, the assertion that everything and every fact must have an effect (or as Leibniz would put it: “nothing is sterile”). (shrink)

This paper is about what we call Deontically-flavored Nominal Constructions (DNCs) in English, such as "No ice cream" or "Dogs on leash only". DNCs are often perceived as commands and have been argued to be a type of non-canonical imperative, much like root infinitives in German or Russian. We argue instead that DNCs at their core are declaratives that cite a rule but can be used performatively in the right context. We propose that DNCs contain an elided deontic modal, i.e., (...) allowed, whose presence explains their distributional restrictions and interpretational properties. Among other things, we speculate on the licensing conditions of DNCs (the presence of 'only' or the negative determiner 'no'), suggesting that these are tied to the properties of discourses in which rules can be used naturally. (shrink)

The topic of this article is the closure of a priori knowability under a priori knowable material implication: if a material conditional is a priori knowable and if the antecedent is a priori knowable, then the consequent is a priori knowable as well. This principle is arguably correct under certain conditions, but there is at least one counterexample when completely unrestricted. To deal with this, Anderson proposes to restrict the closure principle to necessary truths and Horsten suggests to restrict it (...) to formulas that belong to less expressive languages. In this article it is argued that Horsten’s restriction strategy fails, because one can deduce that knowable ignorance entails necessary ignorance from the closure principle and some modest background assumptions, even if the expressive resources do not go beyond those needed to formulate the closure principle itself. It is also argued that it is hard to find a justification for Anderson’s restricted closure principle, because one cannot deduce it even if one assumes very strong modal and epistemic background principles. In addition, there is an independently plausible alternative closure principle that avoids all the problems without the need for restriction. (shrink)