In this paper, I will defend the thesis that fundamental natural laws are distinguished from accidental empirical generalizations neither by metaphysical necessity, 147–155, 2005, 2007) nor by contingent necessitation. The only sort of modal force that distinguishes natural laws, I will argue, arises from the peculiar physical property of mutual independence of elementary interactions exemplifying the laws. Mutual independence of elementary interactions means that their existence and their nature do not depend in any way on which other interactions (...) presently occur. It is exactly this general physical property of elementary interactions in the actual world that provides natural laws with their specific modal force and grounds the experience of nature’s ‘recalcitrance’. Thus, the modal force of natural laws is explained by contingent non-modal properties of nature. In the second part of the paper, I deal with some alleged counterexamples to my approach: constraint laws, compositional laws, symmetry principles and conservation laws. These sorts of laws turn out to be compatible with my approach: constraint laws and compositional laws do not represent the dynamics of interaction-types by themselves, but only as constitutive parts of a complete set of equations, whereas symmetry principles and conservation laws do not represent any specific dynamics, but only impose general constraints on possible interactions. (shrink)

In this paper, I will defend the thesis that fundamental natural laws are distinguished from accidental empirical generalizations neither by metaphysical necessity (e.g. Ellis 1999, 2001; Bird in Analysis, 65(2), 147–155, 2005, 2007) nor by contingent necessitation (Armstrong 1983). The only sort of modal force that distinguishes natural laws, I will argue, arises from the peculiar physical property of mutual independence of elementary interactions exemplifying the laws. Mutual independence of elementary interactions means that their existence and their nature (...) do not depend in any way on which other interactions presently occur. It is exactly this general physical property of elementary interactions in the actual world that provides natural laws with their specific modal force and grounds the experience of nature’s ‘recalcitrance’. Thus, the modal force of natural laws is explained by contingent non-modal properties of nature. In the second part of the paper, I deal with some alleged counterexamples to my approach: constraint laws, compositional laws, symmetry principles and conservation laws. These sorts of laws turn out to be compatible with my approach: constraint laws and compositional laws do not represent the dynamics of interaction-types by themselves, but only as constitutive parts of a complete set of equations, whereas symmetry principles and conservation laws do not represent any specific dynamics, but only impose general constraints on possible interactions. (shrink)

We consider the modality “ $\varphi $ is true in every $\sigma $ -centered forcing extension,” denoted $\square \varphi $, and its dual “ $\varphi $ is true in some $\sigma $ -centered forcing extension,” denoted $\lozenge \varphi $, which give rise to the notion of a principle of $\sigma $ -centered forcing. We prove that if ZFC is consistent, then the modal logic of $\sigma $ -centered forcing, i.e., the ZFC-provable principles of $\sigma $ -centered forcing, is exactly (...) $\mathsf {S4.2}$. We also generalize this result to other related classes of forcing. (shrink)

This paper investigates when and how children figure out the force of modals: that possibility modals (e.g., _can_/_might_) express possibility, and necessity modals (e.g., _must_/_have to_) express necessity. Modals raise a classic subset problem: given that necessity entails possibility, what prevents learners from hypothesizing possibility meanings for necessity modals? Three solutions to such subset problems can be found in the literature: the first is for learners to rely on downward-entailing (DE) environments (Gualmini and Schwarz in J. Semant. 26(2):185–215, 2009 (...) ); the second is a bias for strong (here, necessity) meanings; the third is for learners to rely on pragmatic cues stemming from the conversational context (Dieuleveut et al. in Proceedings of the 2019 Amsterdam colloqnium, pp. 111–122, 2019a ; Rasin and Aravind in Nat. Lang. Semant. 29:339–375, 2020 ). This paper assesses the viability of each of these solutions by examining the modals used in speech to and by 2-year-old children, through a combination of corpus studies and experiments testing the guessability of modal force based on their context of use. Our results suggest that, given the way modals are used in speech to children, the first solution is not viable and the second is unnecessary. Instead, we argue that the conversational context in which modals occur is highly informative as to their force and sufficient, in principle, to sidestep the subset problem. Our child results further suggest an early mastery of possibility—but not necessity—modals and show no evidence for a necessity bias. (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)

Three popular views regarding the modal status of the laws of nature are discussed: Humean Supervenience, nomic necessitation, and scientific/dispositional essentialism. These views are examined especially with regard to their take on the apparent modal force of laws and their ability to explain that modal force. It will be suggested that none of the three views, at least in their strongest form, can be maintained if some laws are metaphysically necessary, but others are metaphysically contingent. (...) Some reasons for thinking that such variation in the modal status of laws exists will be presented with reference to physics. This drives us towards a fourth, hybrid view, according to which there are both necessary and contingent laws. The prospects for such a view are studied. (shrink)

Modals in St’át’imcets (Lillooet Salish) show two differences from their counterparts in English. First, they have variable quantificational force, systematically allowing both possibility and necessity interpretations; and second, they lexically restrict the conversational background, distinguishing for example between deontic and (several kinds of) epistemic modality. We provide an analysis of the St’át’imcets modals according to which they are akin to specific indefinites in the nominal domain. They introduce choice function variables which select a subset of the accessible worlds. Following (...) Klinedinst, we assume distributivity over the resulting set of worlds. St’át’imcets modals thus receive a uniform interpretation as (distributive) pluralities. The appearance of variability in modal force arises because the choice function can select a larger or smaller subset of accessible worlds. Finally, we discuss the implications of our analysis for the investigation of modal systems in other languages. (shrink)

This paper examines "moderate modal skepticism", a form of skepticism about metaphysical modality defended by Peter van Inwagen in order to blunt the force of certain modal arguments in the philosophy of religion. Van Inwagen’s argument for moderate modal skepticism assumes Yablo's (1993) influential world-based epistemology of possibility. We raise two problems for this epistemology of possibility, which undermine van Inwagen's argument. We then consider how one might motivate moderate modal skepticism by relying on a (...) different epistemology of possibility, which does not face these problems: Williamson’s (2007: ch. 5) counterfactual-based epistemology. Two ways of motivating moderate modal skepticism within that framework are found unpromising. Nevertheless, we also find a way of vindicating an epistemological thesis that, while weaker than moderate modal skepticism, is strong enough to support the methodological moral van Inwagen wishes to draw. (shrink)

We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and Löwe [14], including the use of buttons, switches, dials and ratchets. Among the potentialist conceptions we consider are: rank potentialism, Grothendieck–Zermelo potentialism, transitive-set potentialism, forcing potentialism, countable-transitive-model potentialism, countable-model potentialism, and others. In each case, we identify lower bounds for the modal validities, which are generally either S4.2 (...) or S4.3, and an upper bound of S5, proving in each case that these bounds are optimal. The validity of S5 in a world is a potentialist maximality principle, an interesting set-theoretic principle of its own. The results can be viewed as providing an analysis of the modal commitments of the various set-theoretic multiverse conceptions corresponding to each potentialist account. (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)

I think that there are good reasons to adopt a relativist semantics for epistemic modal claims such as ``the treasure might be under the palm tree'', according to which such utterances determine a truth value relative to something finer-grained than just a world (or a <world, time> pair). Anyone who is inclined to relativise truth to more than just worlds and times faces a problem about assertion. It's easy to be puzzled about just what purpose would be served by (...) assertions of this kind, and how to understand what we'd be up to in our use of sentences like ``the treasure might be under the palm tree'', if they have such peculiar truth conditions. After providing a very quick argument to motivate a relativist view of epistemic modals, I bring out and attempt to resolve this problem in making sense of the role of assertions with relativist truth conditions. Solving this problem should be helpful in two ways: first, it eliminates an apparently forceful objection to relativism, and second, spelling out the relativist account of assertion and communication will help to make clear just what the relativist position is, exactly, and why it's interesting. (shrink)

Abstract“Force dynamics” refers to a previously neglected semantic category—how entities interact with respect to force. This category includes such concepts as: the exertion of force, resistance to such exertion and the overcoming of such resistance, blockage of a force and the removal of such blockage, and so forth. Force dynamics is a generalization over the traditional linguistic notion of “causative”: it analyzes “causing” into finer primitives and sets it naturally within a framework that also includes (...) “letting,”“hindering,”“helping,” and still further notions. Force dynamics, moreover, appears to be the semantic category that uniquely characterizes the grammatical category of modals, in both their basic and epistemic usages. In addition, on the basis of force dynamic parameters, numerous lexical items fall into systematic semantic patterns, and there exhibit parallelisms between physical and psychosocial reference. Further, from research on the relation of semantic structure to general cognitive structure, it appears that the concepts of force interaction that are encoded within language closely parallel concepts that appear both in early science and in naive physics and psychology. Overall, force dynamics thus emerges as a fundamental notional system that structures conceptual material pertaining to force interaction in a common way across a linguistic range: the physical, psychological, social, inferential, discourse, and mental-model domains of reference and conception. (shrink)

The paper considers the role of modality in the rational reconstruction of standpoints and arguments. The paper examines in what conditions modal markers can act as argumentative indicators and what kind of cues they provide for the reconstruction of argument. The paper critically re-examines Toulmin’s hypothesis that the meaning of the modals can be analyzed in terms of a field-invariant argumentative force and field-dependent criteria in the light of the Theory of Relative Modality developed within linguistic semantics, showing (...) how this theory can provide a more adequate model for exploiting the modals as indicators. The resulting picture confirms Toulmin’s intuition only in part: on the one hand the modals are always relational in nature and dependent on a contextual conversational background of propositions; on the other hand only epistemic-doxastic modals directly express a speech-act level inferential relation between a set of premises and a standpoint. Other modalities express relations (e.g. causal or final relations) better seen as part of the content of the argument whose argumentative relevance depends on the argumentation scheme employed. Thus non-epistemic modals function as argumentative indicators only indirectly. (shrink)

An increasing amount of contemporary philosophy of mathematics posits, and theorizes in terms of special kinds of mathematical modality. The goal of this paper is to bring recent work on higher-order metaphysics to bear on the investigation of these modalities. The main focus of the paper will be views that posit mathematical contingency or indeterminacy about statements that concern the `width' of the set theoretic universe, such as Cantor's continuum hypothesis. Within a higher-order framework I show that contingency about the (...) width of the set-theoretic universe refutes two orthodoxies concerning the structure of modal reality: the view that the broadest necessity has a logic of S5, and the "Leibniz biconditionals" stating that what is possible, in the broadest sense of possible, is what is true in some possible world. Nonetheless, I suggest that the underlying picture of modal set-theory is coherent and has attractions. (shrink)

“Force dynamics” refers to a previously neglected semantic category—how entities interact with respect to force. This category includes such concepts as: the exertion of force, resistance to such exertion and the overcoming of such resistance, blockage of a force and the removal of such blockage, and so forth. Force dynamics is a generalization over the traditional linguistic notion of “causative”: it analyzes “causing” into finer primitives and sets it naturally within a framework that also includes (...) “letting,”“hindering,”“helping,” and still further notions. Force dynamics, moreover, appears to be the semantic category that uniquely characterizes the grammatical category of modals, in both their basic and epistemic usages. In addition, on the basis of force dynamic parameters, numerous lexical items fall into systematic semantic patterns, and there exhibit parallelisms between physical and psychosocial reference. Further, from research on the relation of semantic structure to general cognitive structure, it appears that the concepts of force interaction that are encoded within language closely parallel concepts that appear both in early science and in naive physics and psychology. Overall, force dynamics thus emerges as a fundamental notional system that structures conceptual material pertaining to force interaction in a common way across a linguistic range: the physical, psychological, social, inferential, discourse, and mental‐model domains of reference and conception. (shrink)

This paper replies to Nanay’s response to my recent paper. My suggestions are the following. First, “should” or “ought” does not need to be deontic. Second, etiological theories of function, like provability logic, do not need to attribute modal force to their explanans. Third, the explanans of the homological account of trait type individuation does not appeal to a trait’s etiological function, that is, what a trait should or ought to do. Finally, my reference to Cummins’s notion of (...) function was intended to note that the homological account is permitted to use this non-etiological notion of function. (shrink)

Kant contends that necessity is a criterion of the a priori—that is, that all knowledge of necessary propositions is a priori. This contention, together with two others that Kant took to be evident—we know some mathematical propositions and such propositions are necessary—leads directly to the conclusion that some knowledge is a priori. Although many contemporary philosophers endorse Kant’s criterion, supporting arguments are hard to come by. Gordon Barnes provides one of the few examples. My purpose in this chapter is to (...) articulate and examine his argument. I have two goals in doing so. The first is to uncover several significant gaps in the argument. The second is to show that it suffers from a common defect in rationalist arguments. If the argument were successful against empiricist accounts of modal knowledge, it would apply with equal force to extant rationalist accounts of such knowledge. Hence, the cost of refuting modal empiricism is modal scepticism. (shrink)

Modal Meinongianism is the most recent neo-Meinongian theory. Its main innovation consists in a Comprehension Principle which, unlike other neo-Meinongian approaches, seemingly avoids limitations on the properties that can characterize objects. However, in a recent paper A. Sauchelli has raised an objection against modal Meinongianism, to the effect that properties and relations involving reference to worlds at which they are instantiated, and specifically to the actual world or parts thereof, force a limitation of its Comprehension Principle. The (...) theory, thus, is no better off than other neo-Meinongian views in this respect. This article shows that the notion part of actuality in Sauchelli’s paper is ambiguous from the modal Meinongian viewpoint. Accordingly, his objection splits into two, depending on its disambiguation. It is then explained how neither interpretation forces modal Meinongianism to limit its Comprehension Principle. A third problem connected to Sauchelli’s objection is addressed: how to account for our felicitously referring to nonexistent objects via descriptions that embed reference to properties not actually instantiated by the objects. Overall, the replies to these difficulties provide good insights into the workings of the new Meinongian theory. (shrink)

This article discusses some of the ways in which natural language can express modal information – information which is, to a first approximation, about what could be or must be the case, as opposed to being about what actually is the case. It motivates, explains, and raises problems for Angelika Kratzer's influential theory of modal auxiliaries, and introduces a new approach to one important debate about the relationships between modality, evidentiality, context change, and imperative force.

This study asserts that W.V.O. Quine’s eliminative philosophical gaze into mereological composition affects inevitably his interpretations of composition theories of ontology. To investigate Quine’s property monism from the account of modal eliminativism, I applied to his solution for the paradoxes of de re modalities’ . Because of its vital role to figure out how dispositions are encountered by Quine, it was significantly noted that the realm of de re modalities doesn’t include contingent and impossible inferences about things. Therefore, for (...) him, all the intrinsic forces and elements of entities such as powers and causal or teleological dispositions for ontology demand to be seen necessarily as bound variables from a monist perspective. Although his denial of analyticity and the elimination of dispositional field of ontology, S. Mumford criticizes the monist perspective of Quine’s paradoxical approach to superveniences. Because superveniences create problems while determining type-type identities from a monist mereological perspective. It is observed that Quine faces with a reduction again in terms of his dispositional monism despite his critiques to repulse vagueness from the ontology in his well-known article Two Dogmas of Empiricism. -/- . (shrink)

In [9], Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of quantum mechanics attempt to escape contradictions, there are many hints that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause [1, 2, 3] have raised several arguments against this approach and claimed that —taking into account (...) the square of opposition— quantum superpositions are better understood in terms of contrariety propositions rather than contradictory propositions. In [14] we defended the Paraconsistent Approach to Quantum Superpositions and provided arguments in favor of its development. In the present paper we attempt to analyze the meanings of modality, potentiality and contradiction in QM, and provide further arguments of why the PAQS is better suited, than the Contrariety Approach to Quantum Superpositions proposed by Arenhart and Krause, to face the interpretational questions that quantum technology is forcing us to consider. (shrink)

The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails (...) that \\) is high but non-maximal and might \ that \\) is significantly greater than 0. Drawing on several observations concerning the behavior of must, might and similar epistemic operators in evidential contexts, deductive inferences, downplaying and retractions scenarios, and expressions of epistemic tension, I argue that those two influential accounts have systematic descriptive shortcomings. To better make sense of their complex behavior, I propose instead a broadly Kratzerian account according to which must \ entails that \ = 1\) and might \ that \ > 0\), given a body of evidence and a set of normality assumptions about the world. From this perspective, must and might are vehicles for expressing a common mode of reasoning whereby we draw inferences from specific bits of evidence against a rich set of background assumptions—some of which we represent as defeasible—which capture our general expectations about the world. I will show that the predictions of this Kratzerian account can be substantially refined once it is combined with a specific yet independently motivated ‘grammatical’ approach to the computation of scalar implicatures. Finally, I discuss some implications of these results for more general discussions concerning the empirical and theoretical motivation to adopt a probabilisitic semantic framework. (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)

After introductory reminder of and comments on Gödel’s ontological proof, we discuss the collapse of modalities, which is provable in Gödel’s ontological system GO. We argue that Gödel’s texts confirm modal collapse as intended consequence of his ontological system. Further, we aim to show that modal collapse properly fits into Gödel’s philosophical views, especially into his ontology of separation and union of force and fact, as well as into his cosmological theory of the nonobjectivity of the lapse (...) of time. As a result, modal collapse should not be conceived in Gödel so much as a deficit, but rather as a kind of the rise of modalities to the “perfect” being. We further show that, in accordance with Gödel’s ontology, the concepts of modality and time should be derived in terms of the “fundamental philosophical concept” of cause. To give an example of how a formalization of such causative Gödelian ontology and ontological proof might look, we propose the transformation of GO into a kind of causally re-interpreted justification logic. (shrink)

Ontic Structural Realism (OSR) gives ontic priority to structures over objects. In its perhaps most extreme form (captured, admittedly, by a slogan) it states that “all that there is, is structure” (da Costa and French 2003, 189). If this is true, if there is nothing but structure(s) in the world, the very idea of contrasting structure to nonstructure loses any force it might have. Actually, if the slogan is right, the very idea of characterising what there is as structure—as (...) opposed to anything else—becomes incoherent. Traditionally, characterising something as a structure has made full sense —and has served excellent scientific and philosophical purposes—precisely because structure was understood as an entity with slots, which could be occupied by objects and whose individuation-conditions involved objects only qua slot-fillers. If objects altogether go, whatever remains can be called ‘structure’ only if we take ‘structure’ to be a term of art. Well, Ontic Structuralists are happy to ‘mimic’ talk of non-structure, or objects in particular, but they hasten to add that this mimicking does not imply any serious metaphysical commitment to them. Here are a couple of characteristic passages. (shrink)

Modal intuitions are the primary source of modal knowledge but also of modal error. According to the theory of modal error in this paper, modal intuitions retain their evidential force in spite of their fallibility, and erroneous modal intuitions are in principle identifiable and eliminable by subjecting our intuitions to a priori dialectic. After an inventory of standard sources of modal error, two further sources are examined in detail. The first source - (...) namely, the failure to distinguish between metaphysical possibility and various kinds of epistemic possibility - turns out to be comparatively easy to untangle and poses little threat to intuition-driven philosophical investigation. The second source is the local misunderstanding of one's concepts . This pathology may be understood on analogy with a patient who is given a clean bill of health at his annual check-up, despite his having a cold at the time of the check-up: although the patient's health is locally disrupted, his overall health is sufficiently good to enable him to overcome the cold without external intervention. Even when our understanding of certain pivotal concepts has lapsed locally, our larger body of intuitions is sufficiently reliable to allow us, without intervention, to ferret out the modal errors resulting from this lapse of understanding by means of dialectic and/or a process of a priori reflection. This source of modal error, and our capacity to overcome it, has wide-ranging implications for philosophical method - including, in particular, its promise for disarming skepticism about the classical method of intuition-driven investigation itself. Indeed, it is shown that skeptical accounts of modal error are ultimately self-defeating. (shrink)

In recent years the doctrine of divine simplicity has become a topic of interest in the philosophical theological community. In particular, the modal collapse argument against divine simplicity has garnered various responses from proponents of divine simplicity. Some even claiming that the modal collapse argument is invalid. It is our contention that these responses have either misunderstood or misstated the argument, and have thus missed the force of the objection. Our main aim is to clarify what the (...) modal collapse argument in fact says, and explain why the recent responses do not succeed. In order to argue our case, we will proceed in several steps. First, we aim to systematically articulate the doctrine of divine simplicity. Second, articulate the Christian conviction that God is free to create any feasible world or no world at all. Third, argue that divine simplicity suffers a modal collapse and thus undermines God's freedom. Fourth, respond to potential objections to modal collapse. Fifth, we offer some concluding remarks. (shrink)

Naturalistic teleological accounts of mental content rely on an etiological theory of function. Nanay has raised a new objection to an etiological theory, and proposed an alternative theory of function that attributes modal force to claims about function. The aim of this paper is both to defend and to cast a new light on an etiological theory of function. I argue against Nanay’s “trait type individuation objection,” suggesting that an etiological theory also attributes modal force to (...) claims about function. An etiological theory of function can be thought to analyze claims about function with modal force, not relying on any theory of counterfactuals. (shrink)

This paper articulates the structure of a two species of weakly aggregative necessity in a common idiom, neighbourhood semantics, using the notion of a k-filter of propositions. A k-filter on a non-empty set I is a collection of subsets of I which contains I, is closed under supersets on I, and contains ∪{Xi ≤ Xj : 0 ≤ i < j ≤ k} whenever it contains the subsets X0,…, Xk. The mathematical content of the proof that weakly aggregative modal (...) logic is complete relative to k-ary frame theory, the standard semantic idiom for weakly aggregative modal logic is presented in language-independent terms as a representation theorem for k-filters: every non-trivial k-filter is included in the union of ≤ k non-trivial filters. The elementary theory of k-filters is developed and then applied in the form of an ultrafilter extension result for k-ary frame theory. (shrink)

Ancient Chinese philosophers were inclined to preserve the doctrine of a unified body and mind rather than to engage in a discussion on the separation of the two. In addition, most traditional Chinese philosophers stressing in particular the function of mind. Based on the tradition of believing in the concept of qi, they traced the cause of their spiritual activities to the natural effect of the qi. The modalities display a phenomenological characteristic that looks at mental activities lightly, and examines (...) language and action as a natural revelation of material force, qi. (shrink)

Recent work on the philosophy of modality has tended to pass over questions about iterated modalities in favour of constructing ambitious metaphysical theories of possibility and necessity, despite the central importance of iterated modalities to modal logic. Yet there are numerous unresolved but fundamental issues involving iterated modalities: Chandler and Salmon have provided forceful arguments against the widespread assumption that all necessary truths are necessarily necessary, for example. The current paper examines a range of ways in which one might (...) seek to identify limited regions within which some of the most well-known principles featuring iterated modalities may safely be assumed. (shrink)

Forensic authorship analysis is based on two assumptions: that every individual has a unique idiolect, and that features characteristic of that idiolect will recur with a relatively stable frequency. Yet, a speaker’s language can change with age, affective states, according to audience, or genre. Thus, studies on authorship analysis should adopt the theory that while some linguistic parameters of an idiolect can remain stable, others can change depending on various circumstances. This investigation, which takes a constructional and functional-based approach to (...) discourse-level phenomena in idiolectal stability, analyzes cross-genre data produced by nine Mexican participants throughout a twelve-year time span. This study contributes to a greater understanding of the linguistic elements that survive genre effects and are potentially useful in both investigative and evidential forensic linguistic work. We provide a detailed description of linguistic features, their specific values, and context-dependent interpretation, keeping in mind the context of expert linguistic testimony, with its preference for methods which “employ linguistically motivated analyses in combination with quantitative tools” (Solan & Tiersma, 2004, p.463). Our findings show that idiolectal style tends to remain stable across genres and communication modes in epistemic modality constructions. Epistemic markers —specifically, markers indicating low commitment by the speaker (e.g., _no sé_ ‘I don’t know’) or expressing indirectness when introducing the illocutionary force (e.g., _la verdad [es que]_ ‘the truth [is that]’)— display idiolectal stability, as these markers seem to be the most effective in terms of allowing speakers to strategically manifest the extent of their knowledge regarding what is said. (shrink)

Paul Cohen’s method of forcing, together with Saul Kripke’s related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I will discuss the (...) aspects of forcing that are useful in this respect, and some sample applications. The latter include ways of obtaining conservation results for classical and intuitionistic theories, interpreting classical theories in constructive ones, and constructivizing model-theoretic arguments. (shrink)

In Naming and Necessity, Kripke argues that intuitions about what is possible play a limited, but important, role in challenging philosophical theses, counting as evidence against them only if they cannot be reconstrued as intuitions about something else, compatible with the thesis in question. But he doesn't provide clear guidelines for determining when such intuitions have been successfully reconstrued, leading some to question their status as evidence for modal claims. In this paper I focus on some worries, articulated by (...) Michael Della Rocca, about whether modal intuitions can be evidence for claims about essential properties, and argue that there is a way of viewing the role of modal intuition in philosophical argument that can preserve their evidential force. (shrink)

In this paper I discuss, on behalf of the materialist, a consideration against the modal or conceivability argument against materialism which was first voiced in the third lecture of Naming and Necessity. This consideration is based on intertheoretic identities, statements in which both terms flanking the identity sign are theoretical. I argue that the defender of the conceivability argument has trouble to account for the appearance of contingency in those types of necessary identities. In fact, intertheoretic identities pose a (...) formidable dilemma for the defender of the modal argument and actually force the antimaterialist to say more about the semantics of theoretical terms than is implicit in standard discussions of the argument. I myself consider several options in this regard, the upshot being, however, that none of the alternative semantics for theoretical terms available to the antimaterialist is good enough to achieve the twofold aim which her modal argument requires, namely, to account for the a posteriori necessity of identities of this sort and, at the same time, to preserve her antimaterialist argument. Finally, in the last part of the paper, I argue that my defense of materialism can withstand some worries coming from David Chalmers’ recent views on a priori scrutability. (shrink)

Modality is standardly thought to come in two varieties: de dicto and de re. De re modality concerns the attribution of modal features to things or individuals, and enshrines a commitment to Aristotelian essentialism. This chapter considers how David Lewis's conception of de re modality fits into his overall metaphysics. The hypothesis is that the driving force behind his metaphysics in general, and his adherence to counterpart theory in particular, is the distinctly Humean thought that necessary connections between (...) distinct existences are literally unintelligible. Lewis's appeal to counterpart theory in his account of truthmakers is explicitly aimed at delivering a truthmaker principle that eschews necessary connections. Lewis's attitude towards several well‐rehearsed debates in contemporary ontology and the reasons underlying that attitude closely mirror Hume's incendiary verdict on "divinity and school metaphysics." Finally, de re modality is connected with his adherence to the doctrine of "Humean supervenience". (shrink)

According to relativist accounts of discourse about, e.g., epistemic possibility and matters of taste, the truth of propositions must be relativized to nonstandard parameters. This paper argues that the central thrust of such accounts should be understood independently of relative truth, in terms of a perspectival account of assertoric force. My point of departure is a stripped-down version of Brandom’s analysis of the normative structure of discursive practice. By generalizing that structure, I make room for an analogue of the (...) “assessment sensitivity” MacFarlane characterizes in terms of relative truth. I argue that my reformulation supplies a stronger rationale for the most distinctive feature of MacFarlane’s brand of relativism, its account of when speakers ought to retract assertions. Furthermore, I show that the view usually regarded as a “moderate” alternative to MacFarlane’s “radical” relativism requires the more radical deviation from an absolutist account of assertoric force. (shrink)

The primary theoretical focus of this paper is on Free Choice uses of any, in particular on two phenomena that have remained largely unstudied. One involves the ability of any phrases to occur in affirmative episodic statements when aided by suitable noun modifiers. The other involves the difference between modals of necessity and possibility with respect to licensing of any. The central thesis advanced here is that FC any is a universal determiner whose domain of quantification is not a set (...) of particular individuals but the set of possible individuals of the relevant kind. In a theory of genericity utilizing situations, an any phrase can be seen as having a universal quantifier binding the situation variable of the common noun. This inherent genericity is argued to be at the heart of the intuition that any statements support counterfactual inferences and do not involve existential commitments. A conflict in presuppositions is shown to account for the incompatibility of unmodified any phrases in affirmative episodic statements and the crucial role played by modification in ameliorating this clash is explicated. In the case of modals of necessity, the interaction between the universal force of any and the particular modal base is shown to be crucial. In view of these facts it is argued that FC any is not directly licensed by modal or generic operators as generally assumed but that its felicitous use is sensitive to the pragmatics of epistemic modality. Turning to its polarity sensitive uses, language internal as well as crosslinguistic evidence is presented to distinguish it from FC any in having the existential quantificational force typical of indefinites. The paper concludes by suggesting that the common tie between them is that they both occur in statements that apply to a class of entities, rather than to particular members of the class. (shrink)

The theme of the paper is that what is true cannot be false and conversely. This position was anticipated by Aristotle in De Interpretatione and by G. H. von Wright. The latter calls it “a truth of the logic of relative modalities.”Aristotle has been taken to task by Susan Haack and others for arguing fallaciously from the Principle of Bivalence, that every statement is either true or false, to fatalism. The implication holds, but we show that it is unreasonable to (...) assume that Aristotle grounded his argument on this implication rather than on what we call the force of truth. (shrink)

This paper presents and discusses a range of counterexamples to the common view that quantifiers cannot take scope over epistemic modals. Some of the counterexamples raise problems for ‘force modifier’ theories of epistemic modals. Some of the counterexamples raise problems for Robert Stalnaker’s theory of counterfactuals, according to which a special kind of epistemic modal must be able to scope over a whole counterfactual. Finally, some of the counterexamples suggest that David Lewis must countenance ‘would’ counterfactuals in which (...) a covert ‘would’ scopes over the whole consequent of the counterfactual, including an overt ‘might.’. (shrink)

In the propositional modal treatment of two-variable first-order logic equality is modelled by a ‘diagonal’ constant, interpreted in square products of universal frames as the identity relation. Here we study the decision problem of products of two arbitrary modal logics equipped with such a diagonal. As the presence or absence of equality in two-variable first-order logic does not influence the complexity of its satisfiability problem, one might expect that adding a diagonal to product logics in general is similarly (...) harmless. We show that this is far from being the case, and there can be quite a big jump in complexity, even from decidable to the highly undecidable. Our undecidable logics can also be viewed as new fragments of first-order logic where adding equality changes a decidable fragment to undecidable. We prove our results by a novel application of counter machine problems. While our formalism apparently cannot force reliable counter machine computations directly, the presence of a unique diagonal in the models makes it possible to encode both lossy and insertion-error computations, for the same sequence of instructions. We show that, given such a pair of faulty computations, it is then possible to reconstruct a reliable run from them. (shrink)

The theme of the paper is that what is true cannot be false and conversely. This position was anticipated by Aristotle in De Interpretatione and by G. H. von Wright. The latter calls it “a truth of the logic of relative modalities.”Aristotle has been taken to task by Susan Haack and others for arguing fallaciously from the Principle of Bivalence, that every statement is either true or false, to fatalism. The implication holds, but we show that it is unreasonable to (...) assume that Aristotle grounded his argument on this implication rather than on what we call the force of truth. (shrink)

The primary theoretical focus of this paper is on Free Choice uses of any, in particular on two phenomena that have remained largely unstudied. One involves the ability of any phrases to occur in affirmative episodic statements when aided by suitable noun modifiers. The other involves the difference between modals of necessity and possibility with respect to licensing of any. The central thesis advanced here is that FC any is a universal determiner whose domain of quantification is not a set (...) of particular individuals but the set of possible individuals of the relevant kind. In a theory of genericity utilizing situations, an any phrase can be seen as having a universal quantifier binding the situation variable of the common noun. This inherent genericity is argued to be at the heart of the intuition that any statements support counterfactual inferences and do not involve existential commitments. A conflict in presuppositions is shown to account for the incompatibility of unmodified any phrases in affirmative episodic statements and the crucial role played by modification in ameliorating this clash is explicated. In the case of modals of necessity, the interaction between the universal force of any and the particular modal base is shown to be crucial. In view of these facts it is argued that FC any is not directly licensed by modal or generic operators as generally assumed but that its felicitous use is sensitive to the pragmatics of epistemic modality. Turning to its polarity sensitive uses, language internal as well as crosslinguistic evidence is presented to distinguish it from FC any in having the existential quantificational force typical of indefinites. The paper concludes by suggesting that the common tie between them is that they both occur in statements that apply to a class of entities, rather than to particular members of the class. (shrink)

Now it cannot be denied, I think, that this argument has the appearance of being sound, that is, both true in its premises and valid in its conclusion. But one surely ought to harbor suspicions concerning an argument which establishes the most momentous of all conclusions upon nothing more than a few propositions. In this paper I shall attempt to show that these suspicions are well-founded by pointing out that the above "proof" derives whatever force it has from an (...) equivocation. (shrink)

The aim of the paper is twofold: i) to give a logically explicit formulation of a slight generalization of Quine's master argument about de re modality—an argument which imposes important constraints on modal semantics, ii) to briefly present my favored account of modal locutions (especially locutions of the de re metaphysical flavor) and show how it successfully copes with Quine's argument. Though Quine made this argument so many years ago, it is still widely misunderstood, and so careful attention (...) to detail seems warranted. From what I have seen, philosophers' attitudes towards Quine's master argument fall into two kinds: i) there are those that think that the argument has no force, because it is based on some mistake (usually, something about definite descriptions), and ii) there are those that think that the argument poses some insuperable barrier to any kind of de re modality. Neither of these attitudes is justified. So, I hope to make plain along the way that a) the original version of Quine's argument is sound, b) there is a version of this same basic argument which imposes very definite constraints on any proposed account of de re "metaphysical" modality in particular, an c) there is an account that satisfies these constraints. Part 1 of the paper is concerned with laying out and discussing three versions of Quine's argument, in the service of establishing points (a) and (b). -/- In Part 2 of the paper, I briefly sketch what I take to be a very promising, and also very Quinean account of de re modality -- one that respects the constraint on modal semantics that Quine's argument reveals and comports well with the few positive remarks Quine makes, for example, in Word and Object regarding our use of modal locutions. This will put us in a position to see that the proposed account does not fly in the face of Quine's master argument. (shrink)

Timothy Smiley has made ground-breaking contributions to modal logic, free logic, multiple-conclusion logic, and plural logic. He has illuminated Aristotle’s syllogistic, the ideas of logical form and consequence, and the distinction between assertion and rejection, and has worked to debunk the theory of descriptions. This volume brings together new articles by an international roster of leading logicians and philosophers in order to honour Smiley’s work. Their essays will be of significant interest to those working across the logical spectrum—in philosophy (...) of language, philosophical and mathematical logic, and philosophy of mathematics. (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)

Humans possess the ability to extract highly organized perceptual structures from sequences of temporal stimuli. For instance, we can organize specific rhythmical patterns into hierarchical, or metrical, systems. Despite the evidence of a fundamental influence of the motor system in achieving this skill, few studies have attempted to investigate the organization of our motor representation of rhythm. To this aim, we studied—in musicians and non-musicians—the ability to perceive and reproduce different rhythms. In a first experiment participants performed a temporal order-judgment (...) task, for rhythmical sequences presented via auditory or tactile modality. In a second experiment, they were asked to reproduce the same rhythmic sequences, while their tapping force and timing were recorded. We demonstrate that tapping force encodes the metrical aspect of the rhythm, and the strength of the coding correlates with the individual’s perceptual accuracy. We suggest that the similarity between perception and tapping-force organization indicates a common representation of rhythm, shared between the perceptual and motor systems. (shrink)

Newton began his Principia with three Axiomata sive Leges Motus. We offer an interpretation of Newton’s dual label and investigate two tensions inherent in his account of laws. The first arises from the juxtaposition of Newton’s confidence in the certainty of his laws and his commitment to their variability and contingency. The second arises because Newton ascribes fundamental status both to the laws and to the bodies and forces they govern. We argue the first is resolvable, but the second is (...) not. However, the second tension shows that Newton conceives laws as formal causes of bodies and forces. This neo-Aristotelian conception goes missing in Kantian accounts of laws, as well as accounts that stress laws’ grounding in powers and capacities. (shrink)