A modal theory Z using the Guaspari witness comparison signs $\leq, is developed. The theory Z is similar to, but weaker than, the theory R of Guaspari and Solovay. Nevertheless, Z proves the independence of the Rosser fixed-point. A Kripke semantics for Z is presented and some arithmetical interpretations of Z are investigated. Then Z is enriched to ZI by adding a new modality sign for interpretability and by axioms expressing some facts about interpretability of theories. Two arithmetical interpretations (...) of ZI are presented. The proofs of the validity of the axioms of ZI in arithmetical interpretations use some strengthening of Solovay's result about interpretability in Godel-Bernays set theory. (shrink)

In this article I argue that phenomenal intentionality fundamentally consists in a horizonality structure, rather than in a relation to a representational content or the determination of accuracy conditions. I provide a distinctive modal model of intentionality that conceives of phenomenal intentionality as the enjoyment of a plus ultra that points beyond what is actual. The directedness of intentionality on the world, thus, consists in “pointing ahead” to possibilities. The principal difficulty for the modal model is logical: the (...) most obvious way of implementing such a structure results in an analogue of Russell’s paradox. However, this paradox can be avoided by fine-tuning the modal logic deployed in this setting. This way of fine-tuning the logic ultimately amounts to intuitive benefits. For, it captures the intensional character of intentionality, since the way that our mental states refer to things is conception-dependent. Moreover, the way I interpret the modal model leads to a conception of intentionality as a feature of dynamic, diachronic patterns in the way that mental acts subjectively appear, rather than as a synchronic property. We ought to think of intentionality as fundamentally a temporal, subjective determination. In a generalization on Sellars’ approach to concepts, I hold that phenomenally intentional mental presentations involve modal laws and are inconceivable without them. (shrink)

Modal logic has been used to analyze potential infinity and potentialism more generally. However, the standard analysis breaks down in cases of divergent possibilities, where there are two or more possibilities that can be individually realized but which are jointly incompatible. This paper has three aims. First, using the intuitionistic theory of choice sequences, we motivate the need for a modal analysis of divergent potentialism and explain the challenges this involves. Then, using Beth–Kripke semantics for intuitionistic (...) logic, we overcome those challenges. Finally, we apply our modal analysis of divergent potentialism to make choice sequences comprehensible in classical terms. (shrink)

Computational systems are traditionally approached from control-oriented perspectives; however, as soon as we move from centralized to decentralized computational infrastructures, direct control needs to be replaced by distributed coordination mechanisms that are on par with institutional constructs observable in human societies (contracts, agreements, enforcement mechanisms, etc.). This paper presents a formalization of Hohfeld's framework building upon a logic whose language includes primitive operators of ability and parametric deontic operators. The proposal is meant to highlight the fundamental interaction between deontic and (...) potestative concepts and contains proofs of soundness and completeness with respect to a class of relational models. (shrink)

A general method for generating contraction- and cut-free sequent calculi for a large family of normal modal logics is presented. The method covers all modal logics characterized by Kripke frames determined by universal or geometric properties and it can be extended to treat also Gödel-Löb provability logic. The calculi provide direct decision methods through terminating proof search. Syntactic proofs of modal undefinability results are obtained in the form of conservativity theorems.

The paper outlines and immediately discusses the so-called ‘soft’ impossibility, i.e., non-logical impossibility generated by modal realism. It will be shown that although in a particular case genuine modal realism, straightforwardly applied, deems impossible a proposition that other philosophers have claimed to be (intuitively) possible, there is a variety of methodologically acceptable moves available in order to avoid the problem. The impossibility at issue is the existence of island universes. Given the Lewisian analysis there are three points (...) at which we might try to square genuine modal realism with such a controversial and problematic claim of (im)possibility, namely: a) the contraction of our pre-theoretical opinions about possibility, b) the revision of some Lewisian definitions and/or c) the extension of our ontological commitments. I shall look at each of these approaches applied to the problematic case. (shrink)

It follows from Humean principles of plenitude, I argue, that island universes are possible: physical reality might have 'absolutely isolated' parts. This makes trouble for Lewis's modal realism; but the realist has a way out. First, accept absolute actuality, which is defensible, I argue, on independent grounds. Second, revise the standard analysis of modality: modal operators are 'plural', not 'individual', quantifiers over possible worlds. This solves the problem of island universes and confers three additional benefits: an 'unqualified' (...) principle of compossibility can be accepted; the possibility of nothing can be accommodated; and the identity of indiscernible worlds can be decisively refuted. (shrink)

The passionate and staunch defence of logic of the controversial thinker Ibn Ḥazm, Abū Muḥammad ʿAlī b. Aḥmad b. Saʿīd of Córdoba (384-456/994-1064), had lasting consequences in the Islamic world. Indeed, his book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples (Kitāb al-Taqrīb li-ḥadd al-manṭiq wa-l-mudkhal ilayhi bi-l-alfāẓ al-ʿāmmiyya wa-l-amthila al-fiqhiyya), composed in 1025-1029, was well known and discussed during and after his time; and it paved the way for the studies (...) of his compatriots Ibn Bājjah (d. 1138), Ibn Ṭufayl (1185), and Ibn Rushd (1198), who each gave demonstrative reasoning a privileged place within the methods of attaining knowledge. Unfortunately, as too often in the history of science, Ibn Ḥazm’s innovative perspectives and contributions in logic have been overlooked or considered with an attitude of contempt. On the one hand, his work has been seen, at best, as promulgating the benefits of studying Aristotle’s logic, so that his contribution is assessed as more didactical than conceptual. And on the other hand, those who do examine his innovations often consider them to be mistaken. As indicated by Chejne (1984, p. 2) contempt towards the logical work of Ibn Ḥazm was also present in its reception by the Eastern philosophers who accused him of deviating from Aristotelian logic and of dabbling in things beyond his capability. However, a reassessment of his work on logic has since begun, by delving into the ways the thinker of Córdoba studied the links between deontic and modal qualification of propositions. In this context Lameer’s (2013) paper on the logical sources of Ibn Ḥazm is worth mentioning; the author (p. 417, footnote 1) observes that, although, strictly speaking, it was al-Fārābī who first drew the parallelism between deontic and modal concepts, it was Ibn Ḥazm who developed it and worked it out in a more precise manner. A primary aim of this paper is to help fill some of these gaps by stressing the role of the work of Ibn Ḥazm in developing a notion of deontic necessity deeply rooted in legal normativity, and in explicitly discussing the transference between deontic and modal concepts. According to our view; the basic units of Islamic deontic logic are what we might call, indulging in terminological anachronism, heteronomous imperatives. As it turns out, the heteronomy of imperatives within Islamic legal systems contrasts with those of the purely moral realm, which seem to be closer to an autonomous conception of moral law. There it concurs again with Leibniz’s proposal to define obligatory as “what is necessary for a good person to do”. In the present paper, we will focus on the heteronomous imperatives of legal systems rather than on the imperatives of the purely moral realm. In this context, the work of Ibn Ḥazm extends the parallelism between the necessity of events and that of human actions stressed by his predecessors. According to our understanding, Ibn Ḥazm’s parallelism can be rendered explicit formally by means of a conditional (or hypothetical) structure shared by both deontic and modal propositions. Moreover, this structure makes apparent that this parallelism displays an underlying system of “degrees”. Indeed, while in the domain of events, given some conditions, it makes sense to distinguish between an event that is more likely to happen than another. Ibn Ḥazm speaks of near and distant possibility (such as the higher degree of likelihood of rain, given the condensation of clouds in December, and its lower degree, when the condensation occurs in summer); and, in the domain of actions, the Islamic notion of weighting actions determines degrees of virtue (or of legal and moral value). So whereas the degree of virtue of performing a forbidden act as determined by the distribution of sanction and reward is 0, we obtain the same value by pondering the likelihood of an impossible event to take place. Furthermore, as discussed in section II.3.2, the system of values at work in the parallelism can be seen as opening the way to a more direct correspondence. Thus, while in the realm of nature, likelihood of occurrence of an event is dependent upon the conditions specific to the occurrence of that event; while, in the realm of jurisprudence, likelihood of performing an action is dependent upon the distribution of reward and sanction specific to that action (being that, given the choice to perform or not perform a given action, those that will be rewarded are more likely to be performed than those that are not). According to this perspective, the point of the parallelism is that both deontic and modal qualifications measure the degree of an action or event to become actual; that is – indulging once more in anachronism (but this time from the Leibnizian background) – the degree measures how feasible (facile) an action or event may be. This suggests that Ibn Ḥazm’s perspectives already herald the links to probability and possibility explored by Leibniz six centuries later – see for example Leibniz’s (1671, A VI, I, p. 424-26) use of probability in the context of conditional right. Nevertheless, it also shows a crucial difference to the approach developed in the Elementa Jura Naturalis: whereas Leibniz’s studies seek to define what is to be just or virtuous, the logical system of deontic imperatives within Islamic jurisprudence presupposes that what is to be virtuous has already been settled. Determining what is to be virtuous is not achieved by logical reasoning within the system of legal jurisprudence, but by delving into the higher objectives of the Sharīʿa. While developing our point, we will delve into the logical structure of the heteronomous imperatives. This distinguishes our contribution from the existing literature, such as the papers of Chejne (1984), Lameer (2014), and Guerrero (1997, 2010, 2014), which do not provide a logical analysis of the deontic concepts put into work by Ibn Ḥazm. The true antecedent to the present paper is the work of Farid Zidani (2007, 2015), who, so far as we know, was the first to undertake such a task. Some of our own developments and general epistemological thoughts go beyond Ibn Ḥazm’s framework and motivations; mainly those contained in sections II.3.2 and IV. However, according to our view, these reflections suggest that Ibn Ḥazm’s approach has the substance for a broader and deeper exploration of the logic of norms. The paper is structured as follows:I.Ibn Ḥazm’s Logic of Heteronomous Imperatives. After presenting some extracts of the relevant text, we proceed by providing a formal reconstruction of the five forms of deontic modalities. II. A Landmark in the History of the Logical Analysis of Norms. Duties and Modalities. In this section, we study the transferences from deontic to modal necessity and possibility. We briefly compare the deontic system of Islamic Jurisprudence with that of Leibniz.III. Leibniz and Hypothetical Imperatives in Law.IV. Beyond Ibn Ḥazm: Conclusions and the Work Ahead. We will conclude the paper by discussing briefly some conceptual points that distinguish the logic of heteronomous imperatives from contemporary deontic logic. Our final words will discuss deontic-modal parallelism in the context of Ibn Ḥazm’s rejection of reasoning by conjecture and what we call “the internalization of nature.”. (shrink)

We offer an analysis of future morphemes as epistemic operators. The main empirical motivation comes from the fact that future morphemes have systematic purely epistemic readings—not only in Greek and Italian, but also in Dutch, German, and English will. The existence of epistemic readings suggests that the future expressions quantify over epistemic, not metaphysical alternatives. We provide a unified analysis for epistemic and predictive readings as epistemic necessity, and the shift between the two is determined compositionally by the (...) lower tense. Our account thus acknowledges a systematic interaction between modality and tense—but the future itself is a pure modal, not a mixed temporal/modal operator. We show that the modal base of the future is nonveridical, i.e. it includes p and ¬p worlds, parallel to epistemic modals such as must, and present arguments that future morphemes are a category that stands in between epistemic modals and predicates of personal taste. We identify, finally, a subclass of epistemic futures which are ratificational, and argue that will is a member of this class. (shrink)

Theories of possible worlds abound. Since the introduction of modal logic, the term of a possible world, and the very nature of an entity denoted by the term, have stood on the top of metaphysical inquiries. A possible world, roughly speaking, is a complete way things could have been. On the face of it, whatever is possible takes place in some possible world, and whatever is not possible, does not. The aim of the present book is to argue that (...) even impossible things happen. By taking David Lewis’s Modal Realism (henceforth as “MR”) seriously, I claim that besides infinitely many concrete ways things could have been, there exist ways things could not have been. I call them concrete impossible worlds. In Chapter I, I outline Lewis’s well-defined conception of philosophical analysis. I present its structure, aims, methodology and criteria for success. Besides the virtues of the Lewisian conception, I point out several limitations the theory has and offer very simple solution: the admission of concrete impossible worlds. In Chapter II, I present a version of an epistemological objection against MR and a positive account in favour of Modal Fictionalism (henceforth as “MF”). I then present the puzzle in this matter and attempt to generalise my point. 9 Introduction Chapter III demonstrates how flexible Lewis’s theory is. I consider a putative impossibility of there being island universes – spatiotemporally disjoint spacetimes – and show what a proponent of modal realism can do in order to account for it. I present three possible moves: a revision of our pre-theoretical opinions, a modification of our definitions and, finally, an ex- tension of our metaphysical commitments. I consider two ersatz theories of impossible worlds in Chapter IV. In particular, I scrutinize Franz Berto’s and Edwin Mares’s (hybrid) theories of MR. Although I admit that the theories radically extend the scope of applications of MR without extending its metaphysical commitments, the approaches do have some limits. Finally, in Chapter V, I present Extended Modal Realism (henceforth EMR), a theory according to which the best way to go in order to account for impossible phenomena is to ex- tend our metaphysical base by genuine impossibilia. I try to (at least) weaken, if not meet, the crucial objections to the proposal. Namely, I challenge the proclaimed universality of classical logic and, subsequently, motivate certain kind of paraconsistent approach to modal reality. Although the consequences are very hard to swallow, I argue that it is because of the fact that we are unsure of our pre-theoretical opinions concerning the impossible. (shrink)

We use a mechanized verification system, PVS, to examine the argument from Anselm’s Proslogion Chapter III, the so-called “Modal Ontological Argument.” We consider several published formalizations for the argument and show they are all essentially similar. Furthermore, we show that the argument is trivial once the modal axioms are taken into account. This work is an illustration of Computational Philiosophy and, in addition, shows how these methods can help detect and rectify errors in modal reasoning.

Some argue that Lewisian realism fails as a reduction of modality because in order to meet some criterion of success the account needs to invoke primitive modality. I defend Lewisian realism against this charge; in the process, I hope to shed some light on the conditions of success for a reduction. In §1 I detail the resources the Lewisian modal realist needs. In §2 I argue against Lycan and Shalkowski’s charge that Lewis needs a modal notion of ‘world’ (...) to ensure that worlds correspond to possibilities. In §3 I respond to Divers and Melia’s objection that Lewis needs to invoke primitive modality to give a complete account of what worlds there are. In §4 I ask what it is for a notion to ‘involve’ modality. I conclude that the question is either in bad standing or at best offers little traction on the debate, and propose a different way of assessing when materials are appropriately included in a reductive base. (shrink)

Inquiry into the metaphysics of essence tends to be pursued in a realist and model-theoretic spirit, in the sense that metaphysical vocabulary is used in a metalanguage to model truth conditions for the object-language use of essentialist vocabulary. This essay adapts recent developments in proof-theoretic semantics to provide a nominalist analysis for a variety of essentialist vocabularies. A metalanguage employing explanatory inferences is used to individuate introduction and elimination rules for atomic sentences. The object-language assertions of sentences concerning essences (...) are then interpreted as devices for marking off structural features of the explanatory inferences that, under a given interpretation, constitute the contents of the atoms of the language. On this proposal, object-language essentialist vocabulary is mentioned in a proof-theoretic metalanguage that uses a vocabulary of explanation. The result is a nominalist interpretation of essence as a modality, understood in the grammatical sense as a modification of the copula, and a view of metaphysical inquiry that is closely connected to the explanatory commitments present in first-order inquiry into things like sets, chemicals, and organisms. This result illustrates that some of the presuppositions that have animated analytic metaphysics over the last few decades can be profitably substituted with more practice-oriented conceptions of the forms of reasoning at work in different domains of human knowledge. (shrink)

Discussions on the concept of Marifatullah as the foundation of belief hold a significant place in theology. There are different opinions among schools of theology regarding whether those who do not receive divine messages must know God. The majority of scholars belonging to the Mu'tazila and Māturīdī schools, including Imam Māturīdī, state that human beings must know God. Although al-Ashʿarī accepts that the most prominent obligatory duties are the methods of reasoning that lead to marifatullah, he states that responsibility in (...) this matter is formed by transmission. However, we can say that whether the human mind is sufficient to reach the knowledge of God, the method of reasoning has reached a different dimension today from the sciences of psychology, genetics, and neurobiology. This study explored whether individuals can achieve marifatullah from a holistic perspective. Whether human beings can be held responsible for this issue has been evaluated through the sciences of psychology, genetics, and neurobiology, and the opinions of schools of theology on this issue have been criticized. When we think in terms of Marifatullah, we can say that man’s psychological sense of obligation to adapt to society leaves him intellectually under the influence of society. In terms of genetic determinism, human personality, behavior, and intellectual adventure are completely determined by genes. Therefore, it is impossible for men to reach marifatullah in the context of their mental abilities. From an epigenetic perspective, we see that human thought structure, behavior, and personality are formed as a result of interactions with the environment. Serious hesitation arises in this idea in terms of intellect being a source of responsibility. Humans are genetically influenced by the environment and society, and they have a suitable nature for this, revealing that their genetic structure is open to environmental influences. In terms of brain plasticity, factors such as the society, environment, and family in which people live can change their brains and enable them to live accordingly. Although life adventures appear to be within the framework of social harmony, there must also be intellectual and religious harmony within social harmony. This reinforces the idea that individuals tend to align more with the thoughts and beliefs instilled by culture given the adaptable nature of the human brain influenced by cultural factors. When the views of the schools of theology are considered considering these evaluations, it becomes clear that the Mu'tazilites and Māturīdīs' belief that the source of the wujūb of marifatullah is intellect is at a point that needs to be reconsidered in terms of human biology and psychology. Although the Asharites emphasize human beings attaining knowledge of God through intellect, their focus on prophethood indicates that a revelation offer appears more accurate concerning human nature in the context of Marifatullah. (shrink)

Superlative adjectives accompanied by certain modal adjectives like possible (e.g. John bought the largest possible present) are ambiguous between a reading where possible is a regular noun modifier and a reading paraphrasable as ‘as Adj as possible’, called ‘modal superlative reading’. Three interesting restrictions have been observed in the literature. First, possible and some other adjectives ending in -able, but not potential and probable, support the latter reading. Second, when the modal adjective appears postnominally, only the (...) class='Hi'>modal superlative reading is available. Third, prenominal possible needs to be in a local configuration to -est in order for the modal superlative reading to arise. Using LF structures independently motivated for degree constructions, the present paper develops a compositional semantic analysis of the modal superlative reading, makes correct new predictions concerning this reading, and—by reconciling previous, opposed syntactic analyses—allows us to derive the three empirical restrictions above. The key innovations are: (i) the previously proposed constituent [possible ▲ellipsis] is interpreted as an amount relative clause, and (ii) this constituent is treated as overtly expressing the comparison class argument of -est. (shrink)

According to Thagard and Stewart :1–33, 2011), creativity results from the combination of neural representations, and combination results from convolution, an operation on vectors defined in the holographic reduced representation framework. They use these ideas to understand creativity as it occurs in many domains, and in particular in science. We argue that, because of its algebraic properties, convolution alone is ill-suited to the role proposed by Thagard and Stewart. The semantic pointer concept allows us to see how we can apply (...) the full range of HRR operations while keeping the modal representations so central to Thagard and Stewart’s theory. By adding another combination operation and using semantic pointers as the combinatorial basis, this modified version overcomes the limitations of the original theory and perhaps helps us explain aspects of creativity not covered by the original theory. While a priori reasons cast doubts on the use of HRR operations with modal representations :5039–5054, 1987) such as semantic pointers, recent models point in the other direction, allowing us to be optimistic about the success of the revised version. (shrink)

We do a quantitative analysis of modal logic. For example, for each Kripke structure M, we study the least ordinal μ such that for each state of M, the beliefs of up to level μ characterize the agents' beliefs (that is, there is only one way to extend these beliefs to higher levels). As another example, we show the equivalence of three conditions, that on the face of it look quite different, for what it means to say that (...) the agents' beliefs have a countable description, or putting it another way, have a "countable amount of information". The first condition says that the beliefs of the agents are those at a state of a countable Kripke structure. The second condition says that the beliefs of the agents can be described in an infinitary language, where conjunctions of arbitrary countable sets of formulas are allowed. The third condition says that countably many levels of belief are sufficient to capture all of the uncertainty of the agents (along with a technical condition). The fact that all of these conditions are equivalent shows the robustness of the concept of the agents' beliefs having a "countable description". (shrink)

A proper understanding of agentive modals promises to clarify issues to do with free will, know how, and other philosophically interesting topics. In this paper I identify one constraint on, and one structural feature of, trying-based versions of the conditional analysis of the agentive modals. I suggest that the constraint and structural feature together provide a novel account of why the famous Lehrer-Chisholm objection to conditional analyses of ability modals is so powerful. I argue that Mandelkern et al.’s ‘Agentive (...) Modals’ (Philosophical Review,126/3, 301–343, 2017) conditional analysis of the agentive modals fails to avoid this problem. I also identify two further problems for their account. I close by summarising a number of criteria which any successful semantic analysis of the agentive modals should satisfy. (shrink)

The Semantic-Pragmatic Analysis of Persian Modal Verbs Based on Papafragou's Model This paper aims at analyzing the semantics and pragmatics of Persian modal verbs based on Papafragou's relevance-theoretic model. Persian modals are defined in terms of logical relations and propositional domains. According to the findings of the research, two of the three modals, namely, šodan and tavân express the logical relation of compatibility with respect to different propositional domains: the three forms mišavad, mišod and mišode are unspecified (...) with respect to their propositional domains and take them directly from the context, whereas betavân and bešavad accept the desirability domain. Mitavân also expresses compatibility in relation to the propositions in the factual domain. However, bˇyad is the only modal that encodes the logical relation of entailment and is unspecified with respect to the type of propositional domain it accepts. (shrink)

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

Three variants of Kurt Gödel's ontological argument, proposed by Dana Scott, C. Anthony Anderson and Melvin Fitting, are encoded and rigorously assessed on the computer. In contrast to Scott's version of Gödel's argument the two variants contributed by Anderson and Fitting avoid modal collapse. Although they appear quite different on a cursory reading they are in fact closely related. This has been revealed in the computer-supported formal analysis presented in this article. Key to our formal analysis is (...) the utilization of suitably adapted notions of ultrafilters, and a careful distinction between extensions and intensions of positive properties. (shrink)

According to the modal view, essence admits of reductive analysis in exclusively modal terms. Fine (1994) argues that modal view delivers an inadequate analysis of essence. This paper defends the modal view from Fine's challenge. This defense proceeds by examining the disagreement between Finean primitivists and Quinean eliminativists about essence. In order to model this disagreement, a distinction between essence and a separable concept, nature, is required. This distinction is then used to show that (...) Fine's challenge is misdirected and therefore unsuccessful. (shrink)

According to Thagard and Stewart :1–33, 2011), creativity results from the combination of neural representations, and combination results from convolution, an operation on vectors defined in the holographic reduced representation framework. They use these ideas to understand creativity as it occurs in many domains, and in particular in science. We argue that, because of its algebraic properties, convolution alone is ill-suited to the role proposed by Thagard and Stewart. The semantic pointer concept allows us to see how we can apply (...) the full range of HRR operations while keeping the modal representations so central to Thagard and Stewart’s theory. By adding another combination operation and using semantic pointers as the combinatorial basis, this modified version overcomes the limitations of the original theory and perhaps helps us explain aspects of creativity not covered by the original theory. While a priori reasons cast doubts on the use of HRR operations with modal representations :5039–5054, 1987) such as semantic pointers, recent models point in the other direction, allowing us to be optimistic about the success of the revised version. (shrink)

This essay proposes a new theory of agentive modals: ability modals and their duals, compulsion modals. After criticizing existing approaches—the existential quantificational analysis, the universal quantificational analysis, and the conditional analysis—it presents a new account that builds on both the existential and conditional analyses. On this account, the act conditional analysis, a sentence like ‘John can swim across the river’ says that there is some practically available action that is such that if John tries to do (...) it, he swims across the river. The essay argues that the act conditional analysis avoids the problems faced by existing accounts of agentive modality and shows how the act conditional analysis can be extended to an account of generic agentive modal claims. The upshot is a new vantage point on the role of agentive modal ascriptions in practical discourse: ability ascriptions serve as a kind of hypothetical guarantee, and compulsion ascriptions as a kind of nonhypothetical guarantee. (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)

In philosophical logic necessity is usually conceived as a sentential operator rather than as a predicate. An intensional sentential operator does not allow one to express quantified statements such as 'There are necessary a posteriori propositions' or 'All laws of physics are necessary' in first-order logic in a straightforward way, while they are readily formalized if necessity is formalized by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one to reject (...) many philosophical accounts involving necessity that are based on the use of operator modal logic. We argue that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate 'is necessary' can then be replaced by 'is necessarily true'. We prove a result showing that this substitution is technically feasible. To this end we provide partial possible-worlds semantics for the language with a predicate of necessity and perform the reduction of necessities to necessary truths. The technique applies also to many other intensional notions that have been analysed by means of modal operators. (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)

In the presentation I will analyse Kant’s conception of modalities and consider its relevance to his critical metaphysics. With his Tables of Judgements and of Categories Kant makes an important division between two kinds of modality, of which the former is only logical and the latter transcendental, i.e., objective. Only judgements that are necessary in both ways are properly metaphysical. This distinction is important for Kant’s distinction between Transcendental Analytic and Transcendental Dialectic, i.e., between acceptable and unacceptable metaphysics. I submit (...) that not only is Kant’s theory of modality useful for properly understanding his arguments in the Dialectic, but that only by distinguishing between the two types of modality can one can make sense of his theory that the ideas of reason are simultaneously inevitable and erroneous. This modal analysis thus offers a new and important point of view to Kant’s metaphysics and its critique. (shrink)

In this paper, we consider recent attempts to metaphysically explain agentive modality in terms of conditionals. We suggest that the best recent accounts face counterexamples, and more worryingly, they take some agentive modality for granted. In particular, the ability to perform basic actions features as a primitive in these theories. While it is perfectly acceptable for a semantics of agentive modal claims to take some modality for granted in getting the extension of action claims correct, a metaphysical explanation of (...) agentive modality cannot, at least not in the way that conditional approaches to agentive modality do. We argue that this problem was present even in the classical conditional analysis. By a pessimistic induction, we suggest that, probably, no conditional approach to agentive modality will succeed. (shrink)

The first edition, published by Acumen in 2000, became a prescribed textbook on modal logic courses. The second edition has been fully revised in response to readers' suggestions, including two new chapters on conditional logic, which was not covered in the first edition. "Modal Logics and Philosophy" is a fully comprehensive introduction to modal logics and their application suitable for course use. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, (...) "Modal Logics and Philosophy" places its emphasis firmly on showing how useful modal logic can be as a tool for formal philosophical analysis. In part 1 of the book, the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, obligation and permission. (shrink)

Modal logic has been applied in many different areas, as reasoning about time, knowledge and belief, necessity and possibility, to mention only some examples. In the present paper, an attempt is made to use modal logic to account for the semantics of theoretical sentences in scientific language. Theoretical sentences have been studied extensively since the work of Ramsey and Carnap. The present attempt at a modal analysis is motivated by there being several intended interpretations of the (...) theoretical terms once these terms are introduced through the axioms of a theory. (shrink)

We show in this paper that some expressions indicating source of evidence are part of propositional content and are best analyzed as special kind of epistemic modal. Our evidence comes from the Japanese evidential system. We consider six evidentials in Japanese, showing that they can be embedded in conditionals and under modals and that their properties with respect to modal subordination are similar to those of ordinary modals. We show that these facts are difficult for existing theories of (...) evidentials, which assign evidentials necessarily widest scope, to explain. We then provide an analysis using a logical system designed to account for evidential reasoning; this logic is the first developed system of probabilistic dynamic predicate logic. This analysis is shown to account for the data we provide that is problematic for other theories. (shrink)

We discuss the semantic significance of a puzzle concerning ‘ought’ and conditionals recently discussed by Kolodny and MacFarlane. We argue that the puzzle is problematic for the standard Kratzer-style analysis of modality. In Kratzer’s semantics, modals are evaluated relative to a pair of conversational backgrounds. We show that there is no sensible way of assigning values to these conversational backgrounds so as to derive all of the intuitions in Kolodny and MacFarlane’s case. We show that the appropriate verdicts can (...) be derived by extending Kratzer’s framework to feature a third conversational background and claiming that the relevant reading of ‘ought’ is sensitive to this parameter. (shrink)