This paper develops an account of the meaning of `ought', and the distinction between weak necessity modals (`ought', `should') and strong necessity modals (`must', `have to'). I argue that there is nothing specially ``strong'' about strong necessity modals per se: uses of `Must p' predicate the (deontic/epistemic/etc.) necessity of the prejacent p of the actual world (evaluation world). The apparent ``weakness'' of weak necessity modals derives from their bracketing whether (...) the necessity of the prejacent is verified in the actual world. `Ought p' can be accepted without needing to settle that the relevant considerations (norms, expectations, etc.) that actually apply verify the necessity of p. I call the basic account a modal-past approach to the weak/strong necessity modal distinction (for reasons that become evident). Several ways of implementing the approach in the formal semantics/pragmatics are critically examined. The account systematizes a wide range of linguistic phenomena: it generalizes across flavors of modality; it elucidates a special role that weak necessity modals play in discourse and planning; it captures contrasting logical, expressive, and illocutionary properties of weak and strong necessity modals; and it sheds light on how a notion of `ought' is often expressed in other languages. These phenomena have resisted systematic explanation. In closing I briefly consider how linguistic inquiry into differences among necessity modals may improve theorizing on broader philosophical issues. (shrink)

1 This paper has been presented at the workshop “Time and Modality: A Round Table on Tense, Mood, and Modality”, Paris, December 2005, at a CUNY linguistics colloquium in May 2006, and at the 6th Workshop on Formal Linguistics in Florian´opolis, Brazil, August 2006. We thank the audiences at those presentations, in particular Orin Percus, Tim Stowell, Marcel den Dikken, Anna Szabolcsi, Chris Warnasch, Roberta Pires de Oliveira, Renato Miguel Basso, and Ana M¨uller. We thank Noam Chomsky, Cleo Condoravdi, and (...) Irene Heim for very helpful conversations about this material. We thank Bridget Copley for sharing with us her recent manuscript “What Should Should.. (shrink)

Kolodny and MacFarlane have made a pioneering contribution to our understanding of how the interpretation of deontic modals can be sensitive to evidence and information. But integrating the discussion of information-sensitivity into the standard Kratzerian framework for modals suggests ways of capturing the relevant data without treating deontic modals as “informational modals” in their sense. I show that though one such way of capturing the data within the standard semantics fails, an alternative does not. Nevertheless I (...) argue that we have good reasons to adopt an information-sensitive semantics of the general type Kolodny and MacFarlane describe. Contrary to the standard semantics, relative deontic value between possibilities sometimes depends on which possibilities are live. I develop an ordering semantics for deontic modals that captures this point and addresses various complications introduced by integrating the discussion of information-sensitivity into the standard semantic framework. By attending to these complexities, we can also illuminate various roles that information and evidence play in logical arguments, discourse, and deliberation. (shrink)

A prevailing thought is that generics have a covert modal operator at logical form. I claim that if this is right, the covert generic modality is a weak necessity modal. In this paper, I pr...

A possible world semantics for standard modal languages is presented, where the valuation functions are allowed to be partial, the truth--functional connectives are interpreted according to weak Kleene matrices, and the necessity operator is given a "weak" interpretation. Completeness and incompleteness results for some (axiomatic) systems are then established. Extensions of these modal logics in which figure "statability" operators are also examined.

A possible world semantics for standard modal languages is presented, where the valuation functions are allowed to be partial, the truth–functional connectives are interpreted according to weak Kleene matrices, and the necessity operator is given a “weak” interpretation. Completeness and incompleteness results for some (axiomatic) systems are then established. Extensions of these modal logics in which figure “statability” operators are also examined.

We consider a version of so called T x W logic for historical necessity in the sense of R.H. Thomason (1984), which is somewhat special in three respects: (i) it is explicitly based on two-dimensional modal logic in the sense of Segerberg (1973); (ii) for reasons of applicability to interesting fields of philosophical logic, it conceives of time as being discrete and finite in the sense of having a beginning and an end; and (iii) it utilizes the technique of (...) systematic frame constants in order to handle the problem of irreflexivity in tense logics, well known since Gabbay (1981). Axiomatizations are given for two infinite hierarchies of two-dimensional modal tense logics, one without and one with the characteristic operators for historical necessity and possibility. Strong and weak completeness results are obtained for both hierarchies as well as a result to the effect that two approaches to their semantics are equivalent, much in the spirit of Di Maio and Zanardo (1996) and von Kutschera (1997). (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)

In this paper I argue that there are some sentences whose truth makes no demands on the world, being trivially true in that their truth-conditions are trivially met. I argue that this does not amount to their truth-conditions being met necessarily: we need a non-modal understanding of the notion of the demands the truth of a sentence makes, lest we be blinded to certain conceptual possibilities. I defend the claim that the truths of pure mathematics and set theory are trivially (...) true, and hence accepting their truth brings no ontological commitment; I further defend the claim that the truths of applied mathematics and set theory do not demand the existence of numbers or sets. While the notion of a demand must not be reduced to anything modal, I nonetheless argue that sentences that are trivially true must also be necessary, lest we violate a very weak version of the principle that truth depends on the world. I further argue that all necessary truths are trivially true, lest we admit unexplained necessities. I end by showing one important consequence of this: I argue that if there are truthmakers for intrinsic predications, they must be states of affairs rather than tropes. (shrink)

The logics of the modal operators and of the quantifiers show striking analogies. The analogies are so extensive that, when a special class of entities (possible worlds) is postulated, natural and non-arbitrary translation procedures can be defined from the language with the modal operators into a purely quantificational one, under which the necessity and possibility operators translate into universal and existential quantifiers. In view of this I would be willing to classify the modal operators as ‘disguised’ quantifiers, and I (...) think that wholehearted acceptance of modal language should be considered to carry ontological commitment to something like possible worldsConsidered as two languages for describing the same subject matter, modal and purely quantificational languages show interesting differences. The operator variables of the purely quantificational languages give them more power than the modal languages, but at least some of the functions performed by the apparatus of operator variables are also performed, in a more primitive and less versatile way, by actuality operators in modal languages.A final note. Quine has written much on the inter-relations of quantifiers, identity, and the concept of existence. These, he holds, form a tightly knit conceptual system which has been evolved to a high point of perfection, but which might conceivably change yet further.29 He has also dropped hints about the possibility of a simpler, primitive or defective version of the system, in which the quantifiers are not backed up in their accustomed way by the concept of identity. He has dubbed the resulting concept a ‘pre-individuative’ concept of existence, or a concept of ‘entity without identity.’ What would a pre-individuative concept of existence be like? Quine has sometimes suggested that one might be embodied in the use of mass nouns, but the identity concept is used in connection with stuff as well as with things: “is that the same coffee that was in the cup last night?” I would submit that modality provides a better case. In view of the comparative weakness of modal languages, compared to the explicitly quantificational ones Quine takes as canonical, there is surely a sense in which the concept of existence embodied in that disguised existential quantifier, the possibility operator, is a defective one. And as we have seen, one of the differences between modal operators and explicit quantifiers is that modal operators cannot be joined with the identity predicate in the way quantifiers with operator variables can. Surely, then, there is a sense in which ordinary speech, as opposed to the metaphysical theorizing of a Leibniz or a David Lewis, conceives of possible worlds as entities without identity. (shrink)

In conclusion, then, the notion of temporal necessity is certainly queer and perhaps a misnomer. It really has little to do with temporality per se and everything to do with counterfactual openness or closedness. We have seen that the future is as unalterable as the past, but that this purely logical truth is not antithetical to freedom or contingency. Moreover, we have found certain past facts are counterfactually open in that were future events or actualities to be other than (...) they will be, these past facts would have been different as a consequence. God's beliefs about the future are such past facts. Moreover, the effects of actions which God would have taken had He believed differently are also such past facts. Oddly enough, then, virtually any past fact is potentially counterfactually open, and the only necessity that remains is purely de facto. We, of course, do not in general know which events of the past depend counterfactually on present actions, and those cases we do know about seem rather trivial. Our intuitions of the necessity, unalterability, and unpreventability of the past as opposed to the future stem from the impossibility of backward causation, which is precluded by the dynamic nature of time and becoming. But the counterfactual dependence of God's beliefs on future events or actualities is not a case of backward causation: rather future-tense propositions are true in virtue of what will happen, given a view of truth as correspondence, and God simply has the essential property of knowing all and only true propositions. With regard to the future, virtually all facts are counterfactually open, and therefore future-tense propositions are not temporally necessary. Propositions thus move from being temporally contingent to being temporally necessary when all the opportunities to affect things counterfactually have slipped by. Hence, the mere fact that an event is past is no indication that it is counterfactually closed. This is especially evident in the case of God's foreknowledge. If we say that God foreknows that I shall do x and therefore I cannot refrain from doing x, lest I change God's past foreknowledge, we are being deceived by a modality which has nothing to do with my power or freedom. All that is impossible is the conjunction of God's foreknowledge that p and of ~ p; but this modality in sensu composito has no bearing on my ability to act such that ~ p would be true and God would have foreknown differently. Temporal necessity, then, turns out to be only obliquely temporal and modally weak, certainly no threat to freedom or divine foreknowledge. (shrink)

Modal Platonism utilizes "weak" logical possibility, such that it is logically possible there are abstract entities, and logically possible there are none. Modal Platonism also utilizes a non-indexical actuality operator. Modal Platonism is the EASY WAY, neither reductionist nor eliminativist, but embracing the Platonistic language of abstract entities while eliminating ontological commitment to them. Statement of Modal Platonism. Any consistent statement B ontologically committed to abstract entities may be replaced by an empirically equivalent modalization, MOD(B), not so ontologically committed. (...) This equivalence is provable using Modal/Actuality Logic S5@. Let MAX be a strong set theory with individuals. Then the following Schematic Bombshell Result (SBR) can be shown: MAX logically yields [T is true if and only if MOD(T) is true], for scientific theories T. The proof utilizes Stephen Neale's clever model-theoretic interpretation of Quantified Lewis S5, which I extend to S5@. (shrink)

As we’ve seen in the last chapter, there is good linguistic reason to categorize negations (and negative operators in general) by which De Morgan laws they support. The weakest negative operators (merely downward monotonic) support only two De Morgan laws;1 medium-strength negative operators support a third;2 and strong negative operators support all four. As we’ve also seen, techniques familiar from modal logic are of great use in giving unifying theories of negative operators. In particular, Dunn’s (1990) distributoid theory allows us (...) to generate relational semantics for many negations. However, the requirements of distributoid theory are a bit too strict for use in modeling the weakest negations. For a relational semantics to work, an operator must either distribute or antidistribute over either conjunction or disjunction; but the merely downward monotonic operators do not. Thus, a unifying semantics cannot be had in distributoid theory. In the (more familiar) study of positive modalities, there is a parallel result. Normal necessities distribute over conjunction, and normal possibilities over disjunction. When these distributions break down, a relational semantics is no longer appropriate. Here, there is a somewhat familiar solution: neighborhood semantics. In this chapter, I’ll adapt neighborhood semantics to the less familiar case of negative modalities, showing how it can be used to give a single semantic framework appropriate to all the pertinent sorts of negative operators. (shrink)

In the first chapter I have introduced Carnapian intensional logic against the background of Frege's and Quine's puzzles. The main body of the dissertation consists of two parts. In the first part I discussed Carnapian modal logic and arithmetic with descriptions. In the second chapter, I have described three Carnapian theories, CCL, CFL, and CNL. All three theories have three things in common. First, they are formulated in languages containing description terms. Second, they contain a system of modal logic. Third, (...) they do not contain the unrestricted classical substitution principle, but they do contain the classical substitution principle restricted to non-modal formulas and the Carnapian substitution principle, which says that two terms can be substituted salva veritate if they are necessarily coreferential. There are two major differences between the three theories. First, CCL and CFL allow universal instantiation with description terms, whereas CNL does not. Moreover, the quantificational theory of the CCL is classical, whereas the quantificational theory of CFL is a free logic. Another difference is that CCL and CFL contain different description principles. Most importantly, the description principle of CCL ensures that even improper descriptions have a denotation, whereas the description principle of CFL does not guarantee this. CNL does not have a description principle. In the third chapter, I have studied collapse arguments for CCL, CFL, and CNL. A collapse argument is an argument for the following statement: if p is true, then it is necessarily true. A crucial role in the proofs of these collapse results was played by so-called self-predication principles, which say that under certain conditions the predicate that expresses the descriptive condition can be combined by the description term formed out of that predicate with the result being a true sentence. In this chapter I have discussed a collapse argument for the extension of CCL with a self-predication principle, I have given a collapse argument for a similarly extended CFL, and most importantly, I have given a collapse argument for the extension of CNL with a self- predication principle. Finally, I have argued that the relevant self-predication principles are unsound under a Carnapian interpretation. In the fourth chapter, I have studied the extension of Peano Arithmetic with a Carnapian modal logic C, which is a dummy letter standing for either CCL or CFL. One can prove that the principle of the necessity of identity is a theorem of CPA. This implies that one gets a collapse result for CPA. The standard principle of weak induction was crucial for the proof. One can also prove that, if one assumes a particular self-predication principle, and if one assumes the principle of strong induction or, equivalently, the least-number principle, then one gets a partial collapse of de re modal truths in de dicto modal truths. I have argued that, if the box operator is interpreted as a metaphysical necessity operator, then Platonists would not be inimical to the collapse result. But if CPA is extended with a physical theory, then there is a threat that physical truths become physical necessiti es. It was shown that, under a Carnapian interpretation, the standard principle of weak induction is unsound, and that it can be replaced by a Carnapian principle of weak induction that is sound. The problem of logical and mathematical omniscience prevents ordinary Carnapian intensional logic from being taken seriously as a logic adequate for describing the principles of demonstrability. Yet many of the proof-theoretic results of the first part carry over to the part on Carnapian epistemic arithmetic with descriptions, since proof-theoretic results are independent of the informal reading of the operators. In the fifth chapter, I looked at extensions of arithmetic with a modal logic in which the box operator is interpreted as a demonstrability operator. A first extension in that sense is Shapiro s Epistemic Arithmetic. Shapiro himself offered the problem of mathematical omniscience as a reason why it is difficult to find a model theory for EA. Horsten attempted to provide a model theory via the detour of Modal-Epistemic Arithmetic. The attention of the reader was drawn to an incoherence in the model theory of. Two alternative solutions were presented and, after a short discussion of the problem of de re demonstrability one of those alternatives was chosen. The discussion of the problem of de re demonstrability made it clear that it would be interesting to study the epistemic properties of notation systems. Horsten himself provided a framework for this, viz. Carnapian Epistemic Arithmetic, and he started a systematic study of the epistemic properties of notation systems within that framework. However, he did not provide non-trivial but adequate models. To make a start with solving the problem of finding good models for CEA, I introduced Carnapian Modal-Epistemic Arithmetic In constructing CMEA I incorporated the lesson about the principle of weak induction learnt in the fourth chapter. In the sixth chapter, I gave a critical assessment of an argument concerning the limits of de re demonstrability about the natural numbers. The conclusion of the Description Argument is that it is undemonstrable that there is a natural number that has a certain property but of which it is undemonstrable that it has that property. A crucial step in the Description Argument involved a self-predication principle. Making good use of one of the results obtained in the third chapter, I proved a collapse result for the background theory against which the Description Argument was formulated. I concluded that either the either the Description Argument is sound but its conclusion is trivial, o r the Description Argument is unsound, or it is a cheapshot. As an appendix I included an article co-authored by prof. dr. Leon Horsten and me. The topic of the article is indirectly related to some other topics investigated in my dissertation. Also, it backs up one of the addition al theses I might be asked to publicly defend during my doctoral exam. T he topic of the appendix is the set of the so-called paradoxes of strict implication. Jonathan Lowe has argued that a particular variation on C.I. Lewis notion of strict implication avoids the paradoxes of strict implication. Pace Lowe, it is argued that Lowe s notion of implication does not achieve this aim. Moreover, a general argument is offered to the effect that no other variation on Lewis notion of constantly strict implication describes the logical behaviour of natural language conditional s in a satisfactory way. (shrink)

According to deontological approaches to justification, we can analyze justification in deontic terms. In this paper, I try to advance the discussion of deontological approaches by applying recent insights in the semantics of deontic modals. Specifically, I use the distinction between weak necessity modals and strong necessity modals to make progress on a question that has received surprisingly little discussion in the literature, namely: ‘What’s the best version of a deontological approach?’ The two most (...) obvious hypotheses are the Permissive View, according to which justified expresses permission, and the Obligatory View, according to which justified expresses some species of obligation. I raise difficulties for both of these hypotheses. In light of these difficulties, I propose a new position, according to which justified expresses a property I call faultlessness, defined as the dual of weak necessity modals. According to this view, an agent is justified in phi-ing iff it’s not the case that she should [/ought] not phi. I argue that this ‘Faultlessness View’ gives us precisely what’s needed to avoid the problems facing the Permissive and Obligatory Views. (shrink)

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

Available from UMI in association with The British Library. Requires signed TDF. ;Two elements in Kripke's notion of "rigid designation" are distinguished: "genuine reference", which has to do with the semantic function of a singular term, and "rigid designation", which has to do with the behaviour of a singular term in modal contexts. Accordingly, the discussion is divided into two parts. ;In Part I, arguments from functionalism against "genuine reference" are considered and rejected, but it is claimed that certain Cartesian (...) arguments constitute a formidable objection against this notion. Therefore, while descriptivism must be rejected "genuine reference" is too strong as an alternative. "Weak reference" is suggested as the required notion, and some of its characteristics are delineated. ;In Part II, the problems concerning the contingent a priori and the necessary a posteriori arising from the second element in Kripke's notion are discussed, depending on whether the names involved are ordinary proper names, or "descriptive" names. Evans' arguments concerning descriptive names are considered, and it is argued that, because of a new distinction between deep vs. superficial rigidity, Davies and Humberstone fail in formulating them more exactly; but the informal arguments, though inconclusive, are intuitive. As for ordinary proper names, and on the basis of conclusions reached in Part I, the case for contingent a priori truths involving such names is undermined. In the case of necessary a posteriori truths involving ordinary proper names, the strategies of denying the necessity or the a posteriority of the examples are discussed, and found wanting. However, since there are reasons from other areas for denying the coincidence of the necessary and the a priori, Kripke's examples do not call for a radical departure from currently held views. (shrink)

Upward monotonic semantics for necessity modals give rise to Ross’s Puzzle: they predict that □φ entails □(φ ∨ ψ), but common intuitions about arguments of this form suggest they are invalid. It is widely assumed that the intuitive judgments involved in Ross’s Puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from □(φ ∨ ψ), interpreters infer that the truth of each disjunct (φ, ψ) is compatible with the relevant set of worlds. I introduce two (...) pieces of data that this analysis fails to explain. Analyzing this data, I argue, suggests that necessity modals with embedded disjunctions license ‘Independence’ inferences: from the truth of □(φ ∨ ψ), interpreters infer that φ-without-ψ and ψ-without-φ are each compatible with the relevant set of worlds. I outline a bilateral inquisitive semantics for necessity modals that predicts the validity of the Independence inferences. I then argue that the resulting theory should be understood as one on which disjunctions denote pluralities of propositions, and necessity modals behave like collective predicates applied to these pluralities. (shrink)

Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic logic and logic of games, so we study some basic model theoretical aspects of WAML in this paper. Specifically, we give a van Benthem-Rosen characterization theorem of WAML based on an intuitive notion of bisimulation and show that each basic WAML system Kn lacks Craig Interpolation.

We assume a central thesis about modal auxiliaries due to Angelika Kratzer, the modal base presupposition: natural language expressions that contain a modal component in their meaning, including all English modal auxiliaries and epistemic modal auxiliaries (EMA)s in particular, presuppose a modal base, a function that draws from context a relevant set of propositions which contribute to a premise-semantics for the modal. Accepting this thesis for EMAs leaves open (at least) the following two questions about the meaning of English EMAs (...) like _must_ and _might_: (i) What constraints, if any, are there on the character of the premise set for an EMA? And (ii) what is the nature of the relationship between premises and conclusion that is required for truth of the EMA statement? I argue for at least a partial answer to (i), with a hypothesis about constraints on the modal base for an EMA: EMAs, unlike some other types of modals, are indexical: They are anchored to an agent-in-a-situation whose doxastic state is currently under discussion in the context of utterance. Realized in a Kratzerian semantics, indexicality sheds new light on a number of outstanding puzzles, including the widely observed variability of anchoring of EMAs, the ways in which EMAs differ from so-called root modals, Yalcin’s (Mind 116:983–1026, 2007) puzzle (a version of Moore’s paradox for epistemic modals embedded under attitudes), how to explain the apparent weakness of necessity EMAs, and problems with second order belief and disagreement. (shrink)

Discussions about the meaning of the word “ought” are pulled in two apparently competing directions. First, in ethical theory this word is used in the paradigmatic statement of ethical principles and conclusions about what some agent is obligated to do. This leads some ethical theorists to claim that the word “ought” describes a real relation, roughly, of being obligated to (realism) or expresses some non-cognitive attitude toward agents acting in certain ways (expressivism). Second, in theoretical linguistics this word is classified (...) as a modal auxiliary verb alongside words like “might,” “may,” “can,” “must,” etc. This leads some theoretical linguists to claim that the word “ought” is a weak necessity modal, which can be modeled with universal quantification over a restricted set of possible worlds. This chapter seeks some resolution of this tension by showing how versions of realism and expressivism can be modified in light of the best semantics of “ought” as a weak necessity modal. In addition, the chapter explains how this semantics might point to a third view—inferentialism—that accounts for the meaning of “ought” not in terms of what relation it describes, nor in terms of what attitude it expresses, but rather in terms of its inferential role. (shrink)

This paper develops a compositional, type-driven constraint semantic theory for a fragment of the language of subjective uncertainty. In the particular application explored here, the interpretation function of constraint semantics yields not propositions but constraints on credal states as the semantic values of declarative sentences. Constraints are richer than propositions in that constraints can straightforwardly represent assessments of the probability that the world is one way rather than another. The richness of constraints helps us model communicative acts in essentially the (...) same way that we model agents’ credences. Moreover, supplementing familiar truth-conditional theories of epistemic modals with constraint semantics helps capture contrasts between strong necessity and possibility modals, on the one hand, and weak necessity modals, on the other. (shrink)

Se afirma que los enunciados necesarios a posteriori, propuestos por S. Kripke, exigen una comprensión débil de la necesidad; esto quiere decir: a) existencia contingente del designatum y b) dependencia racionalista en principios lógicos a priori, particularmente los de diferencia y de identidad. La principal consecuencia es que los enunciados necesarios a posteriori corresponden a instancias de dichos principios lógicos. Contrario al racionalismo, esto no exige que dichos enunciados sean a priori, pues su justificación requiere información empírica. Finalmente, se defiende (...) que la distinción entre denotación y designación permite sostener que la necesidad débil se aplica a las instancias de la clase, y no a esta, con lo que se evita el indeterminismo referencial. The article states that a posteriori necessary sentences as proposed by S. Kripke require a weak understanding of necessity. This means: a) contingent existence of designatum, and b) rationalist dependence on a priori logical principles, particularly those of difference and identity. The main consequence is that a posteriori necessary sentences correspond to instances of these logical principles. Contrary to rationalism, this does not require that these be a priori sentences, given that their justification requires empirical information. Finally, the article argues that the distinction between denotation and designation supports the idea that weak necessity applies to instances of the class, and cannot be applied to the class itself, thus avoiding referential indeterminism. (shrink)

This paper investigates set-theoretical semantics for logics that contain unary connectives, which can be viewed as modalities. Indeed, some of the logics we consider are closely related to linear logic. We use insights from the relational semantics of relevance logics together with a new version of the squeeze lemma in our semantics for logics with disjunction. The ideal-based semantics, which takes co-theories to be situations, dualizes the theory-based semantics for logics with conjunction.

This paper discusses an important puzzle about the semantics of indicative conditionals and deontic necessity modals (should, ought, etc.): the Miner Puzzle (Parfit, ms; Kolodny and MacFarlane, J Philos 107:115–143, 2010). Rejecting modus ponens for the indicative conditional, as others have proposed, seems to solve a version of the puzzle, but is actually orthogonal to the puzzle itself. In fact, I prove that the puzzle arises for a variety of sophisticated analyses of the truth-conditions of indicative conditionals. A (...) comprehensive solution requires rethinking the relationship between relevant information (what we know) and practical rankings of possibilities and actions (what to do). I argue that (i) relevant information determines whether considerations of value may be treated as reasons for actions that realize them and against actions that don’t, (ii) incorporating this normative fact requires a revision of the standard ordering semantics for weak (but not for strong) deontic necessity modals, and (iii) an off-the-shelf semantics for weak deontic necessity modals, due to von Fintel and Iatridou, which distinguishes “basic” and “higher-order” ordering sources, and interprets weak deontic necessity modals relative to both, is well-suited to this task. The prominence of normative considerations in our proposal suggests a more general methodological lesson: formal semantic analysis of natural language modals expressing normative concepts demands that close attention be paid to the nature of the underlying normative phenomena. (shrink)

Discussions about the meaning of the word “ought” are pulled in two apparently competing directions. First, in ethical theory this word is used in the paradigmatic statement of ethical principles and conclusions about what some agent is obligated to do. This leads some ethical theorists to claim that the word “ought” describes a real relation, roughly, of being obligated to or expresses some non-cognitive attitude toward agents acting in certain ways. Second, in theoretical linguistics this word is classified as a (...) modal auxiliary verb alongside words like “might,” “may,” “can,” “must,” etc. This leads some theoretical linguists to claim that the word “ought” is a weak necessity modal, which can be modeled with universal quantification over a restricted set of possible worlds. This chapter seeks some resolution of this tension by showing how versions of realism and expressivism can be modified in light of the best semantics of “ought” as a weak necessity modal. In addition, the chapter explains how this semantics might point to a third view—inferentialism—that accounts for the meaning of “ought” not in terms of what relation it describes, nor in terms of what attitude it expresses, but rather in terms of its inferential role. (shrink)

In this paper, we study the distribution and interpretation of a non-temporal use of the future tense in Italian, called ‘presumptive’ or ‘epistemic’, which we label here PF. We first distinguish PF from its closest modal relatives, namely epistemic necessity/possibility/likelihood modals, as well as weak necessity modals. We then propose an account of PF in declaratives and interrogatives that treats it as a special comparative subjective likelihood modal, and test its empirical predictions. A theoretical lesson (...) drawn from this detailed study of the semantics of PF is that semantics needs sharpened theoretical tools to be able to capture the fine-grained distinctions languages make when it comes to signaling modulated epistemic commitment to a proposition. (shrink)

This paper extends David Lewis' result that all first degree modal logics are complete to weakly aggregative modal logic by providing a filtration-theoretic version of the canonical model construction of Apostoli and Brown. The completeness and decidability of all first-degree weakly aggregative modal logics is obtained, with Lewis's result for Kripkean logics recovered in the case k = 1.

Weakly Aggregative Modal Logic ) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. \ has interesting applications on epistemic logic, deontic logic, and the logic of belief. In this paper, we study some basic model theoretical aspects of \. Specifically, we first give a van Benthem–Rosen characterization theorem of \ based on an intuitive notion of bisimulation. Then, in contrast to many well known normal or non-normal modal logics, we show that (...) each basic \ system \ lacks Craig interpolation. Finally, by model theoretical techniques, we show that an extension of \ does have Craig interpolation, as an example of amending the interpolation problem of \. (shrink)

This paper connects the following three apparently unrelated topics: an epistemic framework fighting logical omniscience, a class of generalized graphs without the arities of relations, and a family of non-normal modal logics rejecting the aggregative axiom. Through neighborhood frames as their meeting point, we show that, among many completeness results obtained in this paper, the limit of a family of weakly aggregative logics is both exactly the modal logic of hypergraphs and also the epistemic logic of local reasoning with veracity (...) and positive introspection. The logics studied are shown to be decidable based on a filtration construction. (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)

This paper connects the following four topics: a class of generalized graphs whose relations do not have fixed arities called hypergraphs, a family of non-normal modal logics rejecting the aggregative axiom, an epistemic framework fighting logical omniscience, and the classical group knowledge modality of ‘someone knows’. Through neighborhood frames as their meeting point, we show that, among many completeness results obtained in this paper, the limit of a family of weakly aggregative logics is both exactly the modal logic of hypergraphs (...) and also the epistemic logic of local reasoning with veracity and positive introspection, and upon adding a single combinatorial axiom, it is also the logic of ‘someone knows’ for a fixed finite number of positively introspective agents. At the core of all these completeness results is a new canonical neighborhood model construction for monotone modal logics that is capable of dealing with all these diverse cases. We also provide an axiomatization for the logic of all non-n-colorable hypergraphs based on a filtration argument that also shows the decidability of the logics of hypergraphs we study. (shrink)

This paper concerns the semantic difference between strong and weak neces-sity modals. First we identify a number of explananda: their well-known in-tuitive difference in strength between ‘must’ and ‘ought’ as well as differ-ences in connections to probabilistic considerations and acts of requiring and recommending. Here we argue that important extant analyses of the se-mantic differences, though tailored to account for some of these aspects, fail to account for all. We proceed to suggest that the difference between ’ought’ and (...) ’must’ lies in how they relate to scalar and binary standards. Briefly put, must(φ) says that among the relevant alternatives, φ is selected by the relevant binary standard, whereas ought(φ) says that among the relevant al-ternatives, φ is selected by the relevant scale. Given independently plausi-ble assumptions about how standards are provided by context, this ex-plains the relevant differences discussed. (shrink)

I defend a contextualist account of bare epistemic modal claims against recent objections. I argue that in uttering a sentence of the form ‘It might be that p,’ a speaker is performing two speech acts. First, she is (directly) asserting that in view of the knowledge possessed by some relevant group, it might be that p. The content of this first speech act is accounted for by the contextualist view. But the speaker's utterance also generates an indirect speech act that (...) consists in a weak suggestive that p. Since this second speech act is typically the main point of a bare epistemic modal utterance, our (negative or positive) responses to the utterance actually target this second speech act. I show how this two-speech-act account can explain the data recently adduced against contextualism. (shrink)

Orthodox semantics for natural language modals give rise to two puzzles for their interactions with disjunction: Ross’s puzzle and the puzzle of free choice permission. It is widely assumed that each puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from the truth of a possibility or necessity modal with an embedded disjunction, hearers infer that each disjunct is compatible with the relevant set of worlds. I argue that Diversity inferences are too weak to (...) explain the full range of data. Instead, I argue, modals with embedded disjunctions license ‘Independence’ inferences: from the truth of a modal with an embedded disjunction, hearers infer that each disjunct is an independent alternative among the relevant set of worlds. I then develop a bilateral inquisitive semantics for modals that predicts the validity of these Independence inferences. My account vindicates common intuitions about both Ross’s puzzle and the puzzle of free choice permission, and explains the full range of data. (shrink)

This paper argues that the innovation of an ordering source parameter in the standard Lewis-Kratzer semantics for modals was a mistake, at least for English auxiliaries like ‘ought’, and that a simpler dyadic semantics (as proposed in my earlier work) provides a superior account of normative uses of modals. I programmatically investigate problems arising from (i) instrumental conditionals, (ii) gradability and “weak necessity”, (iii) information-sensitivity, and (iv) conflicts, and show how the simpler semantics provides intuitive solutions (...) given three basic moves: (1) an end-relational analysis of normative modality, (2) a “most” analysis of “weak necessity”, and (3) well-motivated appeals to pragmatics. I conclude with metasemantic observations about the desiderata for a semantics for ‘ought’. (shrink)

A consequence relation is strongly classical if it has all the theorems and entailments of classical logic as well as the usual meta-rules (such as Conditional Proof). A consequence relation is weakly classical if it has all the theorems and entailments of classical logic but lacks the usual meta-rules. The most familiar example of a weakly classical consequence relation comes from a simple supervaluational approach to modelling vague language. This approach is formally equivalent to an account of logical consequence according (...) to which α1, ..., αn entails β just in case □α1, ..., □αn entails □β in the modal logic S5. This raises a natural question: If we start with a different underlying modal logic, can we generate a strongly classical logic? This paper explores this question. In particular, it discusses four related technical issues: (1) Which base modal logics generate strongly classical logics and which generate weakly classical logics? (2) Which base logics generate themselves? (3) How can we directly characterize the logic generated from a given base logic? (4) Given a logic that can be generated, which base logics generate it? The answers to these questions have philosophical interest. They can help us to determine whether there is a plausible supervaluational approach to modelling vague language that yields the usual meta-rules. They can also help us to determine the feasibility of other philosophical projects that rely on an analogous formalism, such as the project of defining logical consequence in terms of the preservation of an epistemic status. (shrink)

Interest in the metaphysics and logic of possible worlds goes back at least as far as Aristotle, but few books address the history of these important concepts. This volume offers new essays on the theories about the logical modalities held by leading philosophers from Aristotle in ancient Greece to Rudolf Carnap in the twentieth century. The story begins with an illuminating discussion of Aristotle's views on the connection between logic and metaphysics, continues through the Stoic and mediaeval traditions, and then (...) moves to the early modern period with particular attention to Locke and Leibniz. The views of Kant, Peirce, C. I. Lewis and Carnap complete the volume. Many of the essays illuminate the connection between the historical figures studied, and recent or current work in the philosophy of modality. The result is a rich and wide-ranging picture of the history of the logical modalities. (shrink)

Medical necessity (claiming that a medical intervention or care is – at minimum – reasonable, appropriate and acceptable) depends on empirical evidence and on the interpretation of that evidence. Evidence and its interpretation define the standard of care. This commentary argues that both the evidence base and its interpretation are currently weak gatekeepers. Empirical meta-research suggests that very few medical interventions have high quality evidence in support of their effectiveness and very few of them also have relatively thorough (...) assessments of their potential harms. Therefore, evidence on the risk-benefit ratios carries almost always very large uncertainty. Arbitration about medical necessity is thus left to the interpretation process. Professional guidelines are notoriously unreliable and biased in this regard. Regulatory approval ends up being the key arbitrator, but over the years the regulatory process has been subverted. Regulatory approval currently does not mean that an intervention has a favourable risk-benefit ratio, but simply that it can be marketed, sold and made profit from. The process leads to a tragedy of commons where the final victim is society at large: medical necessity is invoked as an alibi for medicine to absorb societal resources. (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)

"This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence.

I survey a number of views about how we can obtain knowledge of modal propositions, propositions about necessity and possibility. One major approach is that whether a proposition or state of affairs is conceivable tells us something about whether it is possible. I examine two quite different positions that fall under this rubric, those of Yablo and Chalmers. One problem for this approach is the existence of necessary a posteriori truths and I deal with some of the ways in (...) which these authors respond to the problem, including the use of two-dimensional modal semantics. Conventionalism about modality offers a complementary approach to modal epistemology, prompting us to identify our knowledge of modal truths with our mastery of linguistic or conceptual conventions. Finally, I discuss an approach to modal epistemology deriving from David Lewis's work that seeks to identify structural features of the modal space over which necessity and possibility are defined. (shrink)

The paper argues against a commitment to metaphysical necessity, semantic modalities are enough. The best approaches to elucidate the semantic modalities are (still) versions of lingustic ersatzism and fictionalism, even if only developed in parts. Within these necessary properties and the difference between natural and semantic laws can be accounted for. The proper background theory for this is an updated version of Logical Empiricism, which is congenial to recent trends in Structural Realism. The anti-metaphysical attitude of Logical Empiricism deserves (...) revitalization. Another target besides metaphysical necessity are substantial forms of iterated modalities, as used, for instance, in the philosophy of religion. (shrink)

Recently it has become almost the received wisdom in certain quarters that Kripke models are appropriate only for something like metaphysical modalities, and not for logical modalities. Here the line of thought leading to Kripke models, and reasons why they are no less appropriate for logical than for other modalities, are explained. It is also indicated where the fallacy in the argument leading to the contrary conclusion lies. The lessons learned are then applied to the question of the status of (...) the formula. (shrink)