Standard conditionals $\varphi > \psi$, by which I roughly mean variably strict conditionals à la Stalnaker and Lewis, are trivially true for impossible antecedents. This article investigates three modifications in a doxastic setting. For the neutral conditional, all impossible-antecedent conditionals are false, for the doxastic conditional they are only true if the consequent is absolutely necessary, and for the metaphysical conditional only if the consequent is ‘model-implied’ by the antecedent. I motivate these conditionals logically, and (...) also doxastically by properties of conditional belief and belief revision. For this I show that the Lewisian hierarchy of conditional logics can be reproduced within ranking semantics, provided we slightly stretch the notion of a ranking function. Given this, acceptance of a conditional can be interpreted as a conditional belief. The epistemic and the neutral conditional deviate from Lewis’ weakest system $V$, in that ID or even CN are dropped, and new axioms appear. The logic of the metaphysical conditional is completely axiomatised by $V$ to which we add the known Kripke axioms T5 for the outer modality. Related completeness results for variations of the ranking semantics are obtained as corollaries. (shrink)

This thesis extends Kit Fine's truthmaker semantics for counterfactuals to indicative conditionals. First, I provide Fine's truthmaker semantics and his extension to counterfactuals. Then I introduce a notion of context state into the semantics and provide the verification-conditions for indicative conditionals by employing this notion of context state. Afterwards, I turn to the logic of indicative conditionals under exact semantics and discuss the principles and inference rules which raise disagreements between variably strict and (...) class='Hi'>strict conditionals accounts. The account I provide shows its promise by validating a plausible combination of principles and strikes a balance between variably strict and strict conditional theories. I discuss certain principles in logic of indicative conditionals under exact semantics in detail and show how the present account validates the plausible combination of them. In the end, I draw comparisons between the viable theories for indicatives and the present one, and argue that the present account takes the advantage in several respects. (shrink)

ABSTRACT The apparent consistency of Sobel sequences famously motivated David Lewis to defend a variably strict conditional semantics for counterfactuals. If Sophie had gone to the parade, she would have seen Pedro. If Sophie had gone to the parade and had been stuck behind someone tall, she would not have seen Pedro. But if the order of the counterfactuals in a Sobel sequence is reversed—in the example, if is asserted prior to —the second counterfactual asserted no (...) longer rings true. This is the Heim sequence problem. That the order of assertion makes this difference is surprising on the variably strict account. Some argue that this is reason to reject the Lewis-Stalnaker semantics outright. Others argue that the problem motivates a contextualist rendering of counterfactuals. Still others maintain that the explanation for the phenomenon is merely pragmatic. I argue that none of these is right, and I defend a novel way to understand the phenomenon. My proposal avoids the problems faced by the alternative analyses and enjoys independent support. There is, however, a difficulty for my view: it entails that many ordinarily accepted counterfactuals are not true. I argue that this cost is acceptable. (shrink)

In this paper I try to show that semantics can explain word-to-world relations and that sentences can have meanings that determine truth-conditions. Critics like Chomsky typically maintain that only speakers denote, i.e., only speakers, by using words in one way or another, represent entities or events in the world. However, according to their view, individual acts of denotations are not explained just by virtue of speakers’ semantic knowledge. Against this view, I will hold that, in the typical cases considered, (...) semantic knowledge can account for the denotational uses of words of individual speakers. (shrink)

In this dissertation I provide a novel logic of the ordinary-language conditional. First, however, I endeavor to make clearer and more precise just what the objects of the study of the conditional are, as a lack of clarity as to what counts as an instance of a given category of conditional has resulted in deep and significant confusions in subsequent analysis. I motivate for a factual/counterfactual distinction, though not at the level of particular instances of the (...) class='Hi'>conditional. Instead, I argue that each individual instance of the conditional may be interpreted either factually or counterfactually, rather than these instances dividing into distinct types. I examine the classic Oswald–Kennedy pair of sentences, typically taken to be the quintessential example of how conditionals must be split into two different categories, to show that they in fact do not demonstrate this. I then present my account of the logic underlying the ordinary-language conditional, the system C3, and a justification of the form it takes. This logic provides distinct interpretations of the conditional as it concerns what is factual or what is counterfactual, respectively. The factual interpretation is true when both antecedent and consequent are true at the actual world, false when the antecedent is true and consequent false, and not truth-apt otherwise. The counterfactual interpretation incorporates a ceteris paribus clause, ensuring that it is not falsified by extraordinary, unforeseeable occurrences, and is true when, at all worlds at which the antecedent is ceteris paribus true, the consequent too is true. It is false when, at any of these worlds the consequent is false; and not truth-apt otherwise. I go on to examine alternative theories of the conditional—from the suppositionalist approach to evaluating the putative indicative conditional, to Stalnaker’s combined indicative and counterfactual account, and Lewis’s analysis of the counterfactual; among a number of others—and offer comparison to my own theory. Finally, I look at various challenges to my account of the conditional. Being a strict conditional (albeit variably so), that of C3 is open to the objection that it fails to match ordinary speakers’ intuitions as regards its truth-value assignments to, for instance, conditionals with necessarily true consequents. I address these so- called paradoxes of the strict conditional, and also discussion the question of truth-preservation in the C3 system in the case of such inferences as those relying on transitivity and that of modus ponens. I maintain that these inferences are indeed truth-preserving under certain, specifiable, conditions, and I close by offering possible avenues for further research. (shrink)

Our understanding of subjunctive conditionals has been greatly enhanced through the use of possible world semantics and, more precisely, by the idea that they involve variably strict quantification over possible worlds. I propose to extend this treatment to ceteris paribus conditionals – that is, conditionals that incorporate a ceteris paribus or ‘other things being equal’ clause. Although such conditionals are commonly invoked in scientific theorising, they traditionally arouse suspicion and apprehensiveness amongst philosophers. By treating ceteris paribus conditionals (...) as a species of variably strict conditional I hope to shed new light upon their content and their logic. (shrink)

This essay calls attention to a set of linguistic interactions between counterfactual conditionals, on one hand, and possibility modals like could have and might have, on the other. These data present a challenge to the popular variably strict semantics for counterfactual conditionals. Instead, they support a version of the strict conditional semantics in which counterfactuals and possibility modals share a unified quantificational domain. I’ll argue that pragmatic explanations of this evidence are not available to (...) the variable analysis. And putative counterexamples to the unified strict analysis, on careful inspection, in fact support it. Ultimately, the semantics of conditionals and modals must be linked together more closely than has sometimes been recognized, and a unified strict semantics for conditionals and modals is the only way to fully achieve this. (shrink)

von Fintel and Gillies : 329–360, 2007) have proposed a dynamic strict conditional account of counterfactuals as an alternative to the standard variably strict account due to Stalnaker and Lewis. Von Fintel’s view is motivated largely by so-called reverse Sobel sequences, about which the standard view seems to make the wrong predictions. More recently Moss :561–586, 2012) has offered a pragmatic/epistemic explanation that purports to explain the data without requiring abandonment of the standard view. So far (...) the small amount of subsequent literature has focused primarily on the original class of cases motivating the strict conditional view. What is needed in the debate is an examination of the predictions of the dynamic strict conditional account for a broader range of data. I undertake this task here, presenting a slew of cases that are problematic for the strict conditional view but not for Moss’s view, and considering some possible responses. Ultimately I take my contribution to constitute a significant blow to the dynamic strict conditional view, though not a decisive verdict against it. (shrink)

Philippe Schlenker gives a method of deriving local contexts from an expression’s classical semantics. In this paper I show that this method, when applied to the traditional variably strict semantics for subjunctive conditionals of Robert Stalnaker, David Lewis, and Angelika Kratzer, delivers an empirically incorrect prediction. The prediction is that the antecedent of a conditional should have the whole domain of possible worlds as its local context and therefore should be allowed to have only necessary (...) presuppositions. In the later part of the paper, I suggest the outlines of a solution to the problem. The solution involves adding a shifting contextual restriction on the domain of possible worlds. (shrink)

Philippe Schlenker gives a method of deriving local contexts from an expression’s classical semantics. In this paper I show that this method, when applied to the traditional variably strict semantics for subjunctive conditionals of Robert Stalnaker, David Lewis, and Angelika Kratzer, delivers an empirically incorrect prediction. The prediction is that the antecedent of a conditional should have the whole domain of possible worlds as its local context and therefore should be allowed to have only necessary (...) presuppositions. In the later part of the paper, I suggest the outlines of a solution to the problem. The solution involves adding a shifting contextual restriction on the domain of possible worlds. (shrink)

According to existing accounts of indicative conditionals, any argument of the following form is valid: ϕ → ψ, ( ϕ ∧ ψ ) → χ ∴ ϕ → χ. Here, I present a set of counterexamples to show that there exist invalid arguments of this form. I argue that this data poses serious problems to variably strict accounts of conditionals, as such accounts are structurally unable to accommodate it. Dynamic strict accounts, however, are a different story. While (...) existing dynamic strict accounts do not accommodate the data, they are in principle able to, and I propose a modified dynamic strict account, drawing from von Fintel, that does. The key modification is this: whereas existing dynamic strict accounts take into account only the effects of conditional antecedents in changing the semantic context, the data shows that we must also take into account the effects of conditional consequents in changing the semantic context. (shrink)

Francesco Berto proposed a logic for imaginative episodes. The logic establishes certain (in)validities concerning episodic imagination. They are not all equally plausible as principles of episodic imagination. The logic also does not model that the initial input of an imaginative episode is deliberately chosen.Stit-imagination logic models the imagining agent’s deliberate choice of the content of their imagining. However, the logic does not model the episodic nature of imagination. The present paper combines the two logics, thereby modelling imaginative episodes with deliberately (...) chosen initial input. We use a combination ofstit-imagination logic and a content-sensitive variably strict conditional à la Berto, for which we give a Chellas–Segerberg semantics. The proposed semantics has the following advantages over Berto’s: (i) we model thedeliberate choiceof initial input of imaginative episodes (in a multi-agent setting), (ii) we showframe correspondencesfor axiomatic analogues of Berto’s validities, which (iii) allows thepossibility to disregard axiomsthat might be considered not plausible as principles concerning imaginative episodes. We do not take a definite stance on whether theseshouldbe disregarded but give reasons for why one might want to disregard them. Finally, we compare our semantics briefly with recent work, which aims to model voluntary imagination, and argue that our semantics models different aspects. (shrink)

In this paper, we offer an argument in favor of the modular character of mind, based on a more detailed proof of the modular character of the linguistic capacity: in comparing the properties of different components of grammar in a specific area we will draw general consequences about the properties of the cognitive system. More specifically, we analyze and compare the properties, in logical form (LF)and in phonology, of “empty eIements” - eIements that are “visible” or “full” at some level (...) of representation, but not at another level.Our analysis shows that empty eIements are governed at LF by principIes on variables. binding conditions, and thematic principles, that relate eIements at a distance. In phonology, on the other hand, empty elements, i.e., empty segments and empty properties, can be obtaines by deletion and are governed by very different principles (underspecification, principles relating to recoverability of deletion effects), andthese principles relates eIements under strict adjacency. In addition, when a principle seems to be operating in a similar fashion in both components, as in the case of the Projection Principle, it involves lexical properties, which are properties affecting all components. We conclude, hence, that grammar is a modular system, with different components following different principles but related of course, among other things, by the properties of lexical structure.It follows from this analysis that a theory that views language as part of a homogeneous cognitive capacity cannot be mantained: cognition cannot be nonmodular in a strict sense, since a subpart of it, the linguistic capacity is modular itself. We conclude also that the linguistic capacity being modular, we ean only expect that, when studied in more detail, other cognitive capacities will be shown to differ intheir structure still more from the language system. (shrink)

This paper examines the stage-level/individual-level hypothesis (Kratzer 1989; Diesing 1988) from the point of view of modern Scottish Gaelic. This language exhibits two syntactically distinct predicational structures, and in particular, two distinct subject positions distinguishable on the basis of word order. While the distinction between the two positions can be shown to support the stage/individual-level hypothesis in one sense, the picture is muddied by the fact that many habitual or ‘characteristic’ sentences seem to be formed according to the stage-level subject (...) construction type.The solution proposed relies on two novel elements. First, it distinguishes the classical Davisonian event variable from the Kratzerian one hypothesized to be the hallmark of the stage-level sentence type. And secondly, it makes a strict logical separation between two types of generics: generics proper, which involve quantifying over an individual variable; and habituals, which only involve quantification over an event variable. These are represented by two distinct logical types which may nevertheless give rise to similar truth conditions in context.I show that the analysis can be made to account for tense interpretation, the scope of genericity, and the facts of syntactic complementation in Scottish Gaelic. To the extent that the solution is successful, it is evidence for a quite direct mapping between syntactic and semantic representations and for the important intuitions behind the initial Kratzer/Diesing stage vs. individual-level hypothesis. (shrink)

Counterfactuals are typically thought--given the force of Sobel sequences--to be variably strict conditionals. I go the other way. Sobel sequences and (what I call) Hegel sequences push us to a strict conditional analysis of counterfactuals: counterfactuals amount to some necessity modal scoped over a plain material conditional, just which modal being a function of context. To make this worth saying I need to say just how counterfactuals and context interact. No easy feat, but I have (...) something to say on the matter. (shrink)

This paper endorses and defends M. J. Cresswell's view that the distinction drawn in linguistic semantics between strictly "logical" implication and merely lexical implication is bogus, and then explores the bad consequences that concession has for the Davidsonian semantic program. A pattern of semantic explanation made famous by Davidson's "The logical form of action sentences" is shown to be far less interesting than has been thought.

This paper expounds a simple and non-trivial Ramsey Test. Drawing on the work of Peter Gärdenfors, it aims to help establish an epistemic alternative to the semantics of variably strict conditionals by Robert Stalnaker (in: Rescher (ed), Studies in logical theory, Blackwell, Oxford, 1968) and David Lewis (Counterfactuals, Blackwell, Oxford, 1973). The novelty of the present contribution lies in considering the framework of Preferred Subtheories as model of belief change upon which conditionals are defined. The resulting (...) class='Hi'>semantics avoids triviality in the sense that a major premise of the proof of Gärdenfors’ triviality theorem is violated. (shrink)

This book combines insights from philosophy and linguistics to develop a novel framework for theorizing about linguistic meaning and the role of context in interpretation. A key innovation is to introduce explicit representations of context — assignment variables — in the syntax and semantics of natural language. The proposed theory systematizes a spectrum of “shifting” phenomena in which the context relevant for interpreting certain expressions depends on features of the linguistic environment. Central applications include local and nonlocal contextual dependencies (...) with quantifiers, attitude ascriptions, conditionals, questions, and relativization. The result is an innovative, philosophically informed compositional semantics compatible with the truth-conditional paradigm. (shrink)

There is abundant evidence of contextual variation in the use of “S knows p.” Contextualist theories explain this variation in terms of semantic hypotheses that refer to standards of justification determined by “practical” features of either the subject’s context (Hawthorne & Stanley) or the ascriber’s context (Lewis, Cohen, & DeRose). There is extensive linguistic counterevidence to both forms. I maintain that the contextual variation of knowledge claims is better explained by common pragmatic factors. I show here that one is variable (...) strictness. “S knows p” is commonly used loosely to implicate “S is close enough to knowing p for contextually indicated purposes.” A pragmatic account may use a range of semantics, even contextualist. I use an invariant semantics on which knowledge requires complete justification. This combination meets the Moorean constraint as well as any linguistic theory should, and meets the intuition constraint much better than contextualism. There is no need for ad hoc error theories. The variation in conditions of assertability and practical rationality is better explained by variably strict constraints. It will follow that “S knows p” is used loosely to implicate that the condition for asserting “p” and using it in practical reasoning are satisfied. (shrink)

The use of ‘S knows p’ varies from context to context. The contextualist theories of Cohen, Lewis, and DeRose explain this variation in terms of semantic hypotheses: ‘S knows p’ is indexical in meaning, referring to features of the ascriber’s context like salience, interests, and stakes. The linguistic evidence against contextualism is extensive. I maintain that the contextual variation of knowledge claims results from pragmatic factors. One is variable strictness :395–438, 2007). In addition to its strict use, ‘S knows (...) p’ may be used loosely to implicate that S is close enough to knowing p for contextually indicated purposes. Here I explore another variable: belief about what is known. This factor is pragmatic rather than semantic in that it affects the use of ‘S knows p’ without affecting its truth conditions. While variation in strictness accounts for the variation in the bank, parking, and some lottery cases, variation in belief accounts for the variation in other lottery cases and the epistemology cases. Along the way, I sketch an insensitive invariantist semantics that is strict but non-skeptical, and show how it works with these pragmatic factors. (shrink)

Modus ponens is the argument from premises of the form If A, then B and A to the conclusion B. Nearly all participants agree that the modus ponens conclusion logically follows when the argument appears in this Basic form. However, adding a further premise can lower participants’ rate of agreement—an effect called suppression. We propose a theory of suppression that draws on contemporary ideas about conditional sentences in linguistics and philosophy. Semantically, the theory assumes that people interpret an indicative (...) conditional as a context-sensitive strict conditional: true if and only if its consequent is true in each of a contextually determined set of situations in which its antecedent is true. Pragmatically, the theory claims that context changes in response to new assertions, including new conditional premises. Thus, the conclusion of a modus ponens argument may no longer be accepted in the changed context. Psychologically, the theory describes people as capable of reasoning about broad classes of possible situations, ordered by typicality, without having to reason about individual possible worlds. The theory accounts for the main suppression phenomena, and it generates some novel predictions that new experiments confirm. (shrink)

In this paper, I examine al-Fārābī's and Avicenna's conceptions of the conditional. I show that there are significant differences between the two frames, despite their closeness. Al-Fārābī distinguishes between an accidental conditional and two “essential” conditionals. The accidental conditional can occur only once and pragmatically involves succession. In the first “essential” conditional, the consequent follows regularly the antecedent; pragmatically it involves likeliness. The second “essential” conditional can be either complete or incomplete. Semantically the former means (...) “if and only if”; pragmatically it means “necessarily if and only if”. The latter is expressed by ‘if, then’ and means entailment; pragmatically, it involves necessity and the inclusion of the antecedent into the consequent. As to Avicenna, he rejects explicitly al-Fārābī’s complete conditional and distinguishes between the luzūm and what he calls ittifāq. He quantifies over situations to express the various conditionals. The two universals AC and EC are expressed by “In all situations, if…, then…”, while the two particulars IC and OC are expressed by “In some situations, if…, then..”. This gives them a modal connotation, and makes the universals close to strict implications. Pragmatically, AC presupposes the truth of the antecedent, but there is no such presupposition in EC, while what is presupposed in both IC and OC is a conjunction. (shrink)

Recent experimental work has shown that the truth-value judgments of color predications, i.e. utterances of the form “the leaves on my tree are green” or “these walls are brown,” are influenced by slight changes in the context of utterance (Hansen and Chemla 2013, Ziółkowski, 2021). Most explanations of this phenomenon focus on the semantics of color adjectives. However, it is not clear if these explanations do justice to the nuances of the empirical data on context-sensitivity of color predications (Ziółkowski, (...) 2021). In contrast to the adjectival explanations, Agustin Vicente (2015) has recently proposed that the context-sensitivity of color predications can be explained by invoking the polysemy of the noun. In this paper, we present the results of three studies designed to empirically test this hypothesis: a traditional survey experiment (Study 1), an exploratory correlational study inspired by the semantic integration paradigm (Study 2a), and a follow-up experiment (Study 2b) that was designed to mitigate possible shortcomings of Study 2a. The results of our studies present preliminary evidence against Vicente’s theory. (shrink)

In the recent literature on proof-theoretic semantics, there is mention of a generality condition on defining rules. According to this condition, the schematic formulation of the defining rules must be maximally general, in the sense that no restrictions should be placed on the contexts of these rules. In particular, context variables must always be present in the schematic rules and they should range over arbitrary collections of formulae. I argue against imposing such a condition, by showing that it has (...) undesirable results and that it is ill-supported by the arguments brought in its favour. (shrink)

Folklore has it that Sobel sequences favor a variably strict analysis of conditionals over its plainly strict alternative. While recent discussions for or against the lore have focussed on Sobel sequences involving counterfactuals, this paper draws attention to the fact that indicative Sobel sequences are just as felicitous as are their counterfactual cousins. The fact, or so I shall argue here, disrupts the folklore: given minimal assumptions about the semantics and pragmatics of indicative conditionals, a textbook (...) variably strict analysis fails to predict that indicative Sobel sequences are felicitous. The correct lesson to draw from Sobel sequences is that their felicity challenges classical implementations of the variably strict and of the plainly strict analysis alike. In response to this challenge I develop a dynamic strict analysis of conditionals that handles indicative Sobel sequences with grace while preserving intuitive constraints on the semantics and pragmatics of their members. A discussion of how such an analysis may handle the challenge from reverse Sobel sequences is provided. (shrink)

I argue that modal terms have an epistemic interpretation on which concessive knowledge attributions are semantically contradictory. This is compatible with the fallibilist view that the basis on which we know something need not entail it, but not with the view that what is known need not be epistemically certain or necessary. The apparent contradictoriness of concessive knowledge attributions is not due to mere implicature, nor to assertion updating the modal base. And it is contextually invariant. Concessive knowledge attributions contrast (...) markedly with concessive assertions and Moorean conjunctions, whose infelicity is plausibly due to norms of assertion. I briefly explain why the strict fallibilism I recommend is compatible with our ordinary use of ‘know,’ and with our knowing much on the basis of perception. Its contextual shiftiness closely parallels our variably strict use of temporal and other invariant terms with strict application conditions. (shrink)

The variably strict analysis of conditionals does not only largely dominate the philosophical literature, since its invention by Stalnaker and Lewis, it also found its way into linguistics and psychology. Yet, the shortcomings of Lewis–Stalnaker’s account initiated a plethora of modifications, such as non-vacuist conditionals, presuppositional indicatives, perfect conditionals, or other conditional constructions, for example: reason relations, difference-making conditionals, counterfactual dependency, or probabilistic relevance. Many of these new connectives can be treated as strengthened or weakened conditionals. They (...) are definable conditionals. This article develops a technique to infer the logic for such definable conditionals from the known logic of the underlying defining conditional. The technique is applied to central examples. The results show that a large part of the zoo of conditionals arises from a basic conditional—a constant nucleus of the different contextual and conceptual variations of variably strict conditionals. (shrink)

This paper extends Kripke’s theory of truth to a language with a variably strict conditional operator, of the kind that Stalnaker and others have used to represent ordinary indicative conditionals of English. It then shows how to combine this with a different and independently motivated conditional operator, to get a substantial logic of restricted quantification within naive truth theory.

Polysemy seems to be a relatively neglected phenomenon within philosophy of language as well as in many quarters in linguistic semantics. Not all variations in a word’s contribution to truth-conditional contents are to be thought as expressions of the phenomenon of polysemy, but it can be argued that many are. Polysemous terms are said to contribute senses or aspects to truth-conditional contents. In this paper, I will make use of the notion of aspect to argue that some (...) apparently wild variations in an utterance’s truth conditions are instead quite systematic. In particular, I will focus on Travis’ much debated green leaves case and explain it in terms of the polysemy of the noun; and in particular, in terms of the as-it-is and the as-it-looks aspects associated with kind words. (shrink)

In Lowe (1995), instead of endorsing a Stalnaker/Lewis-style account of counterfactuals, E. J. Lowe claims that a variation of C. I. Lewis’s strict implication alone captures the essence of everyday conditionals and avoids the paradoxes of strict implication. However, Lowe’s approach fails to account for the validity of simple and straightforward arguments such as ‘if 2=3 then 2+1=3+1’, and Heylen & Horsten (2006) even claims that no variation of strict implication can successfully describe the logical behavior of (...) natural language conditionals. By incorporating the German logician O. Becker’s modal intuition with the insight of Ramsey’s Test, we show that there does exist a unified, strict-conditional based account of everyday conditionals, which withstands all attacks previously raised against truth-conditional accounts of conditionals. Furthermore, a subtle distinction between autistic and realistic readings of the indexical ‘I’ involved in a conditional helps us resolve a recent debate concerning the Thomason conditionals. (shrink)

In this paper, I argue on empirical grounds that (VL-initial) Asymmetric Coordination in German cannot be reduced to a syntactic structure of the form [if S1, then S2], but rather needs to be analyzed as some kind of adjunction to the if-clause, i.e., along the lines of [[if S1] and S2]. This conclusion gives rise to an apparent mismatch between syntactic structure (narrow scope of if) and semantic interpretation (wide scope of if). To resolve this paradoxical situation, I propose a (...) compositional semantics for conditionals that is based on the idea that (indexed) if is to be construed as some kind of anaphor (variable) that ranges over objects of type modal base picking up a modal background in the actual context. Even though this analysis assigns a non-vacuous semantics to the complementizer if, it is still compatible with the syntax of Asymmetric Coordination in German, and, in contrast to alternative accounts, avoids the generation of non-existent distributive readings. (shrink)

This article introduces the classic accounts of the meaning of conditionals (material implication, strict implication, variably strict conditional) and discusses the difference between indicative and subjunctive/counterfactual conditionals. Then, the restrictor analysis of Lewis/Kratzer/Heim is introduced as a theory of how conditional meanings come about compositionally: if has no meaning other than serving to mark the restriction to an operator elsewhere in the conditional construction. Some recent alternatives to the restrictor analysis are sketched. Lastly, the (...) interactions of conditionals (i) with modality and (ii) with tense and aspect are discussed. Throughout the advanced research literature is referenced while the discussion stays largely non-technical. (shrink)

Second-order quantifier elimination in the context of classical logic emerged as a powerful technique in many applications, including the correspondence theory, relational databases, deductive and knowledge databases, knowledge representation, commonsense reasoning and approximate reasoning. In the current paper we first generalize the result of Nonnengart and Szałas [17] by allowing second-order variables to appear within higher-order contexts. Then we focus on a semantical analysis of conditionals, using the introduced technique and Gabbay’s semantics provided in [10] and substantially using a (...) third-order accessibility relation. The analysis is done via finding correspondences between axioms involving conditionals and properties of the underlying third-order relation. (shrink)

Many biologists still believe in a sort of post-Cartesian foundation of reality wherein objects are independent of subjects which cognize them. Recent research in behaviour, cognition, and psychology, however, provides plenty of evidence to the effect that the perception of an object differs depending on the kind of animal observer, and also its personality, hormonal, and sensorial set-up etc. In the following, I argue that exposed surfaces of organisms interact with other organisms’ perception to form semiautonomous relational entities called semantic (...) organs, which participate in biological reality as discrete heritable evolutionary units. The inner dimensions and potentialities of an organism can enter the senses of another living being when effectively expressed on the outer surfaces of the former and meaningfully perceived by the latter. Semantic organs have three basic sources of variability: intrinsic, i.e., genetic, epigenetic, and developmental processes; extrinsic, meaning the biotic and abiotic environmental conditions which affect the developmental generators of intrinsic variability; and perceptual, stemming from differences in the subject-specific interpretation of a SO’s structural basis. Extrinsic and intrinsic sources of variability are, however, just precursors to semantic organs. SOs are relational entities which always come into existence through an act of perception and their actual form depends both on the physical potentialities of the bearer and the species- or group-specific interpretation of the receiver. (shrink)

I present two Triviality results for Kratzer's standard “restrictor” analysis of indicative conditionals. I both refine and undermine the common claim that problems of Triviality do not arise for Kratzer conditionals since they are not strictly conditionals at all.

The standard truth-conditional semantics for substitutional quantification, due to Saul Kripke, does not specify what proposition is expressed by sentences containing the particular substitutional quantifier. In this paper, I propose an alternative semantics for substitutional quantification that does. The key to this semantics is identifying an appropriate propositional function to serve as the content of a bound occurrence of a formula containing a free substitutional variable. I apply this semantics to traditional philosophical reasons for interest (...) in substitutional quantification, namely, theories of truth and ontological commitment. (shrink)

This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. $${p\Rightarrow q}$$ p ⇒ q is thus defined as $${\lnot } \Diamond {(p \wedge \lnot q) \wedge } \Diamond {p \wedge } \Diamond (...) {\lnot q}$$ ¬ ◊ ( p ∧ ¬ q ) ∧ ◊ p ∧ ◊ ¬ q. We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle’s theses and weak Boethius’ thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut. (shrink)

Parity games are combinatorial representations of closed Boolean μ-terms. By adding to them draw positions, they have been organized by Arnold and Santocanale [3] and [27] into a μ-calculus whose standard interpretation is over the class of all complete lattices. As done by Berwanger et al. [8] and [9] for the propositional modal μ-calculus, it is possible to classify parity games into levels of a hierarchy according to the number of fixed-point variables. We ask whether this hierarchy collapses w.r.t. the (...) standard interpretation. We answer this question negatively by providing, for each n≥1, a parity game Gn with these properties: it unravels to a μ-term built up with n fixed-point variables, it is not semantically equivalent to any game with strictly less than n−2 fixed-point variables. (shrink)

Potts et seq. presents an analysis of gap-containing supplements where the gap is modelled as a variable over the semantic type of the constituent that the as-clause adjoins to. This much allows the meaning of the gap to be resolved purely compositionally, by defining as as a function that allows the anchor to bind the gap variable. This article presents a class of as-clauses where Potts’s analysis seems to break down, in that the gap cannot be modelled as a variable (...) over the semantic type of the anchor. I propose that these cases can be unified with those in Potts’s work, as well as a larger class of ellipsis phenomena, by assuming that, under certain conditions, surface gaps are composite entities, containing a bound variable and a free variable that are resolved independently of each other. The bound variable is bound by the anchor, and the free variable is resolved by anaphora to a salient discourse object. (shrink)

The paper focuses on a recent challenge brought forward against the interventionist approach to the meaning of counterfactual conditionals. According to this objection, interventionism cannot account for the interpretation of right-nested counterfactuals, the problem being its strict interventionism. We will report on the results of an empirical study supporting the objection. Furthermore, we will extend the well-known logic of intervention with a new operator expressing an alternative notion of intervention that does away with strict interventionism. This new notion (...) of intervention operates on the valuation of the variables in a causal model, and not on their functional dependencies. (shrink)

Our concern is the completeness problem for spi-logics, that is, sets of implications between strictly positive formulas built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer science, spi-logics have two natural semantics: meet-semilattices with monotone operators providing Birkhoff-style calculi and first-order relational structures (aka Kripke frames) often used as the intended structures in applications. Here we lay foundations for a completeness theory that aims to answer the question whether the two semantics define (...) the same consequence relations for a given spi-logic. (shrink)

We can use language to say what people did, often describing the same action in different complex ways. Davidson offered an illuminating analysis of action reports like “Miss Scarlet stabbed Colonel Mustard with a dagger in the library,” which involve adverbial modifiers. Part of the challenge here is to say how such modifiers are semantically related to the rest of the sentence. Building on the ancient observation that verbs are often used to describe what happened, Davidson argued that an action (...) report implies the occurrence of an eventthat meets the conditions specified by the report; where an event can be described in endlessly many ways. In this chapter, I review Davidson's account, his arguments in favor of it, and his responses to some initial objections. I also discuss some subsequent work that supports central aspects of Davidson's proposal while also presenting challenges for combining his analysis of action reports with his broader conception of linguistic meaning. (shrink)

Various laws and theories in the natural and social sciences are presented with a view to discerning the syntactic and semantic characteristics of many idealizations in science. Three different kinds of idealizations are discussed: ideal conditions, ideal cases, and idealized theories. An ideal condition is a formula in which state variables occur, whose existential closure is false, and for which there is another formula that can be constructed out of the original formula such that the existential closure of the new (...) formula is true. An ideal case is a statement which is logically equivalent to a universal conditional which has an ideal condition as its antecedent. And an idealized theory is a set of false universal conditional statements. Alternative syntactic and semantic analyses are viewed and criticized. (shrink)

Bare conditionals, I argue, exhibit Conditional Duality in that when they appear in downward entailing environments they differ from bare conditionals elsewhere in having existential rather than universal force. Two recalcitrant phenomena are shown to find a new explanation under this thesis: bare conditionals under only, and bare conditionals in the scope of negative nominal quantifiers, or what has come to be known as Higginbotham’s puzzle. I also consider how bare conditionals behave when embedded under negation, arguing that such (...) conditionals often involve denial negation. One important conclusion that emerges from the discussion is that an account of bare conditionals that validates Conditional Excluded Middle is not warranted. By limiting the scope of the strict analysis Conditional Duality is also a way of maintaining such an account. (shrink)

In this paper, we defend a traditional approach to semantics, that holds that the outputs of compositional semantics are propositional, i.e. truth conditions. Though traditional, this view has been challenged on a number of fronts over the years. Since classic work of Lewis, arguments have been offered which purport to show that semantic composition requires values that are relativized, e.g. to times, or other parameters that render them no longer propositional. Focusing in recent variants of these arguments involving (...) quantification and binding, we argue that a correct understanding of how composition works gives no reason to relativize semantic values, and that propositional semantic values are in fact the preferred option. We take our argument to be mainly empirical, but along the way, we defend some more general theses. Simple propositional semantic values are viable in composition, we maintain, because composition is itself a complex phenomenon, involving multiple modes of composition. Furthermore, some composition principles make adjustments to the meanings of constituents in the course of composition. These adjustments are by triggered syntactic environments. We argue such small contributions of meaning from syntactic structure are acceptable. (shrink)

According to logical theories of meaning, a meaning of an expression can be formalized and encoded in truth conditions. Vagueness of the language and individual differences between people are a challenge to incorporate into the meaning representations. In this paper, we propose a new approach to study truth-conditional representations of vague concepts. For a case study, we selected two natural language quantifiers most and more than half. We conducted two online experiments, each with 90 native English speakers. In the (...) first experiment, we tested between-subjects variability in meaning representations. In the second experiment, we tested the stability of meaning representations over time by testing the same group of participants in two experimental sessions. In both experiments, participants performed the verification task. They verified a sentence with a quantifier (e.g., “Most of the gleerbs are feezda.”) based on the numerical information provided in the second sentence, (e.g., “60% of the gleerbs are feezda”). To investigate between-subject and within-subject differences in meaning representations, we proposed an extended version of the Diffusion Decision Model with two parameters capturing truth conditions and vagueness. We fit the model to responses and reaction times data. In the first experiment, we found substantial between-subject differences in representations of most as reflected by the variability in the truth conditions. Moreover, we found that the verification of most is proportion-dependent as reflected in the reaction time effect and model parameter. In the second experiment, we showed that quantifier representations are stable over time as reflected in stable model parameters across two experimental sessions. These findings challenge semantic theories that assume the truth-conditional equivalence of most and more than half and contribute to the representational theory of vague concepts. The current study presents a promising approach to study semantic representations, which can have a wide application in experimental linguistics. (shrink)

Michael Dummett's anti-realism is founded on the semantics of natural language which, he argues, can only be satisfactorily given in mathematics by intuitionism. It has been objected that an analog of Dummett's argument will collapse intuitionism into strict finitism. My purpose in this paper is to refute this objection, which I argue Dummett does not successfully do. I link the coherence of strict finitism to a view of confirmation — that our actual practical abilities cannot confirm we (...) know what would happen if we could compute impracticably vast problems. But to state his case, the strict finitists have to suppose that we grasp the truth conditions of sentences we can't actually decide. This comprehension must be practically demonstrable, or the analogy with Dummett's argument fails. So, our actual abilities must be capable of confirming that we know what would be the case if actually undecidable sentences were true, contradicting the view of confirmation. I end by considering objections. (shrink)

The quantified relevant logic RQ is given a new semantics in which a formula for all xA is true when there is some true proposition that implies all x-instantiations of A. Formulae are modelled as functions from variable-assignments to propositions, where a proposition is a set of worlds in a relevant model structure. A completeness proof is given for a basic quantificational system QR from which RQ is obtained by adding the axiom EC of 'extensional confinement': for all x(A (...) V B) -> (A V for all xB). with x not free in A. Validity of EC requires an additional model condition involving the boolean difference of propositions. A QR-model falsifying EC is constructed by forming the disjoint union of two natural arithmetical structures in which negation is interpreted by the minus operation. (shrink)