Disjunctive antecedent conditionals —conditionals of the form if A or B, C—sometimes seem to entail both of their simplifications and sometimes seem not to. I argue that this behavior reveals a genuine ambiguity in DACs. Along the way, I discuss a new observation about the role of focal stress in distinguishing the two interpretations of DACs. I propose a new theory, according to which the surface form of a DAC underdetermines its logical form: on one possible logical form, if (...) A or B, C does entail both of its simplifications, while on the other, it does not. (shrink)

We propose a modification of the exhaustivity operator from Fox Presupposition and implicature in compositional semantics, Palgrave Macmillan, London, pp 71–120, 2007. https://doi.org/10.1057/9780230210752_4) that on top of negating all the Innocently Excludable alternatives affirms all the ‘Innocently Includable’ ones. The main result of supplementing the notion of Innocent Exclusion with that of Innocent Inclusion is that it allows the exhaustivity operator to identify cells in the partition induced by the set of alternatives whenever possible. We argue for this property of (...) ‘cell identification’ based on the simplification of disjunctive antecedents and the effects on free choice that arise as the result of the introduction of universal quantifiers. We further argue for our proposal based on the interaction of only with free choice disjunction. (shrink)

It is widely held that counterfactuals, unlike attitude ascriptions, preserve the referential transparency of their constituents, i.e., that counterfactuals validate the substitution of identicals when their constituents do. The only putative counterexamples in the literature come from counterpossibles, i.e., counterfactuals with impossible antecedents. Advocates of counterpossibilism, i.e., the view that counterpossibles are not all vacuous, argue that counterpossibles can generate referential opacity. But in order to explain why most substitution inferences into counterfactuals seem valid, counterpossibilists also often maintain that (...) counterfactuals with possible antecedents are transparency‐preserving. I argue that if counterpossibles can generate opacity, then so can ordinary counterfactuals with possible antecedents. Utilizing an analogy between counterfactuals and attitude ascriptions, I provide a counterpossibilist‐friendly explanation for the apparent validity of substitution inferences into counterfactuals. I conclude by suggesting that the debate over counterpossibles is closely tied to questions concerning the extent to which counterfactuals are more like attitude ascriptions and epistemic operators than previously recognized. (shrink)

A number of recent authors (Galles and Pearl, Found Sci 3 (1):151–182, 1998; Hiddleston, Noûs 39 (4):232–257, 2005; Halpern, J Artif Intell Res 12:317–337, 2000) advocate a causal modeling semantics for counterfactuals. But the precise logical significance of the causal modeling semantics remains murky. Particularly important, yet particularly under-explored, is its relationship to the similarity-based semantics for counterfactuals developed by Lewis (Counterfactuals. Harvard University Press, 1973b). The causal modeling semantics is both an account of the truth conditions of counterfactuals, and (...) an account of which inferences involving counterfactuals are valid. As an account of truth conditions, it is incomplete. While Lewis's similarity semantics lets us evaluate counterfactuals with arbitrarily complex antecedents and consequents, the causal modeling semantics makes it hard to ascertain the truth conditions of all but a highly restricted class of counterfactuals. I explain how to extend the causal modeling language to encompass a wider range of sentences, and provide a sound and complete axiomatization for the extended language. Extending the truth conditions for counterfactuals has serious consequences concerning valid inference. The extended language is unlike any logic of Lewis's: modus ponens is invalid, and classical logical equivalents cannot be freely substituted in the antecedents of conditionals. (shrink)

Natural language conditionals seem to be subject to three logical requirements: they invalidate Antecedent Strengthening, they validate so-called Simplification of Disjunctive Antecedents, and they allow for the replacement of logically equivalent clauses in antecedent position. Unfortunately, these requirements are jointly inconsistent. Conservative solutions to the puzzle drop Simplification, treating it as a pragmatic inference. I show that pragmatic accounts of Simplification fail, and develop a truthmaker semantics for conditionals that captures all the relevant data. Differently (...) from existing truthmaker semantics, my semantics extends, rather than replaces, standard possible worlds semantics. The main innovation is the notion of a truthmaker in play: this notion is cognitive, rather than metaphysical, and can be defined in a purely syntactic way. (shrink)

This paper offers a unified semantic explanation of two observations that prove to be problematic for classical analyses of modals, conditionals, and disjunctions: the fact that disjunctions scoping under possibility modals give rise to the free choice effect and the fact that counterfactuals license simplification of disjunctive antecedents. It shows that the data are well explained by a dynamic semantic analysis of modals and conditionals that uses ideas from the inquisitive semantic tradition in its treatment of disjunction. (...) The analysis explains why embedding a disjunctive possibility under negation reverts disjunction to its classical behavior, is general enough to predict less studied simplification patterns, and also makes progress toward a unified perspective on the distinction between informative, inquisitive, and attentive content. (shrink)

Philosophy and Phenomenological Research, EarlyView.

Causal Modeling Semantics (CMS, e.g., Galles and Pearl 1998; Pearl 2000; Halpern 2000) is a powerful framework for evaluating counterfactuals whose antecedent is a conjunction of atomic formulas. We extend CMS to an evaluation of the probability of counterfactuals with disjunctive antecedents, and more generally, to counterfactuals whose antecedent is an arbitrary Boolean combination of atomic formulas. Our main idea is to assign a probability to a counterfactual (A ∨ B) > C at a causal model M as (...) a weighted average of the probability of C in those submodels that truthmake A∨ B (Briggs 2012; Fine 2016, 2017). The weights of the submodels are given by the inverse distance to the original model M, based on a distance metric proposed by Eva, Stern, and Hartmann (2019). Apart from solving a major problem in the epistemology of counterfactuals, our paper shows how work in semantics, causal inference and formal epistemology can be fruitfully combined. (shrink)

I present data that suggest the universal entailments of counterfactual donkey sentences aren’t as universal as some have claimed. I argue that this favors the strategy of attributing these entailments to a special property of the similarity ordering on worlds provided by some contexts, rather than to a semantically encoded sensitivity to assignment.

Grice observes that the primary discourse function of disjunction is the presentation of alternatives, each of which is relevant in the same way to a given topic. After a brief introduction , I offer in Chapter Two an account of Grice's observation and of further felicity conditions on disjunction, for example, the constraint against disjunctions in which one disjunct entails another. Using an enriched version of the Stalnakerian model of assertion, I define two constraints on information update--Relevant Informativity and Simplicity--and (...) show that these suffice to account for the observations. ;I then argue that the requirement to abide by Relevant Informativity and Simplicity provides a basis for an account of two further properties of disjunctive sentences: their presupposition projection properties and the possibility of anaphora between disjuncts. I argue that presuppositions project in disjunction except where projection would lead to infelicity of the kind characterized in Chapter Two. To state this account, a treatment of presupposition which allows projection to be sensitive to considerations of felicity is required. I show that the Stalnakerian view of presupposition, combined with Heim's notion of local accommodation, provides the necessary framework. ;Similarly, I argue that anaphora across disjunction is disallowed only when it leads to an infelicitous disjunction. In certain configurations, anaphora between disjuncts leads to entailment between disjuncts, which is ruled out independently. The account is given using a version of Neale's E-type analysis of unbound anaphora. I show that the analysis has further desirable consequences with respect to more complex examples of inter-disjunct anaphora. ;Throughout Chapters Three and Four, I contrast my own proposals with accounts given in the Dynamic Semantic literature, offering a critique of Dynamic Semantic approaches to the phenomena discussed. ;In Chapter Five, I examine anaphora between NPs contained inside a disjunction and a pronoun in a following sentence. I argue that these pronouns are also E-type, but show that these cases require a reformulation of the E-type analysis. I develop a new account in which the interpretation of E-type pronouns is derived compositionally from the content of the antecedent clause. (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)

The natural interpretation of counterfactuals with disjunctive antecedents involves selecting from each of the disjuncts the worlds that come closest to the world of evaluation. It has been long noticed that capturing this interpretation poses a problem for a minimal change semantics for counterfactuals, because selecting the closest worlds from each disjunct requires accessing the denotation of the disjuncts from the denotation of the disjunctive antecedent, which the standard boolean analysis of or does not allow (Creary and (...) Hill, Philosophy of Science 43:341–344, 1975; Nute, Journal of Philosophy 72:773–778, 1975; Fine, Mind 84(335):451–458, 1975; Ellis et al. Journal of Philosophical Logic 6:335–357, 1977). This paper argues that the failure to capture the natural interpretation of disjunctive counterfactuals provides no reason to abandon a minimal change semantics. It shows that the natural interpretation of disjunctive counterfactuals is expected once we refine our assumptions about the semantics of or and the logical form of conditionals, and (i) we assume that disjunctions introduce propositional alternatives in the semantic derivation, in line with independently motivated proposals about the semantics of or (Aloni, 2003a; Simons, Natural Language Semantics 13:271–316, 2005; Alonso-Ovalle, Disjunction in Alternative Semantics. PhD thesis, 2006); and (ii) we treat conditionals as correlative constructions, as advocated in von Fintel (1994), Izvorski (Proceedings of NELS 26, 1996), Bhatt and Pancheva (2006), and Schlenker (2004). (shrink)

The main goal of this paper is to investigate the relation between the meaning of a sentence and its truth conditions. We report on a comprehension experiment on counterfactual conditionals, based on a context in which a light is controlled by two switches. Our main finding is that the truth-conditionally equivalent clauses (i) "switch A or switch B is down" and (ii) "switch A and switch B are not both up" make different semantic contributions when embedded in a conditional antecedent. (...) Assuming compositionality, this means that (i) and (ii) differ in meaning, which implies that the meaning of a sentential clause cannot be identified with its truth conditions. We show that our data have a clear explanation in inquisitive semantics: in a conditional antecedent, (i) introduces two distinct assumptions, while (ii) introduces only one. Independently of the complications stemming from disjunctive antecedents, our results also challenge analyses of counterfactuals in terms of minimal change from the actual state of affairs: we show that such analyses cannot account for our findings, regardless of what changes are considered minimal. (shrink)

The connective or can be treated as an inclusive disjunction or else as an exclusive disjunction. Although researchers are aware of this distinction, few have examined the conditions under which each interpretation should be anticipated. Based on linguistic-pragmatic analyses, we assume that interpretations are initially inclusive before either (a) remaining so, or (b) becoming exclusive by way of an implicature ( but not both ). We point to a class of situations that ought to predispose disjunctions to inclusive interpretations and (...) to situations that encourage exclusive interpretations. A disjunction's ultimate interpretation is based on its potential informativeness, where the interpretation of the disjunctive utterance having the smallest number of true conditions is considered most informative. Our investigation leads to five experiments employing arbitrary materials. Among the problems expected to encourage inclusive interpretations are those that present disjunctions in the antecedents of conditionals and in question forms. The best candidates to produce implicatures are those disjunctions that underdetermine an expected conjunctive conclusion, although other disjunctive utterances that are more informative as exclusive are discussed and tested. (shrink)

A uniform theory of conditionals is one which compositionally captures the behavior of both indicative and subjunctive conditionals without positing ambiguities. This paper raises new problems for the closest thing to a uniform analysis in the literature (Stalnaker, Philosophia, 5, 269–286 (1975)) and develops a new theory which solves them. I also show that this new analysis provides an improved treatment of three phenomena (the import-export equivalence, reverse Sobel-sequences and disjunctive antecedents). While these results concern central issues in (...) the study of conditionals, broader themes in the philosophy of language and formal semantics are also engaged here. This new analysis exploits a dynamic conception of meaning where the meaning of a symbol is its potential to change an agent’s mental state (or the state of a conversation) rather than being the symbol’s content (e.g. the proposition it expresses). The analysis of conditionals is also built on the idea that the contrast between subjunctive and indicative conditionals parallels a contrast between revising and consistently extending some body of information. (shrink)

The aim of this paper is to investigate the function of the aesthetic paradigm of German idealism within Adorno’s thought. In order to do so, I have chosen to focus on the issue of the social significance of the work of art and the role played by the concept of literary material. Adorno’s aesthetics, in fact, can be read as a reinterpretation of the idealist aesthetic model based precisely on a non-idealist notion such as that of aesthetic material.If one is (...) to allow a seemingly brutal simplification, there are two ways to think about the social meaning of literature. One identifies somehow the subject of the text, assesses whether or not this challenges the society from which the literary work stems, and on this ground establishes its social character. According to this perspective, Brecht’s Threepenny Opera and Sciascia’s The Day of the Owl can be seen as socially engaged literature, while Proust’s Recherche cannot, or can only to a lesser extent. The other approach argues instead that any literary work, and in any of its instances, says something about the society in which it takes shape. In this contribution I would like to focus on this latter approach. In particular, I am interested in understanding how literature is connected to society, that is, through which identifiable elements literary works express certain aspects of society. The Hegelian idealistic idea according to which Greek tragedy expresses the constitutive features of Athenian society, and which is found again and again in the authors who in various ways have taken up Hegel’s legacy, is generally accepted as such and valued for the explanatory opportunities it offers. It is my opinion, however, that one notion in particular can be retrieved within the whole inherited baggage of that aesthetic tradition, which may be able to further clarify the relationship between literature and society. This concept is that of material and the author who has most thoroughly investigated it is Adorno. In this paper I will try to outline the main features of a counterintuitive notion such as that of “literary material” and thereby explain why it plays such an important role in Adorno’s rework of the aesthetic paradigm of German idealism. The concept of material, in fact, is key to the definition of another aesthetic category around which, according to Adorno, most of the problems connected to works of art gravitate, that is to say, the notion of form. From Adorno’s aesthetics, in fact, one of his most insightful readers, Peter Szondi, draws the main principle for his study of the historical form of modern drama, namely the idea that form is essentially a precipitation, a sedimentation of contents. The work of art, then, at least according to this definition, is essentially identified by its form. Or, better said, the artwork must be interpreted as the way in which a certain (historical) content sediments in a certain external form. That the form of the work of art is precipitated content means, in simple terms, that no effective disjunction can be assumed between form and content. This is how Adorno reinterprets the concept of “identity of form and content” stressed by classical aesthetics. The content is such only insofar as it is precipitated into a certain form. This amounts to saying that no objective distinction can be established between one and the other. Now, if one were to ask how the form is made, Adorno’s answer is quite straightforward: the form is made by means of organization and, precisely, by means of the organization of the material. As one reads in Aesthetic Theory, in fact, “the substantial element of genres and forms has its locus in the historical needs of their materials,” and the particular form of an artwork is defined as the “organization” of its “materials” (Adorno 1970, transl. 1997: 201). The concept of material, therefore, is key to the definition of the very notion of work of art in its constituent components, namely the relationship between form and content. In this paper I will first of all clarify the notion of artistic material in general and subsequently I will turn to strictly literary material. Finally, and this is the main goal of this essay, I will show to what extent this definition of the material possibly contributes to a better understanding of a widely and variedly debated literary phenomenon of our time, namely the form of the so-called postmodern novel. (shrink)

Based on a crowdsourced truth value judgment experiment, we provide empirical evidence challenging two classical views in semantics, and we develop a novel account of counterfactuals that combines ideas from inquisitive semantics and causal reasoning. First, we show that two truth-conditionally equivalent clauses can make different semantic contributions when embedded in a counterfactual antecedent. Assuming compositionality, this means that the meaning of these clauses is not fully determined by their truth conditions. This finding has a clear explanation in inquisitive semantics: (...) truth-conditionally equivalent clauses may be associated with different propositional alternatives, each of which counts as a separate counterfactual assumption. Second, we show that our results contradict the common idea that the interpretation of a counterfactual involves minimizing change with respect to the actual state of affairs. We propose to replace the idea of minimal change by a distinction between foreground and background for a given counterfactual assumption: the background is held fixed in the counterfactual situation, while the foreground can be varied without any minimality constraint. (shrink)

Much has been said about the logical difference between rules and principles, yet few authors have focused on the distinct logical connectives linking the normative conditions of both norms. I intend to demonstrate that principles, unlike rules, are norms whose antecedents are linguistically formulated in a generic fashion, and thus logically described as inclusive disjunctions. This core feature incorporates the relevance criteria of normative antecedents into the world of principles and also explains their aptitude to conflict with opposing (...) norms, namely that their consequents are fulfilled to varying extents more frequently than those of rules. I conclude that the property of genericity should be predicated to the norm antecedent of principles, more precisely to the hypothetical action. This is of paramount importance to explain, in terms of logical implication and exclusion, the expansibility of competing principles, in contrast with the exclusive character of conflicting rules. (shrink)

An operator of contraction for a belief set (a theory) can be obtained by assigning to it a belief base and an operator of partial meet contraction for that base. It is argued that closure of the base under disjunction is an intuitively reasonable condition. Axiomatic characterizations are given of the contractions of belief sets that can be generated by (various types of) partial meet contraction on disjunctively closed bases. The corresponding revision operators are also characterized. Finally, some results are (...) reported on operations on bases that are closed under material implication. (shrink)

We present a set of algorithms for automated simplification of symbolic constants of the form ∑iαixi with αi rational and xi complex. The included algorithms, called SimplifySum2 and implemented in Mathematica, remove redundant terms, attempt to make terms and the full expression real, and remove terms using repeated application of the multipair PSLQ integer relation detection algorithm. Also included are facilities for making substitutions according to user-specified identities. We illustrate this toolset by giving some real-world examples of its usage, (...) including one, for instance, where the tool reduced a symbolic expression of approximately 100 000 characters in size enough to enable manual manipulation to one with just four simple terms.2Available from https://github.com/alexkaiser/SimplifySum. (shrink)

Nelson Goodman has constructed two theories of simplicity: one of predicates; one of hypotheses. I offer a simpler theory by generalization and abstraction from his. Generalization comes by dropping special conditions Goodman imposes on which unexcluded extensions count as complicating and which excluded extensions count as simplifying. Abstraction is achieved by counting only nonisomorphic models and subinterpretations. The new theory takes into account all the hypotheses of a theory in assessing its complexity, whether they were projected prior to, or result (...) from, projection of a given hypothesis. It assigns simplicity post-projection priority over simplicity pre-projection. It better orders compound conditionals than does the theory of simplicity of hypotheses, and it does not inherit an anomaly of the theory of simplicity of predicates — its failure to order the ordering relations. Drop Goodman's special conditions, and the problems fall away with them. (shrink)

The modal completeness proofs of Guaspari and Solovay (1979) for their systems R and R – are improved and the relationship between R and R – is clarified.

The present paper proposes a generalisation of the notion of disjunctive sequence, that is, of an infinite sequence of letters having each finite sequence as a subword. Our aim is to give a reasonable notion of disjunctiveness relative to a given set of sequences F. We show that a definition like “every subword which occurs at infinitely many different positions in sequences in F has to occur infinitely often in the sequence” fulfils properties similar to the original unrelativised notion (...) of disjunctiveness. Finally, we investigate our concept of generalised disjunctiveness in spaces of Cantor expansions of reals. (shrink)

At the beginning of his influential De Nominum Analogia, Thomas de Vio Cajetan mentions three mistaken positions on analogy. He does not attach names to these positions, but each one was held by distinguished Thomists of the fourteenth and fifteenth centuries. Furthermore, their proponents were responding to the same set of challenges from John Duns Scotus that set the agenda for the De Nominum Analogia. In this paper, I would like to do something that Cajetan did not do, and that (...) is, directly consider the merits of the first position in his list of mistaken accounts of analogy; namely, the position that analogy is constituted by disjunction. More specifically, this paper investigates the polemical use for which Hervaeus Natalis deployed analogy of disjunction; the reply of John Duns Scotus; and the implications of this back and forth for understanding the Thomist-Scotist dispute over the concept of being. (shrink)

This study is concerned with the properties of the disjunction operator, or, and the acquisition of these properties by English-speaking children. Previous research has concluded that adult truth conditions for logical connectives are acquired relatively late in the course of language development. With particular reference to disjunction, the results of several studies have led to two claims. First, it has been argued that the full range of truth-conditions associated with inclusive-or is not initially available to children; instead, children are supposed (...) to interpret disjunction using the truth conditions that are associated with exclusive-or (e.g., Beilin and Lust 1975; Braine and Rumain 1981, 1983; Paris 1973). A second, related claim is that even when children respond as if they have access to the complete range of truth conditions, their responses result from the failure to distinguish or from and (Paris, 1973). Different conclusions were reached in recent work by Chierchia, Crain, Guasti and Thornton (1998). The experiments conducted by Chierchia et al. (1998) draw upon a distinction between linguistic contexts. In one type of context, the inclusive-or reading of disjunction is available. By contrast, in another type of context, the exclusive-or reading of disjunction is highly preferred; the truth conditions that are uniquely associated with the inclusive-or reading are eliminated in such contexts due to conversational implicatures. One context that cancels conversational implicatures is called the Prediction Mode by Chierchia et al. (1998). Notice that a prediction like (1) is consistent with different scenarios. (shrink)