I explore the logic of the conditional, using credence judgments to argue against Duality and in favor of Conditional Excluded Middle. I then explore how to give a theory of the conditional which validates the latter and not the former, developing a variant on Kratzer (1981)'s restrictor theory, as well as a proposal which combines Stalnaker (1968)'s theory of the conditional with the theory of epistemic modals I develop in Mandelkern 2019a. I argue that the latter approach fits naturally with (...) a conception of conditionals as referential devices which allow us to talk about particular worlds. (shrink)

Higginbotham (1986) observed that quantified conditionals have a stronger meaning than might be expected, as attested by the apparent equivalence of examples like No student will pass if he goofs off and Every student will fail if he goofs off. Higginbotham's observation follows straightforwardly given the validity of conditional excluded middle (CEM; as observed by von Fintel & Iatridou 2002), and as such could be taken as evidence thereof (e.g. Williams forthcoming). However, the empirical status of CEM has been disputed, (...) and it is invalid under many prominent theories of conditionals—notably Lewis (1973) for counterfactuals, also Kratzer (1979, 1991). More acutely, Higginbotham's observation holds even for quantified counterparts of conditionals that appear not to obey CEM (Higginbotham 2003), and the standard way of explaining (away) such apparent counterexamples to the principle, à la Stalnaker (1981), does not directly yield an account of our apparent truth-conditional intuitions about the quantified counterparts (Leslie 2009). This article provides an explanation for the latter intuitions within Stalnaker's framework, the upshot being that CEM does remain a viable explanation, in principle, for Higginbotham's observation. (shrink)

This paper discusses and relates two puzzles for indicative conditionals: a puzzle about indeterminacy and a puzzle about triviality. Both puzzles arise because of Ramsey's Observation, which states that the probability of a conditional is equal to the conditional probability of its consequent given its antecedent. The puzzle of indeterminacy is the problem of reconciling this fact about conditionals with the fact that they seem to lack truth values at worlds where their antecedents are false. The puzzle of triviality is (...) the problem of reconciling Ramsey's Observation with various triviality proofs which establish that Ramsey's Observation cannot hold in full generality. In the paper, I argue for a solution to the indeterminacy puzzle and then apply the resulting theory to the triviality puzzle. On the theory I defend, the truth conditions of indicative conditionals are highly context dependent and such that an indicative conditional may be indeterminate in truth value at each possible world throughout some region of logical space and yet still have a nonzero probability throughout that region. (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)

Deontic necessity modals (e.g. 'have to', 'ought to', 'must', 'need to', 'should', etc.) seem to vary in how they interact with negation. According to some accounts, what forces modals like 'ought' and 'should' to outscope negation is their polarity sensitivity -- modals that scope over negation do so because they are positive polarity items. But there is a conflict between this account and a widely assumed theory of if-clauses, namely the restrictor analysis. In particular, the conflict arises for constructions containing (...) a bound pronoun in the if-clause. This note spells out the core conflict. (shrink)

This paper concerns a thorny problem posed by conditional requirements: we expect some modal conditionals of the form ‘if p, then it must be that p’ to be false, yet they all come out true given two basic assumptions needed to account for ordinary conditional requirement like ‘If the light turns red, then cars must stop’. The first assumption is a semantic expectation linking conditional requirements with absolute ones, the second is the possible-worlds-based definition of modal sentences. Keeping the former (...) means giving up the latter, a result with profound implications for Kratzer’s formal semantics, modifications thereof, as well as deontic logics. (shrink)

A compositional theory of perceptual representations would explain how the accuracy conditions of a given type of perceptual state depend on the contents of constituent perceptual representations and the way those constituents are structurally related. Such a theory would offer a basic framework for understanding the nature, grounds, and epistemic significance of perception. But an adequate semantics of perceptual representations must accommodate the holistic nature of perception. In particular, perception is replete with context effects, in which the way one perceptually (...) represents one aspect of a scene (including the position, size, orientation, shape, color, motion, or even unity of an object) normally depends on how one represents many other aspects of the scene. The ability of existing accounts of the semantics of perception to analyze context effects is at best unclear. Context effects have even been thought to call into question the very feasibility of a systematic semantics of perception. After outlining a compositional semantics for a rudimentary set of percepts, I draw on empirical models from perceptual psychology to show how such a theory must be modified to analyze context effects. Context effects arise from substantive constraints on how perceptual representations can combine and from the different semantic roles that perceptual representations can have. I suggest that context effects are closely tied to the objectivity of perception. They arise from a perceptual grammar that functions to facilitate the composition of reliably accurate representations in an uncertain but structured world. (shrink)

§§3-4 of the Begriffsschrift present Frege’s objections to a dominant if murky nineteenth-century semantic picture. I sketch a minimalist variant of the pre-Fregean picture which escapes Frege’s criticisms by positing a thin notion of semantic content which then interacts with a multiplicity of kinds of truth to account for phenomena such as modality. After exploring several ways in which we can understand the existence of multiple truth properties, I discuss the roles of pointwise and setwise truth properties in modal logic. (...) I argue that thinking of supertruth and determinate truth as setwise truth properties allows an understanding of supervaluationist approaches to vagueness which escapes both Williamson’s objections to and a needless metalinguistic orientation of traditional supervaluationism. (shrink)

The goal of inquiry in this essay is to ascertain to what extent the Principle of Compositionality – the thesis that the meaning of a complex expression is determined by the meaning of its parts and its mode of composition – can be justifiably imposed as a constraint on semantic theories, and thereby provide information about what meanings are. Apart from the introduction and the concluding chapter the thesis is divided into five chapters addressing different questions pertaining to the overarching (...) goal of inquiry. Chapter Two is an attempt to determine whether the Principle of Compositionality is a trivial principle. It is argued that this is not the case in the context of providing the semantics of natural languages since it is an open question whether the best theories that respect available syntactic and semantic data are compositional. Chapter Three and Chapter Four ask whether there are reasons to think that the Principle of Compositionality is true. It is argued that the three most commonly cited reasons for thinking that correct semantic theories must be compositional – Linguistic Creativity, Productivity and Systematicity – in fact only give us reasons to think that the meaning of complex expressions depend on the meanings of their parts and their modes of composition, but not that the meaning of complex expressions depend ONLY on those factors. Chapter Five asks whether there are any reasons to think that the Principle of Compositionality is false. It is argued that all the phenomena that have been suggested entail non-compositionality are in fact compatible with some versions of compositionality. Even if this conclusion is reached in this chapter, the conclusion of the previous two chapters entails that we are not justified in imposing the Principle of Compositionality as an adequacy constraint on Semantic theories. Chapter Six explores the ways in which information about what meanings are can be derived by imposing constraints on semantic theories. It is argued that the distinction emphasized in Chapter Three and Chapter Four between depending on and depending ONLY on is of critical importance. It is demonstrated that the informative potential of the Principle of Compositionality goes far beyond that of the principle we are in fact justified in imposing on semantic theories. So not only is it the case that we cannot learn anything about meanings from the justified imposition of the Principle of Compositionality – since we cannot justifiably impose it as a constraint on semantic theories – what we could have learned from it had we been justified in imposing it is very different from what we can learn from the principle that we are justified in imposing. (shrink)

This note identifies and corrects some problems in developments of the thesis that predictive expressions, such as English "will", are modals. I contribute a new argument supporting Cariani and Santorio's recent claim that predictive expressions are non-quantificational modals. At the same time, I improve on their selectional semantics by fixing an important bug. Finally, I show that there are benefits to be reaped by integrating the selection semantics framework with standard ideas about the future orientation of modals.

Higginbotham argues that conditionals embedded under quantifiers constitute a counterexample to the thesis that natural language is semantically compositional. More recently, Higginbotham and von Fintel and Iatridou have suggested that compositionality can be upheld, but only if we assume the validity of the principle of Conditional Excluded Middle. I argue that these authors’ proposals deliver unsatisfactory results for conditionals that, at least intuitively, do not appear to obey Conditional Excluded Middle. Further, there is no natural way to extend their accounts (...) to conditionals containing ‘unless’. I propose instead an account that takes both ‘if’ and ‘unless’ statements to restrict the quantifiers in whose scope they occur, while also contributing a covert modal element to the semantics. In providing this account, I also offer a semantics for unquantified statements containing ‘unless’. (shrink)