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)

Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form $$p\wedge \Diamond \lnot p$$ (‘p, but it might be that not p’) appears to be a contradiction, $$\Diamond \lnot p$$ does not entail $$\lnot p$$, which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. (...) Some theories predict that $$ p\wedge \Diamond \lnot p$$, a so-called epistemic contradiction, is a contradiction only in an etiolated sense, under a notion of entailment that does not always allow us to replace $$p\wedge \Diamond \lnot p$$ with a contradiction; these theories underpredict the infelicity of embedded epistemic contradictions. Other theories savage classical logic, eliminating not just rules that intuitively fail, like distributivity and disjunctive syllogism, but also rules like non-contradiction, excluded middle, De Morgan’s laws, and disjunction introduction, which intuitively remain valid for epistemic modals. In this paper, we aim for a middle ground, developing a semantics and logic for epistemic modals that makes epistemic contradictions genuine contradictions and that invalidates distributivity and disjunctive syllogism but that otherwise preserves classical laws that intuitively remain valid. We start with an algebraic semantics, based on ortholattices instead of Boolean algebras, and then propose a possibility semantics, based on partial possibilities related by compatibility. Both semantics yield the same consequence relation, which we axiomatize. We then show how to lift an arbitrary possible worlds model for a non-modal language to a possibility model for a language with epistemic modals. The goal throughout is to retain what is desirable about classical logic while accounting for the non-classicality of epistemic vocabulary. (shrink)

Data involving epistemic modals suggest that some classically valid argument forms, such as _reductio_, are invalid in natural language reasoning as they lead to modal collapses. We adduce further data showing that the classical argument forms governing the existential quantifier are similarly defective, as they lead to a _de re–de dicto_ collapse. We observe a similar problem for disjunction. But if the classical argument forms for negation, disjunction and existential quantification are invalid, what are the correct forms that govern the (...) use of these items? Our diagnosis is that epistemic modals interfere with hypothetical reasoning. We present a modal first-order logic and model theory that characterizes hypothetical reasoning with epistemic modals in a principled manner. One upshot is a sound and complete natural deduction system for reasoning with epistemic modals in first-order logic. (shrink)

Mind &Language, Volume 35, Issue 1, Page 115-138, February 2020.

This paper has three main goals. First, to motivate a puzzle about how ignorance-expressing terms like maybe and if interact: they iterate, and when they do they exhibit scopelessness. Second, to argue that there is an ambiguity in our theoretical toolbox, and that exposing that opens the door to a solution to the puzzle. And third, to explore the reach of that solution. Along the way, the paper highlights a number of pleasing properties of two elegant semantic theories, explores some (...) meta-theoretic properties of dynamic notions of meaning, dips its toe into some hazardous waters, and offers characterization theorems for the space of meanings an indicative conditional can have. (shrink)

If modus ponens is valid, then you should take up smoking.

Arguments have always played a central role within logic and philosophy. But little attention has been paid to arguments as a distinctive kind of discourse, with its own semantics and pragmatics. The goal of this essay is to study the mechanisms by means of which we make arguments in discourse, starting from the semantics of argument connectives such as `therefore'. While some proposals have been made in the literature, they fail to account for the distinctive anaphoric behavior of `therefore', as (...) well as uses of argument connectives in complex arguments, suppositional arguments, arguments with non-declarative conclusions, as well as arguments with parenthetical remarks. A comprehensive account of arguments requires imposing a distinctive tree-like structure on contexts. We show how to extend our account to accommodate modal subordination and and di fferent flavors of `therefore'. (shrink)

The standard semantics for modality, together with the influential restrictor analysis of conditionals (Kratzer, 1986, 2012) renders conditional ought claims like “If John’s stealing, he ought to be stealing” trivially true. While this might seem like a problem specifically for the restrictor analysis, the issue is far more general. Any account must predict that modals in the consequent of a conditional sometimes receive obligatorily unrestricted interpretation, as in the example above, but sometimes appear restricted, as in, e.g., “If John’s speeding, (...) he ought to pay the fine.” And the problem runs deeper, for there are non-conditional variants of the data. Thus, the solution cannot lie in adopting a particular analysis of conditionals, nor a specific account of the interaction between conditionals and modals. Indeed, with minimal assumptions, the standard account of modality will render a myriad of claims about what one ought to, must, or may, do trivially true. Worse, the problem extends to a wide range of non-deontic modalities, including metaphysical modality. But the disaster has a remedy. I argue that the source of the problem for the standard account lies in its failure to capture an inferential evidence constraint encoded in the meaning of a wide range of modal constructions. I offer an account that captures this constraint, and show it provides a general and independently motivated solution to the problem. (shrink)

In this paper, I consider a variant of the ancient Idle Argument involving so‐called “unconditionals” with interrogative antecedents. This new Idle Argument provides an ideal setting for probing the logic of these close relatives of if‐conditionals, which has been comparatively underexplored. In the course of refuting the argument, I argue that contrary to received wisdom, many unconditionals do not entail their main clauses, yet modus ponens is still unrestrictedly valid for this class of expressions. I make these lessons precise in (...) a formal system drawing on recent work in inquisitive semantics. My larger aim is to challenge standard truth preservation accounts of logic and deductive argumentation. (shrink)

Utterances of natural language sentences can be used to communicate not just contents, but also forces. This paper examines this topic from a cross-linguistic perspective on sentential mood. Recent work in this area focuses on conversational dynamics: the three sentence types can be associated with distinctive kinds of conversational effects called sentential forces, modeled as three kinds of updates to the discourse context. This paper has two main goals. First, it provides two arguments, on empirical and methodological grounds, for treating (...) sentential force as part of a compositional dynamic semantics, rather than a dynamic pragmatics. Second, it formulates a minimal dynamic semantic analysis that covers the data at the heart of these arguments, incorporating existing analyses of the three major moods, evidentials and conjunction. A further aim of the paper is to sharpen the distinction between sentential force and utterance force, and discuss its implications. (shrink)

Reasoning with conditionals is central to everyday life, yet there is long-standing disagreement about the meaning of the conditional. One example is the puzzle of so-called missing-link conditionals such as "if raccoons have no wings, they cannot breathe under water." Their oddity may be taken to show that conditionals require a connection between antecedent ("raccoons have no wings") and consequent ("they cannot breathe under water"), yet most accounts of conditionals attribute the oddity to natural language pragmatics. We present an experimental (...) study disentangling the pragmatic requirement of discourse coherence from a stronger notion of connection: probabilistic relevance. Results indicate that mere discourse coherence is not enough to make conditionals assertable. (shrink)

Propositions are posited to perform a variety of explanatory roles. One important role is being what is designated by a dedicated linguistic expression like a "that"-clause. In this paper, the case that propositions are needed for such a role is bolstered by defending that there are other expressions dedicated to designating propositions. In particular, it is shown that natural language has anaphors for propositions. Complement "so" and the response markers "yes" and "no" are argued to be such expressions.

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)

Many recent theories of epistemic discourse exploit an informational notion of consequence, i.e. a notion that defines entailment as preservation of support by an information state. This paper investigates how informational consequence fits with probabilistic reasoning. I raise two problems. First, all informational inferences that are not also classical inferences are, intuitively, probabilistically invalid. Second, all these inferences can be exploited, in a systematic way, to generate triviality results. The informational theorist is left with two options, both of them radical: (...) they can either deny that epistemic modal claims have probability at all, or they can move to a nonstandard probability theory. (shrink)

Drawing on the puzzling behavior of ordinary knowledge ascriptions that embed an epistemic (im)possibility claim, we tentatively conclude that it is untenable to jointly endorse (i) an unfettered classical logic for epistemic language, (ii) the general veridicality of knowledge ascription, and (iii) an intuitive ‘negative transparency’ thesis that reduces knowledge of a simple negated ‘might’ claim to an epistemic claim without modal content. We motivate a strategic trade-off: preserve veridicality and (generalized) negative transparency, while abandoning the general validity of contraposition. (...) We criticize various approaches to incorporating veridicality into domain semantics, a paradigmatic ‘information-sensitive’ framework for capturing negative transparency and, more generally, the non-classical behavior of sentences with epistemic modals. We then present a novel information-sensitive semantics that successfully executes our favored strategy: stable acceptance semantics, extending a vanilla bilateral state-based semantics for epistemic modals with a knowledge operator loosely inspired by the defeasibility theory of knowledge. (shrink)

Arguments and conditionals are powerful means language provides us to reason about possibilities and to reach conclusions from premises. These two kinds of constructions exhibit several affinities—e.g., they both come in different varieties depending on the mood; they share some of the same connectives (i.e., ‘then’); they allow for similar patterns of modal subordination. In the light of these affinities, it is not surprising that prominent theories of conditionals—old and new suppositionalisms as well as dynamic theories of conditionals—as well as (...) certain reductive theories of arguments tend to semantically assimilate conditionals and arguments. In this paper, I shall marshall some linguistic evidence as well as some theoretical considerations for thinking that, despite these similarities, arguments and conditionals should be given a different semantics and I shall lay out a framework that can capture at least some of their affinities while accounting for their outstanding differences. (shrink)

In this paper I focus on a recently discussed phenomenon illustrated by sentences containing predicates of taste: the phenomenon of " perspectival plurality " , whereby sentences containing two or more predicates of taste have readings according to which each predicate pertains to a different perspective. This phenomenon has been shown to be problematic for (at least certain versions of) relativism. My main aim is to further the discussion by showing that the phenomenon extends to other perspectival expressions than predicates (...) of taste and by proposing a general solution to the problem raised by it on behalf of the relativist. The core claim of the solution (" multiple indexing ") is that utterances of sentences containing perspectival expressions should be evaluated with respect to (possibly infinite) sequences of perspective parameters. (shrink)