Papers on Logic and Language

Humberstone on Possibility Frames

In his 1981 paper “From Worlds to Possibilities”, Lloyd Humberstone developed an approach to modal logic using possibilities rather than possible worlds. Possibilities, unlike worlds, may be incomplete. This paper sets out the possibility frame approach to modal logic, proves some results about its logic (including that some logics definable on Humberstone frames are not definable on Kripke frames), and surveys several applications, including to conditionals, vagueness, and fiction.

Brian Weatherson

Deference and Infinite Frames

Three recent results about probabilistic deference, due to Zhang, Geanakoplos, and Dorst et al,. each hold for all finite probability frames but fail when frames are allowed to be infinite. Zhang’s result, that a novice cannot defer to two experts while planning to always have a credence strictly between them when they disagree, requires a finite range of possible expert credences; a counterexample using normal distributions shows it fails otherwise. Geanakoplos’s result, that more informative experiments are more valuable when experiments are reflexive, transitive, and nested, does not extend to uncountable frames with discontinuous payoffs, nor does it extend when both the state space and the option set are infinite. The equivalence Dorst et al. establish between Total Trust and Value breaks down in both directions on infinite frames: Total Trust can hold without Value (when utilities are unbounded), and Value can hold without Total Trust (when the option set is finite but the state space is countably infinite). These failures raise questions about the philosophical significance of results that hold only in the finite case, though the paper largely sets those questions aside in favour of establishing the formal results.

Brian Weatherson

Vagueness as Indeterminacy

Traditionally, we thought vague predicates were predicates with borderline cases. In recent years traditional wisdom has come under attack from several leading theorists. They are motivated by a common idea, that terms with borderline cases, but sharp boundaries around the borderline cases, are not vague. I argue for a return to tradition. Part of the argument is that the alternatives that have been proposed are themselves subject to intuitive counterexample. And part of the argument is that we need a theory of what vagueness is that applies to non-predicates. The traditional picture can be smoothly generalised to non-predicates if we identify vagueness generally with indeterminacy. Modern rivals to tradition do not admit of such smooth generalisation.

Brian Weatherson

Notes on Some Ideas in Lloyd Humberstone’s Philosophical Applications of Modal Logic

Lloyd Humberstone’s recently published Philosophical Applications of Modal Logic presents a number of new ideas in modal logic as well explication and critique of recent work of many others. We extend some of these ideas and answer some questions that are left open in the book.

Steven Kuhn, Brian Weatherson

Relativism

Relativism is the view that the truth of a sentence is relative both to a context of utterance and to a context of assessment. That the truth of a sentence is relative to a context of utterance is uncontroversial in contemporary semantics. This chapter focuses on three points: whether the version of contextualism is vulnerable to the disagreement and retraction arguments, and if so, whether these problems can be avoided by a more sophisticated contextualist theory. The points include: whether relativism really does avoid the four problems posed for the other theories; and whether there are other theories that also avoid the problems, without running into the problems facing relativism or problems of their own. The chapter concentrates on two families of views that have been called relativist: Relativism about propositional truth; and Relativism about utterance truth.

Brian Weatherson, Patrick Shirreff

Analytic-Synthetic and A Priori-A Posteriori

This article focuses on the distinction between analytic truths and synthetic truths (i.e. every truth that isn’t analytic), and between a priori truths and a posteriori truths (i.e. every truth that isn’t a priori) in philosophy, beginning with a brief historical survey of work on the two distinctions, their relationship to each other, and to the necessary/contingent distinction. Four important stops in the history are considered: two involving Kant and W. V. O. Quine, and two relating to logical positivism and semantic externalism. The article then examines questions that have been raised about the analytic–synthetic and a priori–a posteriori distinctions, such as whether all distinctively philosophical truths fall on one side of the line and whether the distinction is relevant to philosophy. It also discusses the argument that there is a lot more a priori knowledge than we ever thought, and concludes by describing epistemological accounts of analyticity.

Brian Weatherson

The Role of Naturalness in Lewis’s Theory of Meaning

Many writers have held that in his later work, David Lewis adopted a theory of predicate meaning such that the meaning of a predicate is the most natural property that is (mostly) consistent with the way the predicate is used. That orthodox interpretation is shared by both supporters and critics of Lewis’s theory of meaning, but it has recently been strongly criticised by Wolfgang Schwarz. In this paper, I accept many of Schwarz’s criticisms of the orthodox interpretation, and add some more. But I also argue that the orthodox interpretation has a grain of truth in it, and seeing that helps us appreciate the strength of Lewis’s late theory of meaning.

Brian Weatherson

In Defense of a Kripkean Dogma

A reply to some empirical arguments against Kripkean meta-semantics.

Jonathan Jenkins Ichikawa, Ishani Maitra, Brian Weatherson

Epistemic Modals and Epistemic Modality

This chapter introduces the main themes of the volume, summarizes the chapters in it, and looks at the various arguments that have been raised for semantic relativism over the past decade. It concludes that two of these arguments seem to be resistant to the anti-relativist replies that have appeared in response to this work on relativism. One of these is an argument from agreement. It is argued that contextualist theories about various puzzling locutions have a hard time explaining why it is so easy for people who would happily utter the same words to describe themselves as agreeing, if those words were really context-sensitive. Another is an argument concerning attitude ascriptions. It seems there are quite different restrictions on what values the (allegedly) context-sensitive expressions can take inside and outside of attitude ascriptions. Since this isn’t how context-sensitive terms usually behave, this phenomena tells against contextualism, and in favour of relativism.

Brian Weatherson, Andy Egan

No Royal Road to Relativism

A reponse to Relativism and Monadic Truth. I argue that while the Cappelen and Hawthorne have good responses to the deductive arguments for relativism, there are various good inductive arguments for relativism that their view can’t adequately respond to.

Brian Weatherson

Assertion, Knowledge, and Action

We argue against the knowledge rule of assertion, and in favour of integrating the account of assertion more tightly with our best theories of evidence and action. We think that the knowledge rule has an incredible consequence when it comes to practical deliberation, that it can be right for a person to do something that she can’t properly assert she can do. We develop some vignettes that show how this is possible, and how odd this consequence is. We then argue that these vignettes point towards alternate rules that tie assertion to sufficient evidence-responsiveness or to proper action. These rules have many of the virtues that are commonly claimed for the knowledge rule, but lack the knowledge rule’s problematic consequences when it comes to assertions about what to do.

Ishani Maitra, Brian Weatherson

Conditionals and Indexical Relativism

I set out and defend a view on indicative conditionals that I call “indexical relativism”. The core of the view is that which proposition is (semantically) expressed by an utterance of a conditional is a function of (among other things) the speaker’s context and the assessor’s context. This implies a kind of relativism, namely that a single utterance may be correctly assessed as true by one assessor and false by another.

Brian Weatherson

Attitudes and Relativism

Data about attitude reports provide some of the most interesting arguments for, and against, various theses of semantic relativism. This paper is a short survey of three such arguments. First, I’ll argue (against recent work by von Fintel and Gillies) that relativists can explain the behaviour of relativistic terms in factive attitude reports. Second, I’ll argue (against Glanzberg) that looking at attitude reports suggests that relativists have a more plausible story to tell than contextualists about the division of labour between semantics and meta-semantics. Finally, I’ll offer a new argument for invariantism (i.e. against both relativism and contextualism) about moral terms. The argument will turn on the observation that the behaviour of normative terms in factive and non-factive attitude reports is quite unlike the behaviour of any other plausibly context-sensitive term.

Brian Weatherson

Doing Philosophy With Words

This paper discusses the coverage of ordinary language philosophy in Scott Soames’ “Philosophical Analysis in the Twentieth Century”. After praising the book’s virtues, I raise three points where I dissent from Soames’ take on the history. First, I suggest that there is more to ordinary language philosophy than the rather implausible version of it that Soames sees to have been destroyed by Grice. Second, I argue that confusions between analyticity, necessity and priority are less important to the ordinary language period than Soames takes them to be. Finally, I claim that Soames’ criticisms of Ryle turn in part on attributing reductionist positions to Ryle that Ryle did not hold.

Brian Weatherson

Questioning Contextualism

This chapter argues against the pragmatism that shows that there is a striking disanalogy between the behavior of “knows” in questions and the behavior of “knows” in terms. The chapter discusses that different people may have different standards for knowledge, so perhaps they may mean different things by a statement, because they communicate to meet their preferred standards for knowledge. Standards for knowledge are not the kind of thing that people can differ on without making a mistake, in the way one would say that different people can have different immediate goals (about what to have for dinner) without making a mistake. This explains that one does not just adopt questioners’ standards for knowledge while answering their knowledge questions. So, it is argued that questions involving “knows” should have the three properties—speaker, clarification, and different answers. However, the counter argument is that the proposition can be true relative to some contexts and false relative to other contexts, just as temporality about propositions that a proposition can be true at some times and false at other times, and the utterance is true if the proposition is true only in the context of the utterance.

Brian Weatherson

Epistemic Modals in Context

A very simple contextualist treatment of a sentence containing an epistemic modal, e.g. a might be F, is that it is true iff for all the contextually salient community knows, a is F. It is widely agreed that the simple theory will not work in some cases, but the counterexamples produced so far seem amenable to a more complicated contextualist theory. We argue, however, that no contextualist theory can capture the evaluations speakers naturally make of sentences containing epistemic modals. If we want to respect these evaluations, our best option is a relativist theory of epistemic modals. On a relativist theory, an utterance of a might be F can be true relative to one context of evaluation and false relative to another. We argue that such a theory does better than any rival approach at capturing all the behaviour of epistemic modals.

Andy Egan, John Hawthorne, Brian Weatherson

True, Truer, Truest

My theory of vagueness.

Brian Weatherson

Review of “Real Conditionals”

Review of William Lycan, “Real Conditionals”. Oxford: Clarendon Press, 2001.

Brian Weatherson

Review of “Words Without Meaning”

Review of Christopher Gauker, “Words Without Meaning”. Cambridge: MIT Press, 2002.

Brian Weatherson

Review of “Theories of Vagueness”

Review of Rosanna Keefe, “Theories of Vagueness”. Cambridge: Cambridge University Press, 2000.

Brian Weatherson

Many Many Problems

Recently four different papers have suggested that the supervaluational solution to the Problem of the Many is flawed. Stephen Schiffer has argued that the theory cannot account for reports of speech involving vague singular terms. Vann McGee and Brian McLaughlin say that theory cannot, yet, account for vague singular beliefs. Neil McKinnon has argued that we cannot provide a plausible theory of when precisifications are acceptable, which the supervaluational theory needs. And Roy Sorensen argues that supervaluationism is inconsistent with a directly referential theory of names. McGee and McLaughlin see the problem they raise as a cause for further research, but the other authors all take the problems they raise to provide sufficient reasons to jettison supervaluationism. I will argue that none of these problems provide such a reason, though the arguments are valuable critiques. In many cases, we must make some adjustments to the supervaluational theory to meet the posed challenges. The goal of this paper is to make those adjustments, and meet the challenges.

Brian Weatherson

Epistemicism, Parasites, and Vague Names

John Burgess has recently argued that Timothy Williamson’s attempts to avoid the objection that his theory of vagueness is based on an untenable metaphysics of content are unsuccessful. Burgess’s arguments are important, and largely correct, but there is a mistake in the discussion of one of the key examples. In this note I provide some alternative examples and use them to repair the mistaken section of the argument.

Brian Weatherson

Review of “Vagueness and Contradiction”

Review of Roy Sorensen, “Vagueness and Contradiction”. Cambridge: Cambridge University Press, 2000.

Brian Weatherson

Misleading Indexicals

I argue against well informed observer theories about the referent of indexicals.

Brian Weatherson

From Classical to Intuitionistic Probability

We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of “essentially Kolmogorovian” probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of belief are those representable by probability functions from the class appropriate to that logic. Classical Bayesianism, which fixes the logic as classical logic, is only one version of this general approach. Another, which we call Intuitionistic Bayesianism, selects intuitionistic logic as the preferred logic and the associated class of probability functions as the right class of candidate representions of epistemic states (rational allocations of degrees of belief). Various objections to classical Bayesianism are, we argue, best met by passing to intuitionistic Bayesianism – in which the probability functions are taken relative to intuitionistic logic – rather than by adopting a radically non-Kolmogorovian, e.g. non-additive, conception of (or substitute for) probability functions, in spite of the popularity of the latter response amongst those who have raised these objections. The interest of intuitionistic Bayesianism is further enhanced by the availability…

Brian Weatherson

Indicative and Subjunctive Conditionals

In any plausible semantics for conditionals, the semantics for indicatives and subjunctives will resemble each other closely. This means that if we are to keep the possible‐worlds semantics for subjunctives suggested by Lewis, we need to find a possible‐worlds semantics for indicatives. One reason for thinking that this will be impossible is the behaviour of rigid designators in indicatives. An indicative like ‘If the stuff in the rivers, lakes and oceans really is H₃O, then water is H₃O’ is non‐vacuously true, even though its consequent is true in no possible worlds, and hence not in the nearest possible world where the antecedent is true. I solve this difficulty by providing a semantics for conditionals within the framework of two‐dimensional modal logic. In doing so, I show that we can have a reasonably unified semantics for indicative and subjunctive conditionals.

Brian Weatherson