We present an inferentialist account of the epistemic modal operator might. Our starting point is the bilateralist programme. A bilateralist explains the operator not in terms of the speech act of rejection ; we explain the operator might in terms of weak assertion, a speech act whose existence we argue for on the basis of linguistic evidence. We show that our account of might provides a solution to certain well-known puzzles about the semantics of modal vocabulary whilst retaining classical logic. (...) This demonstrates that an inferentialist approach to meaning can be successfully extended beyond the core logical constants. (shrink)

What does 'might' mean? One hypothesis is that 'It might be raining' is essentially an avowal of ignorance like 'For all I know, it's raining'. But it turns out these two constructions embed in different ways, in particular as parts of larger constructions like Wittgenstein's 'It might be raining and it's not' and Moore's 'It's raining and I don't know it', respectively. A variety of approaches have been developed to account for those differences. All approaches agree that both Moore sentences (...) and Wittgenstein sentences are classically consistent. In this paper I argue against this consensus. I adduce a variety of new data which I argue can best be accounted for if we treat Wittgenstein sentences as being classically inconsistent. This creates a puzzle, since there is decisive reason to think that 'Might p' is classically consistent with 'Not p'. How can it also be that 'Might p and not p' and 'Not p and might p' are classically inconsistent? To make sense of this situation, I propose a new theory of epistemic modals and their interaction with embedding operators. This account makes sense of the subtle embedding behavior of epistemic modals, shedding new light on their meaning and, more broadly, the dynamics of information in natural language. -/- . (shrink)

Famous results by David Lewis show that plausible-sounding constraints on the probabilities of conditionals or evaluative claims lead to unacceptable results, by standard probabilistic reasoning. Existing presentations of these results rely on stronger assumptions than they really need. When we strip these arguments down to a minimal core, we can see both how certain replies miss the mark, and also how to devise parallel arguments for other domains, including epistemic “might,” probability claims, claims about comparative value, and so on. A (...) popular reply to Lewis's results is to claim that conditional claims, or claims about subjective value, lack truth conditions. For this strategy to have a chance of success, it needs to give up basic structural principles about how epistemic states can be updated—in a way that is strikingly parallel to the commitments of the project of dynamic semantics. (shrink)

ABSTRACTLinguistic evidence supports the claim that certain, weak rejections are less specific than assertions. On the basis of this evidence, it has been argued that rejected sentences cannot be premisses and conclusions in inferences. We give examples of inferences with weakly rejected sentences as premisses and conclusions. We then propose a logic of weak rejection which accounts for the relevant phenomena and is motivated by principles of coherence in dialogue. We give a semantics for which this logic is sound and (...) complete, show that it axiomatizes the modal logic KD45 and prove that it still derives classical logic on its asserted fragment. Finally, we defend previous logics of strong rejection as being about the linguistically preferred interpretations of weak rejections. (shrink)

According to recent suggestions within the global pragmatism discussion, metaethical debate must be fundamentally re-framed. Instead of carving out metaethical differences in representational terms, it has been argued that metaethics should be given an inferentialist footing. In this paper, I put inferentialist metaethics to the test by subjecting it to the following two criteria for success: Inferentialist metaethicists must be able to save the metaethical differences between moral realism and expressivism, and do so in a way that employs understandings of (...) these metaethical accounts which would be acceptable to moral realists or expressivists who endorse an inferentialist theory of meaning. Two results follow from my discussion. The first concerns inferentialist metaethics more narrowly, casting doubts on inferentialists’ ability to fulfil the two criteria for success by showing that proposed metaethical demarcation attempts either meet the first criterion but violate the second, or pass the second criterion but fail the first. The second upshot pertains to the global pragmatism debate more widely, pressing the point that inferentialists have not as yet provided a convincing account of ontological commitment. (shrink)

The paper argues that much of the difficulty with making progress on the issue of the normativity of logic for thought, as discussed in the literature, stems from a misapprehension of what logic is normative for. The claim is that, rather than mono-agent mental processes, logic in fact comprises norms for quite specific situations of multi-agent dialogical interactions, in particular special forms of debates. This reconceptualization is inspired by historical developments in logic and mathematics, in particular the pervasiveness of such (...) dialogical conceptions in the early days of logic in ancient Greece. The multi-agent, dialogical perspective then allows for the formulation of compelling 'bridge principles’ between the relation of logical consequence and dialogical normative principles, something that is notoriously difficult to achieve in a mono-agent setting pertaining exclusively to thought and belief. The upshot is also that the truth-preserving rules of logic generally do not have a primary normative bearing on mono-agent mental processes, and in this sense the paper sides with Harman's critique of the idea that logic has a normative import for thought and belief. (shrink)

Mark Schroeder has argued that all reasonable forms of inconsistency of attitude consist of having the same attitude type towards a pair of inconsistent contents (A-type inconsistency). We suggest that he is mistaken in this, offering a number of intuitive examples of pairs of distinct attitudes types with consistent contents which are intuitively inconsistent (B-type inconsistency). We further argue that, despite the virtues of Schroeder's elegant A-type expressivist semantics, B-type inconsistency is in many ways the more natural choice in developing (...) an expressivist account of moral discourse. We close by showing how to adapt ordinary formality-based accounts of logicality to define a B-type account of logical inconsistency and distinguish it from both semantic and pragmatic inconsistency. In sum, we provide a roadmap of how to develop a successful B-type expressivism. (shrink)

Michael Ridge presents an original expressivist theory of normative judgments--Ecumenical Expressivism--which offers distinctive treatments of key problems in metaethics, semantics, and practical reasoning. He argues that normative judgments are hybrid states partly constituted by ordinary beliefs and partly constituted by desire-like states.

Moral realism and antirealist-expressivism are of course incompatible positions. They disagree fundamentally about the nature of moral states of mind, the existence of moral states of affairs and properties, and the nature and role of moral discourse. The central realist view is that a person who has or expresses a moral thought is thereby in, or thereby expresses, a cognitive state of mind; she has or expresses a belief that represents a moral state of affairs in a way that might (...) be accurate or inaccurate. The view of antirealist-expressivism is that such a person is in, or expresses, a conative state of mind, one that consists in a certain kind of attitude or motivational stance toward something, such as an action or a person. Realism holds that moral thoughts have truth conditions and that in some cases these truth conditions are satisfied so that our moral thoughts are true. Antirealist-expressivism holds, to a first approximation, that the distinctive moral content of a moral thought does not have truth conditions. (shrink)

Here is one argument against realism. (1) Realists are committed to the classical rules for negation. But (2) legitimate rules of inference must conserve evidence. And (3) the classical rules for negation do not conserve evidence. So (4) realism is wrong. Most realists reject 2. But it has recently been argued that if we allow denied sentences as premisses and conclusions in inferences we will be able to reject 3. And this new argument against 3 generates a new response to (...) the antirealist argument: keep 1 and 2, avoiding 4 by rejecting 3. My aim in this paper is to see how much work in the fight against anti-realism this new response can really do. I argue that there is a powerful objection to the response: 2 is in tension with the claim that denied sentences can be premisses and conclusions in inferences. But I show that, even given this objection, the new response has an important role to play. (shrink)

This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.

Our topic is the notion of logical consequence: the link between premises and conclusions, the glue that holds together deductively valid argument. How can we understand this relation between premises and conclusions? It seems that any account begs questions. Painting with very broad brushtrokes, we can sketch the landscape of disagreement like this: “Realists” prefer an analysis of logical consequence in terms of the preservation of truth [29]. “Anti-realists” take this to be unhelpful and o:er alternative analyses. Some, like Dummett, (...) look to preservation of warrant to assert [9, 36]. Others, like Brandom [5], take inference as primitive, and analyse other notions in terms of it. There is plenty of disagreement on the “realist” side of the fence too. It is one thing to argue that logical consequence involves preservation of truth. It is another to explain how far truth must be preserved. Is the preservation essentially modal (in all circumstances [25]) or analytic (vouchsafed by.. (shrink)

Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...

We consider a paradox involving indicative conditionals (‘ifs’) and deontic modals (‘oughts’). After considering and rejecting several standard options for resolv- ing the paradox—including rejecting various premises, positing an ambiguity or hidden contextual sensitivity, and positing a non-obvious logical form—we offer a semantics for deontic modals and indicative conditionals that resolves the paradox by making modus ponens invalid. We argue that this is a result to be welcomed on independent grounds, and we show that rejecting the general validity of modus (...) ponens is compatible with vindicating most ordinary uses of modus ponens in reasoning. (shrink)

In the 1960s, Peter Geach and John Searle independently posed an important objection to the wide class of 'noncognitivist' metaethical views that had at that time been dominant and widely defended for a quarter of a century. The problems raised by that objection have come to be known in the literature as the Frege-Geach Problem, because of Geach's attribution of the objection to Frege's distinction between content and assertoric force, and the problem has since occupied a great deal of the (...) attention both of defenders of broadly noncognitivist views, and of their critics. In this article I explain Geach and Searle's historical objections, and put the subsequent discussion into dialectical context, paying some attention to the developments along the way and how they have enhanced our overall understanding of the problem. The article covers a lot of territory, so we will only be able to see the highlights, along the way. For further reading, see the Works Cited. (shrink)

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context are explored.

Expressivists, such as Blackburn, analyse sentences such as 'S thinks that it ought to be the case that p' as S hoorays that p'. A problem is that the former sentence can be negated in three different ways, but the latter in only two. The distinction between refusing to accept a moral judgement and accepting its negation therefore cannot be accounted for. This is shown to undermine Blackburn's solution to the Frege-Geach problem.

I develop a conception of expressivism according to which it is chiefly a pragmatic thesis about some fragment of discourse, one imposing certain constraints on semantics. The first half of the paper uses credal expressivism about the language of probability as a stalking-horse for this purpose. The second half turns to the question of how one might frame an analogous form of expressivism about the language of deontic modality. Here I offer a preliminary comparison of two expressivist lines. The first, (...) expectation expressivism, looks again to Bayesian modelling for inspiration: it glosses deontically modal language as characteristically serving to express decision-theoretic expectation (expected utility). The second, plan expressivism, develops the idea (due to Gibbard 2003) that this language serves to express 'plan-laden' states of belief. In the process of comparing the views, I show how to incorporate Gibbard's modelling ideas into a compositional semantics for attitudes and modals, filling a lacuna in the account. I close with the question whether and how plan expressivism might be developed with expectation-like structure. (shrink)

A difficulty is exposed in Allan Gibbard's solution to the embedding/Frege-Geach problem, namely that the difference between refusing to accept a normative judgement and accepting its negation is ignored. This is shown to undermine the whole solution.

This paper addresses the “creeping minimalism” challenge to quasi-realist forms of expressivism by arguing that the solution suggested by Dreier doesn’t work and proposing an alternative solution based on the different inferential roles of ethical and descriptive judgments.

I develop a new argument for an expressivist account of epistemic modals, which starts from a puzzle about epistemic modals which Seth Yalcin recently presented. I reject Yalcin's own solution to the puzzle, and give a better explanation based on expressivism concerning epistemic modals. I also address two alleged problems for expressivism: do embeddings of epistemic modals pose a serious threat to expressivism, and how can expressivism account for disagreements about statements containing epistemic modals?

Hybrid metaethical theories attempt to incorporate essential elements of expressivism and cognitivism, and thereby to accrue the benefits of both. Hybrid theories are often defended in part by appeals to slurs and other pejoratives, which have both expressive and cognitivist features. This paper takes far more seriously the analogy between pejoratives and moral predicates. It explains how pejoratives work, identifies the features that allow pejoratives to do that work, and models a theory of moral predicates on those features. The result (...) is an expressivist theory that, among other advantages, is immune to embedding difficulties and avoids an overlooked difficulty concerning attitude ascriptions that is lethal to most other hybrid theories. (shrink)

The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: negative introduction and (...) elimination rules, and positive and negative introduction rules. The paper suggests a proof-theoretical definition of duality, using which double harmony is defined. The paper proves that in a doubly-harmonious system, the coordination rule, typical to bilateral systems, is admissible. (shrink)

Moral realismandantirealist-expressivismare of course incompatible positions. They disagree fundamentally about the nature of moral states of mind, the existence of moral states of affairs and properties, and the nature and role of moral discourse. The central realist view is that a person who has or expresses a moral thought is thereby in, or thereby expresses, acognitivestate of mind; she has or expresses abeliefthat represents a moral state of affairs in a way that might be accurate or inaccurate. The view of (...) antirealist-expressivism is that such a person is in, or expresses, aconativestate of mind, one that consists in a certain kind of attitude or motivational stance toward something, such as an action or a person. Realism holds that moral thoughts have truth conditions and that in some cases these truth conditions are satisfied so that our moral thoughts are true. Antirealist-expressivism holds, to a first approximation, that the distinctive moral content of a moral thought does not have truth conditions. (shrink)

Whether assent ("acceptance") and dissent ("rejection") are thought of as speech acts or as propositional attitudes, the leading idea of rejectivism is that a grasp of the distinction between them is prior to our understanding of negation as a sentence operator, this operator then being explicable as applying to A to yield something assent to which is tantamount to dissent from A. Widely thought to have been refuted by an argument of Frege's, rejectivism has undergone something of a revival in (...) recent years, especially in writings by Huw Price and Timothy Smiley. While agreeing that Frege's argument does not refute the position, we shall air some philosophical qualms about it in Section 5, after a thorough examination of the formal issues in Sections 1-4. This discussion draws on - and seeks to draw attention to - some pertinent work of Kent Bendall in the 1970s. (shrink)

The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between (positive) introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: (i) negative (...) introduction and elimination rules, and (ii) positive and negative introduction rules. The paper suggests a proof-theoretical definition of duality (not referring to truthtables), using which double harmony is defined. The paper proves that in a doubly-harmonious system, the coordination rule, typical to bilateral systems, is admissible. (shrink)