Tarski's Undefinability of Truth Theorem comes in two versions: that no consistent theory which interprets Robinson's Arithmetic (Q) can prove all instances of the T-Scheme and hence define truth; and that no such theory, if sound, can even express truth. In this note, I prove corresponding limitative results for validity. While Peano Arithmetic already has the resources to define a predicate expressing logical validity, as Jeff Ketland has recently pointed out (2012, Validity as a primitive. Analysis 72: 421-30), no theory (...) which interprets Q closed under the standard structural rules can define nor express validity, on pain of triviality. The results put pressure on the widespread view that there is an asymmetry between truth and validity, viz. that while the former cannot be defined within the language, the latter can. I argue that Vann McGee's and Hartry Field's arguments for the asymmetry view are problematic. (shrink)

In this paper, I explore a question about deductive reasoning: why am I in a position to immediately infer some deductive consequences of what I know, but not others? I show why the question cannot be answered in the most natural ways of answering it, in particular in Descartes’s way of answering it. I then go on to introduce a new approach to answering the question, an approach inspired by Hume’s view of inductive reasoning.

Is logic normative for reasoning? In the wake of work by Gilbert Harman and John MacFarlane, this question has been reduced to: are there any adequate bridge principles which link logical facts to normative constraints on reasoning? Hitherto, defenders of the normativity of logic have exclusively focussed on identifying adequate validity bridge principles: principles linking validity facts—facts of the form 'gamma entails phi'—to normative constraints on reasoning. This paper argues for two claims. First, for the time being at least, Harman’s (...) challenge cannot be surmounted by articulating validity bridge principles. Second, Harman’s challenge can be met by articulating invalidity bridge principles: principles linking invalidity facts of the form 'gamma does not entail phi' to normative constraints on reasoning. In doing so, I provide a novel defence of the normativity of logic. (shrink)

Logic is widely held to be a normative discipline. Various claims have been offered in support of this view, but they all revolve around the idea that logic is concerned with how one ought to reason. I argue that most of these claims—while perhaps correct—only entail that logic is normative in a way that many, if not all, intellectual disciplines are normative. I also identify some claims whose correctness would make logic normative in a way that sets it apart from (...) other disciplines. I argue that we have no reason think that these claims are correct. In other words, logic is not a distinctively normative discipline. (shrink)

Logic, the tradition has it, is normative for reasoning. But is that really so? And if so, in what sense is logic normative for reasoning? As Gilbert Harman has reminded us, devising a logic and devising a theory of reasoning are two separate enterprises. Hence, logic's normative authority cannot reside in the fact that principles of logic just are norms of reasoning. Once we cease to identify the two, we are left with a gap. To bridge the gap one would (...) need to produce what John MacFarlane has appropriately called a bridge principle, i.e. a general principle articulating a substantive and systematic link between logical entailment and norms of reasoning. This is Harman's skeptical challenge. In this paper I argue that Harman's skeptical challenge can be met. I show how candidate bridge principles can be systematically generated and evaluated against a set of well‐motivated desiderata. Moreover, I argue that bridge principles advanced by MacFarlane himself and others, for all their merit, fail to address the problem originally set forth by Harman and so do not meet the skeptical challenge. Finally, I develop a bridge principle that meets Harman's requirements as well as being substantive. (shrink)

The dominant route to nondescriptivist views of normative and evaluative language is through the expressivist idea that normative terms have distinctive expressive roles in conveying our attitudes. This paper explores an alternative route based on two ideas. First, a core normative term ‘ought’ is a modal operator; and second, modal operators play a distinctive nonrepresentational role in generating meanings for the statements in which they figure. I argue that this provides for an attractive alternative to expressivist forms of nondescriptivism about (...) normative language. In the final section of the paper, I explore ways it might be extended to evaluative language. (shrink)

It is commonly held that the ascription of truth to a sentence is intersubstitutable with that very sentence. However, the simplest subclassical logics available to proponents of this view, namely K3 and LP, are hopelessly weak for many purposes. In this article, I argue that this is much more of a problem for proponents of LP than for proponents of K3. The strategies for recapturing classicality offered by proponents of LP are far less promising than those available to proponents of (...) K3. This undermines the ability of proponents LP to engage in public reasoning in classical domains. (shrink)

True beliefs and truth-preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth-preserving, but truth-preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: the orthodox definition given (...) in terms of interpretations or models, a metaphysical definition given in terms of possible worlds, and a substitutional definition defended by Quine. I argue that the orthodox notion is poorly suited to explain what's good about a Modus Ponens inference. I argue that there is something good that is explained by a certain kind of truth across possible worlds, but the explanation is not provided by metaphysical validity in particular; nothing of value is explained by truth across all possible worlds. Finally, I argue that the substitutional notion of validity allows us to correctly explain what is good about a valid inference. (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)

This paper argues that the prominent accounts of logical knowledge have the consequence that they conflict with ordinary reasoning. On these accounts knowing a logical principle, for instance, is having a disposition to infer according to it. These accounts in particular conflict with so-called ‘reasoned change in view’, where someone does not infer according to a logical principle but revise their views instead. The paper also outlines a propositional account of logical knowledge which does not conflict with ordinary reasoning.

In this paper, I examine Gilbert Ryle’s claim that ordinary competence with logical principles or rules is a kind of knowing how, where such knowledge is understood as a skill, a multi-track disposition. Ryle argues that his account of ordinary logical competence helps avoid Lewis Carroll’s famous regress argument (Carroll 1895), which suggests that elementary deductive reasoning might be impossible. Indeed, Carroll’s regress is the central motivation for Ryle’s account. I argue that this account is inadequate on two counts: it (...) cannot serve to articulate the way ordinary reasoners might exercise their knowledge in reasoning and it does not do much to help us avoid Carroll’s regress. I sketch an alternative view, still Rylean in spirit, that fares better on both counts. (shrink)

In this paper I present a new theory of propositions, according to which propositions are abstract mathematical objects: well-formed formulas together with models. I distinguish the theory from a number of existing views and explain some of its advantages  chief amongst which are the following. On this view, propositions are unified and intrinsically truth-bearing. They are mind- and language-independent and they are governed by logic. The theory of propositions is ontologically innocent. It makes room for an appropriate interface with (...) formal semantics and it does not enforce an overly fine or overly coarse level of granularity. (shrink)

This paper concerns connection between knowing or accepting a logical principle such as Modus Ponens and actions of reasoning involving it. Discussions of this connection typically mention the so-called ‘Lewis Carroll Regress’ and there is near consensus that the regress shows something important about it. Also, although the regress explicitly concerns logic, many philosophers think that it establishes a more general truth, about the structurally similar connection between epistemic or practical principles and actions involving them. This paper’s first aim is (...) to address key interpretations Carroll’s regress as clearly as possible so as to show precisely how it might be relevant to questions concerning the connection between logical knowledge and reasoning, and, more broadly, to discussions of how epistemic or practical principles may be action-guiding. Its second aim is to show that the regress fails to establish anything of substance about the connection between logical knowledge and reasoning, or any other structurally similar relation, unless substantive, contentious and typically undefended assumptions are made. The consensus is thus on shaky ground. (shrink)

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...) of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)

The traditional connection between logic and reasoning has been under pressure ever since Gilbert Harman attacked the received view that logic yields norms for what we should believe. In this article I first place Harman's challenge in the broader context of the dialectic between logical revisionists like Bob Meyer and sceptics about the role of logic in reasoning like Harman. I then develop a formal model based on contemporary epistemic and doxastic logic in which the relation between logic and norms (...) for belief can be captured. (shrink)

Saul Kripke cuestionó el enfoque de la justificación de la lógica provisto por el modelo de Quine de la red de creencias sobre la base de un resultado que Romina Padró llamó “Problema de la adopción”. Sugiero una solución al problema de la adopción y una defensa de la estrategia quineana para la justificación de la lógica.