Once upon a time, logical conventionalism was the most popular philosophical theory of logic. It was heavily favored by empiricists, logical positivists, and naturalists. According to logical conventionalism, linguistic conventions explain logical truth, validity, and modality. And conventions themselves are merely syntactic rules of language use, including inference rules. Logical conventionalism promised to eliminate mystery from the philosophy of logic by showing that both the metaphysics and epistemology of logic fit into a scientific picture of reality. For naturalists of all (...) stripes, this was paradise. Alas, paradise was lost. By the end of the twentieth century, logical conventionalism had been almost universally abandoned. But more recently, it has been revitalized. This chapter provides an overview of logical conventionalism and its history, clears away misunderstandings, and briefly responds to both the canonical objections to conventionalism (from Quine, Dummett, Boghossian, and many others) as well as new objections (from Field and Golan). From paradise lost, to paradise regained: logical conventionalism is back. (shrink)

Philosophers debate about which logical system, if any, is the One True Logic. This involves a disagreement concerning the sufficient conditions that may single out the correct logic among various candidates. This paper discusses whether there are necessary conditions for the correct logic; that is, I discuss whether there are features such that if a logic is correct, then it has those features, although having them might not be sufficient to single out the correct logic. Traditional rationalist arguments suggest that (...) the necessary conditions of thought are necessary and sufficient conditions singling out the correct logical and mathematical theories. In the contemporary debate, Chalmers advocates a view along this line. Jago, analogously, suggests that the necessary conditions for thought—or, as he calls them, our basic epistemic expectations—single out a family of logical and mathematical theories. Warren and Williamson, on the other hand, argue that there are no necessary conditions of thought. I argue that there are necessary conditions for thought, and these are necessary but not sufficient conditions to be the correct logic; indeed, these are features that all logics—correct or incorrect—share. No view we can understand is ruled out by the necessary conditions for thought, but we cannot understand quite any view. Human linguistic and conceptual abilities are genetically constrained, and these constraints are our best guide to the boundaries of logic. Arguing for this, I tackle two dogmas of modern rationalism: namely, the view that the biological constraints of human cognition have no bearing on the boundaries of the epistemic space, and the view that the boundaries of thought coincide with the boundaries of language. (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

Inferences are familiar movements of thought, but despite important recent work on the topic, we do not yet have a fully satisfying theory of inference. Here I provide a functionalist theory of inference. I argue that the functionalist framework allows us the flexibility to meet various demands on a theory of inference that have been proposed (such as that it must explain inferential Moorean phenomena and epistemological ‘taking’). While also allowing us to compare, contrast, adapt, and combine features of extant (...) theories of inference into one unified theory. In fleshing out the inference role, I also criticize the common assumption that inference requires rule-following. (shrink)

Some philosophers have argued that putative logical disagreements aren't really disagreements at all since when you change your logic you thereby change the meanings of your logical constants. According to this picture classical logicians and intuitionists don't really disagree, they just mean different things by terms like “not” and “or”. Quine gave an infamous “translation argument” for this view. Here I clarify the change of logic, change of meaning (CLCM) thesis, examine and find fault with Quine's translation argument for the (...) thesis, offer a modified translation argument in its stead, defend my modified argument from a crucial objection, discuss where the CLCM thesis leaves logical disputes, and discuss if and how the thesis coheres with Quine's influential view of logic. (shrink)

Truth by convention, once thought to be the foundation of a uniquely promising approach to explaining our access to the truth in nonempirical domains, is nowadays widely considered an absurdity. Its fall from grace has been due largely to the influence of an argument that can be sketched as follows: our linguistic conventions have the power to make it the case that a sentence expresses a particular proposition, but they can’t by themselves generate truth; whether a given proposition is true—and (...) so whether the sentence that expresses it is true—is a matter of what the world is like, which means it isn’t a matter of convention alone. The consensus is that this argument is decisive against truth by convention. Strikingly, though, it has rarely been formulated with much precision. Here I provide a new rendering of the argument, one that reveals its structure and makes transparent just what assumptions it requires, and then I assess conventionalists’ prospects for resisting each of those assumptions. I conclude that the consensus is mistaken: contrary to what is almost universally thought, there remains a promising way forward for the conventionalist project. Along the way, I clarify conventionalists’ commitments by thinking about what truth by convention would need to be like in order for conventionalism to do the epistemological work it’s intended to do. (shrink)

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Grounding has become all the rage in recent philosophical work and metaphilosophical discussions. While I agree that the concept of ground marks something useful, I am skeptical about the metaphysical weight many imbue it with, and the picture of ‘worldly layering’ that grounding talk inspires. My skepticism centers around the fact that grounding involves necessitation, combined with reasons for thinking matters of necessity are matters of logical or conceptual (semantic, psychological) relations. I sketch an argument for deflationism about ground based (...) on this sort of deflationism about necessity and essence. I also note that in at least some cases, the considerations supporting modal deflationism directly support deflationism about whatever grounding relations may obtain in these cases. (shrink)

The idea that logic is in some sense normative for thought and reasoning is a familiar one. Some of the most prominent figures in the history of philosophy including Kant and Frege have been among its defenders. The most natural way of spelling out this idea is to formulate wide-scope deductive requirements on belief which rule out certain states as irrational. But what can account for the truth of such deductive requirements of rationality? By far, the most prominent responses draw (...) in one way or another on the idea that belief aims at the truth. In this paper, I consider two ways of making this line of thought more precise and I argue that they both fail. In particular, I examine a recent attempt by Epistemic Utility Theory to give a veritist account of deductive coherence requirements. I argue that despite its proponents’ best efforts, Epistemic Utility Theory cannot vindicate such requirements. (shrink)

In this paper we put forward and defend a view of the nature of logic that we call moderate anti-exceptionalism. In the first part of the paper we focus on the problem of genuine logical validity and consequence. We make use of examples from current debates to show that attempts to pinpoint the one and only authentic logic inevitably either yield irrefutable theories or lead to dead ends. We then outline a thoroughly naturalist account of logical consequence as grounded in (...) rules implicit in human linguistic practices. We insist that there are only two existing kinds of language: natural languages, and artificial languages that have been forged by us. There is thus no room for a "genuine" language and hence for "genuine" logic. We conclude that though logical theories are established—and are liable to criticism—in a similar fashion as those of the sciences, and in this sense logic is not exceptional, to fulfill its mission logic must lay a claim to normative authority over our argumentation and reasoning, which makes its methodology somewhat special. Logical theory is not meant to provide just an explanation, the standards it establishes serve also as a tool, providing for a reinforcement of our rational communication. (shrink)

For several decades, Carnap's philosophy of mathematics used to be either dismissed or ignored. It was perceived as a form of linguistic conventionalism and thus taken to rely on the bankrupt notion of truth by convention. However, recent scholarship has revealed a more subtle picture. It has been forcefully argued that Carnap is not a linguistic conventionalist in any straightforward sense, and that supposedly decisive objections against his position target a straw man. This raises two questions. First, how exactly should (...) we characterise Carnap's actual philosophy of mathematics? Secondly, is his position an attractive alternative to established views? I will tackle these issues by looking at Carnap's response to the incompleteness theorems. Drawing on arguments put forward by Gödel and Beth, I show that some crucial aspects of Carnap's positive account have remained underdeveloped. Suggestions on what a full evaluation of Carnap's position requires are made. (shrink)

Conventionalism about logic is the view that logical principles hold in virtue of some linguistic conventions. According to explicit conventionalism, these conventions have to be stipulated explicitly. Explicit conventionalism is subject to a famous criticism by Quine, who accused it of leading to an infinite regress. In response to the criticism, several authors have suggested reconstructing conventionalism as implicit in our linguistic behaviour. In this paper, drawing on a distinction from proof theory between derivable and admissible rules, I argue that (...) implicit conventionalism has not been stated in a sufficiently precise way, as it leaves open what one needs to say about admissible yet underivable rules. Moreover, it turns out that this challenge cannot be easily met, and that any attempt to meet the challenge makes conventionalism much less attractive a thesis. (shrink)

The central philosophical task posed by conventions is to analyze what they are and how they differ from mere regularities of action and cognition. Subsidiary questions include: How do conventions arise? How are they sustained? How do we select between alternative conventions? Why should one conform to convention? What social good, if any, do conventions serve? How does convention relate to such notions as rule, norm, custom, practice, institution, and social contract? Apart from its intrinsic interest, convention is important because (...) philosophers frequently invoke it when discussing other topics. A favorite philosophical gambit is to argue that, perhaps despite appearances to the contrary, some phenomenon ultimately results from convention. Notable candidates include: property, government, justice, law, morality, linguistic meaning, necessity, ontology, mathematics, and logic. (shrink)

I argue against inferentialism about logic. First, I argue against an analogy between logic and chess, before considering a more basic objection to stipulating inference rules as a way of establishing the meaning of logical constants. The objectionthe Mushroom Omelette Objectionis that stipulative acts are partly constituted by logical notions, and therefore cannot be used to explain logical thought. I then argue that the same problem also attaches to following existing conventional rules, since either those rules have logical contents, or (...) following those conventional rules is done for logical reasons. Lastly, I compare this argument with other arguments found in Quine’s early work, and consider two attempts to reply to Quine. (shrink)

The laws of classical logic are taken to be logical truths, which in turn are taken to hold objectively. However, we might question our faith in these truths: why are they true? One general approach, proposed by Putnam [8] and more recently Dickson [3] or Maddy [5], is to adopt empiricism about logic. On this view, logical truths are true because they are true of the world alone – this gives logical truths an air of objectivity. Putnam and Dickson both (...) take logical truths to be true in virtue of the world’s structure, given by our best empirical theory, quantum mechanics. This assumes a determinate logical structure of the world given by quantum mechanics. Here, I argue that this assumption is false, and that the world’s logical structure, and hence the related ‘true’ logic, is underdetermined. This leads to what I call empirical conventionalism. (shrink)