Self-taught mathematician and father of Boolean algebra, George Boole (1815-1864) published An Investigation of the Laws of Thought in 1854. In this highly original investigation of the fundamental laws of human reasoning, a sequel to ideas he had explored in earlier writings, Boole uses the symbolic language of mathematics to establish a method to examine the nature of the human mind using logic and the theory of probabilities. Boole considers language not just as a mode of expression, but as a (...) system one can use to understand the human mind. In the first 12 chapters, he sets down the rules necessary to represent logic in this unique way. Then he analyses a variety of arguments and propositions of various writers from Aristotle to Spinoza. One of history's most insightful mathematicians, Boole is compelling reading for today's student of intellectual history and the science of the mind. (shrink)

What are people who disagree about logic disagreeing about? The paper argues that (in a wide range of cases) they are primarily disagreeing about how to regulate their degrees of belief. An analogy is drawn between beliefs about validity and beliefs about chance: both sorts of belief serve primarily to regulate degrees of belief about other matters, but in both cases the concepts have a kind of objectivity nonetheless.

As a procedure, reflective equilibrium is simply a familiar kind of standard scientific method with a new name. A theory is constructed to account for a set of observations. Recalcitrant data may be rejected as noise or explained away as the effects of interference of some sort. Recalcitrant data that cannot be plausibly dismissed force emendations in theory. What counts as a plausible dismissal depends, among other things, on the going theory, as well as on background theory and on knowledge (...) that may be relevant to under-standing the experimental design that is generating the observations, including knowledge of the apparatus and observation conditions. This sort of mutual adjustment between theory and data is a familiar feature of scientific practice. Whatever authority RE seems to have comes, I think, from a tacit or explicit recognition that it has the same form as this familiar sort of scientific inference. One way to see the rationale underlying this procedure in science is to focus on prediction. Think of prediction as a matter of projecting what is known onto uncharted territory. To do this, you need a vehicle—a theory—that captures some invariant or pattern in what is known so that you can project it onto the unknown. How convincing the projection is depends on two factors: how sure one is of the observational base, and how sure one is that the theory gets the invariants right. The two factors are not independent, of course. One's confidence in the observational base will be affected by how persuasively the theory identifies and dismisses noise; one's confidence in the theory, on the other hand, will depend on one's confidence in the observations it takes seriously. Prediction is important as a test of theory precisely because verified predictions seem to show that the theory has correctly captured the general in the particular, that it has got the drift of the observational evidence in which our confidence is ultimately grounded. (shrink)

In this paper I investigate how differences in approach to truth and logic (in particular, a deflationist vs. a substantivist approach to these fields) affect philosophers’ views concerning pluralism and normativity in these fields. My perspective on truth and logic is largely epistemic, focusing on the role of truth in knowledge (rather than on the use of the words “true” and “truth” in natural language), and my reference group includes Carnap (1934), Harman (1986), Horwich (1990), Wright (1992), Beall and Restall (...) (2006), Field (2009), Lynch (2009), and Sher (2016a).1 Whenever possible, I focus on positive rather than negative views on the issues involved, although in some cases this is not possible. (shrink)

Anti-exceptionalism about logic is the Quinean view that logical theories have no special epistemological status, in particular, they are not self-evident or justified a priori. Instead, logical theories are continuous with scientific theories, and knowledge about logic is as hard-earned as knowledge of physics, economics, and chemistry. Once we reject apriorism about logic, however, we need an alternative account of how logical theories are justified and revised. A number of authors have recently argued that logical theories are justified by abductive (...) argument (e.g. Gillian Russell, Graham Priest, Timothy Williamson). This paper explores one crucial question about the abductive strategy: what counts as evidence for a logical theory? I develop three accounts of evidential confirmation that an anti-exceptionalist can accept: (1) intuitions about validity, (2) the Quine-Williamson account, and (3) indispensability arguments. I argue, against the received view, that none of the evidential sources support classical logic. (shrink)

According to tradition, logic is normative for reasoning. Gilbert Harman challenged the view that there is any straightforward connection between logical consequence and norms of reasoning. Authors including John MacFarlane and Hartry Field have sought to rehabilitate the traditional view. I argue that the debate is marred by a failure to distinguish three types of normative assessment, and hence three ways to understand the question of the normativity of logic. Logical principles might be thought to provide the reasoning agent with (...) first-personal directives; they might be thought to serve as third-personal evaluative standards; or they might underwrite our third-personal appraisals of others whereby we attribute praise and blame. I characterize the three normative functions in general terms and show how a failure to appreciate this threefold distinction has led disputants to talk past one another. I further show how the distinction encourages fruitful engagement with and, ultimately, resolution of the question. (shrink)

Carnap and Goodman developed methods of conceptual re-engineering known respectively as explication and reflective equilibrium. These methods aim at advancing theories by developing concepts that are simultaneously guided by pre-existing concepts and intended to replace these concepts. This paper shows that Carnap’s and Goodman’s methods are historically closely related, analyses their structural interconnections, and argues that there is great systematic potential in interpreting them as aspects of one method, which ultimately must be conceived as a component of theory development. The (...) main results are: an adequate method of conceptual re-engineering must focus not on individual concepts but on systems of concepts and theories; the linear structure of Carnapian explication must be replaced by a process of mutual adjustments as described by Goodman; Carnap’s condition of similarity can be analysed into two components, one securing a relation to the specific extensions of the pre-existing concepts, one regulating the transition to the new system of concepts; these two criteria of adequacy can be built into Goodman’s account of reflective equilibrium to ensure that the resulting concepts promote theoretical virtues while being sufficiently similar to the concepts we started out with. (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)

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)

This book offers a comprehensive account of logic that addresses fundamental issues concerning the nature and foundations of the discipline. The authors claim that these foundations can not only be established without the need for strong metaphysical assumptions, but also without hypostasizing logical forms as specific entities. They present a systematic argument that the primary subject matter of logic is our linguistic interaction rather than our private reasoning and it is thus misleading to see logic as revealing "the laws of (...) thought". In this sense, fundamental logical laws are implicit to our "language games" and are thus more similar to social norms than to the laws of nature. Peregrin and Svoboda also show that logical theories, despite the fact that they rely on rules implicit to our actual linguistic practice, firm up these rules and make them explicit. By carefully scrutinizing the project of logical analysis, the authors demonstrate that logical rules can be best seen as products of the so called reflective equilibrium. They suggest that we can profit from viewing languages as "inferential landscapes" and logicians as "geographers" who map them and try to pave safe routes through them. This book is an essential resource for scholars and researchers engaged with the foundations of logical theories and the philosophy of language. (shrink)

The article addresses two closely related questions: What are the criteria of adequacy of logical formalization of natural language arguments, and what gives logic the authority to decide which arguments are good and which are bad? Our point of departure is the criticism of the conception of logical formalization put forth, in a recent paper, by M. Baumgartner and T. Lampert. We argue that their account of formalization as a kind of semantic analysis brings about more problems than it solves. (...) We also argue that the criteria of adequate formalization need not be based on truth conditions associated with logical formulas; in our view, they are better based on structural (inferential) grounds. We then put forward our own version of the criteria. The upshot of the discussion that follows is that the quest for an adequate formalization in a suitable logical language is best conceived of as the search for a Goodmanian reflective equilibrium. (shrink)