This chapter explores the intersection of experimental philosophy and philosophical logic. It considers a distinction between pure and applied logic. It sketches some ways in which experimental results and empirical results more broadly, can inform and have informed debates within philosophical logic. The chapter lays out a way of looking at the situation that makes plain at least one way in which people should expect experimental and logical concerns to overlap. It turns to the phenomenon of vagueness, where people can (...) see this overlap explored and developed from multiple angles, showing just how intimately related experiment and logic can be. Logic is not only useful for exploring hypotheses about truth conditions and entailments but also for exploring hypotheses about reasoning. Logical and experiment can fruitfully interact in a variety of applications, and that is all people need for experimental philosophical logic to be worthwhile. (shrink)

This book discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the problem of explaining the (defeasible) justification of our mathematical beliefs (‘the justificatory challenge’), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the problem of explaining their reliability (‘the reliability challenge’), arises to the extent that we could have easily had different beliefs. The book shows that mathematical facts are not, in general, empirically accessible, contra Quine, (...) and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is intelligible. The book concludes with a complementary ‘pluralism’ about modality, logic and normative theory, highlighting its revisionary implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap’s pragmatism, transposed to the key of realism. (shrink)

In this article, we discuss a simple argument that modal metaphysics is misconceived, and responses to it. Unlike Quine's, this argument begins with the observation that there are different candidate interpretations of the predicate ‘could have been the case’. This is analogous to the observation that there are different candidate interpretations of the predicate ‘is a member of’. The argument then infers that the search for metaphysical necessities is misguided in much the way the ‘set-theoretic pluralist’ claims that the search (...) for the true axioms of set theory is. We show that the obvious responses to this argument fail. However, a new response has emerged that purports to prove, from higher-order logical principles, that metaphysical possibility is the broadest kind of possibility applying to propositions, and is to that extent special. We distill two lines of reasoning from the literature, and argue that their import depends on premises that any ‘modal pluralist’ should deny. Both presuppose that there is a unique typed hierarchy, which is what the modal pluralist, in the context of higher-order logic, should disavow. In other words, both presupposes that there is a unique candidate for what higher-order claims could mean. We consider the worry that, in a higher-order setting, modal pluralism faces an insuperable problem of articulation, collapses into modal monism, is vulnerable to the Russell-Myhill paradox, or even contravenes the truism that there is a unique actual world, and argue that these worries are misplaced. We also sketch the bearing of the resulting ‘Higher-Order Pluralism’ on the theory of content. One theme of the discussion is that, if Higher-Order Pluralism is correct, then there is no fixed metatheory from which to characterize higher-order reality. (shrink)

I discuss methodology in epistemology. I argue that settling the facts, even the epistemic facts, fails to settle the questions of intellectual policy at the center of our epistemic lives. An upshot is that the standard methodology of analyzing concepts like knowledge, justification, rationality, and so on is misconceived. More generally, any epistemic method that seeks to issue in intellectual policy by settling the facts, whether by way of abductive theorizing or empirical investigation, no matter how reliable, is inapt. The (...) argument is a radicalization of Moore’s Open Question Argument. I conclude by considering the ramifications of this conclusion for the debate surrounding “Modal Security”, a proposed necessary condition on undermining defeat. (shrink)

In explaining the notion of a fundamental property or relation, metaphysicians will often draw an analogy with languages. The fundamental properties and relations stand to reality as the primitive predicates and relations stand to a language: the smallest set of vocabulary God would need in order to write the “book of the world.” This paper attempts to make good on this metaphor. To that end, a modality is introduced that, put informally, stands to propositions as logical truth stands to sentences. (...) The resulting theory, formulated in higher-order logic, also vindicates the Humean idea that fundamental properties and relations are freely recombinable and a variant of the structural idea that propositions can be decomposed into their fundamental constituents via logical operations. Indeed, it is seen that, although these ideas are seemingly distinct, they are not independent, and fall out of a natural and general theory about the granularity of reality. (shrink)

We need to understand the impossible. Francesco Berto and Mark Jago start by considering what the concepts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition have in common. They are all concepts which divide the world up more finely than logic does. Logically equivalent sentences may carry different meanings and information and may differ in how they're believed. Fictions can be inconsistent yet meaningful. We can suppose impossible things without collapsing into total incoherence. Yet for the leading philosophical (...) theories of meaning, these phenomena are an unfathomable mystery. To understand these concepts, we need a metaphysical, logical, and conceptual grasp of situations that could not possibly exist: Impossible Worlds. This book discusses the metaphysics of impossible worlds and applies the concept to a range of central topics and open issues in logic, semantics, and philosophy. It considers problems in the logic of knowledge, the meaning of alternative logics, models of imagination and mental simulation, the theory of information, truth in fiction, the meaning of conditional statements, and reasoning about the impossible. In all these cases, impossible worlds have an essential role to play. (shrink)

This edited volume brings together 18 state-of-the art essays on pluralism about truth and logic. Parts I and II are dedicated to respectively truth pluralism and logical pluralism, and Part III to their interconnections. Some contributors challenge pluralism, arguing that the nature of truth or logic is uniform. The majority of contributors, however, defend pluralism, articulate novel versions of the view, or contribute to fundamental debates internal to the pluralist camp. The volume will be of interest to truth theorists and (...) philosophers of logic, as well as philosophers interested in relativism, contextualism, metaphysics, philosophy of language, semantics, paradox, epistemology, or normativity. (shrink)

To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to (...) being empirically justified than our moral beliefs. It is also incorrect that reflection on the "genealogy" of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together -- and for a surprising reason. Moral questions, insofar as they are practical, are objective in a sense that mathematical questions are not. Moreover, the sense in which they are objective can be explained only by assuming practical anti-realism. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the objective questions in the neighborhood of questions of logic, modality, grounding, and nature are practical questions too. Practical philosophy should, therefore, take center stage. (shrink)

Abstract‘Logical Realism’ is taken to mean many different things. I argue that if reality has a privileged structure, then a view I call metaphysical logical realism is true. The view says that, first, there is ‘One True Logic’; second, that the One True Logic is made true by the mind‐and‐language‐independent world; and third, that the mind‐and‐language‐independent world makes it the case that the One True Logic is better than any other logic at capturing the structure of reality. Along the way, (...) I discuss a few alternatives, and clarify two distinct kinds of metaphysical logical realism. (shrink)

Logical monists and pluralists disagree about how many correct logics there are; the monists say there is just one, the pluralists that there are more. Could it turn out that both are wrong, and that there is no logic at all?

Much recent metaphysics is built around notions such as naturalness, fundamentality, grounding, dependence, essence, and others besides. In this article I raise a problem for this kind of metaphysics, the “problem of missing value.” I survey a number of possible solutions to the problem and find them all wanting. This suggests a return to a kind of Goodmanian view that the world is a structureless mess onto which we project our own categorizations, not something with categories already built in.

In The Boundary Stones of Thought, Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project.

The concepts we use to value and prescribe are historically contingent, and we could have found ourselves with others. But what does it mean to say that some concepts are better than others for purposes of action-guiding and deliberation? What is it to choose between different normative conceptual frameworks?

It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If there were nothing otherwise “uniquely metaphysically significant” about (...) metaphysical necessity, then paradigmatic metaphysical necessities would be necessary in one sense of “necessary”, not necessary in another, and that would be it. The question of whether they were necessary simpliciter would be like the question of whether the Parallel Postulate is true simpliciter – understood as a pure mathematical conjecture, rather than as a hypothesis about physical spacetime. In a sense, the latter question has no objective answer. In this article, I argue that paradigmatic questions of modal metaphysics are like the Parallel Postulate question. I then discuss the deflationary ramifications of this argument. I conclude with an alternative conception of the space of possibility. According to this conception, there is no objective boundary between possibility and impossibility. Along the way, I sketch an analogy between modal metaphysics and set theory. (shrink)

The article is centered on the question of how best to understand the logical pluralism/logical monism debate. A number of suggestions are brought up and rejected on the ground that they re...

Can quite different values be rationally weighed against one another? Can the value of one thing always be ranked as greater than, equal to, or less than the value of something else? If the answer to these questions is no, then in what areas do we find commensurability and comparability unavailable? And what are the implications for moral and legal decision making? This book struggles with these questions, and arrives at distinctly different answers.".

_Metaphysics: A Contemporary Introduction_ is for students who have already completed an introductory philosophy course and need a fresh look at the central topics in the core subject of metaphysics. It is essential reading for any student of the subject. This Fourth Edition is revised and updated and includes two new chapters on Parts and Wholes, and Metaphysical Indeterminacy or vagueness. This new edition also keeps the user-friendly format, the chapter overviews summarizing the main topics, concrete examples to clarify difficult (...) concepts, annotated further reading at the end of each chapter, endnotes, and a full bibliography. Topics addressed include: the problem of universals the nature of abstract entities the problem of individuation the nature of modality identity through time the nature of time the nature of parts and wholes the problem of metaphysical indeterminacy the Realism/anti-Realism debate. Wherever possible, Michael J. Loux and Thomas M. Crisp relate contemporary views to their classical sources in the history of philosophy. As experienced teachers of philosophy and important contributors to recent debates, Loux and Crisp are uniquely qualified to write this book. (shrink)

The first systematic exposition of all the central topics in the philosophy of logic, Susan Haack's book has established an international reputation for its accessibility, clarity, conciseness, orderliness, and range as well as for its thorough scholarship and careful analyses. Haack discusses the scope and purpose of logic, validity, truth-functions, quantification and ontology, names, descriptions, truth, truth-bearers, the set-theoretical and semantic paradoxes, and modality. She also explores the motivations for a whole range of non-classical systems of logic, including many-valued logics, (...) fuzzy logic, moddal and tense logics, and relevance logics. Persupposing only an elementary knowledge of formal logic, this book includes many useful summary tables and diagrams, as well as a helpful glossary of technical terms. Wide-ranging, informative, and eminently readable, this book has proven a valuable resource for generations of students and scholars in a variety of disciplines outside philosophy needing guidance on the philosophy of logic. (shrink)

One logic or many? I say—many. Or rather, I say there is one logic for each way of specifying the class of all possible circumstances, or models, i.e., all ways of interpreting a given language. But because there is no unique way of doing this, I say there is no unique logic except in a relative sense. Indeed, given any two competing logical theories T1 and T2 (in the same language) one could always consider their common core, T, and settle (...) on that theory. So, given any language L, one could settle on the minimal logic T0 corresponding to the common core shared by all competitors. That would be a way of resisting relativism, as long as one is willing to redraw the bounds of logic accordingly. However, such a minimal theory T0 may be empty if the syntax of L contains no special ingredients the interpretation of which is independent of the specification of the relevant L-models. And generally—I argue—this is indeed the case. (shrink)

David Enoch develops, argues for, and defends a strongly realist and objectivist view of ethics and normativity more broadly. This view--according to which there are perfectly objective, universal, moral and other normative truths that are not in any way reducible to other, natural truths--is familiar, but this book is the first in-detail development of the positive motivations for the view into reasonably precise arguments. And when the book turns to defend Robust Realism against traditional objections, it mobilizes the original positive (...) arguments for the view to help with fending off the objections. (shrink)

How do axioms, or first principles, in ethics compare to those in mathematics? In this companion piece to G.C. Field's 1931 "On the Role of Definition in Ethics", I argue that there are similarities between the cases. However, these are premised on an assumption which can be questioned, and which highlights the peculiarity of normative inquiry.

It is often claimed that irreducibly normative truths would have unacceptable metaphysical implications, and are incompatible with a scientific view of the world. The book argues, on the basis of a general account of the relevance of ontological questions, that this claim is mistaken. It is also a mistake to think that interpreting normative judgments as beliefs would make it impossible to explain their connection with action. An agent’s acceptance of a normative judgment can explain that agent’s subsequent action because (...) it is part of being a rational agent that such an agent’s beliefs about reasons normally, but not invariably, make a difference to the agent’s subsequent behavior. Because facts about reasons are not entities existing apart from us, there is no epistemological problem of how we can “be in touch with” such facts. There are serious worries about normative knowledge, but the problems involved are internal to the normative domain itself. The best solution to these problems would be an overall account of the domain of reasons in normative terms, supported by an argument from reflective equilibrium. But no existing account, constructivist, or based on desires or on an idea of rationality, is plausible, and no alternative is likely to succeed. Conclusions about reasons for action must rest on more piecemeal applications of the method of reflective equilibrium. (shrink)

The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous range of set-theoretic possibilities, a phenomenon that challenges the universe (...) view. In particular, I argue that the continuum hypothesis is settled on the multiverse view by our extensive knowledge about how it behaves in the multiverse, and as a result it can no longer be settled in the manner formerly hoped for. (shrink)

Paul Boghossian defends a meaning‐based approach to the apriority of the propositions of logic. His model is based on the idea that the logical constants are implicitly defined by some of the axioms and inference rules in which they are involved, thereby offering an alternative to those theories that deny that grasp of meaning can contribute to the explanation of a thinker's entitlement to a particular type of transition or belief.

In order to perfectly describe the world, it is not enough to speak truly. One must also use the right concepts - including the right logical concepts. One must use concepts that "carve at the joints", that give the world's "structure". There is an objectively correct way to "write the book of the world". Much of metaphysics, as traditionally conceived, is about the fundamental nature of reality; in the present terms, this is about the world's structure. Metametaphysics - inquiry into (...) the status of metaphysical questions - turns on structure. The question of whether ontological, causal, or modal questions are "substantive" is in large part a question of whether the world has ontological, causal, and modal structure - whether quantifiers, causal relations, and modal operators carve at the joints. (shrink)

Logical pluralism is the claim that different accounts of validity can be equally correct. Beall and Restall have recently defended this position. Validity is a matter of truth-preservation over cases, they say: the conclusion should be true in every case in which the premises are true. Each logic specifies a class of cases, but differs over which cases should be considered. I show that this account of logic is incoherent. Validity indeed is truth-preservation, provided this is properly understood. Once understood, (...) there is one true logic, relevance logic. The source of Beall and Restall’s error is a recent habit of using a classical metalanguage to analyse non-classical logics generally, including relevance logic. (shrink)

" In a book that seeks to shift the ground of debate within theory of knowledge, William P. Alston finds that the century-lo.

This book defends a form of ethical intuitionism, according to which (i) there are objective moral truths; (ii) we know some of these truths through a kind of immediate, intellectual awareness, or "intuition"; and (iii) our knowledge of moral truths gives us reasons for action independent of our desires. The author rebuts all the major objections to this theory and shows that the alternative theories about the nature of ethics all face grave difficulties.

In Contradiction advocates and defends the view that there are true contradictions, a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the center of the controversies surrounding dialetheism ever since its first publication in 1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author’s reflections on developments over the last two decades. Further aspects of dialetheism are discussed in the companion (...) volume, Doubt Truth to be a Liar, also published by Oxford University Press in 2006. (shrink)

The Realm of Reason develops a new, general theory of what it is for a thinker to be entitled to form a given belief. The theory locates entitlement in the nexus of relations between truth, content, and understanding. Peacocke formulates three principles of rationalism that articulate this conception. The principles imply that all entitlement has a component that is justificationally independent of experience. The resulting position is thus a form of rationalism, generalized to all kinds of content. To show how (...) these principles are realized in specific domains, Peacocke applies the theory in detail to several classical problems of philosophy, including the nature of perceptual entitlement, induction, and the status of moral thought. These discussions involve an elaboration of the structure of entitlement in ways that have applications in many other areas of philosophy. He also relates the theory to classical and recent rationalist thought, and to current issues in the theory of meaning, reference and explanation. In the course of these discussions, he proposes a general theory of the a priori. The focus of the work lies in the intersection of epistemology, metaphysics, and the theory of meaning, and will be of interest both to students and researchers in these areas, and to anyone concerned with the idea of rationality. (shrink)

In his new foreword to this edition, Hilary Putnam forcefully rejects these nativist claims.

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

This paper criticises necessitarianism, the thesis that there is at least one necessary truth; and defends possibilism, the thesis that all propositions are contingent, or that anything is possible. The second section maintains that no good conventionalist account of necessity is available, while the third section criticises model theoretic necessitarianism. The fourth section sketches some recent technical work on nonclassical logic, with the aim of weakening necessitarian intuitions and strengthening possibilist intuitions. The fifth section considers several a prioristic attempts at (...) demonstrating that there is at least one necessary proposition and finds them inadequate. The final section emphasises the epistemic aspect of possibilism. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

What would something unlike us--a chimpanzee, say, or a computer--have to be able to do to qualify as a possible knower, like us? To answer this question at the very heart of our sense of ourselves, philosophers have long focused on intentionality and have looked to language as a key to this condition. Making It Explicit is an investigation into the nature of language--the social practices that distinguish us as rational, logical creatures--that revises the very terms of this inquiry. Where (...) accounts of the relation between language and mind have traditionally rested on the concept of representation, this book sets out an alternate approach based on inference, and on a conception of certain kinds of implicit assessment that become explicit in language. Making It Explicit is the first attempt to work out in detail a theory that renders linguistic meaning in terms of use--in short, to explain how semantic content can be conferred on expressions and attitudes that are suitably caught up in social practices. -/- At the center of this enterprise is a notion of discursive commitment. Being able to talk--and so in the fullest sense being able to think--is a matter of mastering the practices that govern such commitments, being able to keep track of one’s own commitments and those of others. Assessing the pragmatic significance of speech acts is a matter of explaining the explicit in terms of the implicit. As he traces the inferential structure of the social practices within which things can be made conceptually explicit, the author defines the distinctively expressive role of logical vocabulary. This expressive account of language, mind, and logic is, finally, an account of who we are. (shrink)