Logical pluralism and logical normativity - forthcoming in Philosopher's Imprint
This paper explores an apparent tension between two widely held views about logic: that logic is normative and that there are multiple equally legitimate logics. The tension is this. If logic is normative, it tells us something about how we ought to reason. If, as the pluralist would have it, there are several correct logics, those logics make incompatible recommendations as to how we ought to reason. But then which of these logics should we look to for normative guidance? I argue that inasmuch as pluralism draws its motivation from its ability to defuse logical disputes---that is, disputes between advocates of rival logics--it is unable to provide an answer: pluralism collapses into monism with respect to either the strongest or the weakest admissible logic.
Consequence and normative guidance - forthcoming in Philosophy and Phenomenological Research
Logic is said to be 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.
Three ways logic may be normative - forthcoming in Journal of Philosophy
Draft paper: Logic, the tradition has it, is normative for reasoning. Famously, the tradition was challenged by Gilbert Harman who argued that there is no straightforward connection between logical consequence and norms of reasoning. A number of authors (including John MacFarlane and Hartry Field) have sought to rehabilitate the traditional view of the normative status of logic against Harman. In this paper, I argue that the debate as a whole is marred by a failure of the disputing parties to distinguish three different types of normative assessment, and hence three distinct ways in which the question of the normativity of logic might be understood. Logical principles might be thought to provide first-personal directives to the reasoning agent, they might be thought to serve as third-personal evaluative standards, or they might underwrite our third-personal appraisals of others whereby be attribute praise and blame. I characterize the three normative functions in general terms. I then show how a failure to appreciate this three-fold distinction has impeded progress since it has led the participants in the debate to talk past one another. Moreover, I show how the distinction paves the way for a more fruitful engagement with the issue.
Frege and Carnap on the normativity of logic - Special edition "Carnap on Logic" of Synthese, G. Schiemer (ed.) 2017
In this paper I examine the question of logic's normative status in the light of Carnap's Principle of Tolerance. I begin by contrasting Carnap's conception of the normativity of logic with that of his teacher, Frege. I identify two core features of Frege's position: first, the normative force of the logical laws is grounded in their descriptive adequacy; second, norms resulting from logic are constitutive for thinking as such (in a sense to be clarified). While Carnap breaks with Frege's absolutism about logic and hence with the notion that any system of logic should have a privileged claim to correctness, I argue that there is a sense in which Carnap's framework-relative conception of logical norms has a constitutive role to play: though they are not constitutive for the conceptual activity for thinking, they do nevertheless set the ground rules that make certain forms of scientific inquiry possible in the first place.
Philosophie der Logik
Draft of a survey article on the philosophy of logic in German.
Inferentialism (with J. Murzi) for Blackwell Companion to Philosophy of Language, B. Hale, A. Miller and C. Wright (ed.) 2017
Draft of an article on inferentialism in the philosophy of language.
How tolerant can you be? Carnap on rationality - Philosophy and Phenomenological Research forthcoming 2016
In this paper I examine a neglected question concerning the centerpiece of Carnap's philosophy: the principle of tolerance. The principle of tolerance states that we are free to devise and adopt any well-defined form of language or linguistic framework we please. A linguistic framework defines framework-internal standards of correct reasoning that guide is in our first-order scientific pursuits. The choice of a linguistic framework, on the other hand, is an `external' question to be settled on pragmatic grounds and so not itself constrained by these (framework-internal) standards. However, even if choosing a framework is a practical matter, we would nevertheless expect the process of framework selection to be subject to rational norms. But which norms might those be? And where do they come from? I begin by showing that these questions are crucial to the success of Carnap's entire philosophical project. I then offer a response on behalf of the Carnapian which guarantees the rationality of the process of framework selection, while remaining true to Carnap's firm commitment to tolerance.
The normative status of logic - entry in Stanford Encyclopedia of Philosophy 2017
Draft of a survey article about the question of the normativity of logic. The final version can be found here: https://plato.stanford.edu/entries/logic-normative/
Explosion and the normativity of logic - Mind 2016
Logic has traditionally been construed as a normative discipline; it sets forth standards of correct reasoning. Explosion is a valid principle of classical logic. It states that an inconsistent set of propositions entails any proposition whatsoever. However, ordinary agents presumably do---occasionally, at least---have inconsistent belief sets. Yet it is false that such agents may, let alone ought, to believe any proposition they please. Therefore, our logic should not recognize explosion as a logical law. Call this the `normative argument against explosion'. Arguments of this type play---implicitly or explicitly---a central role in motivating paraconsistent logics. Branden Fitelson (2008), in a throwaway remark, has conjectured that there is no plausible 'bridge principle' articulating the normative link between logic and reasoning capable of supporting such arguments. This paper offers a critical evaluation of Fitelson's conjecture and hence of normative arguments for paraconsistency and the conceptions of logic's normative status on which they repose. It is argued that Fitelson's conjecture turns out to be correct: normative arguments for paraconsistency probably fail.
Entries in Cambridge Dictionary of Philosophy, third edition, R. Audi (Ed.) 2015:
adverbs, logic of; bootstrapping; cumulative case arguments; dialetheism; explosion; harmony, proof-theoretic; Lockean thesis; logical pluralism; normalization theorem; preface paradox; proof; principal principle; probabilism; radical interpretation; regulative-constitutive distinction; substructural logics.
Editorial and interview with Branden Fitelson - The Reasoner 2015
This is an interview with Branden Fitelson about his book manuscript Coherence.
David Lewis' sprachbegabte Esel - Cogito 2014
This is a light-hearted piece on David Lewis's modal realism written for a general audience in German. A version of it has appear in the LMU philosophy student journal Cogito.
Is logical knowledge dispositional? (with Julien Murzi) - Philosophical Studies 2013
In a series of recent papers, Corine Besson argues that dispositionalist accounts of logical knowledge conflict with ordinary reasoning. She cites cases in which, rather than applying a logical principle to deduce certain implications of our antecedent beliefs, we revise some of those beliefs in the light of their unpalatable consequences. She argues that such instances of, in Gilbert Harman’s phrase, ‘reasoned change in view’ cannot be accommodated by the dispositionalist approach, and that we would do well to conceive of logical knowledge as a species of propositional knowledge instead. In this paper, we propose a dispositional account that is more general than the one Besson considers, viz. one that does not merely apply to beliefs, and claim that dispositionalists have the resources to account for reasoned change in view. We then raise what we take to be more serious challenges for the dispositionalist view, and sketch some lines of response dispositionalists might offer.
Special Issue on Formal Epistemology (Ed. with Vincenzo Crupi, Branden Fitelson and Ole Hjortland) - Erkenntnis 2013
On the equivalence conjecture for proof-theoretic harmony - Notre Dame Journal of Formal Logic 2013
The requirement of proof-theoretic harmony has played a pivotal role in a number of debates in the philosophy of logic. Different authors have attempted to precisify the notion in different ways. Among these, three proposals have been prominent in the literature: Harmony-as-conservative extension, Harmony-as-levelling procedure and Tennant’s Harmony-as-deductive equilibrium. In this paper I propose to clarify the logical relationships between these accounts. In particular, I demon- strate that what I call the equivalence conjecture—that these three notions essentially come to the same thing—is erroneous.
Harmony in a sequent setting: a reply to Tennant - Analysis 2011
In this paper I reply to Neil Tennant's response to my 'Not so stable'.
What harmony could and could not be - Australasian Journal of Philosophy 2011
The notion of harmony has played a pivotal role in a number of debates in the philosophy of logic. Yet there is little agreement as to how the requirement of harmony should be spelled out in detail or even what purpose it is to serve. Most if not all conceptions of harmony can already be found in Michael Dummett’s seminal discussion of the matter in The Logical Basis of Metaphysics. Hence, if we wish to gain a better understanding of the notion of harmony, we do well to start here. Unfortunately, however, Dummett’s discussion is not always easy to follow. The following is an attempt to disentangle the main strands of Dummett’s treatment of harmony. The different variants of harmony as well as their interrelations are clarified and their individual shortcomings qua interpretations of harmony are demonstrated. Though no attempt is made to give a detailed alternative account of harmony here, it is hoped that our discussion will lay the ground for an adequate rigorous treatment of this central notion.
Why conclusions should remain single - Journal of Philosophical Logic 2011
This paper argues that logical inferentialists should reject multiple-conclusion logics. Logical inferentialism is the position that the meanings of the logical constants are determined by the rules of inference they obey. As such, logical inferentialism requires a proof-theoretic framework within which to operate. However, in order to fulfil its semantic duties, a deductive system has to be suitably connected to our inferential practices. I argue that, contrary to an established tradition, multiple-conclusion systems are ill-suited for this purpose because they fail to provide a 'natural' representation of our ordinary modes of inference. Moreover, the two most plausible attempts at bringing multiple conclusions into line with our ordinary forms of reasoning, the disjunctive reading and the bilateralist denial interpretation, are unacceptable by inferentialist standards.
Not so stable - Analysis 2009
In this paper I present a counterexample to Neil Tennant's account of proof-theoretic harmony.
Harmony and logical inferentialism - Ph.D. Thesis Cambridge University 2009
My thesis is an attempt to supply answers to what I take to be the three central questions facing inferentialism about the logical constants (which I call logical inferentialism). What are the assumptions about meaning that underpin logical inferentialism? What is the correct formulation of the principle of harmony? And finally: What follows from logical inferentialism? Accordingly, the dissertation falls into three parts.
I begin by laying out the fundamental meaning-theoretic principles that underpin logical inferentialism: it is use-theoretic; it subscribes to the two-aspect theory of meaning; as the name makes plain, it is inferentialist in approach; and it is committed to a weak form of molecularism. Having spelled out its founding assumptions, I defend inferentialism against the charge that, contrary to its defining motto, the meanings of the logical operators are not fully determined by the rules of inference they obey, but also in part by structural assumptions. The second part offers a comprehensive treatment of the notion of harmony. After giving an analysis of the notion, I review and criticize existing accounts of harmony in the literature. In particular, I show that Michael Dummett’s and Stephen Read’s theories are unsatisfactory and I present a counterexample to Neil Tennant’s principle of harmony. I then advance my own version of harmony, which not only avoids the difficulties that plagued the accounts mentioned, but also boasts additional advantageous features. In the final part I examine the consequences of these results for so-called proof-theoretic arguments. Such arguments purport to show that the principle of harmony supports broadly intuitionistic revisions of our logic. I argue that, given our inferentialist commit- ments, a defence of classical logic based on the adoption of multiple-conclusion sequent calculi is misguided. Multiple-conclusion systems, I submit, are illegitimate from an inferentialist point of view. Moreover, I defend the principle of separability against realist attacks.
Tennant on multiple conclusions - Logique et analyse 2008
This section is under construction.