Books by Ole T Hjortland
Foundations of Logical Consequence
Logical consequence is the relation that obtains between premises and conclusion(s) in a valid ar... more Logical consequence is the relation that obtains between premises and conclusion(s) in a valid argument. Orthodoxy has it that valid arguments are necessarily truth-preserving, but this platitude only raises a number of further questions, such as: how does the truth of premises guarantee the truth of a conclusion, and what constraints does validity impose on rational belief? This volume presents thirteen essays by some of the most important scholars in the field of philosophical logic. The essays offer ground-breaking new insights into the nature of logical consequence; the relation between logic and inference; how the semantics and pragmatics of natural language bear on logic; the relativity of logic; and the structural properties of the consequence relation.
Insolubles and Consequences: Essays in honour of Stephen Read
Throughout his career, Stephen Read has been at the forefront of research in the history and phil... more Throughout his career, Stephen Read has been at the forefront of research in the history and philosophy of logic. Distinctive of his work is his effort both to bring ideas from the history of logic into contemporary debates, and to apply formal logic in his historical analyses. He has made decisive contributions to the study of medieval logic, paradoxes, proof-theoretic semantics, relevant logic, logical consequence, and many other topics. On the occasion of his retirement, friends and colleagues join forces to honor him with a collection of papers reflecting his wide range of interests. Topics covered are: modern treatments of medieval solutions to the Liar paradox, reflections on logical consequence, proof-theoretic semantics, logical pluralism, studies in the history of logic (Latin and Arabic medieval logic in particular), among others. The collection reflects both the breadth and the depth of Read's unique approach to the history and philosophy of logic, containing papers by prominent researchers in these areas. As a whole, it strives to live up to the quality of Stephen's own work.
Papers by Ole T Hjortland
Norsk filosofisk tidsskrift, 2021
Synthese
While anti-exceptionalism about logic (AEL) is now a popular topic within the philosophy of logic... more While anti-exceptionalism about logic (AEL) is now a popular topic within the philosophy of logic, there’s still a lack of clarity over what the proposal amounts to. currently, it is most common to conceive of AEL as the proposal that logic is continuous with the sciences. Yet, as we show here, this conception of AEL is unhelpful due to both its lack of precision, and its distortion of the current debates. Rather, AEL is better understood as the rejection of certain traditional properties of logic. The picture that results is not of one singular position, but rather a cluster of often connected positions with distinct motivations, understood in terms of their rejection of clusters of the various traditional properties. In order to show the fruitfulness of this new conception of AEL, we distinguish between two prominent versions of the position, metaphysical and epistemological AEL, and show how the two positions need not stand or fall together.
Journal of Philosophical Logic, 2020
Motivated by weaknesses with traditional accounts of logical epistemology, considerable attention... more Motivated by weaknesses with traditional accounts of logical epistemology, considerable attention has been paid recently to the view, known as anti-exceptionalism about logic (AEL), that the subject matter and epistemology of logic may not be so different from that of the recognised sciences. One of the most prevalent claims made by advocates of AEL is that theory choice within logic is significantly similar to that within the sciences. This connection with scientific methodology highlights a considerable challenge for the anti-exceptionalist, as two uncontentious claims about scientific theories are that they attempt to explain a target phenomenon and (at least partially) prove their worth through successful predictions. Thus, if this methodological AEL is to be viable, the anti-exceptionalist will need a reasonable account of what phenomena logics are attempting to explain, how they can explain, and in what sense they can be said to issue predictions. This paper makes sense of the anti-exceptionalist proposal with a new account of logical theory choice, logical predictivism, according to which logics are engaged in both a process of prediction and explanation.
The Routledge Handbook of the Philosophy of Evidence (edited by M. Lasnon-Aarnio & C. Littlejohn), 2020
The historical consensus is that logical evidence is special. Whereas empirical evidence is used ... more The historical consensus is that logical evidence is special. Whereas empirical evidence is used to support theories within both the natural and social sciences, logic answers solely to a priori evidence. Further, unlike other areas of research that rely upon a priori evidence, such as mathematics , logical evidence is basic. While we can assume the validity of certain inferences in order to establish truths within mathematics and test scientific theories, logicians cannot use results from mathematics or the empirical sciences without seemingly begging the question. Appeals to rational intuition and analyticity in order to account for logical knowledge are symptomatic of these commitments to the apriority and basicness of logical evidence. This chapter argues that these historically prevalent accounts of logical evidence are mistaken, and that if we take logical practice seriously we find that logical evidence is rather unexceptional, sharing many similarities to the types of evidence appealed to within other research areas.
Inquiry, 2019
What do we disagree about when we disagree about logic? On the face of it, classical and nonclass... more What do we disagree about when we disagree about logic? On the face of it, classical and nonclassical logicians disagree about the laws of logic and the nature of logical properties. Yet, sometimes the parties are accused of talking past each other. The worry is that if the parties to the dispute do not mean the same thing with 'if', 'or', and 'not', they fail to have genuine disagreement about the laws in question. After the work of Quine, this objection against genuine disagreement about logic has been called the meaning-variance thesis. We argue that the meaning-variance thesis can be endorsed without blocking genuine disagreement. In fact, even the type of revisionism and nonapriorism championed by Quine turns out to be compatible with meaning-variance.
Nonclassical theories of truth have in common that they reject principles of classical logic to a... more Nonclassical theories of truth have in common that they reject principles of classical logic to accommodate an unrestricted truth predicate. However, different nonclassical strategies give up different classical principles. The paper discusses one criterion we might use in theory choice when considering nonclassical rivals: the maxim of minimal mutilation (MMM).
Logic isn't special. Its theories are continuous with science; its method continuous with scienti... more Logic isn't special. Its theories are continuous with science; its method continuous with scientific method. Logic isn't a priori, nor are its truths analytic truths. Logical theories are revisable, and if they are revised, they are revised on the same grounds as scientific theories. These are the tenets of anti-exceptionalism about logic. The position is most famously defended by Quine, but has more recent advocates in 2015). Although these authors agree on many methodological issues about logic, they disagree about which logic anti-exceptionalism supports. Williamson uses an antiexceptionalist argument to defend classical logic, while Priest claims that his anti-exceptionalism supports nonclassical logic. This paper argues that the disagreement is due to a difference in how the parties understand logical theories. Once we reject Williamson's deflationary account of logical theories, the argument for classical logic is undercut. Instead an alternative account of logical theories is offered, on which logical pluralism is a plausible supplement to anti-exceptionalism.
An introduction to the Foundations of Logical Consequence. Overview of debates about logical cons... more An introduction to the Foundations of Logical Consequence. Overview of debates about logical consequence.
According to the logical inferentialist, the meaning of a logical connective is determined by the... more According to the logical inferentialist, the meaning of a logical connective is determined by the inference rules that govern its use. Proof theoretic semantics attempts to make this idea precise in a proof theoretic framework, using for example natural deduction or sequent calculus rules. Since Prior's infamous connective tonk much of proof theoretic semantics have been occupied with formal anti-tonk conditions which rule out ill-behaved connectives (e.g. conservativeness, harmony). Common between them is that inference rules only succeed in determining the meaning of a connective if the proof theoretic conditions are fulfilled. On the traditional account, however, such conditions are insensitive to substructural dimensions of proof theory, e.g. the distinction between additive and multiplicative connectives. We argue that proof theoretic semantics ought to have the resources to attribute different meanings to substructurally distinct connectives. Subsequently we show how to develop a notion of proof theoretic harmony that preserves substructural distinctions from introduction to elimination rules. The substructural account of harmony can rule out cases of nonconservativeness that previous accounts have not dealt with.
Journal of Logic and Computation
This article looks at so-called dynamic consequence relations for models of soft information chan... more This article looks at so-called dynamic consequence relations for models of soft information change. We provide a sound, complete calculus for one-step soft dynamic consequence relations. We then study a generalization to sequences of updates, for which we show a number of valid and invalid structural rules.
In bilateral systems for classical logic, assertion and denial occur as primitive signs on formul... more In bilateral systems for classical logic, assertion and denial occur as primitive signs on formulae. Such systems lend themselves to an inferentialist story about how truth-conditional content of connectives can be determined by inference rules. In particular, for classical logic there is a bilateral proof system which has a property that Carnap (1943) called categoricity. We show that categorical systems can be given for any finite many-valued logic using n-sided sequent calculus. These systems are understood as a further development of bilateralism-call it multilateralism. The overarching idea is that multilateral proof systems can incorporate the logic of a variety of denial speech acts. So against Frege we say that denial is not the negation of assertion, and with Mark Twain, that denial is more than a river in Egypt. * This research is supported by the Alexander von Humboldt Foundation. I'd like to thank Pål for helpful feedback and discussion of earlier drafts. Finally, I'm immensely grateful to an anonymous referee for detailed suggestion on how to improve the paper.
Logical Pluralism, Meaning-Variance, and Verbal Disputes
Logical pluralism has been in vogue since JC Beall and Greg Restall 2006 articulated and defended... more Logical pluralism has been in vogue since JC Beall and Greg Restall 2006 articulated and defended a new pluralist thesis. Recent criticisms such as Priest 2006a and Field 2009 have suggested that there is a relationship between their type of logical pluralism and the meaning-variance thesis for logic. This is the claim, often associated with Quine 1970, that a change of logic entails a change of meaning. Here we explore the connection between logical pluralism and meaning-variance, both in general and for Beall and Restall's theory specifically. We argue that contrary to what Beall and Restall claim, their type of pluralism is wedded to meaning-variance. We then develop an alternative form of logical pluralism that circumvents at least some forms of meaning-variance.
Insolubles and Consequences. Essays in honour of Stephen Read (College Publications)
Inferentialism and the categoricity problem: reply to Raatikainen
The structure of logical consequence: proof-theoretic conceptions
The model-theoretic analysis of the concept of logical consequence has come under heavy criticism... more The model-theoretic analysis of the concept of logical consequence has come under heavy criticism in the last couple of decades. The present work looks at an alternative approach to logical consequence where the notion of inference takes center stage. Formally, the model-theoretic framework is exchanged for a proof-theoretic framework. It is argued that contrary to the traditional view, proof-theoretic semantics is not revisionary, and should rather be seen as a formal semantics that can supplement model-theory. Specifically, there are formal resources to provide a proof-theoretic semantics for both intuitionistic and classical logic.
We develop a new perspective on proof-theoretic harmony for logical constants which incorporates elements from the substructural era of proof-theory. We show that there is a semantic lacuna in the traditional accounts of harmony. A new theory of how inference rules determine the semantic content of logical constants is developed. The theory weds proof-theoretic and model-theoretic semantics by showing how proof-theoretic rules can induce truth-conditional clauses in Boolean and many-valued settings. It is argued that such a new approach to how rules determine meaning will ultimately assist our understanding of the apriori nature of logic.
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Books by Ole T Hjortland
Papers by Ole T Hjortland
We develop a new perspective on proof-theoretic harmony for logical constants which incorporates elements from the substructural era of proof-theory. We show that there is a semantic lacuna in the traditional accounts of harmony. A new theory of how inference rules determine the semantic content of logical constants is developed. The theory weds proof-theoretic and model-theoretic semantics by showing how proof-theoretic rules can induce truth-conditional clauses in Boolean and many-valued settings. It is argued that such a new approach to how rules determine meaning will ultimately assist our understanding of the apriori nature of logic.