Articles by Colin R Caret
Asian Journal of Philosophy, 2023
In a recent series of articles, Beall has developed the view that FDE is the formal system most d... more In a recent series of articles, Beall has developed the view that FDE is the formal system most deserving of the honorific "Logic". The Simple Argument for this view is a cost-benefit analysis: the view that FDE is Logic has no drawbacks and it has some benefits when compared with any of its rivals. In this paper, I argue that both premises of the Simple Argument are mistaken. I use this as an opportunity to further reflect on how such arguments can be bolstered to provide more substantial and productive support for revisionary theses about Logic.
The Logica Yearbook 2021, 2022
According to Jago (2014a), logical omniscience is really part of a deeper paradox. Jago develops ... more According to Jago (2014a), logical omniscience is really part of a deeper paradox. Jago develops an epistemic logic with principles of indeterminate closure to solve this paradox, but his official semantics is difficult to navigate, it is motivated in part by substantive metaphysics, and the logic is not axiomatized. In this paper, I simplify this epistemic logic by adapting the hyperintensional semantic framework of Sedlár (2021). My first goal is metaphysical neutrality. The solution to the epistemic paradox should not require appeal to a metaphysics of truth-makers, situations, or impossible worlds, by contrast with Jago's official semantics. My second goal is to elaborate on the proof theory. I show how to axiomatize a family of logics with principles of indeterminate epistemic closure.
Synthese, 2021
This paper scrutinizes the debate over logical pluralism. I hope to make this debate more tractab... more This paper scrutinizes the debate over logical pluralism. I hope to make this debate more tractable by addressing the question of motivating data: what would count as strong evidence in favor of logical pluralism? Any research program should be able to answer this question, but when faced with this task, many logical pluralists fall back on brute intuitions. This sets logical pluralism on a weak foundation and makes it seem as if nothing pressing is at stake in the debate. The present paper aims to improve this situation by looking at a promising case study and drawing general lessons about the kind of evidence that would support logical pluralism. I argue that the best motivation for logical pluralism will ultimately be rooted in certain kinds of performative data.
Episteme, 2021
This paper is about the underlying logical principles of scientific theories. In particular, it c... more This paper is about the underlying logical principles of scientific theories. In particular, it concerns ex contradictione quodlibet (ECQ) the principle that anything follows from a contradiction. ECQ is valid according to classical logic, but invalid according to paraconsistent logics. Some advocates of paraconsistency claim that there are 'real' inconsistent theories that do not erupt with completely indiscriminate, absurd commitments. They take this as evidence in favor of paraconsistency. Michael (2016) calls this the non-triviality strategy (NTS). He argues that this strategy fails in its purpose. I will show that Michael's criticism significantly overreaches. The fundamental problem is that he places more of a burden on the advocate of paraconsistency than on the advocate of classical logic. The weaknesses in Michael's argument are symptomatic of this preferential treatment of one viewpoint in the debate over another. He does, however, make important observations that allow us to clarify some of the complexities involved in giving a logical reconstruction of a theory. I will argue that there are abductive arguments deserving of further consideration for the claim that paraconsistent logic offers the best explanation of the practice of inconsistent science. In this sense, the debate is still very much open.
Erkenntnis, 2017
According to the logical pluralism of Beall and Restall, there are several distinct relations of ... more According to the logical pluralism of Beall and Restall, there are several distinct relations of logical consequence. Some critics argue that logical pluralism suffers from what I call the collapse problem: that despite its intention to articulate a radically pluralistic doctrine about logic, the view unintentionally collapses into logical monism. In this paper, I propose a contextualist resolution of the collapse problem. This clarifies the mechanism responsible for a plurality of logics and handles the motivating data better than the original view. It is a major improvement that should be embraced by all logical pluralists.
This paper contributes to the study of paracompleteness and paraconsistency. We present two logic... more This paper contributes to the study of paracompleteness and paraconsistency. We present two logics that address the following questions in novel ways. How can the paracomplete theorist characterize the formulas that defy excluded middle while maintaining that not all formulas are of this kind? How can the paraconsistent theorist characterize the formulas that obey explosion while still maintaining that there are some formulas not of this kind?
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.
Topoi 34.1, 2015
This note motivates a logic for a theory that can express its own notion of logical consequence-a... more This note motivates a logic for a theory that can express its own notion of logical consequence-a 'syntactically closed' theory of naive validity. The main issue for such a logic is Curry's paradox, which is averted by the failure of contraction. The logic features two related, but different, implication connectives. A Hilbert system is proposed that is complete and non-trivial.
Books by Colin R Caret
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.
The advocate of modal logic or relevant logic has traditionally argued that her preferred system ... more The advocate of modal logic or relevant logic has traditionally argued that her preferred system offers the best regimentation of the theory of entailment. Essential to the projects of modal and relevant logic is the importation of non-truth-functional expressive resources into the object language on which the logic is defined. The most elegant technique for giving the semantics of such languages is that of frame semantics, a variation on which features the device of partitioned frames that divide 'points of evaluation' into two types: normal points and abnormal points. This essay attempts to provide satisfying philosophical interpretations of the partitioned frame semantics for some weak modal logics and relevant logics. According to the current best interpretation, partitioned frame semantics are a kind of possible worlds semantics that appeal to 'logically impossible worlds' where the laws of logic may fail to hold. This is undermined by the fact that all of the target logics fail to satisfy criteria of expressibility needed to support the thesis that laws of logic fail to hold at abnormal points. This suggests that we should not look for a monistic interpretive paradigm for partitioned frame semantics. In response, new interpretations of the weak modal logic S0.5 and the 'basic' relevant logic B are constructed. It is argued that S0.5 is a logic of alethic modality according to a conventionalist conception of necessity, and that B is a logic of meaning inclusion according to a dialetheist conception of the space of possibilities. The given interpretations help to shed light on relations between systems of modal logic and relevant logic, and explain some of the most interesting features of such logics, like failure of the rule of necessitation and failure of contraction principles.
Reviews by Colin R Caret
The Philosophical Quarterly, 2022
The semantic tradition in logic descends from Tarski's seminal work on truth and logical conseque... more The semantic tradition in logic descends from Tarski's seminal work on truth and logical consequence. In the introduction to this volume, Sagi and Woods remind us that this tradition prominently uses model theory to study languages and their interpretations. Tarski's model-theoretic definition of logical consequence is the prime example of this approach, seeking as it does to reduce logical properties to a class of operations on classical, iterative (ZF) sets. Sagi and Woods explain with admirable clarity the origins, implications, and philosophical questions surrounding this project. The contributions to the volume go on to address whether this approach successfully elucidates logicality and how it intersects with the foundations of mathematics and natural language semantics.
Notre Dame Philosophical Reviews, 2017
Mind 120
Spandrels of Truth, by Jc Beall. Oxford: Oxford University Press, 2009. Pp. xii + 154. H/b £30.00... more Spandrels of Truth, by Jc Beall. Oxford: Oxford University Press, 2009. Pp. xii + 154. H/b £30.00, P/b £17.99.
Review of Modern Logic 11, 2008
This is a book about dialetheism, the theory that there are some truth-bearers (sentences, propos... more This is a book about dialetheism, the theory that there are some truth-bearers (sentences, propositions, or what have you) of the form α and ¬α such that both of the pair are true. As Graham Priest puts it, "Dialetheism is the view that some contradictions are true. . . " 1 This book does not, however, offer a sustained defense of dialetheism nor a rigorous exploration of the appropriate logic for a dialetheist to endorse. Those subjects have been sufficiently dealt with in Priest's prior work and they play only a minor role in the present book. Instead, this book is concerned with the relation between dialetheism and the philosophical notions of truth, negation, rationality, and logic. It is meant to supplement the dialetheist project by explaining where and how the commitment to dialetheism intersects with our conceptions of these core philosophical notions. Because it is not principally concerned with the motivations for dialetheism and because it is not too heavy-handed with the formal logic, this book will appeal to philosophers of many stripes.
Uploads
Articles by Colin R Caret
Books by Colin R Caret
Reviews by Colin R Caret