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and Logic
Edited by
Jeremy Wyatt
Nikolaj J. L. L. Pedersen
Nathan Kellen
Palgrave Innovations in Philosophy

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University of Copenhagen
Copenhagen, Denmark

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University of Edinburgh
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 Jeremy Wyatt
Nikolaj J. L. L. Pedersen  •  Nathan Kellen
Editors

Pluralisms in Truth
and Logic
Editors
Jeremy Wyatt Nikolaj J. L. L. Pedersen
Underwood International College Underwood International College
Yonsei University Yonsei University
Incheon, South Korea Incheon, South Korea

Nathan Kellen
University of Connecticut,
Storrs, CT, USA

Palgrave Innovations in Philosophy

ISBN 978-3-319-98345-5    ISBN 978-3-319-98346-2 (eBook)
https://doi.org/10.1007/978-3-319-98346-2

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 Preface

Pluralism has made inroads into a number of areas in philosophy. This

edited collection brings together 18 state-of-the-art articles on pluralism
about truth and logic.
We first discussed the possibility of an edited collection shortly after
the Truth Pluralism and Logical Pluralism Conference, held at the
University of Connecticut in April of 2015. Following this conference,
several additional pluralism-related events took place, including three
workshops hosted by the Cogito Research Centre at the University of
Bologna in 2015 and 2016 and Pluralisms Week, hosted by the Pluralisms
Global Research Network and the Veritas Research Center at Yonsei
University in June of 2016. A fair number of contributors were given the
chance to present and discuss their work at one or several of these events.
The University of Connecticut, University of Bologna, and Yonsei
University all provided financial support. We gratefully acknowledge
their support. Two of the editors, Pedersen and Wyatt, would also like to
thank the National Research Foundation of Korea for support (grants no.
2013S1A2A2035514 and 2016S1A2A2911800).
We are grateful to many colleagues who share our interest in pluralism.
Their collegial, constructive ways of conducting research and discussions
are much appreciated. We are grateful to many people who, in some way
or another, have helped along the way. These include Jc Beall, Elke
Brendel, Colin Caret, Roy Cook, Douglas Edwards, Will Gamester,
v
vi Preface

Patrick Greenough, Sungil Han, Jinho Kang, Jiwon Kim, Junyeol Kim,
Seahwa Kim, Teresa Kouri Kissel, Kris McDaniel, Graham Priest, Agustín
Rayo, Greg Restall, Jisoo Seo, Stewart Shapiro, Gila Sher, Paul Simard
Smith, Erik Stei, Elena Tassoni, Pilar Terrés, Cory D.  Wright, Crispin
Wright, Andy D. Yu, Luca Zanetti, and Elia Zardini. Special thanks go to
Filippo Ferrari, Michael P. Lynch, Sebastiano Moruzzi, and Joe Ulatowski.

Incheon, South Korea Jeremy Wyatt

 Nikolaj J. L. L. Pedersen
Storrs, CT, USA Nathan Kellen
 Contents

Part I Truth    1

Introduction  3
Nikolaj J. L. L. Pedersen, Jeremy Wyatt, and Nathan Kellen

Truth: One or Many or Both? 35

Dorit Bar-On and Keith Simmons

Truth Pluralism, Quasi-Realism, and the Problem of Double-­

Counting 63
Michael P. Lynch

The Metaphysics of Domains 85

Douglas Edwards

Strong Truth Pluralism107

Seahwa Kim and Nikolaj J. L. L. Pedersen

vii
viii Contents

Methodological Pluralism About Truth131

Nathan Kellen

Normative Alethic Pluralism145

Filippo Ferrari

Truth in English and Elsewhere: An Empirically-Informed

Functionalism169
Jeremy Wyatt

Part II Logic  197

Core Logic: A Conspectus199

Neil Tennant

Connective Meaning in Beall and Restall’s Logical Pluralism217

Teresa Kouri Kissel

Generalised Tarski’s Thesis Hits Substructure237

Elia Zardini

Logical Particularism277
Gillman Payette and Nicole Wyatt

Logical Nihilism301
Aaron J. Cotnoir

Varieties of Logical Consequence by Their Resistance to

Logical Nihilism331
Gillian Russell
  Contents  ix

Part III Connections  363

Pluralism About Pluralisms365

Roy T. Cook

A Plea for Immodesty: Alethic Pluralism, Logical Pluralism,

and Mixed Inferences387
Chase B. Wrenn

Logic for Alethic, Logical, and Ontological Pluralists407

Andy D. Yu

Pluralisms: Logic, Truth and Domain-Specificity429

Rosanna Keefe

Aletheic and Logical Pluralism453

Kevin Scharp

Index473
 Notes on Contributors

Dorit  Bar-On is Professor of Philosophy, Department of Philosophy, and

Director of the Expression, Communication, and the Origins of Meaning
Research Group, University of Connecticut. Bar-On is well known for her work
in philosophy of language, mind, and meta­ethics. She is author of Speaking My
Mind: Expression and Self­Knowledge (Clarendon Press, 2004) and has published
in journals such as The Journal of Philosophy, Mind & Language, Philosophy and
Phenomenological Research, Noûs, Synthese, and Philosophical Studies.
Roy T. Cook  is Professor of Philosophy, Department of Philosophy, University
of Minnesota. Cook specializes in the philosophy of logic, philosophical logic,
philosophy of mathematics, and aesthetics. He is the author of Paradoxes (Polity,
2013) and The Yablo Paradox: An Essay on Circularity (OUP, 2014), as well as
many papers in journals such as Mind, Analysis, Journal of Symbolic Logic,
Philosophia Mathematica, and Australasian Journal of Philosophy.
Aaron J. Cotnoir  is Senior Lecturer, Department of Philosophy, University of
St Andrews. Cotnoir’s work is centered around metaphysics and philosophical
logic. He is the editor of Composition as Identity (OUP, 2014, with Donald
Baxter) and co-author of Mereology (OUP, forthcoming). His articles have
appeared in Journal of Philosophy, Mind, Noûs, Australasian Journal of Philosophy,
and more.
Douglas  Edwards is Assistant Professor of Philosophy, Department of
Philosophy, Utica College. Edwards’ research centers around metaphysics, the
philosophy of language, and metaethics. He is the author of Properties (Polity,

xi
xii  Notes on Contributors

2014) and The Metaphysics of Truth (OUP, 2018) and the editor of Truth: A
Contemporary Reader (Bloomsbury, under contract). His articles have appeared
in a number of journals, including the Journal of Philosophy, Australasian Journal
of Philosophy, and Pacific Philosophical Quarterly, amongst others.
Filippo Ferrari  is Postdoctoral Research Fellow at the Institute of Philosophy,
University of Bonn. His research focuses primarily on two clusters of topics: the
normative aspects of enquiry and the debate about the nature of truth. He has
published his work in journals such as Mind, Synthese, Analysis, and Philosophical
Quarterly.
Rosanna  Keefe is Professor of Philosophy and Head, Department of
Philosophy, University of Sheffield. Keefe specializes in philosophy of logic, phi-
losophy of language, and metaphysics. She is the author of Theories of Vagueness
(Cambridge, 2000) and numerous articles in journals such as Mind, Analysis,
Philosophical Studies, Australasian Journal of Philosophy, and Synthese.
Nathan  Kellen works at the Department of Philosophy, University of
Connecticut. Kellen’s work is on truth, the philosophy of logic, philosophy of
mathematics, and ethics. Currently his main research project is an investigation
of truth pluralism and logical pluralism. He explores both of these views indi-
vidually but likewise examines how they might be connected.
Seahwa  Kim  is Professor of Philosophy and Dean, Scranton College, Ewha
Womans University. Kim specializes in metaphysics and the philosophy of
mathematics. Her articles have appeared in journals such as Australasian Journal
of Philosophy, Philosophical Studies, and Erkenntnis.
Teresa  Kouri  Kissel  is Assistant Professor, Department of Philosophy, Old
Dominion University. Kouri Kissel specializes in philosophy of logic, philoso-
phy of mathematics, and mathematical and philosophical logic. Her dissertation
develops a new, neo­Carnapian form of logical pluralism. Her articles have
appeared in Philosophia Mathematica, Erkenntnis, and Topoi.
Michael  P.  Lynch is Professor of Philosophy and Director, Humanities
Institute, University of Connecticut. Lynch’s work focuses on questions in meta-
physics, the philosophy of language, epistemology, and metaethics. He is author
of Truth in Context (MIT, 1998), True to Life (MIT, 2004), and Truth as One
and Many (OUP, 2009), as well as two books for popular audiences and a num-
ber of different articles in journals such as Philosophical Quarterly, Australasian
Journal of Philosophy, and Philosophical Studies.
   Notes on Contributors  xiii

Gillman Payette  is Postdoctoral Fellow at the University of British Columbia.

His main research interests are philosophical logic and the philosophy of logic.
He has published in journals such as Journal of Philosophical Logic, Australasian
Journal of Philosophy, Synthese,  Logique et Analyse,  and  Notre Dame Journal of
Formal Logic.
Nikolaj J. L. L. Pedersen  is Associate Professor of Philosophy and Director of
the UIC Research Institute and Veritas Research Center, Underwood
International College, Yonsei University. He has been the principal investigator
of several collaborative research projects. Pedersen’s main research areas are truth,
epistemology, and metaphysics. He has published in journals such as Noûs,
Analysis, Philosophical Quarterly, Synthese, Erkenntnis, and The Monist. He is a
co­editor of New Waves in Truth (Palgrave Macmillan, 2010), Truth and Pluralism:
Current Debates (Oxford University Press, 2013), Epistemic Pluralism (Palgrave
Macmillan, 2017), Epistemic Entitlement (Oxford University Press, 2019), and
The Routledge Handbook of Social Epistemology (2019).
Gillian  Russell is Professor of Philosophy, Department of Philosophy,
University of North Carolina at Chapel Hill. Russell specializes on the philoso-
phy of language, philosophy of logic, and epistemology. She is the author of
Truth in Virtue of Meaning: A Defence of the Analytic/Synthetic Distinction (OUP,
2008) and her articles have appeared in journals such as Journal of Philosophical
Logic, Philosophical Studies, and Australasian Journal of Philosophy.
Kevin Scharp  is Reader in Philosophy, Department of Philosophy and Director,
Arché Philosophical Research Centre, University of St Andrews. Scharp special-
izes in the philosophy of language, logic, metaphysics, philosophy of science,
and the history of analytic philosophy. He is the author of Replacing Truth (OUP,
2013) and numerous articles in journals such as The Philosophical Review,
Philosophy and Phenomenological Research, Erkenntnis, and Philosophical Studies.
Keith  Simmons is Professor of Philosophy, Department of Philosophy,
University of Connecticut. Simmons specializes in logic, philosophy of lan-
guage, and metaphysics. He is the author of Universality and the Liar (OUP,
1993) and has had articles appear in Philosophical Studies, Philosophy and
Phenomenological Research, and Journal of Philosophical Logic, amongst other
journals.
Neil Tennant  is Arts and Humanities Distinguished Professor of Philosophy,
Department of Philosophy, Ohio State University. Tennant specializes in logic,
philosophy of mathematics, and the philosophy of language. He is the author of
xiv  Notes on Contributors

a number of books, including The Taming of the True (OUP, 2002) and Changes
of Mind: An Essay on Rational Belief Revision (OUP, 2012). His articles have
appeared in many journals, including Mind, Philosophia Mathematica, Review of
Symbolic Logic, and Noûs.
Chase  B.  Wrenn is Professor of Philosophy, Department of Philosophy,
University of Alabama. Wrenn’s research focuses on truth, epistemology, and the
philosophy of mind and cognitive science. He is the author of Truth (Polity,
2014) and has had articles appear in journals including Australasian Journal of
Philosophy, Erkenntnis, Synthese, and The Philosophical Quarterly.
Jeremy Wyatt  is Assistant Professor of Philosophy, Underwood International
College, Yonsei University. Wyatt’s main research interests are the philosophy of
language, metaphysics, and truth. His articles have appeared in Philosophical
Studies, Philosophical Quarterly, American Philosophical Quarterly, and Inquiry.
Andy D. Yu  is JD student, University of Toronto. Yu completed a D.Phil. the-
sis (Fragmented Truth) at the University of Oxford. He works on philosophical
logic, the philosophy of language, metaphysics, and epistemology. He has pub-
lished in the Journal of Philosophy, Philosophical Quarterly, and Thought.
Elia Zardini  is Mid­Career FCT Fellow, LanCog Research Group, University of
Lisbon. Zardini specializes in logic and epistemology and has had articles appear
in many journals, including The Review of Symbolic Logic, Philosophical Studies,
Analysis, and Journal of Philosophical Logic. He is also the editor or co­editor of
Scepticism and Perceptual Justification (OUP, 2014), Substructural Approaches to
Paradox (special issue of Synthese, forthcoming), The Sorites Paradox (CUP, forth-
coming), and The A Priori: Its Significance, Grounds, and Extent (OUP,
forthcoming).
 List of Figures

Truth in English and Elsewhere: An Empirically-Informed

Functionalism
Fig. 1 Alethic functionalism 173
Fig. 2 Consistency of interlinguistic and intralinguistic pluralism 177
Fig. 3 Updated functionalism 184
Core Logic: A Conspectus
Fig. 1 From classical logic to core logic 203
Fig. 2 Important system containments 204
Varieties of Logical Consequence by Their Resistance to Logical
Nihilism
Fig. 1 A truth-table proof of Modus tollens 343
Fig. 2 A paraconsistent truth-table of Modus tollens 344

xv
Part I
Truth
 Introduction
Nikolaj J. L. L. Pedersen, Jeremy Wyatt,
and Nathan Kellen

1 Pluralisms
The history of philosophy displays little consensus or convergence when
it comes to the nature of truth. Radically different views have been pro-
posed and developed. Some have taken truth to be correspondence with
reality, while others have taken it to be coherence with a maximally coher-
ent set of beliefs. Yet others have taken truth to be what it is useful to
believe, or what would be believed at the end of enquiry.1 While these
views differ very significantly in terms of their specific philosophical com-
mitments, they all share two fundamental assumptions: monism and sub-
stantivism. The views all assume that truth is to be accounted for in the

N. J. L. L. Pedersen (*)
Underwood International College, Yonsei University, Incheon, South Korea
e-mail: nikolaj@yonsei.ac.kr
J. Wyatt
Underwood International College, Yonsei University, Incheon, South Korea
N. Kellen
University of Connecticut, Storrs, CT, USA

© The Author(s) 2018 3

J. Wyatt et al. (eds.), Pluralisms in Truth and Logic, Palgrave Innovations in Philosophy,
https://doi.org/10.1007/978-3-319-98346-2_1
4  N. J. L. L. Pedersen et al.

same way across the full range of truth-apt discourse (monism) and that
truth is a substantive property or relation (substantivism).
The deflationist reaction to the traditional debate is to reject substantiv-
ism and, in some cases, to endorse monism. Truth, if it has a nature at all,
has a uniform nature across all truth-apt discourse, but there is not much
to say about it. The traditional debate went off-track exactly because
truth theorists thought that there was a whole lot to say about truth—
that somehow it had a deep or underlying nature that could be uncovered
through philosophical theorizing. Instead, according to many deflation-
ists, the (non-paradoxical) instances of the disquotational schema (“p” is
true if and only p) or the equivalence schema (it is true that p if and only
if p) exhaust what there is to say about truth.2
The pluralist reaction to the traditional debate is to reject monism and
endorse substantivism. Truth pluralists, encouraged by the seminal work
of Crispin Wright and Michael Lynch, appeal to more than one property
in their account of truth. Propositions from different domains of dis-
course are true in different ways. The truth of propositions concerning
the empirical world (e.g., 〈There are mountains〉) might be accounted
for in terms of correspondence, while the truth of legal propositions (e.g.,
〈Speeding is illegal〉) might be accounted for in terms of coherence with
the body of law.3 This amounts to a rejection of monism. By contrast,
truth pluralists have traditionally endorsed substantivism. They have
appealed to properties or relations that are substantive in nature (where
this means, at least, that they directly explain certain facts entirely in
virtue of characteristics pertaining to their natures).4
The history of logic, like the history of truth, displays little consensus.
Advocates of classical logic, intuitionistic logic, and relevant logic, for
instance, have argued back and forth about the merits and demerits of their
preferred systems. Again, as in the case of truth, this seems to suggest a shared
underlying assumption of monism: there is a uniquely correct logic, and
advocates of different systems are disagreeing about which one it is. The plu-
ralist reaction—notably advocated by Jc Beall and Greg Restall (2006)—is
to reject monism and maintain that there are several equally correct logics.
Speaking more generally, pluralist views are becoming increasingly
prominent in different areas of philosophy. Pluralism about truth has been
extensively developed, defended, and critically discussed. The same goes
  Introduction  5

for pluralism about logic.5 Pluralism has also made inroads into ontology
where the idea that there are several ways of being has been defended, sup-
ported, and articulated in various ways. The work of Kris McDaniel is a
particularly rich source.6 In epistemology, a variety of pluralist theses can
likewise be found in the literature. The idea that there are several epistemi-
cally good-making features of belief can be found in different guises, as
pluralism about epistemic justification, warrant, desiderata, and value.
Prominent epistemologists such as Alvin Goldman, Tyler Burge, William
Alston, and Crispin Wright all endorse one of these forms of pluralism.7
These pluralist trends are philosophically significant. They go against a
one-size-fits-all conception of their relevant areas and invite a reconsid-
eration of the nature and character of some of the most fundamental
notions in core areas of philosophy—including truth, validity, being, and
justification. This volume takes as its focus two of kinds of pluralism:
pluralism about truth and pluralism about logic. It brings together 18
original, state-of-the-art essays. The essays are divided into three parts.
Part I is dedicated to truth pluralism, Part II to logical pluralism, and Part
III to the question as to what connections might exist between these two
kinds of pluralism.

2 Truth Pluralism (Part I)

In this section, we will briefly introduce a range of ideas and issues that
have served to shape and define the debate concerning truth pluralism.
We will then introduce the contributions to Part I of the volume.

Background

Truth pluralists are engaged in critical debates on two fronts—one exter-

nal and the other internal. On the external front, we find pluralists debat-
ing monists as to which of these views of truth is superior. The argument
most commonly deployed by pluralists is the scope problem. Pluralists argue
that monist theories do not have a scope that is sufficiently wide to plau-
sibly accommodate all truth-apt discourse. Perhaps the c­orrespondence
6  N. J. L. L. Pedersen et al.

theory can be plausibly applied to empirical discourse, accounting for the

truth of propositions such as 〈Mt. Everest is extended in space〉. However,
it cannot plausibly cover the truth of legal propositions such as 〈Breaking
and entering is illegal〉. Now, maybe coherence with the body of law can
plausibly be applied to legal discourse. However, coherence does not seem
easily extendable to the empirical domain. Pluralists take this point to
generalize and conclude that monism is unsatisfactory. Instead, they let
several theories of truth work in tandem, restricting their range of applica-
bility to certain domains.
In connection with the internal debate, we see advocates of so-called
strong pluralism and moderate pluralism pitched against one another. They
agree that truth pluralism is the right view, but disagree over the details.
According to strong pluralists, there is no single truth property that
applies to all true propositions. Rather, there is a range of properties that
reduce or constitute truth for different propositions belonging to differ-
ent domains. Thus, the truth of 〈There are mountains〉 may reduce to
this proposition’s corresponding to reality while the truth of 〈Speeding is
illegal〉 may reduce to this proposition’s cohering with the body of law.
Crucially, there is no single property that reduces or constitutes the truth
of every true proposition. Moderate pluralists, on the other hand, endorse
a single, generic truth property. This property is possessed by every true
proposition, so that for the moderate pluralist, truth itself is one. However,
moderate pluralists also think that instances of generic truth are grounded
by instances of different truth-relevant properties. In this sense, for the
moderate pluralist, truth is also many. Thus, according to moderate plu-
ralism, truth is both one and many.8
Despite their different views on how to best articulate truth pluralism,
strong and moderate pluralists share significant commitments. One such
commitment is the commitment to domains. Domains are a crucial com-
ponent of the theoretical framework of pluralism, as reflected by the fact
that the core pluralist thesis is that the nature of truth varies across
domains.
Domains also feature prominently in some of the main challenges
faced by truth pluralists. Problems concerning mixed discourse are cases in
point. Mixed discourse is discourse that cuts across domains. Such
­discourse occurs at three different levels: the levels of atomics, com-
pounds, and inferences. Consider the propositions that are expressed in:
  Introduction  7

(mix-atom) π is beautiful.

(mix-comp) Mt. Everest is extended in space and Bob’s drunk driving is

illegal.

(mix-inf ) If Mt. Everest is extended in space, then Bob’s drunk driv-

ing is illegal.
Mr. Everest is extended in space.
Bob’s drunk driving is illegal.

〈π is beautiful〉 is a mixed atomic proposition. It features a mathemati-

cal concept (π) and an aesthetic concept (beauty).9 However, in light of
this, should 〈π is beautiful〉 be classified as belonging to the mathemati-
cal domain, the aesthetic domain, both of these domains, or perhaps
some other domain? This question by no means seems to be a straight-
forward one to answer. However, there seems to be considerable pressure
on the pluralist to provide an answer. After all, for atomic propositions
such as 〈π is beautiful〉, the domain membership of the proposition is
meant to determine the property that is relevant to its truth. Hence,
absent a principled story about the domain membership of mixed atom-
ics, there would be a whole cluster of propositions whose truth would
remain unaccounted for. This is the problem of mixed atomics.
〈Mt. Everest is extended in space and Bob’s drunk driving is illegal〉 is
a mixed conjunction. Its first conjunct belongs to the empirical domain,
and its second conjunct to the legal domain. The conjunction is true, as
both of its conjuncts are. However, it is not clear what story the pluralist
is going to tell about this. We can suppose that correspondence to reality
and coherence with the body of law are, respectively, the truth-relevant
properties for the two conjuncts. However, neither correspondence nor
coherence seems like a plausible candidate when we try to account for the
truth of the conjunction itself. Now, if the truth-relevant property of
neither the first nor the second conjunct is the right property, the con-
junction must have some third property. However, what property would
that be? The problem of mixed compounds challenges pluralists to tell a
story about the truth of mixed compounds.
8  N. J. L. L. Pedersen et al.

The inference from 〈If Mt. Everest is extended in space, then Bob’s
drunk driving is illegal〉 and 〈Mr. Everest is extended in space〉 to 〈Bob’s
drunk driving is illegal〉 is a mixed inference. It is also a valid inference—
that is, necessarily, if the premises are true, then so is the conclusion. In
order to account for the validity of the inference, it would seem that there
must be some truth-relevant property that the premises and conclusion
all share which ensures that truth is preserved from premises to conclu-
sion. However, the pluralist seems to be unable to point to a property
that satisfies this constraint. For, as before, we can suppose that corre-
spondence to reality is the truth-relevant property for 〈Mr. Everest is
extended in space〉 and coherence with the body of law for 〈Bob’s drunk
driving is illegal〉. This means that one of the premises and the conclu-
sion have different truth-relevant properties. The problem of mixed infer-
ences challenges the pluralist to tell a story about the validity of mixed
inferences.10
Another fundamental problem confronting pluralists is what is some-
times called the “double-counting objection.” In essence, the objection is
that pluralists count two differences where only one is needed. They
endorse significant metaphysical differences regarding the nature of vari-
ous subject matters and, in addition, they endorse differences in the
nature of truth. However, in order to accommodate wide-ranging truth-­
aptitude, differences need only be countenanced at one level—at the level
of the things themselves (numbers, trees, moral properties, laws, etc.) or
at the level of the content associated with different domains (expressivist
content vs. representational content). Drawing distinctions at the level of
truth, the objection goes, is superfluous.11

The Contributions

Dorit Bar-On and Keith Simmons’ contribution “Truth: One or

Many?” runs a version of the double-counting objection. Prominent
pluralists such as Wright and Lynch claim that one motivation for
adopting truth pluralism is that it puts one in a position to make
sense of disputes between realists and anti-realists. Adopting the the-
sis that the nature of truth varies across domains, it is possible for the
  Introduction  9

pluralist to account for the “differential appeal of realist and anti-

realist intuitions” about them.12 Bar-On and Simmons counter by
arguing that truth pluralism offers no distinctive explanatory power
vis-à-vis the realism/anti-realism debate. Rather, all that is needed is a
plurality of kinds of worldly conditions that track metaphysical differ-
ences. Bar-On and Simmons’ version of the double-counting objec-
tion targets not only truth pluralists but also certain kinds of truth
monists—namely, those who think that a distinction between differ-
ent kinds of content or meaning offers explanatory power vis-à-vis the
realism/anti-realism debate. Bar-On and Simmons spell out in con-
siderable detail how their proposal differs from those of truth monists
who seek to accommodate realism/anti-realism disputes by appealing
to semantic differences.
Michael P. Lynch’s contribution “Truth Pluralism, Quasi-Realism and
the Problem of Double-Counting” offers a pluralist response to the dou-
ble-counting objection—in particular, as it might be pressed by quasi-
realists such as Simon Blackburn and global expressivists such as Huw
Price. Lynch argues that semantic diversity and cognitive unity are theses
that quasi-realists, global expressivists, and truth pluralists all seek to
accommodate and explain:

(SD) There are real differences in kind between the contents of our
beliefs and indicative statements.

(CU) All beliefs and indicative statements are subject to a single

type of cognitive normative assessment of correctness.

Blackburn proposes to accommodate semantic diversity by appealing to

two sorts of propositions or two sorts of truth-aptitude. Price proposes to
accommodate semantic diversity by appealing to two kinds of representa-
tion: i-representation and e-representation. A proposition i-represents in
virtue of its inferential or functional role, while e-representation is cashed
out in terms of co-variance with the environment. Lynch argues that, in
effect, both Blackburn’s proposal and Price’s proposal result in a form of
truth pluralism. Hence, when it comes to double-counting, truth plural-
ists turn out to be no worse off than quasi-realists or global expressivists.
10  N. J. L. L. Pedersen et al.

Douglas Edwards’ contribution “The Metaphysics of Domains” pro-

vides a systematic account of domains and thus addresses a major lacuna
in the theoretical framework of truth pluralism. Edwards distinguishes
between a semantic and a metaphysical aspect of domains. He accounts
for these via a discussion of, respectively, singular terms and predicates
and their metaphysical counterparts, objects and properties. Edwards
argues that his proposed notion of domain is not a commitment of
pluralists only—it is implicit in a number of philosophical views.
Edwards demonstrates the significance of his account of domains by
arguing that it delivers a solution to two major challenges to truth plu-
ralism: the problem of mixed atomics and the problem of mixed
compounds.
Seahwa Kim and Nikolaj Jang Lee Linding Pedersen’s contribution
“Strong Truth Pluralism” provides a pluralist solution to the problem of
mixed compounds. Kim and Pedersen offer their solution against the
background of a certain form of strong pluralism. They thus deny that
there is any generic truth property that applies across all domains.
Instead they think that an atomic proposition’s being true reduces to its
corresponding to reality, cohering, or having some other “base-level
truth property.” The truth of a compound reduces to its having a com-
pound-specific truth-reducing property. For example, the truth of the
mixed conjunction 〈Mt. Everest is extended in space and Bob’s drunk
driving is illegal〉 reduces to its being a conjunction with conjuncts that
have their respective truth-reducing properties. Note that in this regard
mixed conjunctions are no different from pure conjunctions. Hence,
Kim and Pedersen’s response to the problem of mixed compounds is
that there is nothing special or problematic about them. They are true
in the same way that their pure counterparts are.
The contributions by Nathan Kellen, Filippo Ferrari, and Jeremy
Wyatt explore different ways to reconfigure or add a new dimension to
the debate concerning truth pluralism.
Kellen’s contribution “Methodological Pluralism About Truth” introduces
a meta-­perspective on the truth pluralism debate. According to Kellen,
Wright takes anti-realism to be methodologically fundamental. He does so
in the sense that anti-realist truth is taken to be the default for all domains.
  Introduction  11

This is not to say that Wright is opposed to giving truth a “non-default”

treatment within some domains. However, in order for truth to receive
this kind of treatment, there must be reasons why, within that particular
domain, the default should be abandoned. Kellen likewise attributes a
thesis of methodological fundamentality to Edwards although, in con-
trast to Wright, the default is realist truth. Kellen proposes methodological
pluralism as an alternative to anti-realist and realist default forms of plu-
ralism. According to this methodological doctrine, the pluralist should
have no default for any domain but should remain neutral until reasons
have been given one way or the other.
Filippo Ferrari’s contribution “Normative Alethic Pluralism” articu-
lates a novel view concerning the normativity of truth—what he calls
“normative alethic pluralism.” He articulates this view against the back-
ground of a rejection of normative alethic monism, the view that truth’s
normative profile is uniform across all domains, and can be captured by
a single principle that connects truth and judgment. Ferrari targets nor-
mative alethic monism by employing a normative analogue of the scope
problem. By appealing to disagreements pertaining to different domains,
Ferrari argues that the normative profile of truth varies across domains. If
people disagree over whether, for example, oysters are tasty, there is no
strong sense of fault in play. On the other hand, if two parties disagree as
to whether abortion is a morally acceptable practice, there is a strong
sense of fault in play. This is reflected by each party’s tendency toward
condemnation of the other party. This normative variability cannot satis-
factorily be accommodated within the framework of normative alethic
monism. Hence, according to Ferrari, there is reason to adopt normative
alethic pluralism. There are several ways for truth to normatively regulate
judgment. Having motivated and articulated normative alethic plural-
ism, Ferrari discusses the issue of whether it might bear significant con-
nections to pluralism about truth. He concludes that the two kinds of
pluralism are compatible and may nicely complement one another. Yet,
one does not imply the other.
Jeremy Wyatt’s contribution “Truth in English and Elsewhere: An
Empirically-Informed Functionalism” presents a refined framework that
should help to shape future work on both pluralism and functionalism
12  N. J. L. L. Pedersen et al.

about truth. Wyatt argues that a proper defense of alethic functional-

ism—a view that was pioneered by Lynch—must be informed by empiri-
cal data. The alethic functionalist puts forward an account of the folk
theory of truth, which is meant to consist of the propositions about truth
that those who possess the folk concept of truth are ipso facto disposed to
believe upon reflection. The functionalist’s view on the folk theory of
truth is thus empirical in nature and should be evaluated using empirical
data. Wyatt discusses two kinds of existing data: data pertaining to alethic
vocabulary in English and preliminary data pertaining to the Ghanaian
language Akan. The English-related data suggest variation in the use of
alethic vocabulary among male and female English speakers. The prelimi-
nary data concerning Akan suggest that there are significant differences in
the alethic vocabulary that is used, respectively, by native Akan and native
English speakers. Wyatt argues that these lines of data lend support to
two kinds of pluralism regarding ordinary thought about truth—what he
calls intralinguistic and interlinguistic conceptual pluralism. In addition to
motivating these two sorts of pluralism, Wyatt shows how the functional-
ist, by adopting a more nuanced version of Lynch’s framework, can nicely
accommodate these pluralistic hypotheses.

3 Logical Pluralism (Part II)

Over the past decade, there has been a surge of interest in logical plural-
ism, one major factor being the publication of JC Beall and Greg Restall’s
Logical Pluralism.13 In this section, we will briefly introduce Beall and
Restall’s logical pluralism and the contributions to Part II of the volume.
In one way or another, most of these contributions engage with promi-
nent themes from Beall and Restall’s work.

Background

According to Beall and Restall, logic is plural in the sense that there are
several equally legitimate instances of what they call Generalized Tarski’s
Thesis (GTT):
  Introduction  13

(GTT) An argument is validx if and only if in every casex in which

the premises are true, so is the conclusion.

Beall and Restall argue that there are at least three equally legitimate ways
to construe casex in GTT: cases as (consistent and complete) possible
worlds, cases as (possibly incomplete) constructions, and cases as (possibly
inconsistent) situations. These three notions of case deliver different log-
ics—respectively classical logic, intuitionistic logic, and relevant logic.
To shed further light on the nature of Beall and Restall’s logical plural-
ism, let us highlight a number of key features of their view: legitimacy,
logical functionalism, logical generalism, logical relativism, meaning con-
stancy, and structural rules and properties.

Legitimacy  The standard of legitimacy for cases is given by three features

that Beall and Restall call “necessity”, “formality”, and “normativity.”
Roughly stated, necessity is the idea that valid arguments must be neces-
sarily truth-preserving; formality is the idea that validity is neutral with
respect to content; and normativity is the idea that invalid arguments
must involve a kind of mistake or fault.

Logical Functionalism  The network approach to conceptual analysis can

be regarded as a form of conceptual functionalism. A target concept C is
characterized by a set of principles that connect C to other concepts. In
this way, C is characterized through its role or function within a larger
conceptual network. Beall and Restall’s view can be regarded as an
instance of the network approach. Generalized Tarski’s Thesis and the
three constraints of necessity, formality, and normativity characterize the
concept of validity via its connection to other concepts such as case,
truth, necessity, formality, and normativity. In this way, validity
is characterized through its function or role within a larger conceptual
network, and for this reason Beall and Restall’s logical pluralism involves
a form of functionalism.

Logical Generalism To borrow a phrase from Hartry Field, Beall and

Restall’s logical pluralism is a pluralism about all-purpose logics.14 Their
view is not that classical logic, intuitionistic logic, and relevant logic are
14  N. J. L. L. Pedersen et al.

legitimate only when restricted to certain domains or when used for certain
purposes. Rather, their view is that classical logic, intuitionistic logic, and
relevant logic are equally legitimate across the board. This idea can be
regarded as a form of logical generalism. The legitimacy of the logics admit-
ted by (GTT) and the three constraints is meant to be completely general.

Logical Relativism  Beall and Restall’s logical pluralism involves a form of

logical relativism: statements concerning the validity of arguments only
have a truth-value relative to a particular system.15 Thus, for example, as
far as logic is concerned, there is no absolute fact of the matter as to
whether double negation elimination is valid. Instead there are logic-­
relative facts: in classical logic, double negation elimination is valid while
in intuitionistic logic, it is not.16

Meaning Constancy  Beall and Restall are pluralists about validity and
logical consequence. However, they maintain that the meaning of the
logical connectives is constant across the various logics that qualify as
legitimate. This view contrasts with a view often attributed to Carnap—
namely, that different logics have different connectives.17 According to
the latter view, the meaning of “and”, “not”, “or”, etc. changes from one
logic to another. By contrast, on Beall and Restall’s view, logical expres-
sions share the same—but incomplete—meaning across logics. However,
clauses that govern the connectives in different logics capture different
aspects of that shared meaning.

Structural Rules and Properties  It is common to distinguish between the

operational rules and the structural rules of a system. Operational rules
and properties concern specific logical operations (e.g., negation).
Structural rules and properties of a logic capture general features that
hold purely in virtue of premises and conclusions being structures of
unstructured objects that can be manipulated in certain ways. The fol-
lowing list specifies five well-known structural rules:

(Reflexivity) ϕ ⊨ ϕ

(Monotonicity) If Γ ⊨ ϕ, then Γ, Δ ⊨ ϕ

  Introduction  15

(Transitivity) If Γ ⊨ ϕ and Δ, ϕ ⊨ ψ, then Δ, Γ ⊨ ψ

(Contraction) If Γ, ϕ, ϕ ⊨ ψ, then Γ, ϕ ⊨ ψ

(Commutativity) If Γ, ϕ, ψ, Δ ⊨ χ, then Γ, ψ, ϕ, Δ ⊨ χ

Reflexivity says that anything is a logical consequence of itself.

Monotonicity says that, if ϕ is a logical consequence of Γ, adding more
premises Δ does not change anything (i.e., ϕ is also logical of a conse-
quence of Γ, Δ). Transitivity says that, if ϕ is a logical consequence of Γ
and ψ is a logical consequence of Δ, ϕ, then ψ is a logical consequence of
just Δ, Γ. Contraction says that multiple occurrences of the same premise
can be cut to a single occurrence without impacting consequence.
Commutativity says that the order of premises does not matter: it can be
switched without impacting consequence. Any system that fails to accom-
modate any of the five structural rules listed above is a substructural logic.18

The Contributions

Neil Tennant’s contribution “Core Logic: A Conspectus” presents an

“absolutist pluralist” view on logic. It is absolutist in the sense that there is
a core to logic or deductive reasoning—core logic in Tennant’s terminology.
However, Tennant’s view is pluralist in that there are several legitimate
extensions of the core. Tennant is particularly interested in providing an
account of logic for mathematics. He wants to accommodate both con-
structive and non-constructive (or classical) mathematics, but argues that
all proofs should be “relevantized.” For this reason, core logic is relevant.
Thus, Tennant’s view is revisionist, as he thinks that the logics of construc-
tive and classical mathematics should be revised along relevantist lines.
The logic suitable for c­ onstructive mathematics is relevantized intuitionis-
tic logic (the core logic C) while the logic suitable for non-constructive (or
classical) mathematics is relevantized classical logic (the core logic C+).
Teresa Kouri Kissel’s contribution “Connective Meanings in Beall and
Restall’s Logical Pluralism” contests Beall and Restall’s meaning con-
stancy thesis, that is, their claim that logical expressions have the same
16  N. J. L. L. Pedersen et al.

meaning across logics. She argues that this cannot be the case for intu-
itionistic negation and relevant negation. Thus, contrary to their own
claims, Beall and Restall’s logical pluralism ends up having a Carnapian
flavor.
Elia Zardini’s contribution “Generalised Tarski’s Thesis Hits
Substructure” offers an extended argument to the effect that Beall and
Restall’s logical pluralism is overly restrictive. He shows that (GTT)
implies that logical consequence has the structural features mentioned
above, that is, reflexivity, monotonicity, transitivity, contraction, and
commutativity. For instance, in every casex in which ϕ is true, ϕ is true—
thus (GTT) implies reflexivity. By the lights of Beall-Restall logical plu-
ralism, then, any system that fails to satisfy reflexivity cannot qualify as
logic properly so-­called. Similarly, for any system that fails to satisfy
monotonicity, transitivity, contraction, or commutativity. In general,
Beall-Restall logical pluralism disqualifies any substructural logic from
qualifying as logic proper. Zardini argues that there are philosophical rea-
sons to doubt each of reflexivity, monotonicity, transitivity, contraction,
and commutativity. For instance, one might wish to abandon transitivity
in order to give an account of vagueness, and one might wish to abandon
contraction in order to address the semantic paradoxes. In light of these
considerations, Zardini deems Beall-Restall pluralism unacceptably
restrictive.
Gillman Payette and Nicole Wyatt’s contribution “Logical
Particularism” introduces and spells out a particularist view on logic.
According to logical particularism, there are no completely general
principles concerning validity. Rather, validity is a property of particu-
lar arguments or inferences. Since Payette and Wyatt think that differ-
ent, specific arguments call for different treatments vis-à-­vis validity,
their logical particularism goes hand in hand with a ­particularist ver-
sion of logical pluralism. This particularist pluralism is at odds with the
kind of logical pluralism endorsed by Beall and Restall—which, as seen
above, involves a commitment to logical generalism. Logics on the
Beall-Restall view are all-purpose logics, which means that their rules
are completely general principles concerning validity. Payette and
Wyatt’s particularist pluralism is also at odds with domain-based forms
  Introduction  17

of logical pluralism. Unlike logical generalists, domain-based logical

pluralists do not think that there are completely general logical prin-
ciples. However, they do think that there are somewhat general prin-
ciples, as the rules of a domain-specific logic hold for all arguments or
inferences within the specific domain to which the logic applies. This
commitment, although weaker than generalism, is likewise at odds
with logical particularism.
Aaron Cotnoir’s contribution “Logical Nihilism” makes a case for a
species of logical nihilism. According to this view, there is no logical
consequence relation that correctly represents natural language infer-
ence; formal logics are inadequate to capture informal inference.
Cotnoir gives two clusters of arguments that lend support to logical
nihilism. The first cluster consists of arguments from diversity, the sec-
ond of arguments from expressive limitations. Arguments from diver-
sity contain two steps. The first step is an argument to the effect that no
single logic can provide an adequate account of natural language infer-
ence. The second step is an argument to the effect that at most one logic
can provide an adequate account of natural language inference.
However, nothing satisfies both of these requirements—so, no formal
logic can provide an adequate account of natural language inference.
Arguments from expressive limitations also consist of two steps. The
first is an observation to the effect that natural language contains infer-
ences involving a certain phenomenon. The second step is an argument
to the effect that no formal logic has the expressive resources to capture
inferences of that kind. Hence, due to the expressive limitations of for-
mal logics, no formal logic can provide an adequate account of natural
language inference.
Gillian Russell’s contribution “Varieties of Logical Consequence by
Their Resistance to Logical Nihilism” also speaks to the theme of logi-
cal nihilism, although a different variety than the one d ­ iscussed by
Cotnoir. Logical nihilism, as Russell approaches the view, has it that
there are no valid arguments. This view has emerged as a discussion
point in the logical pluralism debate. A criticism of Beall and Restall
is that validity should be conceived as truth-preservation across all
cases, in contrast to Beall and Restall’s strategy of pairing each type of
18  N. J. L. L. Pedersen et al.

case with a corresponding, case-specific type of validity. If validity is

thus conceived, logical nihilism (or “minimalism”) threatens—maybe
no (or only very few) arguments are truth-preserving across all cases.
Russell investigates what resources different accounts of logical conse-
quence offer when it comes to resisting the threat of nihilism. She con-
siders Etchemendy’s interpretational and representational accounts,
Quine’s substitutional account, and Williamson’s universalist account.
Williamson’s account is found to be the one that offers the strongest
path of resistance to the threat of logical nihilism. However, Russell sug-
gests that the universalist path of resistance may come at a high cost. It
may only work because the universalist account operates at a level that
does not fully engage with the problematic phenomena that fuel the
move toward nihilism (such as empty names, vagueness and incomplete
predicates, and self-reference and overdetermination).

4 Connections (Part III)

Parts I and II of the volume respectively concern truth pluralism and logi-
cal pluralism, considered and discussed (mostly) in isolation from one
another. The contributions in Part III explore potential connections
between these two kinds of pluralism.

Background

The most widely explored form of truth pluralism is domain-based. The

core idea, as we have seen, is that the nature of truth varies across domains.
Several authors have connected domain-based truth pluralism and logic,
arguing that pluralism in the case of truth supports pluralism about logic.
The target kind of logical pluralism inherits a crucial feature from its
alethic counterpart: it is domain-based. Different domains have different
logics.
The kind of argument that truth pluralists have given to support
domain-based logical pluralism can be presented as follows19:
  Introduction  19

(1) If truth is epistemically constrained in one domain and epistemically

unconstrained in another domain, then different logics govern these
domains.
(2) Truth is epistemically constrained in one domain and epistemically
unconstrained in another domain.
(3) So, there are domains that are governed by different logics.

(2) is accepted by most (domain-based) truth pluralists. Many of them take

the realism/anti-realism debate as background for their truth pluralism.
They want to accommodate the appeal of realism and anti-realism with
respect to different domains. It is an integral part of the realism/anti-realism
debate that anti-realist truth is epistemically constrained while realist truth
is epistemically unconstrained. It is with this in mind that many domain-
based truth pluralists go in for (2). The idea behind (1) is that the logic of
epistemically constrained truth is intuitionistic while the logic of epistemi-
cally unconstrained truth is classical. Both (1) and (2) can be regarded as
reflections of Dummett’s influence on the realism/anti-realism debate, as it
figures in the theoretical foundations of the pluralist program.20
Domain-based logical pluralism raises some tough questions. The view
pairs individual domains with logics. However, what is to be said about
the logic of mixed inferences (sec. 2.1)? What logic governs inferences
that cut across domains with different logics? Lynch has proposed the
following principle of modesty:

(mod) The logic of a mixed compound or inference that involves

propositions from domains with distinct logics L1, …, Ln is
the intersection of L1, …, Ln.

The logic of a given mixed compound or inference is thus minimal—it is

the core shared by all the logics of the domains involved in the com-
pound or inference. Lynch himself officially endorses two logics within
his domain-based pluralist framework, viz. intuitionistic and classical