The Realism-Antirealism Debate in the Age of Alternative Logics. Vol 23 LOGIC, EPISTEMOLOGY, AND THE UNITY OF SCIENCE

Les comparto la aparición del Vol.  23 de LOGIC, EPISTEMOLOGY, AND THE UNITY OF SCIENCE
El tema: The Realism-Antirealism
Debate in the Age
of Alternative Logics

Editores: Shahid Rahman · Giuseppe Primiero ·
Mathieu Marion


Contents
1 OnWhen a Disjunction Is Informative . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Patrick Allo

2 My Own Truth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Alexandre Billon

3 Which Logic for the Radical Anti-realist? . . . . . . . . . . . . . . . . . . . . . . . 47
Denis Bonnay and Mikaël Cozic

4 Moore’s Paradox as an Argument Against Anti-realism . . . . . . . . . . . 69
Jon Cogburn

5 The Neutrality of Truth in the Debate Realism vs. Anti-realism . . . . 85
María J. Frápolli

6 Modalities Without Worlds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Reinhard Kahle

7 Antirealism, Meaning and Truth-Conditional Semantics . . . . . . . . . . 119
Neil Kennedy

8 Game Semantics and the Manifestation Thesis . . . . . . . . . . . . . . . . . . . 141
Mathieu Marion

9 Conservativeness and Eliminability for Anti-Realistic Definitions . . . 169
Francesca Poggiolesi

10 Realism, Antirealism, and Paraconsistency . . . . . . . . . . . . . . . . . . . . . . 181
Graham Priest

11 Type-Theoretical Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Giuseppe Primiero

12 Negation in the Logic of First Degree Entailment and Tonk . . . . . . . . 213
Shahid Rahman

13 Necessary Truth and Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Stephen Read

14 Anti-realist Classical Logic and Realist Mathematics . . . . . . . . . . . . . 269
Greg Restall

15 A Tale of Two Anti-realisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Sanford Shieh

16 A Double Diamond of Judgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
Göran Sundholm

17 Stable Philosophical Systems and Radical Anti-realism . . . . . . . . . . . 313
Joseph Vidal-Rosset

18 Two Diamonds Are More Than One . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Elia Zardini

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343


Preface
In the preface to the first volume of LEUS, the editors of the series pointed out,
within the context of the failure of the positivist project of the unity of science, the
difference between science as a body of knowledge and science as process by which
knowledge is achieved. In fact, the editors suggested that a ban on the logical analysis
of science as a dynamic process, which in traditional philosophy was overtaken
by ‘gnoseology’, produced a gap between sciences and logic (including philosophy
of science). In gnoseology the main notion was the one of judgement rather than
that of proposition. Judgement delivered the epistemic aspect of logic, namely the
relation between an (epistemic) agent and a proposition. This represented the basis
of the Kantian approach to logic, which seemed to be in conflict with the post-
Fregean approach where only relations between propositions are at stake and where
the epistemic aspect is seen as outside logic.
As it happens quite often in philosophy, the echoes of the old traditions come
back and point to the mistakes of the younger iconoclast movements. This is indeed
the case in the relation between logic and knowledge where the inclusion or exclusion
of the epistemic moment as linked with the concept of proposition provoked a
heated debate since the 1960s. The epistemic approaches, which started to call themselves,
following Michael Dummett, ‘antirealism’, found their formal argument in
the mathematics of Brouwer and intuitionistic logic, while the others persisted with
the formal background of the Frege-Tarski tradition, where Cantorian set theory
is linked via model theory to classical logic. This picture is, however, incomplete.
Already in the 1960s Jaakko Hintikka tried to join both traditions by means of what
is now known as ‘explicit epistemic logic’, where the epistemic content is introduced
into the object language as an operator which yield propositions from propositions
rather than as metalogical constraint on the notion of inference. The debate
had thus three players: classical logicians, intuitionistic logicians (implicit epistemic
logic) and epistemic logicians (explicit epistemic logic), though the mainstream
continued to think that the discussion reduces to the discussion between classical
and intuitionistic logic.
The editors of the present volume think that in these days and age of Alternative
Logics, where manifold developments in logic happen in a breathtaking pace,
this debate should be revisited. In fact, collaborators to this volume took happily
this challenge and responded with new perspectives on the debate from both
the explicit and the implicit point of view, challenging it from the newly arisen
perspectives in logic. This volume aims therefore at presenting standard issues of
the realism-antirealism debate in a new light, shed from the point of view of different
philosophical perspectives. It is therefore appropriate that we open with Patrick
Allo’s contribution, which analyses the meaning of ambiguous connectives (and
in particular of disjunction) from a logical pluralistic viewpoint, in which content
is explained in terms of informativeness. Logical pluralism can be understood as
the larger conceptual umbrella under which one finds today many different understandings
of the realism-antirealism debate. This certainly still grows on Dummett’s
arguments against truth-conditional semantics, which Neil Kennedy reconstructs
and critically analyses; in general, it refers to well known forms of semantic antirealism,
which Sanford Shieh characterizes by means of the distinction between
epistemically-based and conceptually based ones, and it still triggers today huge
debates such as the one on Moorean validities, that Jon Cogburn reconstructs in view
of the different old and new interpretations. But antirealism today profits of the influences
of many different backgrounds: this is the case for example of Martin-Löf’s
type theory, which is conceptually and historically located within the larger frame of
theories of truth and judgement in Göran Sundholm’s contribution, and which meets
for the first time belief revision dynamics in Giuseppe Primiero’s paper. Departure
from classical principles of reasoning is therefore possible in different forms, and
whereas Denis Bonnay and Mikaël Cozic place the justification of radical forms
of anti-realism in the context of the (to them still unjustified) shift to linear logic,
Joseph Vidal-Rosset suggests a larger philosophical frame for the understanding of
radical antirealism. Many are therefore the new branches of logic that are called
upon in this volume to face non-classical issues raising from an antirealistic perspective:
this is the case of modal logic in the interpretations by Reinhard Kahle
and Elia Zardini; the anti-realistic inspired defence of realist mathematics by Greg
Restall, where (implicit) antirealism is understood as a means to defend logical
pluralism: the extension to Paraconsistency, via a defence of a suitable negation
connective in the Kripke-Hintikka reconstruction of intuitionistic logic, suggested
by Graham Priest, which virtually dialogues with the dialogical interpretation of the
same connective given by Shahid Rahman. The relation of antirealism to dialogical
logic and game semantics appears also inMathieu Marion’s contribution, where it is
considered how to make Dummett’s Manifestation Argument work within this new
programme, and it is argued that a derived Thesis fits (with appropriate reformulations)
within game semantics. Stephen Read, takes the proof theoretical approach
to logic of the antirealists to challenge the epistemic constraints of the intuitionists
and Francesca Poggiolesi analyses properties of anti-realistic definitions starting
from the classical requirements imposed by Lesniewski. Truth is of course always
an open field for new interpretations: Alexandre Billon considers the notion of
assessment-sensitive truth to provide solutions to semantic paradoxes and Maria
Frapolli presents a prosentential account of truth showing that our comprehension
of truth and the use we make of truth expressions are strictly independent of our
views about the relation between mind and world
Some years have passed from the initial proposal to collect a number of contributions
from scholars that are reconsidering the realism-antirealism debate from new
philosophical, logical and metaphysical perspectives. This has led to different lineups
of both authors and editors.What we hope to have achieved through this process
is to have selected significant contributions on the different aspects of research on
anti-realism done today at academic level, a representative body of work that can be
of reference and inspiration for further advancements in this field.
Montreal, Canada Mathieu Marion
Ghent, Belgium Giuseppe Primiero
Lille, France Shahid Rahman
December 2010