The Routledge Handbook of Modality

Otávio Bueno, Scott A. Shalkowski, Otávio Bueno, Scott A. Shalkowski

• Publisher: Routledge
• Year: 2020
• eBook ISBN: 9781317585275
• Topic: Philosophy
• Subtopic: Logic in Philosophy

Modality - the question of what is possible and what is necessary - is a fundamental area of philosophy and philosophical research. The Routledge Handbook of Modality is an outstanding reference source to the key topics, problems and debates in this exciting subject and is the first collection of its kind. Comprising thirty-five chapters by a team of international contributors the Handbook is divided into seven clear parts:

• worlds and modality
• essentialism, ontological dependence, and modality
• modal anti-realism
• epistemology of modality
• modality in science
• modality in logic and mathematics
• modality in the history of philosophy.

Within these sections the central issues, debates and problems are examined, including possible worlds, essentialism, counterfactuals, ontological dependence, modal fictionalism, deflationism, the integration challenge, conceivability, a priori knowledge, laws of nature, natural kinds, and logical necessity.

The Routledge Handbook of Modality is essential reading for students and researchers in epistemology, metaphysics and philosophy of language. It will also be very useful for those in related fields in philosophy such as philosophy of mathematics, logic and philosophy of science.

PART 1

Worlds and modality

Chapter 1

POSSIBLE WORLDS

Michael De

1.1Introduction

Modality concerns what might or must be the case. We use modal expressions such as ‘might’, ‘must’, and cognates in a variety of ways, however. One can truthfully say, for example, that the neither yet proved nor disproved Goldbach’s conjecture (that every natural number greater than two is the sum of two primes) might be true, even if the conjecture is false and hence, in a metaphysical sense, necessarily so. What one means here is that the conjecture is compatible with our evidence, since we have neither proven nor disproven it.

Modal expressions are typically intensional (with an ‘s’). An expression α is intensional just in case the substitution of extensionally equivalent expressions under the scope of α need not preserve truth. For instance, even though ‘8’ and ‘the number of planets’ have the same extension, ‘Necessarily, 8 is greater than 1’ and ‘Necessarily, the number of planets is greater than 1’ do not share their extension (i.e. truth-value). However, while many modal notions are intensional, not all are. Consider e.g. the de re modal relation expressed by ‘it is necessary of x that it be such that A’, where A is to be replaced by a declarative statement. Thus, even though the expressions ‘modal’ and ‘intensional’ are sometimes used interchangeably, modality and intensionality are not equivalent.

How best are we to analyze modality and intensionality? The most popular strategy since the mid-twentieth century is to employ possible worlds. Reference to possible worlds dates back at least to Leibniz (see Mates, 1968), but they do not assume their familiar role until the 1940s when Rudolf Carnap (Carnap, 1946) gave an analysis of modal operators resembling a modern treatment in terms of quantification over what we would now call possible worlds. Such an analysis, often called possible worlds semantics, was later generalized throughout the 1940s and 1950s independently by a number of logicians, including Saul Kripke and Jaakko Hintikka, and is now the standard treatment for a wide variety of intensional notions including modality. An impressive number of intensional notions have been given possible worlds analyses, only some of which include: conditionality, causation, knowledge, de se belief, intrinsicality, dispositionality, aboutness or subject matter, supervenience and dependence, truthmaking, the laws of nature, essence, property, propositional and intentional content, fictional worlds, and truth in fiction. The use of possible worlds in linguistics, logic, and computer science has also seen enormous success. The fact that possible worlds talk has become common parlance in many areas of contemporary analytic philosophy, and other fields, raises important questions concerning their ontological status and the explanatory value they afford.

Rather than answering the question What are possible worlds? I wish to discuss what I think is a more tractable question, namely, What what theoretical roles are possible worlds supposed to play, and are they cut out to play those roles?¹

The question is tractable because we can simply look and see to what purposes possible worlds have been put and whether possible worlds analyses have survived the test of time, or whether they have been succeeded by superior analyses which either do away with worlds altogether or else demote them to a lesser role.

In giving a partial answer to the question, we will begin by looking at traditional possible worlds analyses of intensional and modal concepts (Section 1.2). We will then look at three possible worlds analyses that have played an important role in their perceived success, viz. the analyses of (i) modality and possibilities in counterpart theory (Section 1.3), (ii) belief contents (Section 1.4), and (iii) conditionals (Section 1.5).

1.2Possible worlds semantics

Let us have a more careful look at possible world semantics and the reasons for its success. Let us denote ‘Necessarily’ by ‘□’, ‘Possibly’ by ‘◊’, and ‘It is not the case that’ by ‘¬’. Then, according to the simplest quantificational analysis of the broadest sort of necessity, often called metaphysical,

(□*) □A is true at a world iff A is true at every world.

Given the equivalence of ◊A with ¬□¬A, we have:

(◊) ◊A is true at a world iff A is true at some world.

The quantificational analysis is simple and has the virtue of providing a way of determining whether complex modal sentences (or sentence forms), such as those containing a large number of iterated modalities (e.g. ‘It is possibly necessarily possible that A only if it is necessary that A’), are true (valid) or not. Before the quantificational analysis, determining which modal inferences were valid rested mainly on potentially shaky intuitions concerning the plausibility of individual axioms or rules.² Possible worlds semantics provides a translation of an obscure intensional language into the pristine clarity of an extensional (meta)language.³

More restricted versions of necessity can be given a similar a...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Notes on Contributors
• Introduction: Modal Matters Philosophical Significance
• PART 1: Worlds and Modality
• PART 2: Essentialism, Ontological Dependence, and Modality
• PART 3: Epistemology of Modality
• PART 4: Epistemology of Modality
• PART 5: Modality and the Metaphysics of Science
• PART 6: Modality in Logic and Mathematics
• PART 7: Modality in the History of Philosophy
• Index