An Inquiry on Modal Metaphysical Puzzling Possible Worlds

Berthoud, Valery

An Inquiry on Modal Metaphysical Puzzling Possible Worlds

Philosophy - Theoretical (Realisation, Science, Logic, Language)

Summary

The concept of possible worlds is useful because it defines the four modalities – possibility, necessity, contingency, and impossibility – but a challenge lies in defining it. David Lewis’ polemical hypothesis (“genuine modal realism” as it is called) succeeds in it. Lewis’ modal realism stirred controversy because he maintains that a plurality of worlds exists. Some philosophers suggest that the Lewisian view is a violation to the law of parsimony, also known as Ockham’s Razor, i.e. not multiply entities beyond necessity. While avoiding a circular definition, Lewis constructs an inflated ontology. Is it worth it, and if we do not want to assume too many Lewisian worlds, what alternatives remain? Actualist modal realism and modal antirealism are the most relevant alternatives because modal abstentionism simply will not progress in this direction. This study evaluates the theories of possible worlds.

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Berthoud, Valery: An Inquiry on Modal Metaphysical Puzzling Possible Worlds,

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Abstract

The concept of possible worlds is useful because it defines the

four modalities possibility, necessity, contingency, and impos-

sibility but a challenge lies in defining it. The polemical hy-

pothesis from David Lewis ("genuine modal realism" as it is

called) succeeds in it. Lewis' modal realism stirred controversy

because he maintains that a plurality of worlds exists. Some

philosophers suggest that the Lewisian view is a violation to

the law of parsimony, also known as Ockham's Razor "don't

multiply entities beyond necessity" (Spade and Panaccio 2015).

While avoiding a circular definition, Lewis constructs an in-

flated ontology. Is it worth it, and if we do not want to assume

too many Lewisian worlds, what alternatives remain? Actualist

modal realism and modal antirealism are the most relevant alter-

natives because modal abstentionism simply will not progress in

this direction. This thesis evaluates theories of possible worlds.

iii

Acknowledgements

For his proofreading and all the work he has done to help me

through the learning and writing process of this bachelor thesis,

I would like to offer my special thanks to Jonathan Mai.

Many thanks to all the people who discussed ideas with me,

who provided me with very valuable inspiration and useful com-

ments.

Foremost, I am much obliged to my family for their support

and guidance.

Contents

List of Figures

vii

List of Symbols

viii

Background

Modalities

1.1 Possibility . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2 Contingency . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3 Necessity . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4 Impossibility . . . . . . . . . . . . . . . . . . . . . . . . . .

Modal Logic

2.1 What is Modal Logic? . . . . . . . . . . . . . . . . . . . . .

2.2 Possible Worlds Semantics . . . . . . . . . . . . . . . . . . .

What Are Possible Worlds?

Theories of Possible Worlds

3.1 Modal Realism . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 Actualist Modal Realism . . . . . . . . . . . . . . . . . . . .

3.2.1 Plantingan Modal Realism . . . . . . . . . . . . . . .

3.2.2 Combinatorialism . . . . . . . . . . . . . . . . . . .

CONTENTS

3.2.3 Nature Modal Realism . . . . . . . . . . . . . . . . .

3.2.4 Book Modal Realism . . . . . . . . . . . . . . . . . .

3.3 Concreteness or abstractness? . . . . . . . . . . . . . . . . .

3.4 Genuine Modal Realism . . . . . . . . . . . . . . . . . . . .

3.4.1 Lewis' Analysis of Possible Worlds. . . . . . . . . . .

3.4.2 Counterpart Theory . . . . . . . . . . . . . . . . . .

3.4.3 Arguments in Favour of Genuine Modal Realism . .

3.5 Critique of Genuine Modal Realism . . . . . . . . . . . . . .

3.6 Neo-Meinongianism . . . . . . . . . . . . . . . . . . . . . . .

3.6.1 Meinongian Modal Realism . . . . . . . . . . . . . .

3.7 Hybrid Modal Realism . . . . . . . . . . . . . . . . . . . . .

Evaluation

III

Conclusion

Summary

Final Thoughts

Bibliography

Index

List of Figures

1.1 Relation between modalities . . . . . . . . . . . . . . . . . .

1.2 Tree structure of possible futures . . . . . . . . . . . . . . .

vii

List of Symbols

Necessity (necessarily)

Possible worlds, a W with a subscript numeral is also used instead

of uppercase Greek letters

Possibility (possibly)

Material equivalence, (if and only if; iff)

Existential quantification (there exists)

Universal quantification (for all; for any; for each)

Negation (not), ¬ A is true only if A is false

Inclusive disjunction (or)

Lowercase Greek letters are used for formulae

Therefore sign

Material conditional (implies; if A then B)

Conjunction (and)

Uppercase Roman letters are used for propositions

viii

Part I

Background

Introduction

"Do you come to a philosopher as to a cunning man, to learn

something by magic or witchcraft, beyond what can be known

by common prudence and discretion?"

David Hume (1793)

The title of this bachelor thesis, "An Inquiry on Modal, Metaphysical,

Puzzling Possible Worlds", includes four adjectives that qualify the noun

worlds

: possible, puzzling, metaphysical, and modal. Possible and worlds

coalesce into the concept of possible worlds, and the remaining three adjec-

tives qualify it. Puzzling indicates the enigma that is the concept of pos-

sible worlds, and metaphysical relates possible worlds to things treated

in the framework of metaphysics.

Finally, modal characterises possible

worlds by asserting or denying possibility, impossibility, contingency, or

necessity. This thesis is explanatory, and the debate begins by defining

possible worlds, a concept that contemporary philosophers use often.

I deal with a metaphysical question. My position regarding metaphysi-

cal questions is that we can seek answers, since such questions are part of a

branch of philosophy. Therefore, my method is to seek clarification of the

concepts as it is usual in philosophy.

Metaphysics is a branch of philosophy that examines the nature of reality and inves-

tigates the fundamental nature of being and the world; it answers what there is and what

it is like.

Modalities

This chapter offers a broad perspective on modalities, and I begin by defin-

ing modality and explaining types of them: logical, metaphysical, nomo-

logical, epistemic, doxastic, deontic, and temporal.

I then define the four

modalities: possibility, contingency, necessity, and impossibility. Modal-

ity refers to the way things might have been; if a possibility is asserted,

impossibility is disqualified.

(1) Life is possible.

When stating that (1) impossibility is disqualified, it is impossible that

life is not possible, and we do not have to prove it. The four modalities

interrelate; possibility requires contingency or necessity, but it cannot be

both, inasmuch as contingency contradicts necessity and vice versa. The

difference lies in whether it need not be or it must be. Contingency and

necessity both require possibility, and both disqualify impossibility. Thus,

impossibility disqualifies possibility, contingency, and necessity (cf. Divers

2002, pp. 3-4). Statements that suggest what must be, cannot be, may be,

or need not be are called modal statements, of which there are multiple

types. Modal statements appear to be true.

I do this because it is easier to understand the nature of possible worlds if they are

involved with modal discourse.

1. MODALITIES

(2) Possible worlds exist.

Depending on the understanding of (2), possible worlds exist either in a

logical, metaphysical, or physical space. Shown in figure 1.1 (Vaidya 2015),

Figure 1.1: Relation between modalities

logical modality is the most inclusive, and logical modality is fixed by the

laws of logic. One proposition must be true and the other false, and if they

are contradictory propositions, this is the law of the excluded middle, which

brings us to the law of non-contradiction: there is no proposition such that

both it and its negation are true. Apart from logical modality, other types

can be classified, of which metaphysical modality is one, fixed by the laws

of metaphysics (e.g., the nature and identity conditions of things). Meta-

physical modality includes everything that might have existed. Something

is metaphysically necessary if it is determined by the laws of metaphysics,

and it is possible if compatible with the laws of metaphysics.

The origin

and constitution of something are the type of properties that are thought

to be essential. I cannot lose the property of being human; this property is

metaphysically necessary. Magic is metaphysically possible. An example is

growing larger or smaller after eating cake like Alice in Wonderland. This

is not physically possible. Nomological modality is fixed by the laws of

Some suggest no disparity between logical and metaphysical spaces, but it is difficult

to think of metaphysical modalities that are not concordant with logical modalities.

1. MODALITIES

physical reality; the laws of nature have to allow it. Something is nomolog-

ically necessary if it is determined by the laws of nature, and it is possible

if compatible with the laws of nature. It is nomologically necessary that

an isolated system's entropy always increases over time, and it is nomo-

logically possible to jump five meters (e.g., on the moon) (cf. Priest 2008,

pp. 46-47). Another type is deontic modality, determined by what satisfies

a norm or rule. Something is deontically necessary if it is required by the

laws of morality, and deontically possible if permitted. Temporal modality

is fixed by time; something is temporally necessary if it is true at all times,

and temporally possible if true sometimes (cf. ibid., pp. 46-47). Another

type of modality is epistemic. Facts that can be known or believed (e.g.,

evidence) are epistemic modal notions. Epistemic modality is fixed by what

is known. If something is known to be true, it is epistemically necessary,

and epistemically possible if it might be true. Doxastic modality is fixed by

what is believed. If something is believed true, it is doxastically necessary,

and doxastically possible if it could be believed. A debate exists regard-

ing whether epistemic modalities are different from metaphysical ones (cf.

Kment 2012). Dualists argue for a fundamental distinction between epis-

temic and metaphysical modalities, but monists for only a single type of

modality (cf. ibid.) I argue that it is possible to distinguish a metaphysical

notion of necessity from an epistemic one. Regardless of whether one is a

dualist or monist, it is possible to differentiate them and distinguish both

epistemic and metaphysical reasons to seek a reduction of the definition of

modality. Asking "Why seek such a reduction?" is like asking why philoso-

phers avoid circular reasoning. The reasons have to do with connections

among modality, epistemology, and metaphysics. Modality is important

to philosophy because it connects with epistemology and metaphysics, and

these connections are influential in analytic philosophy. Epistemology of

the modal requires reductionism to define modal notions in terms that do

not include modal notions and can therefore be the epistemology of the

1. MODALITIES

modal secured. A metaphysical reason for seeking reduction is to begin an

ontology with primitive notions that are non-modal (cf. Sider 2003, p. 5).

1.1

Possibility

There are two ways of expressing possibilities: possible for is a qualifi-

able possibility, and possible that is a variable possibility (cf. Girle 2009,

pp. 140-141). The first phrase can be qualified using words such as logically,

metaphysically, and physically. For example:

(3) It is physically possible for light to travel at 299,792,458 m/s.

The second phrase can vary using terms such as quite and definite:

(4) It is definitely not possible for time to stop.

There is a connection between (3) and (4).

(5) If it is impossible to travel at the speed of light, then it is impossible

for time to stop.

The reverse does not hold:

(6) If it is impossible for time to stop, then it is impossible to travel at

the speed of light.

Shown in 1.1, if something is possible, it depends on the considered type

of modality.

(7) I could have done better.

Sentence (7) expresses possibility (i.e., can, might, could). We can imagine

what would have happened were the course of things different. Imagine a

painter choosing the colour blue instead of orange; the resulting painting

is different. What if my parents had not met and I had not been born? I

would not be here writing this thesis because existence is contingent.

1. MODALITIES

1.2

Contingency

A contingent proposition might or might not happen; the event could occur,

but is unnecessary. Logical contingency means something that is neither

logically necessary nor impossible. Maybe, maybe not, might have been,

might not have been and could have been otherwise these are ways of

expressing contingency (cf. Girle 2009, p. 3). In Figure 1.2, Ohrstrom

and Hasle (2015) illustrate an idea from Saul Kripke, concerning branching

time, in which Kripke considers the present as a point of Rank 1, the next

possible event as point of Rank 2, etc.

Figure 1.2: Tree structure of possible futures

(8) It might rain today.

For example, if someone says (8) at point 0, point 1 could be sunny, point

2 cloudy, and point 3 thunderstorm. Plans depend on contingent weather,

and we depend on contingent events because the future is uncertain. This

uncertainty will always change plans.

(9) If it rains, the picnic will be cancelled.

1. MODALITIES

The picnic depends on something that is neither necessarily true nor false.

A proposition is contingent if its contrary does not imply a contradiction.

When speaking, we make statements about the future, and most are con-

tingent.

(10) In 1999, a great King of terror will come from the sky.

When Nostradamus wrote (10), it was neither true nor false because the

year 1999 did not exist. Future contingents are neither true nor false (cf.

Priest 2008, p. 132).

1.3

Necessity

Our lives are full of decisions, leading to endless possibilities, but despite

so many possibilities, necessity expresses that something could not be oth-

erwise. Necessity (i.e., must and has to be) is another case of modality.

Something necessary is understood as an inevitable consequence. There is

a discussion about whether some things could have been otherwise. Many

things appear metaphysically possible, but more disagreement exists re-

garding whether metaphysical principles are necessary. Some philosophers

argue that metaphysical principles are merely contingent.

An important

question is whether anything is necessary does a nomological necessity

exist? Are the laws of nature necessary? There is also an ongoing debate

on whether necessity must associate with the laws of nature, and some

examples suggest doubt. What about mathematical truths?

For example, Ross Cameron argues that metaphysical principles are contingent be-

cause were they necessary, it would lead to an unwarranted universalism (cf. Cameron

2007, p. 99).

1. MODALITIES

1.4

Impossibility

Something impossible cannot be done and cannot happen, and many agree

that something that violates the natural laws is impossible. Lewis argues

that what usually counts as nomologically impossible is possible, "so the

laws are not sacred" (Lewis 1973, p. 567). Another definition of impossibil-

ity contradicts the laws of classical logic, like the law of non-contradiction.

Consensus suggests that contradictions are impossible unless the law of

non-contradiction is invalid, as in the position of dialethism. Dialethists

defend the view that some contradictions are true; hence, for them, logical

laws are not sacred. Graham Priest suggests no problem with discrimina-

tions concerning impossibility (cf. Priest 2008, p. 15).

Modal Logic

I turn to modal logic in this chapter, examining its background and de-

velopment, and then introduce modal logic, assessing axioms and common

possible worlds semantics. Modal logic was created at the same time as

logic. Aristotle provided partial analysis of problems raised by modality,

investigating the validity of modal syllogisms. The history of modal logic

traces to Megarian logicians.

Medieval logic books include principles of

modal syllogism, which indicates that modal logic was discussed during

the Middle Ages. The empiricist tradition embraces skepticism regarding

modalities. The system B was formulated by Kurt Gödel, who was first

to propose that the syntactical notion of provability especially as under-

stood by Luitzen Brouwer, after whom the system was named can be

represented by the modal notion of necessity (cf. Cocchiarella and Freund

2008, p. 37). Clarence Lewis initiated modal logic during the modern pe-

riod; he defined a logic of conditionals that do not have the necessity signs.

At that time, Paul Carnap worked out the Leibnizian idea that necessary

truth is truth across all possible worlds. During the first half of the century,

logicians failed to identify models for modal systems, and were incapable

of providing complete proofs of the systems. The subject was criticised by

Euclid of Megara founded the Megarian school, and Philo the Dialectician was its

most prominent exponent.

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Type of Edition: Erstausgabe
Year: 2017
ISBN (PDF): 9783960676942
ISBN (Softcover): 9783960671947
File size: 17.2 MB
Language: English
Institution / College: University of Stuttgart
Publication date: 2017 (September)
Grade: 1,7
Keywords: Possible Worlds Mögliche Welten David Lewis Metaphysik Ontologie Possibility Impossibility Necessity Contingency Metaphysics Ontology Genuine Modal Realism Ockham’s Razor Modal Antirealism

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Valery Berthoud (Author)

An Inquiry on Modal Metaphysical Puzzling Possible Worlds

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