Possible World Theory
Lewis vs Plantinga (and Kripke)
Introduction to the Issue
1. Necessity and Possibility are modal notions.
Are we allowed to talk this way? Why have we been uncritical of modal language, taking
it seemingly for granted?
We typically seem to explain our modal language by using other modal semantics to
make sense of it. So we say that a thing is “essential” if the thing “could not possibly
have not had it”.
2. Why challenge modality?
a) Empiricist intuitions. Modal concepts cannot be traced back in any way to experience
or with confirmation with the world.
-- typical Humean objection to modal language
-- we can say in line with Hume that our use of modality is linguistic; thus, it is
not revealing anything to us about the world as such, but really just about the ways in
which we are using our language (Ayer).
-- so necessity is just verbal necessity.
b) Empiricists tend to turn towards extensional languages.
-- an extensional language sees coreferential terms as those that can be
interchanged salva veritate without a change in truth value.
-- two terms are co-extensional if they name the same object
-- they name the same object if the same things satisfy the name
Examples:
1 – Bill Clinton is on vacation in Wyoming.
Suppose we replance “BC” with “42nd president of US”. Same truth value.
Extensional languages seem important because only with them can be derive logical
relations that show us how sentences are inferentially related to one another.
3. The Problem: Extensional Languages Don’t Express Necessity
(1) Two plus two equals four and all bachelors are unmarried. (necessary)
(2) It is necessary that two plus two equals four and all bachelors are unmarried.
Unfortuanately, if we put in “BC is the president” in for “two plus two is four” we get
(3) It is necessary that BC is president and bachelors are unmarried. – but this is False!
So it looks like introducing necessity in (2) turns a perfectly extensional sentence in (1)
into an intensional sentence.
As such, and because extensional sentences are what we are aiming for, it looks like the
introduction of modal language will be illicit.
 this will be because we are left with no way to draw up the inferential
relationships that will obtain between sentences using modal language.
4. What is needed is a modal logic.
Unfortunately, there are different non-equivalent modal languages, each of which gives a
different answer to the question “what modal sentences follow from what modal
sentences?”
In the 50s and 60s, philosophers noticed that using Leibniz’s notion of possible worlds
allowed for us to make sense of modal notions.
Possible worlds allow us to give clear answers to “what does a modal sentence mean?”
Virtues:
a) allows us to understand why there are different modal logics
b) allows us to understand why empiricists cannot locate modality
Possible Worlds
If we take seriously the framework of possible worlds and make it part of our ontology,
then we have a framework with which we can make sense of many philosophical
problems.
This may strike us as bizarre, but they claim that PWs have deep pre-philosophical roots.
 all PWs are, are philosophical ways of making sense of the fact that our prephilosophical intuitions about modality need truth makers.
1. De Dicto Modality
 modality as applied to whole propositions.
 Modality as used as a property of a proposition
 Modal language then become ways of quantifying sentences over PWs
2. De Re Modality
 modality as it is applied to an object
 so “BC is only contingently a person” then I am ascribing modal status to BC
the object, not the proposition.
So,
(1) The thing Steven Hawking is thinking about is necessarily an even number
(2) Necessarily the thing SH is thinking about is an even number
(1) is de re modality whereas (2) is de dicto modality. Now supposing that SH is thinking
of the number 2, then (1) will be true whereas (2) will be false.
Although we need to keep these separate, PWs Frameworkers will argue that both ways
of understanding modality can be understood via the PW way of analyzing modality.
So they say that de re modality can be understood by talking about the existence of
objects in possible worlds.
To say that an object has a property necessarily is just to say that wherever that object
exists, it has that property.
X has a property P necessarily: where X exists, it has P.
X is a necessary being: X exists in all PWs
X has a property P contingently: X exists in some PW and lacks P
X is a contingent being: X fails to exist in some PW
Possible Worlds Nominalism
How are we to understand all of this?
1. Two different conceptions of PWs
a. Some argue that the connection between concepts of de dicto and de re modality can
best be understood only through a network of interconnected and supporting concepts.
So to understand one modal notion requires that we show its relationship to other modal
notions in the network.
b. Others argue that we must approach the question of PWs in the way of thinking of
them reductively, so that we can understand modality in a way that does not presuppose a
family of interrelated modal notions.
2. Austere Nominalism (AN)
PWs enable the metaphysician to provide accounts of “proposition” and “property”.
 they are satisfied that these notions cannot be explained merely by talking
about the actual world. They suggest that PWs are needed.
 PWs contain only CRs (in the sense of AN).
 Using only these notions we can reductively explain everything else
a) What is a property?
F-ness is “the set whose members are all and only the CRs that are F”.
Problem 1: Different Properties Seem to Be the Same Property
“Creature with Kidney” and “Creature with Heart” wind up to be the same property,
because the sets that express them are identical.
Reply: Use PWs to fix it
Across PWs, the sets for these two will actually diverge.
So what we want is a set theoretical entity constructed of the sets from all the PWs. This
is the reductive analysis of property, and on this score the problem is dissolved.
So, a property is a set theoretical structure composed of concrete particulars.
b) What is a proposition?
A proposition is a set of possible worlds in which the proposition is true.
But this seems circular. So we need to get rid of “proposition is true”. What does it mean
to say that a proposition is true? That the world in which it expresses is “p-ish”. So;
A proposition is a set of possible worlds that are p-ish. So,
“All swans are white” is the set of possible worlds that are all-swans-are-white-ish.
c) Return to de dicto and de re modality
First: De Dicto Modality
Now we can return to our notions of modality.
What does it mean to say that a proposition is necessarily true?
N(p) just means “a set of worlds that has all PWs as its members”. To say that “2+2=4” is
necessarily trueis just to say that the set of 2_+_2_=_4-ish worlds has every PWs as a
member.
P(p) means “of a set of worlds it is non-empty”
C(p) means “has at least the actual world as a member”
If the ANs are right, then all talk about de dicto modality can be reductively understood
as set-theoretical discourse.
Second: De Re Modality
Object X is P = “X is a member of the set of objects the Set that is the property assigns to
the actual world”.
Object X is (N)p = “X is a member of the set of objects assigned by the property to each
PW”
Possible World Nominalism – David Lewis
1. Possible World Nominalists want to be able to talk about properties and propositions
without being committed to the obscure entities of the realist.
Property: set whose members are concrete particulars.
Propositions: set of PWs those CPs inhabit.
So when we are talking about modality, we are really just using a particular way of
constructing set-theoretic discourse.
So, in the end, all discourse about linguistic meaning can be reduced to PWs and the CPs
in them.
PWs allow us to talk now about counter-factual systems.
2. PW Nominalism is a reductivist theory. Everything, propositions, properties, counter
factuals, and meaning can be understood within a certain way of construing reality or
ontology – CPs and PWs (and set theory) is all we need.
3. The Central Question, is: How do they get to introduce Possible Worlds?
a) Ontology of the PW. Possible worlds are just like the actual world – they are things of
that sort. They are different only in respect to what goes on in them.
Lewis wants to exploit our pre-philosophical intuitions about PWs.
PWs are real, just like the actual world. They have concrete objects in spatial relations.
 no spatial relations or causal relations between PWs
There is no special property that marks out the “actual” world as more ontologically
relevant than any other PW. The use of the term “actual” is really just an indexical like
“here” or “I” or “now”.
 context relative to the utterance used
b) Transworld Individuals. But if the PWs are all equally real, then it seems that I cannot
occupy each world in the sense that I live each of the sets of possibilities peculiar to each
one.
Objection One: Indiscernability of Identicals
The intuitive problem with transworld individuals is that it seems to assume that the
Indiscernability of Identicals is false.
Indiscernability of Identicals: Necessarily, for any objects A and B, if A = B then for any
property P, A exemplifies P iff B exemplifies P.
But here we seem to be suggesting that two individuals with different properties could
actually the one and the same person.
Example. Take W1 and W2 given and X-in-W1 and X-in-W2 as given.
Now, if X-in-W1 is a beachcomber and X-in-W2 is a metaphysician, then it seems as if
X-in-W1 has properties that X-in-W2 does not.
So if X exists in both W1 and W2, then the I of I must be false.
Reply to Objection One: World-Indexed Properties
Say that properties are indexed to worlds, such that X has the property of being swarthy
in W1 and being a metaphysician in W2. This removes the contradiction.
Counter-Reply:
This would force us to deny that people have properties, but rather that the properties are
world-indexed, which is not what we say. We say that individuals have properties
simpliciter.
Lewis’ Conclusion: World-Bound Individuals. In every different world, you have a
separate person.
Cost:
(a) then it appears as if modality doesn’t work in the way I suspect that it should. Things
that are possible aren’t things that happen to me in another world, they happen to
someone else who looks like me.
(b) everything that is true of me is true by necessity
This consequences can be seen when we think of the way in which we talk about de re
modality; to say that a thing has P essentially is to say that it exemplifies it wherever it
exists; but, since it only exists in the actual world, it has it essentially.
(c) but it seemed that PW were a useful framework for trying to figure out how to explain
the difference between contingent and necessary properties.
3. The Counterpart Relationship
According to Lewis, individuals across PW are tied together by means of a qualitative
relationship of similarity.
 this relation does not make them the same; rather, it undergirds our prephilosophical intuitions about modality.
So;
a) property P is essential to X iff P is possessed by X and all of its counterparts.
b) property P is contingent to X iff P is not possessed by some of X’s counterparts.
So what Lewis is saying here is that for something to count as Socrates it must be human,
but for it to count as Socrates it doesn’t have to be white or Greek, say.
 but what is forming the basis for these intuitions on “what counts”?
The Principles of Lewis’ Possible Worlds
1. Possible worlds exist -- they are just as real as our world;
2. Possible worlds are the same sort of things as our world -- they differ in content, not in
kind;
3. Possible worlds cannot be reduced to something more basic -- they are irreducible
entities in their own right.
From here we get,
4. `Actual' is indexical. When we distinguish our world from others by claiming that it
alone is actual, we mean only that it is ours -- we live here.
From here the next two are harder to prove, but seem to follow:
5. Possible worlds are unified by the spatiotemporal interrelations of their parts; possible
worlds are spatiotemporally isolated from each other.
6. Each possible world has at least one member
7. Possible worlds are causally isolated from each other.