Lewis advocates modal realism, which holds that possible worlds are as real as the actual world. Possible worlds resemble different ways the world could have been and do not overlap, so events in one world do not affect others. Lewis draws a parallel between plurality of sets and plurality of worlds to argue this view is theoretically useful. However, some critics argue Lewis does not provide strong evidence for this view and the shift from possible ways things could have been to possible worlds is problematic. A better argument might have been that we make accurate modal claims and there are worlds where these claims are true, but Lewis' argument is not ultimately proven. Modal realism can help analyze modality by quantifying over possible worlds using operators restricted by accessibility relations

1. On Lewis: The Utility of Modal Realism
Robert Morien
990-41-5960
Philosophy 685 – Modality
The University of Wisconsin-Milwaukee

2. Chapter 1.1 The Thesis of Plurality of Worlds
In the first chapter of David Lewis’ book, On the Plurality of Worlds, Lewis advocates
modal realism, or a thesis of plurality of worlds. This view about the plurality of worlds
resembles the different possible ways a world might have been, and one of these
possibilities is the actual world; that is, the world we are a part of. Possible worlds are as
concrete and real as the actual world. They are separate entities with no overlap such that
the consequences that result from one world cannot affect the outcome from any other
world. This is the framework Lewis provides for his thesis of modal realism, the
framework which ought to deliver coherent accounts about modal logic.
Lewis tries to sell this thesis by drawing a parallel between the plurality of sets in
mathematical space with the plurality of worlds in logic space. He claims that it is from
this harmony between sets and worlds that allows for an analog between the fruitfulness
of set theory and the theoretical utility of modal realism. It is due to this fruitfulness that
we should accept the theory of possible worlds as true.
However plausible these claims appear to be, there doesn’t seem to be very compelling
evidence (other than what he supplies) for the skeptic to willingly adhere to this view.
He simply spells out the conditions of his terms without providing an airtight alibi.
Another qualm modal realism faces is, there doesn’t seem to be a smooth transition
during the exchange of ‘ways things might have been’ with ‘possible worlds’. Reason
being, for someone to believe that there exist countless talking donkeys is a false
statement; nevertheless, hold that it might be true seems to be a bit odd.
… for this to be convincing, the shift from ‘ways things might have been’ to ‘possible
worlds’ must be an innocent terminological substitution, and I do not believe that, as Lewis
develops the concept of a possible world, it is. (Stalnaker [1984]: 26)
This anomaly is what is commonly referred to as
… the incredulous stare. (Rosen [1990]: 329)
The punch-line to Lewis’ argument for acceptance of modal realism appears to be1
: we
should take the theory of possible worlds as true. The positive outcome that results from
this theory will allow us to carry out further analyses about modal claims. However
aesthetically pleasing this may sound to the non-skeptic, it still appears to be an invalid
argument. The reason for its invalidity is the fact that simply generating positive
outcomes provides no evidence for its truth.
1
See “Do Modal Claims Imply the Existence of Possible Worlds?,” http://home.sprynet.com/~owl1/lewis.htm.

3. Perhaps a better argument Lewis might have put forward could have been the following:
1) We frequently make accurate assertions involving the modal “Possibly P”.
2) There exist possible worlds where “Possibly P” obtains.
3) Therefore, there are possible worlds.
Although there is no rhyme or reason to indicate that this argument is ultimately true, it is
nevertheless a valid one. An argument such as this might have served a better purpose
during Lewis’ exposition of the utility of possibilia.
Chapter 1.2 Modal Realism at work: modality
Where the theory of modal realism does seem to make the most sense is during the
employment of quantification. By utilizing the theory of possible worlds, we turn
modality into quantification over possible worlds. This is done through restricting
modifiers that sets an upper and lower bound to cover only the worlds or counterparts we
are speaking of.
“In Australia, all swans are black” is then a true statement since we are ignoring
everything that is not inside the domain of Australia.
Usually in modality, quantification over possible worlds is restricted by the following
accessibility relations: nomological necessity and historical necessity. Nomological
necessity refers to all possible worlds that are nomologically accessible from the actual
world where P obtains2
. For instance, when someone claims that aluminum has a density
of2 7 3
.
g
cm
, this is a nomologial fact. On the other hand, if someone claimed that all the
steel in my shop is non-ferrous, this is not a nomological fact since at a later time, t a bar
of HRS might have found its way inside. Historical necessity refers to a perfect match
between worlds up to a time t. Similarly, quantification over possible individuals is
restricted by counterpart relations. These refer to similarities in origin, location, etc.
We apply the two standard modal operators, diamond (possibly) or box (necessarily), to
sentences to make sentences, or to open formulas. When applied to sentences they are
used as restricted quantifiers over possible worlds.
We run into trouble when we apply these operators to open formulas. Lewis provides
two solutions to this dilemma; each works equally well. Simple solution: “Hubert
Humphrey might have won the presidency but didn’t.” Using the diamond as a quantifier
2
See “Accessibility Relations,” http://en.wikipedia.org/wiki/Accessibility_relation

4. over worlds implies that there is a world where he did win the presidency, but how can
this be? How could he win the presidency in a world he never occupied? Lewis claims
that there is a world where somehow he satisfies this in absentia. Complex solution: Let
the diamond quantify over other-worldly counterparts of this-worldly individuals.
Through vicarious satisfaction he possibly wins the election iff at some world w he has a
counterpart who wins.
But what about for the problem, “Humphrey satisfies ‘necessarily x exists’ and fails to
satisfy ‘possibly x does not exist’? In other words, Humphrey has the possibility of not
existing iff some world lacks a counterpart.
This was a bit tricky for me to understand, but from what I interpreted, I think how Lewis
gets out of this problem is by placing less restriction on the operators. We do not need to
quantify over the box or diamond in the strict sense. Instead, we can replace the diamond
with say, probably or could, quantifying over the appropriate modal verb contained
within a particular context.
Chapter 1.4 Modal Realism at Work: Content
I did not present this section of the chapter to the class, however, I would like to
emphasize a few of the key points Lewis manages to convey.
We can characterize the content of someone’s knowledge and belief through epistemic
and doxastic accessible worlds. Doxastic accessibility implies quantification over
possible or counterpart beliefs. These doxastic accessible worlds give the contents of
someone’s belief system about the world and about himself; modality de se, or an
egocentric belief of oneself. This is the entire content of someone’s system of belief,
which should be characterized as a class of possible individuals (doxastic alternatives).
Epistemic accessibility implies quantification over possible or counterpart knowledge.
This knowledge also has an egocentric part – you can know who you are in the world and
what time it is, therefore, these beliefs should also be characterized as a class of possible
individuals (epistemic alternatives).
How this works is, if someone knows that he has a possible individual – or counterpart –
and if this counterpart has some property in common with them, then they know that they
have this property. Therefore, if they live in a world with obtaining propositions, then he
knows the proposition.
Also, since no single belief system can perfectly match that of someone else’s belief
system, we must admit of a probabilistic range of belief systems that fits a particular
individual. This probabilistic range of belief systems also fits a person who can have
multiple belief systems conforming each one to fit a certain situation. By quantifying
over this range of belief systems guarantees cover over someone’s entire belief system.