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ALEX, C., F., LEUNG
A Thesis submitted for
Figures in Analytic Philosophy

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What Does David Lewis’s Notion of Modality and His Thesis on Modal
Realism Entail – Does That Involve any Theoretically Intolerable Defect?
1. Introduction
This essay concerns not merely on David Lewis’s understanding on the notion of
modality and its derivative notions of possibility and impossibility but also on his
thesis on modal realism and his conception about the existence of possible
worlds and the nonexistence of impossible worlds. Also, this essay aims at
examining if his theory of modality, that of possibility, and that of impossibility
involve any intolerable defect based on two of his restrictions, namely
epistemological and metaphysical.
This essay will analyze, firstly, in §2, the meaning of modality, enquiring into
Lewis’s understanding and restrictions on possibility and impossibility. In
details, this essay claims that his understanding of these notions manifests the
meaning of modality, although it is epistemologically and metaphysically
restricted.
Secondly, in §3, it will analyze Lewis’s modal realism. In doing so, it will review
his modal realism based on the abovementioned epistemological and
metaphysical restrictions. And, it will also examine his modal realism through the
anti-realism of modality. Illustratively, Lewis’s modal realism asserts the reality
of possible worlds and the unreality of impossible worlds. In contrast, the anti-
realism on modality asserts the unreality of possible worlds and the reality of
impossible worlds.
Thirdly, in §4, it will synthesize the analysis on Lewis’s understanding on
modality and the analysis on his thesis about modal realism. It will, then,
examine if this unity of Lewis’s theory involves any theoretically intolerable
defect, namely the incompatibility between the aforementioned epistemological
and metaphysical restrictions on the notion of modality and in the modal realism.
Eventually, it will figure out the alternative solutions if his theory involves any
defect.

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2. The Meaning of Modality and The Notions of Possibility and Impossibility
The notion of modality has been being presupposed to be derivable to its
derivative notions of possibility and impossibility. However, there can be various
ways to understand these notions, namely through epistemological
conceivability, conjectural imaginability, metaphysical possibility, logical
possibility, sensory perceivability, physical achievability, and the like.1 These
understandings may have their manifold interplays. Nevertheless, Lewis restricts
his understanding of these notions explicitly in two contents, namely in
epistemology and metaphysics. And, this essay will concentrate in the interplays
between these two contents.
On the one hand, he understands these notions within some epistemic and
doxastic constraints:
“An inventory of the varieties of modality may include epistemic and doxastic
necessity and possibility.”2
On the other hand, he imposes some logical and metaphysical limits on these
notions:
“One comes to philosophy already endowed with a stock of opinions. It is not
the business of philosophy either to undermine or to justify these preexisting
opinions, to any great extent, but only to try to discover ways of expanding
them into an orderly system… So it is throughout metaphysics; and so it is
with my doctrine of realism about possible world… Realism about possible
worlds is an attempt, the only successful attempt I know of, to systematize
these preexisting modal opinions… To the extent that I am modally opinioned,
independently of my philosophizing, I can distinguish between alternative
versions of realism about possible worlds that conform to my opinions and
versions that does not. Because I believe my opinions, I believe that the true
1 Anand Vaidya (2015), "The Epistemology of Modality", The Stanford Encyclopedia of Philosophy,
ed. by Edward N. Zalta (2015).
URL=http://plato.stanford.edu/archives/sum2015/entries/modality-epistemology/.
2 David Lewis (1986), “On The Plurality of Worlds”, Blackwell Publishing, pp.27.

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version is one of the former. For instance, I believe that there are possible
worlds where physics is different from the physics of our worlds, but none
where logic and arithmetic are different from the logic and arithmetic of our
world.”3
These two restrictions are jointly sufficient in constituting Lewis’s understanding
on the notion of modality. If it is the case, then either these two restrictions are
individually operating or one of them supervenes another one of them. This
essay claims by arguing that these restrictions are not separately functioning.
Thence, there are two tracks to go with these limits and constrains. One path is to
conceive that the epistemic and doxastic constraints supervene the metaphysical
and logical constrains. Another way is to conceive that metaphysical and logical
constrains supervene the epistemic and doxastic constraints. It is seemingly
undetermined on which route does Lewis take somehow. Nevertheless, this essay
will analyze both routes. And yet, preliminary to the synthesis of the interplays
between these two sorts of superveniences in section four, these restrictions on
possibility and impossibility shall be clarified.
2.1 Epistemic and Doxastic Possibilities and Impossibilities
Thoroughly, Lewis explains the epistemic and doxastic restrictions on possibility
and necessity by appealing to the accessibility and exerting the truth-conditions
of this accessibility. He asserts that:
“Like other modalities, these may be explained as restricted quantification
over possible worlds. To do so, we may use possible worlds to characterize
the content of thought. The content of someone’s knowledge of the world is
given by his class of epistemologically accessible worlds. These are the worlds
that might, for all he knows, be his world; world W is one of them iff he knows
nothing, either explicitly or implicitly, to rule out the hypothesis that W is the
world where he lives. Likewise, the content of someone’s system of belief
about the world is given by his class of doxastically accessible worlds. World
W is one of those iff he believes nothing, either explicitly or implicitly, to rule
3 David Lewis (1973), “Counterfactual”, Basil Blackwell, pp.88.

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out the hypothesis that W is the world where he lives.
Whatever is true at some epistemically or doxastically accessible world is
epistemically or doxastically possible for him. It might be true, for all he knows
or for all he believes, he does not know or believe it to be false. Whatever is
true throughout all the epistemically or doxastically accessible world is
epistemically or doxastically necessary; which is to say that he knows or
believes it, perhaps explicitly or perhaps only implicitly.”4
In Lewis’s modal language, this claim presupposes that the notion of possibility
and that of impossibility can be explained by the notions of epistemic
accessibility and that of doxastic accessibility. Also, according to Lewis, it
indicates that the truth-conditions for doxastic possibilities and epistemic
possibilities are sufficiently satisfied by doxastically accessible worlds and
epistemically accessible worlds respectively.
Nevertheless, the truth-conditions could have never been satisfied if the contents
of a belief or knowledge are not about the worlds. Accordingly, some beliefs, as
well as knowledge, are about the worlds; but egocentric beliefs and egocentric
knowledge are not about the worlds and merely about the egocentric properties
of individuals.5
In order to substantiate his claim about the truth-conditions for the accessibility
of worlds, Lewis additionally remarks that beliefs about the world and
knowledge about the world are essentially reducible to the egocentric beliefs and
egocentric knowledge respectively. Moreover, Lewis highlights the truth-
conditions for these two sorts of belief and that of knowledge. According to
Lewis, the truth-conditions for the beliefs about the worlds and knowledge about
the worlds are captured respectively by a class of doxastic accessible worlds and
a class of epistemic accessible worlds, whereas the truth-conditions for the
egocentric beliefs and knowledge are captured respectively by a class of doxastic
accessible individuals and epistemic accessible individuals. Furthermore, Lewis
claims that the classes of worlds are manifested by the classes of individuals,
4 David Lewis (1986), “On The Plurality of Worlds”, Blackwell Publishing, pp.27.
5 David Lewis (1986), “On The Plurality of Worlds”, Blackwell Publishing, pp.28-30.

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whereas, the classes of individuals are manifested by the classes of properties
that the individuals may have, which Lewis calls them counterfactual individuals.
Illustratively, if an individual in a world doxastically, or epistemically, processes a
property about his own inhabitation of the world at which a proposition holds,
then he believes, or knows, his inhabitation of the world at which the proposition
holds. Correspondingly, he believes, or knows, that the proposition holds in his
world. Likewise, if an individual of a world doxastically, or epistemically,
processes a property about all of his alternative individuals’ inhabitations of
worlds at which a proposition holds, then he believes, or knows, his necessary
inhabitation of all worlds. Also, he believes, or knows, that the proposition entails
a necessity.6
It shall be noted that the reality of these truth conditions will be investigated in a
coming section, whereas, in this section, the truth-conditions are merely clarified.
However, regardless of the similarities of the truth-conditions that the epistemic
restrictions and the doxastic restrictions share, the epistemic restrictions are
essentially different from the doxastic restrictions. According to Lewis, only truth
can be known universally; and yet, not only can truth be confirmed by every
system of beliefs but also falsehood can be adopted by it.7 Formulating the
system of beliefs, according to Lewis, indicates that the contents from every
system of beliefs are not constrained by its truth-values but are remarked by
belief-desire psychology and not merely individuals’ acceptances of these
contents. To sustain this claim, Lewis presupposes that these contents essentially
belong to the recurrent states of individuals, namely the brain states. So, the
recurrent states sufficiently motivate individuals to have certain contents in
which the contents reasonably fit the states. Additionally, he claims that the
recurrent states of individuals are essentially influenced by the individuals’
desires.8
Remarkably, this essential distinction is influential to the latter discussion of
superveniences in this essay when this epistemic and doxastic restriction is
6 David Lewis (1986), “On The Plurality of Worlds”, Blackwell Publishing, pp.27-30.
7 David Lewis (1986), “On The Plurality of Worlds”, Blackwell Publishing, pp.27.
8 David Lewis (1986), “On The Plurality of Worlds”, Blackwell Publishing, pp.30-40.

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combined with Lewis’s modal realism.
2.2 Metaphysical and Logical Possibilities and Impossibilities
For the metaphysical restrictions, Lewis is not opinioned more than his belief in
logic and arithmetic. As for Lewis’s restrictions on logic and arithmetic, there are
two routines at which he can settle with it. On the one hand, he seemingly takes
certain logical rules as unshakeable logical truth over his epistemic restrictions.
On the other hand, within his doxastic restrictions, apparently, he apparently
intends to assert some semantic values into his system of logic. He phases it in a
claim that:
“This is nothing but the systematic expression of my naı̈ve, pre-philosophical
opinion that physics could be different, but not logic and arithmetic. I do not
know of any non-circular argument that I could give in favour of that opinion;
but so long as that is my firm opinion nevertheless, I must make a place for it
when I do metaphysics.”9
This is, however, undetermined about whether Lewis takes certain logical rules
to be logical truth or he asserts these rules with some sematic values.
Nonetheless, these two routines are essentially different. By taking the former
routine, it implies that his logical restrictions supervene his epistemic
restrictions since, according to Lewis, only truth can be known universally.
Whereas, by taking the latter routine, it implies that his epistemic restrictions
supervene his logical restrictions because, in Lewis’s account, an epistemic
system can adopt any logical rules from which its truth-value is affirmed.
Moreover, by taking the former routine, his whole theory of modality will face an
intolerably theoretical defect if the logical truth prohibiting any violation to it
and yet being found otherwise. Whereas, by taking the latter routine, the logical
rules will just be presupposed, and these presuppositions will be alterable with
other rules without threatening his entire theory of modality.
Taking the rule of non-contradiction as an example, as mentioned by Aristotle
9 David Lewis (1973), “Counterfactual”, Basil Blackwell, pp.88.

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and apparently adopted by Lewis, it asserts the impossibility of contradictory
properties being applied to the same object at the same time and in the same
respect.10 However, it may be found that contradictions are possible. For
example, if the quantum uncertainty is true, then an atom will inhabit both the
state of decaying and the state of non-decayed at the same time at which the
quantum system is isolated.11 And hence, if it is the case, then it entails a
violation to the rule since it designates a falsehood rather than a truth to the rule.
Consequently, if Lewis takes this rule for granted as a logical truth, then this truth
will be known universally. Also, it implies that this truth cannot be otherwise.
But, if now this truth is found otherwise, no matter metaphysically or physically,
then his modal system will carry out an infinite circulation. Illustratively, if this
logical truth, which essentially prohibits any violation to it, is found to be
otherwise, then it involves contradictions, which is not permissible in Lewis’s
theory of modality. But, contradictions will be logically permissible if the rule of
non-contradiction is found otherwise. And, since Lewes’s theory of modality
endures logical truth, it will also find this permissible. And, this just brings us to
the beginning again and so on. Therefore, it will face a theoretically intolerable
defect. It shall be noted that it will only happen when the logical truth is found
otherwise than what Lewis presupposes.
In contrast, if Lewis just presupposes this rule, then it can be replaced another
rule and be adopted by an epistemic system when the truth of this kind is found
to be manifested otherwise.
Taking another example from the rule of excluded middle, as indicated by
Aristotle and apparently accepted by Lewes, it claims that everything is either
true or false.12 And yet, it may be found that something is both true and false, or
that something is neither true nor false. For example, if a truth is asserted to a
sentence to which declares the falsehood of it, per se, then the sentence will
10 Aristotle, “Metaphysics”, Book iv, 1005b19–23, ed. by Jonathan Barnes (1984), “The Complete
Works of Aristotle, Vol.2”, Princeton University Press, pp.1588.
11 Laurence Horn (2014), "Contradiction", The Stanford Encyclopedia of Philosophy, ed. by
Edward N. Zalta (2014).
URL=http://plato.stanford.edu/archives/spr2014/entries/contradiction/.
12 Aristotle, “Metaphysics“, Book iv, 1012a25–29, ed. by Jonathan Barnes (1984), “The Complete
Works of Aristotle, Vol.2”, Princeton University Press, pp.1598.

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entail a falsehood to itself. But, if the sentence is false, then it entails a truth
based on what it claims. So, the sentence does not only designate a truth-value,
which is both true and false, but also designate not a truth-value, which is neither
true nor false.13 And hence, if it is the case, then it simply violates the rule.
Consequently, if Lewis considers this rule to be a logical truth, then this truth will
be known by all and cannot be otherwise. But, if this truth is, in fact, found
otherwise, no matter metaphysically or physically, then his theory of modality
will be involved in the same circular paradox abovementioned. For, if this logical
truth, which essentially forbids any violation to it, is found otherwise, then it
permits not only incompatible truth-values being applied to a statement but also
no truth-values being attributed to it. In consequent, it will be logically
acceptable to have no truth-value. In other words, this option of having no truth-
value will designate the truth since the truth is found this way. And hence, it
entails that the truth is not manifested by the truth-value. So, when Lewes takes
this rule for granted, and this rule is found otherwise, then it will be
unacceptable in Lewes’s theory of modality since there can be truth without
truth-values. But, if it will be logical acceptable, then it will be, again, acceptable
in Lewis’s theory of modality since it is logically acceptable, and Lewis’s theory of
modality accepts the logical truth. Therefore, it manifests an indefinitely circular
and a theoretically intolerable defect. And yet, it shall be noted that it will only
happen when the logical truth is found otherwise but not what Lewis
presupposes.
In contrast, if this rule is just presupposed by Lewis, then it can be substituted by
another rule, which theoretically tolerates a statement to have contradictory
truth-values and no truth-value for an epistemic system.
Therefore, if Lewis intends to save his theory of modality, then he will have to
presuppose these logical restrictions are amenable when those logical
restrictions are arguably open to doubt and found otherwise. By the same
reason, his restrictions on metaphysics shall be available to substitutions if logic
13 Laurence Horn (2014), "Contradiction", The Stanford Encyclopedia of Philosophy, ed. by
Edward N. Zalta (2014).
URL=http://plato.stanford.edu/archives/spr2014/entries/contradiction/.

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and arithmetic are not ultimately grounded as he presupposes. Significantly, this
remark casts a theoretically threatening shadow on the coming discussion of
superveniences in this essay when this metaphysical and logical and restriction
is synthesized with Lewis’s modal realism.
It shall also be noted that the soundness of the abovementioned logical rules has
not been justified but merely analyzed by conditional. So as the soundness of
Lewis’s theory of modality has been neither justified nor falsified, but only the
structure of his metaphysical and logical restrictions are clarified.
3. The Thesis on Modal Realism and The Anti-thesis on The Reality on
Modality:
This section will process an analysis on Lewis’s thesis on modal realism and
examine it through its anti-theses on the anti-realism on modality. In doing so, it
will clarify the extensions of Lewis’s theory on modality and provide a solid base
for the investigation on the theoretical compatibility in the next section.
3.1 Modal Realism
Given Lewis’s restrictions on the notion of modality, he claims that these notions
infer the existence of possible worlds and the nonexistence of impossible worlds.
For, ordinary language permits a paraphrase between these notions and the
reality of that if they share the same semantic value.
On the one hand, Lewis believes in the reality of possibility, the constrained
notions that things could have been. Having abstracted from ordinary language
that he has epistemologically acquainted with, he claims that:
“It is uncontroversially true that things might be otherwise than they are…
Ordinary language permits the paraphrase: there are many ways things could
have been besides the way they actually are. On the face of it, this sentence is
an existential quantification. It says that there exist many entities of a certain
description, to wit ‘ways things could have been’… I prefer to call them

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‘possible worlds’.”14
On top of the abstraction from ordinary language, he asserts a metaphysical
thesis that:
“The world we live in is a very inclusive thing… The ways things are, at its
most inclusive, means the way this entire world is. But things might have been
different, in ever so many ways that a world might be; and one of these many
ways is the way that this world is… I advocate a thesis of plurality of worlds, or
modal realism, which holds that our world is but one world among many.”15
On the other hand, Lewis also believes in the unreality of impossibility, the
constrained notions that things could not have been. Upon his epistemic and
doxastic restrictions, he claims that:
“We already have a good grip, in this way, on at least some of the possible
worlds: those that correspond to mathematical ersatz worlds constructed at
the highest level of generality that our modal opinions clearly require and
permit. It is only because there may be higher levels of generality that we have
failed to think of, and because our modal opinion are indecisive about whether
there really are possibilities corresponding to some of the levels of generality
we have thought of, that we fail to have a good grip on all the worlds.”16
And also, based on his metaphysical and logical restrictions, he claims that:
“There is no difference between a contradiction within the scope of the
modifier and a plain contradiction that has the modifier within it. So to tell the
alleged truth about the marvelously contradictory things that happen is no
different from contradicting yourself. But this is no subject matter, however
marvelous, about which you can tell the truth by contradicting yourself… An
impossible world where contradictions are true would be no better. The
alleged truth about its contradictory goings-on would itself be
14 David Lewis (1973), “Counterfactual”, Basil Blackwell, pp.84.
15 David Lewis (1986), “On The Plurality of Worlds”, Blackwell Publishing, pp.1-2.
16 David Lewis (1973), “Counterfactual”, Basil Blackwell, pp.90.

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contradictory.”17
His claims elude abstract conceptions then, but that is no matter. Lewis
presupposes the synthesis of these notions and the existential quantifications of
that. He takes it for granted that these notions furnish their existential
quantifications. Consequently, what is possible does really exist. In contrast, what
is impossible does not exist.
Moreover, he claims that all worlds are specified and unique in their contents.
Effectively, these worlds are isolated from each other if their components, namely
the possible individuals and their possible properties, are spatiotemporally
distinct. On the contrary, if these components are spatiotemporally related, then
these components shall belong to one and the same world where Lewis calls
them worldmates. Additionally, Lewis simply denies a single world to have two
or even more completely disconnected spacetimes. Nor does he accept a world
consisting purely nothing.
Furthermore, in order to explain the plentitude of these worlds, Lewis asserts
that every counterpart individual who is not alien from the individuals of the
actual world can exist at some worlds. And, these counterfactual individuals can
also coexist with other counterfactual individuals of the same kind insofar as
these individuals occupy distinct spacetimes. To be clarified, according to Lewis,
what are alien from the individuals of the actual world are the properties by
which the individuals at the actual world instantiate not. As for the actuality of a
world, Lewis takes it as an indexical description about the world at which an
individual inhabit.
According to Lewis, modal realism, the belief in the reality of worlds and in the
unreality of impossible worlds services us for a good reason, although it is not
conclusive. It services us for the sake of its benefits in the unity and economy of a
theory.18 These benefits include the explanatory power over metaphysics, logic,
physics, and language. Accordingly, these benefits indicate the reasons of which
modal realism shall be taken into our theoretical consideration.
17 David Lewis (1986), “On The Plurality of Worlds”, Blackwell Publishing, pp.7.
18 David Lewis (1986), “On The Plurality of Worlds”, Blackwell Publishing, pp.3-5.

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For instance, on the one hand, by employing the reality of possible worlds, the
truth-conditions of modal statements are fixed in appealing to possible worlds
and impossible worlds; and these modal statements can, then, be reduced to
logically elementary statements. So, the notion of modality can be explained in
terms of elementary logics and quantifiers.19 On the other hand, by embracing
the unreality of impossible worlds, it provides a solution to the problem of
vacuous truths that a false antecedent always affirms its consequent without
regard to the truth-values of the consequent.20
3.2 Anti-Realism on Modality
However, two sorts of anti-realism on modality have been arguing against
Lewis’s thesis on modality for diverse reasons. On the one hand, anti-realism on
possibility argues against the reality of possible worlds. On the other hand,
realism on impossibility argues against the unreality of impossible worlds.
Arguing for the anti-realism on possibility, Forbes attempts to explain the
semanticsof possibility without presupposing the reality of possible worlds.21
And yet, this attempt does not include the notion of manifesting the truth-
conditions for modal sentences. This attempt shall, however, be taken as
matching the modal language with our first-order logical language without the
use of possible worlds. In detail, he claims that:
“If σ is a sentence of modal language, and σ′ is its rendering in possible worlds
language according to the quantifier treatment of modal operators, then the
hypothesis that σ stands in the candidate relation to σ′ should be sufficient to
guarantee that σ behaves that same way in σ modal argument as σ′ does in the
rendering of that argument in possible worlds language.”22
Consequently, if this attempt from Forbes is successful, then it entails that
19 David Lewis (1986), “On The Plurality of Worlds”, Blackwell Publishing, pp.3.
20 David Lewis (1973), “Counterfactual”, Basil Blackwell, pp.24-31.
21 Charles Chihara (1998), “The Worlds of Possibility: Modal Realism and the Semantics of Modal
Logic”, Oxford University Press, pp.142-151.
22 Graeme Forbes (1985), “The Metaphysics of Modality”, Oxford University Press, pp.73.

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adopting the unreality of possible worlds exhibits the same explanatory power
on modality as employing the reality of possible worlds. Therefore, although
modal realism services us for a good reason, anti-realism on modality can do us
the same favour. Effectively, when anti-realism on modality can service us as
reasonable as modal realism does on explaining modality, Lewis would need to
provide further reason in order to justify modal realism.
As for the realism on impossibility, Vacek argues that Lewis’s restrictions on
modality are problematic. He claims that, according to Yagisawa, all truth about
impossibility can be told by contradictions.23 In detail, he puts it in a way that:
“Following Lewis, I say that actuality is an indexical notion. Actuality usually
means to be in this world. However, I also think that actuality sometimes
means to be in this logical space… I carry the idea even further and say that
possibility is also indexical… It is certainly impossible for impossibilia to exist
under any possible conditions or circumstances. But that does not mean that
impossibilia do not exist under any conditions or circumstances whatever.
They exist under impossible conditions or circumstances… When you
contradict yourself, what you are saying could not possibly be true. That is
indeed a good reason for the conclusion that you cannot tell the truth about
anything possible by contradicting yourself. But it is hardly a good reason
against impossibilia… It seems that you have to contradict yourself to tell the
truth about an impossible thing… Impossible things are impossible!”24
Consequently, if contradictions can entail any truth about impossibility, then this
entailment shall not indicate what Lewis’s modal language originally indicate,
which is the non-existence of impossible worlds. Rather, it shall indicate that
there is a possible world at which contradictions are impermissible. Illustratively,
that is to say, there is a world that a state of affairs cannot manifests itself at a
possible world and manifests itself not at the same possible world at the same
time. Similarly, according to Russell, mentioning the non-existence of an object
23 Martin Vacek (2013), “Concrete Impossible Worlds", Filozofia, Vol.68, No.6, pp.528-529.
24 Takashi Yagisawa (1988), “Beyond Possible Worlds", Philosophical Studies, Vol.53, No.2,
pp.175-204.

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must, in the first place, have already asserted the existence of it.25 Effectively, if
this argument is not error, then either Lewis’s modal language fails or
contradictions are permissible in his restrictions on modality.
It shall be noted that, in this section, Lewes’s modal realism has been examined
by conditional. And yet, it has neither justified nor falsified his modal realism.
4. The Interplay between The Epistemology and The Metaphysics
Given Lewis’s understanding and restrictions on the modal notions and his thesis
on modal realism, this section will proceed to the investigation on whether his
epistemological and metaphysical restrictions are always compatible with each
other and whether this may commit to any theoretical defect.
In details, it will investigate, on the one hand, whether it always makes sense to
suppose that Lewis’s epistemological restrictions supervene his metaphysical
restrictions, and on the other hand, whether it is always appropriate to maintain
that Lewis’s metaphysical restrictions supervene his epistemological restrictions.
4.1 The Supervenience of Epistemological Modality on Metaphysical
Modality
Given Lewis’s definitions on modality, purely speaking, when his epistemological
restrictions supervene his metaphysical restrictions, it means that individuals
can know whatever is true according to their systems of metaphysics and their
systems of logics when it is said to be possible. And yet, whether the
correspondent systems of metaphysics and that of logics are true depends
essentially on the epistemic accessibility of the correspondent worlds. Likewise,
accordingly, this supervenience also means that individuals can believe what are
supported by their recurrent states and their belief-desire psychology, which is
ultimately dependent on the doxastic accessibility of the correspondent worlds,
when it is claimed to be possible.
25 Bertrand Russell (1905), “On Denoting", Mind, New Series, Vol.14, No.56, pp.479–493.

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However, it is not clear whether Lewis presupposes conceivability to be the
sufficient condition of these accessibilities. The notion of conceivability can be,
somehow, considered as involving the ability of perceiving and that of imagining,
by which individuals have acquaintances with relative objects in certain ways. So,
it is not obvious whether Lewis presupposes that what individuals can know is
essentially conceivable, perceivable, and imaginable to them. Also, it is not clear
whether Lewis presupposes that what individuals can believe or desire are
essentially and conceivable, perceivable, and imaginable to them.
On the one hand, if he does presuppose it, then it raises some puzzles to which
may cause an intolerable defect on Lewis’s theory.
The first puzzle can be shown by an instance. To begin, Lewis’s modal language
shall be clarified. For a statement to be known possible by individuals, the
statement is essentially true at some possible worlds at which the metaphysics
and logics designate a truth based on the epistemic accessibilities of the
individuals and their conceivability of the statement. Also, for a statement to be
believed possible by individuals, the statement is essentially true at some
possible worlds at which it is supported by the doxastic accessibilities of the
individuals and by their conceivability of the statement.
So, for instance, if an individual can, for all he knows, conceive a statement about
the non-existences of possible worlds, which is true according to the anti-realism
of possible worlds, then, according to Lewis’ modal language, the statement is
true at some possible worlds at which these possible worlds does not exist.
Accordingly, this situation asserts the non-existences of possible worlds to the
individual and yet accepts the existences of the possible worlds at which the
statement is true. And yet, it shall be noted that it is a puzzle only to those who
consider contradiction is not metaphysically and logically acceptable. A
statement about the non-existences of impossible worlds that an individual can,
for all he knows, conceive, in a similar situation, is no better; surprisingly, being
expressed in Lewis’s modal language, it means that there are impossible worlds
and these impossible worlds do not exist. It is no better because the statement
asserts the existences of the impossible worlds and denies the existences of these
impossible worlds as being claimed in the statement. And also, it is a puzzle

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merely to those who consider contradiction is not permissible in metaphysics
and logics.
The similar situations happen to individuals who can, for all they believe, or
desire, to conceive such statements, namely the non-existences of possible
worlds, and the non-existences of impossible worlds. And then, incompatible
existential quantifiers will be attributed to these worlds. These situations can
happen because Lewis’s modal language permits paraphrases between the
modal notions and the realities of that if they share the same semantic value.
These are the puzzles, however, merely to those who consider contradiction is
prohibited in their system of metaphysics and that of logics.
The second puzzle is about Lewis’s account of realism. An interpretation about
Lewis’s project in this sort of supervenience is that he gives an account on
realism by appealing to the notion of modality, and then explained this notion of
modality not only by metaphysical and logical possibilities but also by epistemic
and doxastic accessibility, which may presuppose conceivability. The puzzle
arises, according to Chalmers, when the epistemological accessibility does not
entail the metaphysical possibility even if the former accessibility supervenes the
latter possibility.26 For, as indicated by Yablo, this supervenience entails merely
that the metaphysical possibility cannot exists without the epistemological
accessibility. But, it does not entail that the epistemological accessibility cannot
exist without the metaphysical possibility.27 Therefore, if it is so, Lewis’s modal
realism will not be obviously supported by the abstraction from the ordinary
language although he can still presuppose this metaphysical thesis on modal
realism.
On the other hand, if he does not presuppose it, then it is undetermined on how
those, which are knowable, believable, or desirable, can be acquainted with an
individual. And it is also undetermined on what grants this accessibility to justify
these possible worlds if this notion of conceivability is not involved.
26 David Chalmers (2002), “Does Conceivability Entails Possibility?”, ed. by Tamar Gendler and
John Hawthorne (2002), “Conceivability and Possibility”, Oxford University Press, pp.145-200.
27 Stephen Yablo (2004), “Is Conceivability a Guide to Possibility?”, ed. by Stephen Yablo (2008),
“Thoughts: Papers on Mind, Meaning, and Modality”, Oxford University Press, pp.39-78.

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Therefore, the puzzle about this epistemological supervenience over Lewis’s
metaphysical restrictions rests merely on his understanding of the ways that
individuals can get acquaintances with objects. However, whether Lewis
presupposes conceivability to be the sufficient conditions to the knowledge and
the belief-desire psychology of individuals or not, he seemingly have to overcome
several difficulties casting on his theory. If he presupposes it, then he has to grant
radical, perhaps indefinite, changes in logics according to different bases of
knowledge and different belief-desire systems. And also, his abstraction from
ordinary language may not be as obvious evidential in sustaining his thesis on
modal realism. If he does not presuppose it, then he has to exhibit for which
reason individuals can know, belief, and desire, without involving the notion of
conceiving, that of perceiving, and that of imagining. In other words, he has to
show how can these accessibilities be manifested without the notion of
conceivability.
4.2 The Supervenience of Metaphysical Modality on Epistemological
Modality
Following Lewis’s view, if his metaphysical restrictions supervene his
epistemological restrictions, then there must be some universal rules governing
of which all individuals can know or belief only within the region of these rules.
Otherwise, individuals can whimsically know or believe according their own
epistemological interests where it has been discussed in the pervious section.
And, if an individual can conceive only whatever these universal rules allow, then
these rules shall rather be universal laws since they offer not tolerable guidance
but forceful imperatives, which prohibit any violation to them.
However, this characterization hints a paradox about what these laws shall be.
There are two routes to go. Either these laws are fixed, functioning as logical
truth, or these laws are flexible, having been ascribed with some semantic values.
On the one hand, if these laws are fixed, then, as argued in the pervious section
by which the characterizations of metaphysical and logical restrictions are given,
it comes to disputes on which particular laws can be taken universally and still

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unshakeable. But if these disputes are found and has not been settled, then it is
unclear about which laws entail the universal truth. Moreover, most importantly,
these disputes indicate that the metaphysical supervenience on epistemological
restrictions fails if conceivability is presupposed in knowledge and belief-desire
psychology. For, in this case, individuals can conceive, perceive, or imagine
violations to the laws in which the laws initially forbid. Furthermore, with same
importance, even if conceivability is not presupposed in this accessibility, it is
still unclear for which reason that these disputes are found and has not been
settled.
On the other hand, however, it seems contradictory to say that these laws are
flexible. It is not only because these laws, which govern Lewis’s epistemological
restrictions, shall be unified to prevent violations to them, but also because it
entails an epistemological supervenience on metaphysical restrictions but not
vice versa. And, it circularly brings us back to the pervious discussion on Lewis’s
metaphysical and logical restrictions.
Therefore, no matter the metaphysical and logical laws are unified or flexible,
Lewis seemingly has to confront several challenges. If these laws are ultimately
taken for granted, then Lewis has to provide more reasons for those
metaphysical and logical disputes to sustain his account. If these laws are
flexible, however, then Lewis seemingly has to deny this metaphysical
supervenience over his epistemological restrictions.
5. Conclusion
This essay has explained Lewis’s project in developing a theory for modality,
firstly in his understanding on possibility and impossibility; and secondly in his
thesis on the reality of possible worlds and the unreality of impossible worlds.
On the one hand, his understanding on possibility and impossibility are merely
rested on two restrictions, namely in epistemological and metaphysical. These
two restrictions are individually functioning, and they are seemingly compatible
with each other when they remain as pure conceptions. However, when the
thesis of modal realism is involved, the compatibility of these two restrictions

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has several challenges to deal with. One of the problems is how Lewis can give an
account to individuals’ acquaintances with objects. Another issue is what can
Lewes state about the metaphysical truth, laws, or rules.
On the other hand, his thesis on modal realism has been confronting to various
challenges. One of the anti-theses has argued for the unreality of possible worlds,
whereas another anti-thesis has argued for the reality of impossible worlds.
However, whether these arguments success depends on which accounts can
provide a better explanation to the notion of modality. And it is, so far as the
instrumental rationality in this essay can reach, undetermined.