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Modal Realism is an idea associated with David Lewis, who wrote its canonical text, On the Plurality of Worlds. A modal realist believes that the possible worlds we speak of when, for example, talking about semantics for modal logics are actual. In Lewis’ words: “I advocate a thesis of plurality of worlds, or modal realism, which holds that our world is but one world among many."

=Modal Realism= As Lewis sees it, a possible world has parts, namely possible individuals; and a world is simply the mereological sum of of its possible individuals.

Worlds are Spatiotemporally Isolated
Two things are "worldmates" when there is any distance, either temporal or spatial, between them. If such a distance exists at all, then those things are worldmates, and part of just one world.

We can also say those things are spatiotemporally related; Lewis claims that:


 * "A world is unified, then, by the spatiotemporal relations of its parts. There are no spatiotemporal relations across the boundary between one world and another; but no matter how we draw a boundary within a world, there will be spatiotemporal relations across it." (1986, p.71)

Worlds are Causally Isolated
Just as there can be no trans-world spatiotemporal relations, there can be no trans-world causation. Lewis argues that if we understand counterfactuals (explained below) in terms of possible worlds, then we have no analysis of trans-world causation that makes sense.

Because there can be no causation between worlds, Lewis argues that we cannot observe other worlds. He uses the example of a telescope that could possibly view other worlds. Gathering informatin is a causal process; the telescope could not be in a causal relationship with the world one was trying to observe, so it is not possible.

Worlds are Concrete
Lewis stipulates that worlds are concrete, rather than abstract, in order to avoid entailing our being abstract.

Worlds are spatiotemporally and causally isolated from one another, so when we talk about other worlds we stand in no spatiotemporal or causal relation to them. But that does not make us abstract. You might say we are concrete at this world and they are abstract; but from their world they are concrete and we are abstract. Lewis does not think this is a good response, and instead proposes that all worlds are concrete.

Principle of Recombination
Lewis needs a way to express the totality of worlds that exist. To that end, he offers the Principle of Recombination:


 * "I require a principle of recombination according to which patching together parts of different possible worlds yields another possible world." (1986, p. 88)

A proviso must be added, according to Lewis, which says that any such recombinations are legitimate, size and shape permitting. This deflects arguments about recombinations yielding a set of worlds larger than there is (which is discussed in section:#).

Actual is Indexical
Finally, Lewis argues that when we say our world is the "actual" world, we do not mean that our world is real and others fictional. Rather, actual just picks out our world. We could have been members of some other world, or our world could easily not have been the way it has; but when we say actual, we're just picking out the world which closest matches our world, which is of course our world.

=Benefits of Modal Realism= Lewis claims that we gain some benefits by accepting his ontology with a plurality of worlds. First, modal realism allows us to clarify the way we speak about certain portions of modal logic. Also, possible worlds make sense of counterfactuals as well as the notion that a theory can be closer to the truth.

Modal Realism and Modal Logic
A common way of speaking about the relational structures that define the semantics for modal logic is to call the set of points 'worlds.'

Thus, we 'read' the modal operators as follows:


 * $$\Diamond$$$$\phi$$ is read "Possibly $$\phi$$ if and only if, for some world W, $$\phi$$"


 * $$\Box$$$$\phi$$ is read "Necessarily $$\phi$$ if and only if, at every world, $$\phi$$"

Lewis argues that the modal operators can be thought of similarly to the quantifiers $$\exists$$ and $$\forall$$; the modal operators are said to quantify over possible worlds. From the above two statements we can see that $$\Diamond$$ functions like $$\exists$$, and $$\Box$$ like $$\forall$$.

Modal Realism also allows us to make sense of many interesting metalogical results. According to Lewis, "where we need possible worlds...is in applying the results of these metalogical investigations." (1986, p. 17) Lewis points to some of the axioms of normal modal logics, such as T, B, and 4. Each of these axioms places a restriction on the accessiblity relation between the worlds in its frame. Although restricting the quantification of the modal operators does allow for the axiom's acceptance into systems of modal logic, Lewis contends that we don't know anything new by virtue of knowing, for example, that the 4 axiom is only valid on transitive frames.

However, with modal realism and talk of possible worlds, Lewis says we have a place to look for illumination about the modal axioms. Lewis provides the following example:

It is nomologically necessary that friction produces heat because at every world nomologically accessible from ours - every world that obeys the laws of ours - friction produces heat.

Rather than asking questions about iterated nomological necessity such as:


 * "Is $$\Box$$$$\phi$$→$$\Box$$$$\Box$$$$\phi$$ valid at nomologically accessible worlds?"

We can, with talk of possilbe worlds, ask instead:


 * "Is it the case that if world w obeys the rules of world u, and world u obeys the laws of world v, that world v obeys the laws of world w?"

Which Lewis contends is a much more interesting question.

Counterfactuals
A counterfactual conditional is a statement of the form:


 * "If $$\phi$$ were true, then $$\psi$$"

Lewis claims that such statements make little sense without possible worlds. Such statements are invitations to think about what goes on in a counterfactual situation, which for Lewis means what is going on at some possible world. Lewis claims that counterfactuals deal with what happens at the set of possible worlds defined by the antecedent, factual background, and contextual influences.

Taking our example above, Lewis would explain the semantics for that counterfactual in the following way:


 * There are all the $$\phi$$-worlds, some of which are closer to our world than others. If some ($$\phi$$ $$\wedge$$ $$\psi$$)-world is closer to our world than any ($$\phi$$ $$\wedge$$ $$\neg$$$$\psi$$)-world, then the counterfactual is true.

Therefore, possible worlds serve as a frame of reference that allows us to characterize our world.

The careful reader may wonder why we need a semantics for counterfactuals. Lewis responds by demonstrating the entanglement of counterfactuals with causation:


 * Let us imagine that two distinct events occur, $$\phi$$ and $$\psi$$. If $$\phi$$ had not happened, $$\psi$$ would not have either.

Lewis says that if one event depends counterfactually on another in this way, then $$\phi$$ causally depends on $$\psi$$. Lewis admits that this is not a complete analysis, and that there are many counter-arguments where the counterfactual would not imply causation. However, he urges the reader to imagine the many events that could be explained in this way; at minimum, Lewis claims, he has demonstrated that causation and counterfactuals are in some way dependent upon each other.

Scientific Theories
Possible worlds also allow us to explain why false theories are still closer to the truth than older theories. Lewis begins by stating:


 * "A theory is close to the truth to the extent that our world resembles some world where that theory is exactly true. A true theory is closest to teh truth, becuase our world is a world where that theory is true. As for false theories, the ones that can come true in way that involve little dissimilarity to the world as it really is are thereby closer to the truth than those that cannot." (1986, p. 24)

Lewis also points out that scientific formulas depend on certain fictions to be able to be true; for example, the fiction of the frictionless surface. We use a frictionless plane to simulate conditions in the real world--on slick ice, however, it is much closer than on a dry bed of sand--and get an answer that is close to the truth. The degree to which our fiction approximates the actual conditions is how much closer it is to the truth. As Lewis explains:


 * "An idealized theory is a theory known to be false at our world, but true at worlds thought to be close to ours. The frictionless plane, the ideal gases, the ideally rational belief systems - one and all, these are things that exist as parts of other worlds than our own." (1986, p. 27)

Lewis argues that possible worlds permit the modal realist to give an analysis of what we mean when we say that one scientific theory is closer to the truth than another.