Extended modal realism

Modal realism is the view that the actual and the non-actual are equally real. It contrasts with actualism, the view that fundamental reality is restricted to actuality. Extended modal realism, as developed by Takashi Yagisawa, differs from other versions of modal realism, such as David Lewis' views, in several important aspects. Possible worlds are conceived as points or indices of the modal dimension rather than as isolated space-time structures. Regular objects are extended not only in the spatial and the temporal dimensions but also in the modal dimension: some of their parts belong to non-actual worlds. Among these non-actual worlds within the modal dimension are not just possible worlds but also impossible worlds. There is only one universe encompassing everything that is real in the widest sense: the actual, the possible and the impossible.
Introduction.
Modal statements, like "Hillary Clinton could have won the 2016 US election" or "it is necessary that cows are animals", are part of everyday language. Common-sense tells us that some modal statements are true while others are false. "Modal metaphysics" is interested in what determines the truth or falsehood of modal statements, i.e. in what the aspects of reality responsible for this look like. Actualists maintain that reality is actual at its most fundamental level and that possibility somehow depends on or is reducible to actuality. Modal realists, by contrast, state that possibility is an irreducible aspect of reality besides actuality. The most well-known version of modal realism is due to David Lewis, who holds that a plurality of possible worlds exist beside the actual world. Every object just belongs to one world but it has counterparts in other worlds. The truth of falsehood of modal statements depends not just on the actual world but also on these other worlds. For example, it is true that "Hillary Clinton could have won the 2016 US election" because there is a possible world in which "a counterpart of Hillary Clinton won the 2016 US election". Extended modal realism differs from Lewis' views in that it states that objects have real parts belonging to other worlds, not just counterparts, and that there are also impossible worlds besides the possible worlds.
Worlds as modal indices.
A possible world is a way things could have been. Lewis sees possible worlds as concrete entities extended in space and time. They are complex entities mereologically composed of possible individuals. Extended modal realism, on the other hand, sees worlds as mere indices of the modal dimension at which regular individuals exist. This approach is best explained in analogy to the other two dimensions of the universe, with which we are more familiar: space and time. Space is commonly pictured as made up of many regions. Spatially extended things, like chairs, trees or ourselves, are composed of different parts that exist at different regions. Often the different parts carry different qualities: e.g. the tree is green on the top and brown on the bottom. This could be expressed by saying that the green color is located at some spatial indices occupied by the tree while the brown color is located at other spatial indices occupied by the tree. Four-dimensionalism extends these ideas to the temporal dimension. The tree as a whole can be pictured as a space-time worm: it is made up of various parts located at different spatial and temporal indices. So for example, if we move the temporal index from summer to autumn, the color occupying the top part of the tree changes from green to yellow and red as the leaves change their color. Extended modal realism applies this approach also to modality. Regular objects are extended not just in space and time but also in the modal dimension. Another way to express these ideas is to say that space, time and modality are "relativizers" of "so-sein", of being in a certain way.
Actuality, possibility and impossibility.
The modal stage of the tree in the actual world is nowhere violet but it has violet parts at other modal indices. The tree as a whole is a modally extended entity encompassing not just the actual tree but also all its modal parts belonging to other worlds. Like in Lewis's modal realism, the term "actual" just has an indexical meaning: it refers to the modal index of the speaker. "Actual" is thus analogous to the spatial "here" and the temporal "now".
Yagisawa holds that while the notion of "a world" is simple, being a modal index, the notion of a possible world is composite: it is a world that is possible. Possibility can be understood in various ways: There is logical possibility, metaphysical possibility, physical possibility, etc. A world is possible if it doesn't violate the laws of the corresponding type of possibility. For example, a world is logically possible if it obeys the laws of logic or physically possible if it obeys the laws of nature. Worlds that don't obey these laws are impossible worlds. There are different types of impossibility corresponding to the different types of possibility. Impossible worlds are real in the same sense as possible worlds are real: they are modal indices. The truths of modal statements about objects are grounded in their modal stages in other worlds. It "is possible" that the tree is violet because it has a modal stage at a possible world in which it "is" violet. If it "is impossible" that the tree is both alive and dead at the same time then it has a modal stage at an impossible world in which it "is" both alive and dead at the same time.
The universe, reality and existence.
The universe, according to extended modal realism, is the vast object extending in the dimensions of space, time and modality. The different possible and impossible worlds are just modal stages of the universe. The universe encompasses everything that is real in the widest sense. For Yagisawa there is a difference between reality and existence. Reality is a primitive notion while existence is relative to a domain. For example, fictional characters like Pegasus are real even though they don't exist in the actual world.
Criticism.
Extended modal realism is subject to most of the criticism direct at modal realism in general. This includes objections to the lack of ontological parsimony and epistemological doubts that beliefs about possible worlds can be justified. But other critiques have been directed specifically at extended modal realism. As John Divers points out, the term "reality" may be useless if we allow possible as well as impossible objects into our ontology. The reason is that it seems to follow that every sentence of the form "_ is real" is true. This consequence would turn metaphysics as the science of reality into a trivial enterprise.
Other critics have pointed out that a commitment to logically impossible worlds leads to contradictions even in possible worlds, including the actual world. This can be seen by considering a logically impossible world in which it is the case that both a proposition and its negation are true. As we reason about this impossible world, from within the actual world, we may reach a conclusion in which we both affirm and deny a proposition about this impossible world. The result would be that the actual world is also an impossible world. Yagisawa suggests that this conclusion is based on a false inference that can be avoided by implementing a strict usage of a modally tensed language.