Modal realism is the view, notably propounded by David Kellogg Lewis, that all possible worlds are as real as the actual world. It is based on the following tenets: possible worlds exist; possible worlds are not different in kind from the actual world; possible worlds are irreducible entities; the term actual in actual world is indexical, i.e. any subject can declare their world to be the actual one, much as they label the place they are "here" and the time they are "now".
The term possible world 
The term goes back to Leibniz's theory of possible worlds, used to analyse necessity, possibility, and similar modal notions. In short: the actual world is regarded as merely one among an infinite set of logically possible worlds, some "nearer" to the actual world and some more remote. A proposition is necessary if it is true in all possible worlds, and possible if it is true in at least one.
Main tenets of modal realism 
At the heart of David Lewis's modal realism are six central doctrines about possible worlds:
- Possible worlds exist – they are just as real as our world;
- Possible worlds are the same sort of things as our world – they differ in content, not in kind;
- Possible worlds cannot be reduced to something more basic – they are irreducible entities in their own right.
- Actuality is indexical. When we distinguish our world from other possible worlds by claiming that it alone is actual, we mean only that it is our world.
- Possible worlds are unified by the spatiotemporal interrelations of their parts; every world is spatiotemporally isolated from every other world.
- Possible worlds are causally isolated from each other.
Reasons given by Lewis 
Lewis backs modal realism for a variety of reasons. First, there doesn't seem to be a reason not to. Many abstract mathematical entities are held to exist simply because they are useful. For example, sets are useful, abstract mathematical constructs that were only conceived in the 19th century. Sets are now considered to be objects in their own right, and while this is a philosophically unintuitive idea, its usefulness in understanding the workings of mathematics makes belief in it worthwhile. The same should go for possible worlds. Since these constructs have helped us make sense of key philosophical concepts in epistemology, metaphysics, philosophy of mind, etc., their existence should be uncritically accepted on pragmatic grounds.
Lewis believes that the concept of alethic modality can be reduced to talk of real possible worlds. For example, to say "x is possible" is to say that there exists a possible world where x is true. To say "x is necessary" is to say that in all possible worlds x is true. The appeal to possible worlds provides a sort of economy with the least number of undefined primitives/axioms in our ontology.
Taking this latter point one step further, Lewis argues that modality cannot be made sense of without such a reduction. He maintains that we cannot determine that x is possible without a conception of what a real world where x holds would look like. In deciding whether it is possible for basketballs to be inside of atoms we do not simply make a linguistic determination of whether the proposition is grammatically coherent, we actually think about whether a real world would be able to sustain such a state of affairs. Thus we require a brand of modal realism if we are to use modality at all.
Details and alternatives 
Lewis himself not only claimed to take modal realism seriously (although he did regret his choice of the expression modal realism), he also insisted that his claims should be taken literally:
By what right do we call possible worlds and their inhabitants disreputable entities, unfit for philosophical services unless they can beg redemption from philosophy of language? I know of no accusation against possibles that cannot be made with equal justice against sets. Yet few philosophical consciences scruple at set theory. Sets and possibles alike make for a crowded ontology. Sets and possibles alike raise questions we have no way to answer. [...] I propose to be equally undisturbed by these equally mysterious mysteries.
How many [possible worlds] are there? In what respects do they vary, and what is common to them all? Do they obey a nontrivial law of identity of indiscernibles? Here I am at a disadvantage compared to someone who pretends as a figure of speech to believe in possible worlds, but really does not. If worlds were creatures of my imagination, I could imagine them to be any way I liked, and I could tell you all you wished to hear simply by carrying on my imaginative creation. But as I believe that there really are other worlds, I am entitled to confess that there is much about them that I do not know, and that I do not know how to find out.
While it may appear to be a simply extravagant account of modality, modal realism has proven to be historically quite resilient. Nonetheless, a number of philosophers, including Lewis himself, have produced criticisms of (what some call) "extreme realism" about possible worlds.
Lewis's own critique 
Lewis's own extended presentation of the theory (On the Plurality of Worlds, 1986) raises and then counters several lines of argument against it. That work introduces not only the theory, but its reception among philosophers. The many objections that continue to be published are typically variations on one or other of the lines that Lewis has already canvassed.
Here are some of the major categories of objection:
- Catastrophic counterintuitiveness The theory does not accord with our deepest intuitions about reality. This is sometimes called "the incredulous stare", since it lacks argumentative content, and is merely an expression of the affront that the theory represents to "common sense" philosophical and pre-philosophical orthodoxy. Lewis is concerned to support the deliverances of common sense in general: "Common sense is a settled body of theory — unsystematic folk theory — which at any rate we do believe; and I presume that we are reasonable to believe it. (Most of it.)" (1986, p. 134). But most of it is not all of it (otherwise there would be no place for philosophy at all), and Lewis finds that reasonable argument and the weight of such considerations as theoretical efficiency compel us to accept modal realism. The alternatives, he argues at length, can themselves be shown to yield conclusions offensive to our modal intuitions.
- Inflated ontology Some object that modal realism postulates vastly too many entities, compared with other theories. It is therefore, they argue, vulnerable to Occam's razor, according to which we should prefer, all things being equal, those theories that postulate the smallest number of entities. Lewis's reply is that all things are not equal, and in particular competing accounts of possible worlds themselves postulate more classes of entities, since there must be not only one real "concrete" world (the actual world), but many worlds of a different class altogether ("abstract" in some way or other).
- Too many worlds This is perhaps a variant of the previous category, but it relies on appeals to mathematical propriety rather than Occamist principles. Some argue that Lewis's principles of "worldmaking" (means by which we might establish the existence of further worlds by recombination of parts of worlds we already think exist) are too permissive. So permissive are they, in fact, that the total number of worlds must exceed what is mathematically coherent. Lewis allows that there are difficulties and subtleties to address on this front (1986, pp. 89–90). Daniel Nolan ("Recombination unbound", Philosophical Studies, 1996, vol. 84, pp. 239–262) mounts a sustained argument against certain forms of the objection; but variations on it continue to appear.
- Island universes On the version of his theory that Lewis strongly favours, each world is distinct from every other world by being spatially and temporally isolated from it. Some have objected that a world in which spatio-temporally isolated universes ("island universes") coexist is therefore not possible, by Lewis's theory (see for example Bigelow, John, and Pargetter, Robert, "Beyond the blank stare", Theoria, 1987, Vol. 53, pp. 97–114). Lewis's awareness of this difficulty discomforted him; but he could have replied that other means of distinguishing worlds may be available, or alternatively that sometimes there will inevitably be further surprising and counterintuitive consequences — beyond what we had thought we would be committed to at the start of our investigation. But this fact in itself is hardly surprising.
- Mathematical versus physical reality Another criticism levelled against modal realism, specifically applied to the mathematical expression of it, Max Tegmark's Ultimate ensemble, is that it equates mathematical reality with physical reality:
Physical existence is something that we have some experience of. We probably can't define it but, like many things we have difficulty defining, we know it when we see it. Mathematical existence is a far weaker thing, but much easier to define. Mathematical existence just means logical self-consistency: this is all that is needed for a mathematical statement to be "true". (Barrow, 2002, pp. 279–80)
A pervasive theme in Lewis's replies to the critics of modal realism is the use of tu quoque argument: your account would fail in just the same way that you claim mine would. A major heuristic virtue of Lewis's theory is that it is sufficiently definite for objections to gain some foothold; but these objections, once clearly articulated, can then be turned equally against other theories of the ontology and epistemology of possible worlds.
Stalnaker's response 
|This section requires expansion. (July 2010)|
Robert Stalnaker, while he finds some merit in Lewis's account of possible worlds finds the position to be ultimately untenable. He himself advances a more "moderate" realism about possible worlds, which he terms modal actualism (since it holds that all that exists is in fact actual, and that there are no "merely possible" entities." In particular, Stalnaker does not accept Lewis's attempt to argue on the basis of a supposed analogy with the epistemological objection to mathematical Platonism that believing in possible worlds as he (Lewis) imagines them is no less reasonable than believing in mathematical entities such as sets or functions.
Kripke's response 
|This section requires expansion. (January 2012)|
Saul Kripke described modal realism as "totally misguided', "wrong", and "objectionable". Kripke argued that possible worlds were not like distant countries out there to be discovered; rather, we stipulate what is true according to them. Kripke also criticized modal realism for its reliance on counterpart theory, which he regarded as untenable, which should surprise nobody as counterpart theory is a rival to Kripke's own possible-worlds semantics.
See also 
- David Lewis, Convention, 1968, p. 208
- David Lewis, Counterfactuals, 1973, pp. 87–88
- W.V.O. Quine, "Proportional Objects" in Ontological Relativity and Other Essays', 1969, pp.140-147
- Stalnaker (1976,1996 both reprinted in Stalnaker 2003)
- Stalnaker (1996)
- Kripke (1972)
- David Lewis, Counterfactuals, (1973 [revised printing 1986]; Blackwell & Harvard U.P.)
- David Lewis, Convention: A Philosophical Study, (1969; Harvard University Press)
- David Lewis, On the Plurality of Worlds (1986; Blackwell)
- Saul Kripke, "Identity and Necessity". (Semantics of Natural Language, D. Davidson and G. Harman [eds.], [Dordrecht: D. Reidel, 1972]
- David Armstrong, A Combinatorial Theory of Possibility (1989; Cambridge University Press)
- John D. Barrow, The Constants of Nature (2002; published by Vintage in 2003)
- Colin McGinn, "Modal Reality" (Reduction, Time, and Reality, R. Healey [ed.]; Cambridge University Press)
- Stalnaker, Robert (2003). Ways a world might be: metaphysical and anti-metaphysical essays. Oxford: Clarendon. ISBN 0-19-925149-5.
-  Andrea Sauchelli, "Concrete Possible Worlds and Counterfactual Conditionals", Synthese, 176, 3 (2010), pp. 345-56.