Possible worlds and modal reasoning have made "counterfactual" arguments extremely popular in current philosophy. Possible worlds, especially the idea of "nearby worlds" that differ only slightly from the actual world, are used to examine the validity of modal notions such as necessity and contingency, possibility and impossibility, truth and falsity.

Information philosophy can quantify over the information in different possible worlds and thus establish the relative possibilities or "information distance" from our actual world.

In ancient times, Lucretius commented on possible worlds. In his De Rerum Natura, he wrote in Book V,

for which of these causes holds in our world it is difficult to say for certain ; but what may be done and is done through the whole universe in the various worlds made in various ways, that is what I teach, proceeding to set forth several causes which may account for the movements of the stars throughout the whole universe; one of which, however, must be that which gives force to the movement of the signs in our world also; but which may be the true one,

(De Rerum Natura, Book V, lines 526-533

The sixteenth-century philosopher Giordano Bruno speculated about an infinite universe, with room for unlimited numbers of other stars and their own planets.

Philotheo. This is indeed what I had to add; for, having pronounced that the universe must itself be infinite because of the capacity and aptness of infinite space; on account also of the possibility and convenience of accepting the existence of innumerable worlds like to our own; it remaineth still to prove it.

I say that the universe is entirely infinite because it hath neither edge, limit, nor surfaces. But I say that the universe is not all-comprehensive infinity because each of the parts thereof that we can examine is finite and each of the innumerable worlds contained therein is finite.

There hath never been found a learned and worthy philosopher who, under any kind of pretext, hath wished to deduce from such a proposition the necessity of human action and thus to destroy free will. Thus, Plato and Aristotle among others, in postulating the necessity and immutability of God, posit no less the moral liberty and power of our free will, for they know well and understand how compatible are that necessity and that free will.

Theophilo. For the solution that you seek you must realize Firstly, that since the universe is infinite and immobile, there is no need to seek the motive power thereof, Secondly, the worlds contained therein such as earths, fires and other species of body named stars are infinite in number, and all move by the internal principle which is their own soul, as we have shewn elsewhere; wherefore it is vain to persist in seeking an extrinsic cause of their motion. Thirdly, these worlds move in the ethereal regions and are not fixed or nailed down on to any body, any more than is our earth, which is one of them. And we prove that this earth doth from innate animal instinct, circle around her own centre in diverse fashion and around the sun. These matters having been thus declared, we are not, according to our principles, obliged to demonstrate either active or passive motion arising from infinite intensive force, for the moving body, as also the motor power, is infinite; moving soul and moved body meet in a finite subject, that is, in each of the aforesaid stars which are worlds. So that the Prime Origin is not that which moveth; but itself still and immobile, it giveth the power to generate their own motion to an infinity of worlds, great and small animals placed in the vast space of the universe, each with a pattern of mobility, of motion and of other accidents, conditioned by its own nature.

(On the Infinite Universe and Worlds, First Dialogue)

The idea of many possible worlds was also proposed by Gottfried Leibniz, who famously argued that the actual world is "the best of all possible worlds." Leibniz says to Arnauld in a letter from 14 July 1686,

I think there is an infinity of possible ways in which to create the world, according to the different designs which God could form, and that each possible world depends on certain principal designs or purposes of God which are distinctive of it, that is, certain primary free decrees (conceived sub ratione possibilitatis) or certain laws of the general order of this possible universe with which they are in accord and whose concept they determine, as they do also the concepts of all the individual substances which must enter into this same universe.

(Die philosophischen Schriften., II 51/L 333)

Leibniz' notion of a substance was so complete that it could be used to deduce from it all the predicates of the subject to which this notion is attributed.

Hugh Everett was one of John Wheeler's most famous graduate students. Others included Richard Feynman. Wheeler supervised more Ph.D. theses than any other Princeton physics professor.

Everett took mathematical physics classes with Eugene Wigner, who argued that human consciousness (and perhaps some form of cosmic consciousness) was essential to the collapse of the wave function.

In his Ph.D thesis finally accepted in 1957, Everett was the inventor of the "universal wave function" and the "relative state" formulation of quantum mechanics, later known as the "many-worlds interpretation."

Everett's many-worlds interpretation of quantum mechanics is an attempt to deny the random "collapse" of the wave function and preserve determinism in quantum mechanics. Everett claims that every time an experimenter makes a quantum measurement with two possible outcomes, the entire universe splits into two new universes, each with the same material content as the original, but each with a different outcome. Everett's thesis violates the conservation of mass/energy in the most extreme way. John Bell called it "extravagant," which by Occam's Razor must be an extreme understatement.

Everett described the results of a measurment by an observer.

As soon as the observation is performed, the composite state is split into a superposition for which each element describes a different object-system state and an observer with (different) knowledge of it. Only the totality of these observer states, with their diverse knowledge, contains complete information about the original object-system state - but there is no possible communication between the observers described by these separate states. Any single observer can therefore possess knowledge only of the relative state function (relative to his state) of any systems, which is in any case all that is of any importance to him.

("The Many-Worlds Interpretation of Quantum Mechanics," pp.97-98)

In the early 1970's, the analytic language philosopher David Lewis developed the philosophical methodology known as modal realism based on the idea of many possible worlds. Lewis, who was at Princeton in philosophy, may well have been influenced by Hugh Everett, who was at Princeton in physics, and whose meeting with Einstein motivated him to restore determinism to quantum physics.

Lewis claims that

• Possible worlds exist and 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.

Modal realism implies the existence of infinitely many parallel universes, an idea similar to Hugh Everett III's many-worlds interpretation of quantum mechanics. In the information interpretation of quantum mechanics, quantum systems evolve in two ways: the first is the wave function deterministically exploring all the possibilities for interaction; the second is the particle randomly choosing one of those possibilities to become actual.

But David Lewis is a materialist and determinist who believes that our world, the actual world, could not have been otherwise. Thus, Lewis is not a true modal realist. He insists that all his possible worlds are real and actual (cf. Hegel's "the real is the actual"). In each of Lewis's possible worlds, there are no possibilities other than the completely determined actualities.
All of David Lewis's possible worlds are actual worlds!

There are no real possibilities in any of David Lewis's possible worlds. For information philosophy, possibilities are of course not real in the sense of actual, but are realized when they are actualized. Possibilities have the same existential or ontological status as ideas, especially multiple ideas in a mind that are evaluated as .alternative possibilities for action.

Possible worlds and modal reasoning made "counterfactual" arguments extremely popular in current philosophy. Possible worlds, especially the idea of "nearby worlds" that differ only slightly from the actual world, are used to examine the validity of modal notions such as necessity and contingency, possibility and impossibility, truth and falsity.

But counterfactuals and Lewis's counterpart theory are just language games, ways of talking, that analytic language philosophers and metaphysicians have found productive. They do have an ontological commitment to possibilities or ideas.

Lewis appears to have believed that the truth of his counterfactuals was a result of believing that for every non-contradictory statement there is a possible world in which that statement is true.

• True propositions are those that are true in the actual world.
• False propositions are those that are false in the actual world.
• Necessarily true propositions are those that are true in all possible worlds.
• Contingent propositions are those that are true in some possible worlds and false in others.
• Possible propositions are those that are true in at least one possible world.
• Impossible propositions are those that are true in no possible world .

In the 1960's, Saul Kripke recommended that his "possible worlds" should be regarded as "possible states (or histories) of the world," or just "counterfactual situations," or simply "ways the world might have been."

Kripke appears to endorse the idea of alternative possibilities, that things could have been otherwise.

I will say something briefly about 'possible worlds'. (I hope to elaborate elsewhere.) In the present monograph I argued against those misuses of the concept that regard possible worlds as something like distant planets, like our own surroundings but somehow existing in a different dimension, or that lead to spurious problems of 'transworld identification'. Further, if one wishes to avoid the Weltangst and philosophical confusions that many philosophers have associated with the 'worlds' terminology, I recommended that 'possible state (or history) of the world', or 'counterfactual situation' might be better... Perhaps such confusions would have been less likely but for the terminological accident that 'possible worlds' rather than 'possible states', or 'histories', of the world, or 'counterfactual situations' had been used.

(Naming and Necessity, p.15)

Kripke is not talking about different worlds, with different persons who might be identified as the same person in some respects (a 'transworld identification'). They are "nearby" worlds that describe a single individual and the alternative counterfactual situations that might have obtained.

In his discussion of the counterfactual situation that Humphrey wins the presidential election in 1968, he says.

although someone other than the U.S. President in 1970 might have been the U.S. President in 1970 (e.g., Humphrey might have), no one other than Nixon might have been Nixon...

proper names are rigid designators, although the man (Nixon) might not have been the President, it is not the case that he might not have been Nixon (though he might not have been called 'Nixon'). Those who have argued that to make sense of the notion of rigid designator, we must antecedently make sense of 'criteria of transworld identity' have precisely reversed the cart and the horse; it is because we can refer (rigidly) to Nixon, and stipulate that we are speaking of what might have happened to him (under certain circumstances), that 'transworld identifications' are unproblematic in such cases.

(Naming and Necessity, p.48)

Where Saul Kripke appears to accept the existence in this world of alternative possibilities, David Lewis was a materialist and determinist. His "modal realism" imagined "possible worlds," but denied the existence of alternative possibilities in any of his worlds. Even more important, for Lewis an individual can exist in only one world. His version of the Nixon/Humphrey counterfactual would be that the Nixon who lost the election would not be the same ("transworld") individual but a "counterpart," as similar to the "actual" Nixon as desired..

Lewis said his counterpart theory avoids what he called the problem of "accidental intrinsics," a single individual both having and not having specific properties. In Kripke's "counterfactual situations," it is the same Nixon, though he does not both win and lose, but is either the winner or the loser depending on what "happens." Lewis's counterparts are not identical. His counterpart relation is only a similarity relation, where Kripke's identity is a reflexive, symmetric, and transitive relation.

Kripke criticizes Lewis's approach...

Strictly speaking, Lewis's view is not a view of 'transworld identification'. Rather, he thinks that similarities across possible worlds determine a counterpart relation which need be neither symmetric nor transitive. The counterpart of something in another possible world is never identical with the thing itself. Thus if we say 'Humphrey might have won the election (if only he had done such-and-such), we are not talking about something that might have happened to Humphrey but to someone else, a "counterpart".' Probably, however, Humphrey could not care less whether someone else, no matter how much resembling him, would have been victorious in another possible world. Thus, Lewis's view seems to me even more bizarre than the usual notions of transworld identification that it replaces. The important issues, however, are common to the two views: the supposition that other possible worlds are like other dimensions of a more inclusive universe, that they can be given only by purely qualitative descriptions, and that therefore either the identity relation or the counterpart relation must be established in terms of qualitative resemblance.

Many have pointed out to me that the father of counterpart theory is probably Leibnitz. I will not go into such a historical question here. It would also be interesting to compare Lewis's views with the Wheeler-Everett interpretation of quantum mechanics. I suspect that this view of physics may suffer from philosophical problems analogous to Lewis's counterpart theory; it is certainly very similar in spirit.

(Naming and Necessity, p.45)

The Harvard cosmologist David Layzer argues from the nature of mathematical infinity that every possible "world" is realized somewhere in the physical universe.

He asks:

Do We Exist in Multiple Copies?

Are the assemblies we have been discussing "real"? Does the Strong Cosmological Principle imply that somewhere in the Universe there is a star very much like the Sun; and orbiting that star, a planet very much like the Earth; and on that planet, a person very much like you, the reader, reading a book very much like this one? Of course, such near-replicas of the Earth and its inhabitants would be very thinly distributed in space. Although I haven't made a serious estimate, I am confident that the nearest one would lie well beyond the most distant galaxy we could observe, even with infinitely sensitive instruments, Even so, the idea is unsettling, however familiar it may be to readers of science fiction.

(Cosmogenesis, pp.127-28)

Layzer commented on the connection between himself and Everett.

The interpretation of quantum theory discussed in this chapter resembles in some respects the "many-worlds" interpretation proposed by Hugh Everett in 1957. Everett, in a Ph.D. thesis supervised by John Wheeler, suggested that every measurement or measurement-like process causes the Universe to split into a vast number of "parallel universes," in each of which one possible outcome of the measurement is realized. In one set of universes, Schroedinger's cat lives; in another, it dies. Quantum theory, according to this interpretation, doesn't describe individual physical systems, as in the orthodox and instrumental interpretations; nor does it describe assemblies of physical systems, as in the interpretation based on the Strong Cosmological Principle. It describes a multitude of universes, each of which splits at every moment into a multitude of parallel universes. All these universes are equally real, but only the one we happen to be in is real to us; all the others are completely inaccessible to us.

According to the many-worlds interpretation, the probability that a measurement has a given outcome is equal to the fraction of the parallel universes in which that outcome occurs. Since probabilities are real numbers that can assume any value between zero and one, the set of parallel universes must be infinite. Every measurement or measurement-like process in every universe therefore creates an infinity of new parallel universes.

The many-worlds interpretation shares two attractive features of the interpretation based on the Strong Cosmological Principle. It avoids the paradoxes that result from the conventional assumption that quantum theory describes individual systems. And it predicts, instead of merely positing, the basic rule mentioned earlier for calculating the probabilities of experimental outcomes. [Probabilities are proportional to the number of outcomes in the assembly.]

(Cosmogenesis, pp.129-30)

In our two-stage model of free will, we might imagine the alternative possibilities for action generated by an agent in the first stage to be "possible worlds" in Kripke's sense. They are counterfactual situations, involving a single individual, alternative ways one person's world may be.

Note that Kripke's possible worlds are extremely close to one another. The quantification of information in each case shows a very small number of bits as the difference between them, especially when compared to the typical examples given in possible worlds cases. In the case of Humphrey winning the election, millions of persons must have done something different. Such worlds are hardly "nearby." For typical cases of a free decision, the possible worlds require only small differences in the mind of a single person. Kripke's worlds are simply ways that our world might be (or become).

By comparison, the possible worlds of Hugh Everett, David Lewis, and David Layzer in general may bear very little resemblance to one another. But note that they all include Layzer's solution to the problem of free will, at least in those worlds with thinking beings, because the inhabitants do not know which of all the possible worlds they are in.

It is important to note that the Everett and Lewis worlds are individually materialist and deterministic. Since Layzer discounts microscopic quantum indeterminism in a given world and locates macroscopic indeterminism as something between worlds, there appears to be no alternative possibilities within each world.

Layzer believes that his macroscopic indeterminism solves the free will problem. The human ignorance of not knowing which universe we are in introduces indeterminacy in the form of the unpredictability of our futures. If Layzer is right, the logically possible worlds of David Lewis and the many physical worlds of Hugh Everett also solve the free will problem in his sense.