The concept of "possible worlds" can be sensationalised into some kind of pseudo-scientific parallel universe nonsense. Instead, a more preferable term would be counterfactual scenarios. One such work of great interest which covers counterfactual scenarios is Saul Kripke's Naming and Necessity. Like all good works, Naming and Necessity almost raises as many questions as it answers. Something lacking is a complete understanding of counterfactual scenarios and how they relate to human beings.
Let's look at some simple examples to try and understand the meaning of a counterfactual. Imagine rolling a dice. We understand that the counterfactuals are all of the possible outcomes of the dice roll. There does not need to be "phantom worlds" in which the dice "really" rolled with different values. Another important point here is the "boiling off" of irrelevancies. This "boiling off" of irrelevancies is discussed quite extensively in Human Action. As Mises says
The natural sciences too deal with past events. Every experience is an experience of something passed away; there is no experience of future happenings. But the experience to which the natural sciences owe all their success is the experience of the experiment in which the individual elements of change can be observed in isolation. The facts amassed in this way can be used for induction, a peculiar procedure of inference which has given pragmatic evidence of its expediency, although its satisfactory epistemological characterization is still an unsolved problem.
The dice roll example raises an empirical question: is there even any counterfactual to discuss? After all, is it not true that the outcome of the dice roll was determined by the initial conditions of the throw? The initial conditions here being the particular way the person holds and throws the dice. After all, it is natural laws which determine how the motion of the dice propagates. In this way, there is no such possible counterfactual, given that particular throw of the dice.
The issue with this perspective is that it does not appreciate the discussion that Mises makes. After all, since there simply is no possibility of rerunning the exact same dice-throw, at least when considered on such a micro level, then some other conception must be brought to bare i.e. the counterfactuals. The mathematical study of probability more or less exists to overcome this limitation. By taking a bulk view of a set of events where we assume the extrinsic variables are uncountable, we can postulate away these external variables and make an abstraction to a more fundamental underlying issue.
Perhaps a more enlightening example comes from the phrase "Aristotle was fond of dogs". The proper understanding of this statement is that it is true if there was a man who existed called Aristotle, who, was fond of dogs. Consider the counterfactuals. In one counterfactual, Aristotle exists, but he is not fond of dogs. Consider the counterfactual in which Aristotle does not exist. In such a counterfactual, it is not even meaningful to discuss whether Aristotle (whoever that is!) liked dogs. Another counterfactual is that "Aristotle" exists, but he is not called Aristotle. This leads onto a much broader discussion, and introduces another concept that Kripke uses extensively: the rigid designator.
How do we keep track of objects across counterfactuals?
Consider first the follow scenario. You are at a party, and you say "that man with the champagne in his glass is happy". What does this mean? Well, in the very basic level, the statement is true if you ostensibly point at a man, he has champagne in his glass, and his happy.
If "the man" has champagne in his glass but is not happy, then the sentence is false. "The man", the object, is identified, but the description of him is false.
Consider now if the intended object, "the man" does not have champagne in his glass but water. There are two variations on this sentence, one in which he is happy and one in which he is not. These two variations don't differ much really, but the thing that we want to get at the heart of is identification. We tried to identify someone by a property of them.
Now, from a social or biological standpoint the question is: am I, the speaker, able to communicate to my listener which man I mean? Even if I am false about what is in his glass, if my listener understands who I mean then I am successful, if he does not I fail. Consider though if there was champagne in his glass but my listener did not understand who I meant. While I have factually identified the man, this was not communicated to my listener. I think this scratches below the surface and reveals an important concept that I personally haven't heard many people talk about before. While some logical statements can be validated without empirical requirements, humans have a "barrier" of communication with one another. This must always be crossed by some empirical means i.e. I must generate real sounds in the real world and my listener must really observe those sounds and then interpret what they mean. I think this covers the problem well - even an unambiguously true statement may be misunderstood or misinterpreted by another person. That is not actually the subject of my inquiry here, but I think it needs to be cleared up before I am able to continue and talk about what I do want to talk about. In other words, I must clarify the philosophical point I am about to raise is not dependent on mere misinterpretation by other people.
Can we be more precise in my use of the term "barrier"? Yes, Reinach, a criminally underlooked philosopher, in his Apriori Foundations of the Civil Law, a criminally underlooked work, brings about a much more solid idea. In it, he introduces the concept of the "social act". Social acts are actions or behaviour which occur in a social context and involve multiple individuals. These acts are characterised by their intersubjective nature, that is, they are defined by involving intentions, beliefs, interactions and so on between individuals. In this context of "that man with the champagne in his glass" the social act is one of informing or communication. I, the speaker, have some knowledge in mind which I wish to impart to you, the listener. I have some gentleman in the party in mind which I want to express to you is happy. How then, do I pick out the exact man I mean from the crowd? The "truth" and "falsehood" of this statement should not come from whether the man does or does not have champagne in his glass - that is broadly irrelevant. The real question is whether the social act of communication has been successful.
The point I want to get at is as follows: while I have some definite person in mind when I form the sentence, the object, "that man", I was at the time mistaken about the status of the liquid in his glass. Does this mean I actually spoke about the man next to him, who did have water in his glass? I think the answer here is clearly no. "That man with the champagne in his glass" is a rigid and definite identifier of a particular person at a particular time in a particular counterfactual scenario when spoken, despite being false as such. If this seems odd, consider the following statement "Aristotle, the last great philosopher of antiquity". Given what I previously stated about counterfactual scenarios, imagine if he wasn't the last great philosopher of antiquity. Suppose in fact that is the case in this universe. Tomorrow, archaeologists discover manuscripts that show that there was some other great philosopher of antiquity (let's call him "Kieth"). And suppose Kieth never wrote a book called "Metaphysics" (but Aristotle did). Now, would the sentence "Aristotle, the last great philosopher, wrote a book called 'Metaphysics'" suddenly be wrong? Would this sentence now mean that Kieth wrote a book called "Metaphysics" because he was the last great philosopher of antiquity? I trust the reader understand that history would not suddenly reform itself such that Kieth did write such a book. I think it is clear that due to the fact that humans can be mistaken about something does not impair the philosophical basis of the fact that the meaning of the sentence "Aristotle, the last great philosopher, wrote a book called 'Metaphysics'" suddenly changes, or that the object of the sentence suddenly changes? I think what is more likely is the sentence would be understood in the context in which it was written.
In other words, what we a seeing here is not an epistemological shortcoming but a human shortcoming.
Kripke goes on to say what I just said but in much fewer words: even though it is not empirically true as such, it is used as a name. As Voltair said: The Holy Roman Empire is neither Holy, nor Roman nor an Empire. Are people who say "Holy Roman Empire" being hoodwinked into somehow magically referring to something else unknown to them? Or is it being linguistically used as a name despite not being true, as such.
In other words, "that man with champagne in his glass" can be thought of as a whole noun rather than a logical condition i.e. "that-man-with-champagne-in-his-glass"
As Kripke says
Philosophers have come to the opposite view through a false dilemma: they have asked, are these objects behind the bundle of qualities or is the object nothing but the bundle. Neither is the case; this is wooden, brown, in the room etc. It has all these properties and is not a thing without properties, behind them; but it should not therefore be identified with the set, or 'bundle', of its properties, or with the subset of its essential properties. Don't ask: how can I identify this in another possible world, except by its properties? I have the table in my hands, I can point to it, and when I ask whether it might have been in another room, I am talking, by definition, about it. I don't have to identify it after seeing it through a telescope
Returning to Reinach and the social acts for a moment, we see the breakthrough he covers is seeing humans as humans. In other words, the "man with the champagne in his glass" "problem" is only a problem in so far as we fail to see the humans involved as humans. Some philosophers have a habit of seeing human beings not as socially interacting instances of limited knowledge but rather as these abstract truth-statement generation machines. Indeed, many philosophers from around the same time as Reinach recognised this simple truth, for instance, as Hoppe says in Economic Science and the Austrian Method
It is true, as Kant says, that true synthetic a priori propositions are grounded in self-evident axioms and that these axioms have to be understood by reflection upon ourselves rather than being in any meaningful sense “observable.” Yet we have to go one step further. We must recognize that such necessary truths are not simply categories of our mind, but that our mind is one of acting persons. Our mental categories have to be understood as ultimately grounded in categories of action. And as soon as this is recognized, all idealistic suggestions immediately disappear. Instead, an epistemology claiming the existence of true synthetic a priori propositions becomes a realistic epistemology. Since it is understood as ultimately grounded in categories of action, the gulf between the mental and the real, outside, physical world is bridged. As categories of action, they must be mental things as much as they are characteristics of reality. For it is through actions that the mind and reality make contact.
However, for some reason, this viewpoint has somewhat faded from fashion, despite the fact that without it, rather strange and unusual descriptions of the "that man with the champagne in his glass" "problem" are given. Philosophers would do well to remember that they themselves are human.
References
Kripke, S. (1972) Naming and Necessity. Harvard University Press.
Reinach, A. (1913) Die apriorischen Grundlagen des bürgerlichen Rechtes Jahrbuch für Philosophie und phänomenologische Forschung. More recently republished as Reinach, A. (2012) The Apriori Foundations of the Civil Law, Along with the Lecture "Concerning Phenomenology" Ontos Verlag, Translated by Crosby, J. F.
von Mises, L. (1949) Human Action. Ludwig von Mises Institute.
Hoppe, H.H. (1995) Economic Science and the Austrian Method. Ludwig von Mises Institute.