Are possible worlds really ‘real’?
It depends on what one means by “real”. And that will depend on one’s underlying metaphysical assumptions about what actual existence means. My underlying metaphysical assumptions are materialistic (physical matter is the only reality and everything, including thought, feeling, mind, and will, can be explained in terms of matter and physical phenomena). So my answer to the question is – No!
My American Heritage Dictionary of the English Language (Microsoft Bookshelf 98) that says “real” means “(1-a) Being or occurring in fact or actuality; having verifiable existence. (b) True and actual; not imaginary, alleged, or ideal. (c) Of or founded on practical matters and concerns. (6) Philosophy. Existing objectively in the world regardless of subjectivity or conventions of thought or language.”
The word “real”, when employed as a general descriptor not limited to a specific field of discourse, I thus understand as referring to something that actually exists in this materialistic reality, and is to be contrasted with things imaginary and non-existent in this reality. Therefore, if possible worlds did in fact exist objectively as true and actual, not imaginary, alleged, or ideal, they would have verifiable existence. Since there is no evidence extant that such “parallel universes” do in fact exist, then they are not “real” by this definition of “real”. Furthermore, if in fact “parallel universes” did actually exist, they would not constitute the philosopher’s notion of “possible worlds”. Actually existing worlds, like this one, cannot be proved to be logically consistent. Therefore, they cannot be proved to constitute the philosopher’s notion of logically possible worlds. A philosopher who maintains that “possible worlds” actually exist, would have to assume that they are logically consistent, or would have to relax the usually requirement that “possible worlds” are necessarily logically consistent.
Possible worlds, then, are conceptual or imaginary constructs like Unicorns or Centaurs or circles or squares.
Any thinker is free to posit the existence of any imaginary construction, with no limits on the creativity of the imagination. Positing the existence of something does not constitute proof of the existence of that thing. Therefore positing the existence of a possible world, is not evidence or proof of the existence of possible worlds. And what we say about some possible world is only true or false to the extent that the statement is consistent with the imagined nature of the particular possible world under discussion. (Or all possible worlds, if that is the topic of the statement.)
All the talk about possible worlds has led me to ponder an associated question. Since some users of possible worlds regard them as “real” in some sense, just what does constitute a “possible world” in such an ontology? First, let’s deal with the question “Just how many possible worlds are there?”
That is surely a fair question: if we cannot actually count possible worlds, we can at least form the conception of how they would be counted. Suppose we regard “the place wherein could exist all things that might possibly exist” (aka “The Universe”) as an n-dimensional set of points. “N” would, of course, have to be an infinite number, since there is no logical limit on the number of spatio-temporal dimensions that “reality” could exhibit. Along any one particular dimension, of course, there are an infinite number of points. So in an n-dimensional universe there are “infinity to the power of infinity” number of spatio-temporal points. Technically this trans-finite number is called “Aleph-1”. Curiously enough, n-dimensional space has the same “number” of points as one-dimensional space (a line), or any finite interval of one-dimensional space (a line segment), as was first recognized by Georg Cantor. So it makes no difference whether any particular dimension (or combination of dimensions) is finite or infinite in extent, bounded or unbounded, closed or unclosed. In other words, the geometry of any particular dimension is irrelevant to our transfinite mathematical calculations.
Suppose, as the next step, we adopt the attitude of Quantum Physics, and treat all forces that might exist as manifested by particles. We can then treat all the logically possible particles of force the same way we do all the logically possible particles of matter. Since there is no logical limit to the number of kinds of particles that might logically exist, we must treat the number of possible kinds of particles as infinite as well. To complicate things, any given particle might assume any of an infinity of logically possible “quantum states”. Furthermore, any given particle in a particular quantum state might logically possess any of an infinite number of logically possible energy levels. Therefore we can regard the number of discrete particle configurations as “(infinity to the power of infinity) to the power of infinity”, or Aleph-1 logically possible particle configurations. (Alpeh-1 to the power of infinity is still Aleph-1. Transfinite mathematics is more than curious, it is downright odd.)
Putting these two suppositions together gives us – at each of the Aleph-1 points in the universe there might exist any one of Aleph-1 particle configurations. This gives us “aleph-1 to the power of aleph-1” possible configurations of “The Universe”. (And, oddly enough, this even larger number of possibilities is also Aleph-1. Trans-finite mathematics is very odd indeed.) So this view would suggest that there are Aleph-1 logically possible “mathematically describable worlds”. (An unanswered question worth pondering is whether or not there could be a “logically possible world” that is not among the aleph-1 “mathematically describable worlds”. Personally, I don’t see how, but I suppose it might be possible. However, alpeh-1 is large enough to serve my purposes here, so I will ignore any potential left-overs.)
Yet each configuration presented by this analysis is timeless. Each of the aleph-1 particular configurations of particles in an n-dimensional universe is static — it does not change. Time is one (or possibly infinitely many) of the dimensions of the n-dimensional universe, and to specify a particular particle’s n-dimensional position is to specify also its specific time. Now is this the image that the possible worlds theorist has when he talks about “logically possible worlds”? Certainly it cannot be if one considers that there might be a logically possible world in which Pontius Pilot really pondered the philosophical import of his question “What is Time?” Or if I can consider that there is a logically possible world in which I tool down London Road in James Bond’s Aston Martin. These images involve processes — things that change in time. So it would seem that the possible worlds theorist’s “logically possible world” is not a static thing, but a dynamic succession of “images” from the aleph-1 catalogue of “mathematically describable worlds”. I suppose this could be thought of as “seeing reality” like a movie film — a rapid succession of individually static images. (Possibly, I suppose, an infinitely rapid sequence of an infinite number of successive “images”.) And the number of ways in which the aleph-1 separate images of “mathematically describable worlds” can be arranged in sequences is called “Aleph-2”. (The possibly infinite number of time-like dimensions that would be “discarded” in creating the temporal sequence is not relevant to the trans-finite mathematics involved.)
So we can, at least as a first approximation, treat the set of all “logically possible worlds” as containing Aleph-2 separate “worlds”. But this enormous set contains aleph-1 many “logically possible worlds” in which I am at one temporal instant sitting at my computer, and in the next temporal instant am spread thinly across the universe with each constituent particle in a widely separate position. And it contains aleph-1 many “logically possible worlds” in which the dropped and shattered glass reassembles itself and jumps back into the hand that dropped it. It is obvious that the Vast majority of “logically possible worlds” in this set of Aleph-2 possibilities would not be recognizable as “meaningful possible worlds”.
(I borrow here the terminology employed by Dennett in “Darwin’s Dangerous Idea”. You can think of the concept of a “Vast majority” [capitalized V] as what is left after a “Vanishingly small” [capitalized V] subset is removed from the whole. And that “Vanishingly small” subset is infinitesimally small — a fraction smaller than one divided by infinity, one divided by aleph-1, or one divided by aleph-2, depending on context.)
The Vast majority of the aleph-2 mathematically describable possible worlds would have spatial and temporal dimensionality different from our own. The Vast majority of the remainder would not contain anything remotely resembling our current world. The Vast majority of the little that’s left would not contain anything that would be remotely recognizable as germane to the question of whether “P” or “not-P” or the question of whether “if counter-factually P then Q”. And by no means finally, the Vast majority of the Very Vanishingly small residual subset would not behave across time in any way remotely recognizable as “normal”. If any member of the set of Aleph-2 “logically possible worlds” is acceptable to the possible worlds theorist as a possible contender for the resolution of “P or not-P” or “if P then Q”, then every possible proposition must be counted as undecidable — as having an indeterminate truth value. For within the set of Aleph-2 possibilities are logically possible worlds in which any evidence we have that “P” ( or that “not-P”), no matter what “P” might be, could have appeared “as if by magic”, “out of thin air”, or exist only in your memory, or was manufactured by an evil conspiracy for the sole purpose of confusing you, and thus really has no meaningful bearing on whether “P” or “not-P” or “if counter-factually P then Q” for any and every possible “P” (and “Q”). Including such propositions “I am a brain in a vat”, or “I exist only as an idea in the mind of God”, or “The Universe was created in toto, by the white mice, just 15 seconds ago — complete with all of its evidence to the contrary.”
Consider the counter-factual proposition “the Holocaust never happened”. Within that set of alpeh-2 logically possible worlds there is at least one in which the Holocaust never happened, and all of the evidence that exists “Today” that it did happen was manufactured by “The Jewish Conspiracy”. Even personal experience doesn’t count, since the relevant memories could also have been manufactured and implanted in the minds of the alleged witnesses. Or the alleged witnesses could actually be part of the conspiracy. Does the possible worlds theorist really want to maintain that the proposition “the Holocaust never happened” is undecidable? Surely this is not the notion that the possible worlds theorist maintains. It is obvious, therefore, that despite the trans-finite enumeration of “logically possible worlds”, what the possible worlds theorist actually has in mind when contemplating the “logically possible worlds” relevant to the resolution of “P or not-P” or “if P then Q” is that Very Very Vanishingly small subset of aleph-2 possibilities that are consistent with what we might refer to as the “normally expected behaviour of reality”.
In all cases of considering the possible worlds that might play a part in resolving any question of “P or not-P” or “if P then Q”, the possible worlds theorist is not considering all Aleph-2 members of the set of “logically possible worlds”. The possible worlds theorist is considering only that Very Very Vanishingly small subset that are “as like this actual world as possible”, except that either “P” (and “Q”) or “not-P”.
The question I asked initially was — just what constitutes a “possible world” in the possible worlds theorist’s scheme of things. It now becomes clear that a more sophisticated interpretation of this question is — just what is the possible worlds theorist’s conception of the “normally expected behaviour of reality”. What does it mean for one of the aleph-2 logically possible worlds to be “as like this current world as possible” and still allow that either “P” (and “Q”) or “not-P”? Surely the possible worlds theorist, when in discussions about the nature of “truth”, or the resolution of counter-factual conditional, must include in his notion of “normally expected behaviour of reality” the constraint that any candidate “logically possible world” will be consistent with the best understanding we have of the physical laws that appear to govern the world we experience. Otherwise, one can argue against the possible worlds theorist by claiming that whatever the “evidence” says, the “evidence” appeared by magic, and does not mean what the possible worlds theorist wants it to mean. And if the possible worlds theorist is not concerned by this challenge, he has reduced “truth” to “whatever I choose to believe”. And I don’t think anyone but a Solipsist would want to maintain that position.
Which leaves the one remaining question — how many “meaningful possible worlds” are left out of the aleph-2 “logically possible worlds” once we eliminate those that are not “as like this actual world as possible”? And does that Really Vanishingly small remaining sub-set actually include worlds where “P” (and “Q”) and worlds where “not-P”? It is obvious that for some propositions “P”, the physical laws that appear to govern the world we experience do not allow acceptable alternative candidates of “logically possible worlds” that are both “as like this current world as possible” and permit both “P” (and “Q”) and “not-P”. If I drop a rock off the tower in Pisa, the rock will hit the ground unless interfered with by magic. Once the pool queue is struck, the billiard balls will proceed in a deterministic fashion, and you can tell which single history each traced if you come in before they stop rolling — unless you permit magic. And it is physically impossible, again unless you permit magic, (given the understanding we have of the physical laws that appear to govern the world we experience) for there not to be a star with a planet in a galaxy beyond our visible horizon.
Being a determinist, and a realist, it is my argument that there is in fact only one single “meaningful possible world” that is “as like this actual world as possible” — one that does not require “magic” to realize one of “P” (and “Q”) or “not-P”. I would argue that without becoming inconsistent with the physical laws that govern the actual world, in other words without allowing “magic”, there is only one single “logically possible world” that can be considered as a “meaningful possible world”. And that single remaining member of the set of aleph-2 logically possible worlds, is the actual world. In that single actual world – past, present, or future – either “P” (and “Q”) or “not-P”.
So my answer to the possible worlds theorist who maintains that “an undecidable proposition would be true in some possible worlds, and false in other possible worlds, but there is no answer in reality to the question which of all these possible worlds is the actual world” is — it is simply not the case that there is both an acceptable possible world where “P” and an acceptable possible world where “not-P”, as long as “magic” is excluded. And my answer to the possible worlds theorist who maintains that “a counter-factual conditional is true if and only if there is a logically possible world wherein both P and Q” is — it is simply not the case that there is an acceptable possible world wherein either P or Q, if P or Q are inconsistent with the known laws of nature, as long as “magic” is excluded.
And the elimination of “magic” is the answer in reality to the question of which possible world is the actual possible world. Even though there might be a logically possible world in which Nero did not fiddle while Rome burned (assuming he did), that possible world could not have become this current world without violating the physical laws that govern this current world. Even though there might be a possible world in which my nephew wins the lottery and tools down London Road in a brand new silver Aston Martin, that possible world will never be the actual world if there is no way that the current world could become that one without violating the physical laws that govern this current world. (Note that the mechanics of lottery draws are not truly random. They are sufficiently chaotic to be unpredictable, but they are none the less deterministic.)
Past, present or future – if “P”, then there is no logically possible world that is “as like this current world as possible” and still permits “not-P”without resorting to “magical” violations of the laws that govern our world. For a realist to maintain that “P” is to maintain that “not-P” is inconsistent with the laws that govern the world. (And vice versa for “not-P”, of course.) To maintain otherwise, as does the possible worlds theorist, is to maintain that the laws of physics that govern reality are radically indeterminate to an extent that challenges the efforts of science and the expectations that govern our choices of behaviour. Or is to maintain that “magic” is an acceptable means of allowing the existence of an actually counter-factual “P”. And if “magic” is allowed, with no determinate constraints on the effects of that magic, then all of the Aleph-2 logically possible worlds are equally feasible alternatives. (If “magic” is allowed, then there is no effective meaning to the notion of the “closeness” of one possible world to another.)
So I would wonder how the possible worlds theorist marries his notions of “logically possible worlds” and the indeterminateness of truth values with the expectations he normally has about alarm clocks and getting up in the morning. I don’t think that the possible worlds theorist would dispute the evaluation that the anti-realist notion of “truth” and the actuality of “logically possible worlds” is inconsistent with the common sense notions on these matters. I think, therefore, that the onus should be on the possible worlds theorist to demonstrate that both “P” and “not-P” is consistent with the physical laws that govern the world before claiming that the question is undecidable, or that the truth-value of “P” is indeterminate.
