Copyright © Norman Swartz 1989
http://www.sfu.ca/~swartz/senses_of_world.htm
This revision: January 2, 1998
Department of Philosophy
Simon Fraser University

Supplementary notes for

Possible Worlds

The senses of "world"

In ordinary speech, the term "world" has a great number of different meanings. However, when we use the term "world" in the book, Possible Worlds, we use it in a highly specialized sense which must be distinguished from its more ordinary uses.

   Sometimes speakers of ordinary English will use the term "world" in a very narrow sense. In the fifties there was a movie entitled "The world of Henry Orient". In that context, "world" meant something like "the life, the thoughts, the actions and the environment".

   A slightly broader sense is found in such expressions as "the prehistoric world", or "the world of the Buddhist", or "the world of the fly-fisher". Here "world" designates a particular time, or place, or life-style, or set of beliefs, etc.

   Perhaps the most common use of the term "world" is to refer to a planet, e.g. Earth, or Mars, or Venus. And sometimes "world" is used to refer to a galaxy. Occasionally, in a few books, galaxies are referred to as 'island universes'. But for our purposes, galaxies are not to be regarded as universes, only as parts of a universe.

   As used in this course, and indeed whenever philosophers talk of possible worlds or the actual world, the term "world" is not used in any of the above senses. It is used only in its most inclusive sense. "World" – as used in philosophical contexts – is used to refer, not just to planets, not just to galaxies, but to an entire universe.

   This particular universe we happen to find ourselves in contains the planet Earth (of course), but a great deal more besides. It includes all the planets (as well as their moons, all the interplanetary dust, asteroids, etc. of the Solar System), but it includes the Solar System itself too, the galaxy in which the Solar System occurs (viz. the Milky Way), and – continuing – all the other galaxies, the galactic clusters and the superclusters, of this universe as well: the Andromeda Galaxy, the Coma cluster, etc. In short, the actual world is simply the entire universe. But to have said this is not quite to have said it all. For by "the actual world" we do not mean the entire universe only as it is now; we mean, again, something more inclusive: the entire universe as it was, is, and will be. That is, we mean the universe complete with its unique history, present, and future.

   The actual world (i.e. the entire universe) is obviously immense in its physical size, in the number, amount and diversity of its contents, and in its temporal extent. On the best theories of modern science, the actual world (the universe) is at present at least five billion (i.e. five thousand million) years old. And it promises to have a future of at least that length of time. The physical distances stagger the imagination. The universe is at least 10 billion light-years in diameter. (One light-year is 5,878,000,000,000 miles.) [Note: A favorite theme in recent years in some science-fiction books, and even indeed in a few physics texts, has been that of so-called 'parallel worlds' (or 'parallel universes'). Again, for our purposes, parallel worlds (whatever they are supposed to be), if they are real, i.e. really exist, are to be regarded as parts of the one actual universe and not as distinct, further universes.]

   If the actual world is so immense, can we suppose that it includes everything?

   The question just asked – whether the actual world includes everything – turns out to be subtly ambiguous. And it is essential to understand the two different senses in which we might talk of "everything".

   In one sense, the actual world does contain everything. Indeed this might almost be taken as the very definition of "the (actual) world": everything that there was, is, and will be. Everything that exists, ever has existed, and ever will exist is to be regarded as part of the actual world (or of the universe, if you prefer).

   But notice carefully what we have just said. We have subtly qualified the term "everything". Notice how, quite naturally, we slipped from talking about "everything", without qualification, to talking of "everything that exists (at any time or place)". It was easy to make that transition because, very often, "everything" is used precisely to refer "everything that exists (at any time or place)".

   But "everything" does not mean (i.e. is not equivalent to) "everything that exists". Indeed, if "everything" did mean "everything that exists", then there would be no point in ever adding the qualification "that exists".

   The fact is that "everything" can be used to refer even more widely than when it is used in the expression "everything that exists". For one can use "everything" equally easily in an expression such as "everything, both existent and nonexistent", or, "everything, both actual and nonactual".

   On this latter, widest interpretation, of "everything", it is clear that the actual world (the universe) does not contain everything. It does not, for example, contain a creature which is you and which is eating a dinosaur leg. True enough, there may be some distant planet in this universe in which there is a creature very like you and which is eating a dinosaur leg. But that creature, however like you he or she may be, is not you. You exist here and now in this local part of the actual universe, and in this place – here and now – you (the bona fide you) are not eating a dinosaur leg.

   As it turns out, the number of things missing from the actual world is considerably greater than the number of things which actually occur. Think of ways you might have been different, but are not: all of those are 'things' missing from the actual world. Think of ways the actual world might be different from the way it in fact is: the Liberals in Canada might have won the 1988 federal election; AIDS might have been cured in June 1990; you might win the lottery three times; you might have a severe toothache tonight and fly to Calcutta for treatment by the tallest person living in that city; lithium might be the most common element; any creature's eating carrots will reverse that creature's aging process; etc., etc. All of these are 'things' which do not occur in, i.e. are not part of, the actual world.

   The actual world encompasses (includes, comprises) everything actual (i.e. everything that has existed, does, or will exist). But it does not include everything possible. The realm of possibility infinitely exceeds the realm of actuality. As immense as actuality (reality) is, its 'size' pales in comparison to the realm of possibility. For every single way the world is (for every individual fact), there is an infinity of alternative ways the world might have been. Each of these alternative ways is a description of a nonactual possible world. These alternative ways, these alternative (nonactual, but possible) worlds are limitless in number. There is exactly one actual world; there is an infinity of nonactual possible worlds.

Actuality and Knowledge

One of the most troubling aspects for some students of this talk of the actual world and of possible worlds occurs when one tries to give examples of ways the actual world is not. In the preceding section, to cite just one case, I claimed that this (the actual) world is a world in which a creature's eating carrots is not guaranteed to reverse that creature's aging process.

   Years of teaching this course and related subjects has made it clear to me how some students will react to such examples. Their immediate response is to object with something of this sort:

But how can you be so sure? The universe, as you yourself say, is enormous. So much of what is going on in the universe – in its distant parts, in its unglimpsed future – is totally unknown to us. How can anyone be sure, then, that somewhere, at some time, there isn't a situation where eating carrots does reverse the aging process?

Is such an objection sound? Does one really have to know what's happening on far-flung planets, perhaps in future times, to have certainty about the falsity of the claim that any creature's eating carrots will reverse its aging process?

   Perhaps there is some distant planet where eating carrots will have the reverse-aging effect on the local inhabitants. But even so, that would not alter the fact that a creature's eating carrots whenever and wherever in the universe it happens to be does not guarantee that its aging process will be reversed. And the latter is something that we can know here and now. We know it by knowing that carrots don't have that effect on us. As long as we know that there is even one creature anywhere, at any time, in the universe on whom carrots do not have the reversing effect, we know that that effect is not universal. We do not, then, have to examine all of the universe or all of the future. For this latter claim is not about some creatures, at some particular time and place in the universe, but about all creatures, at any time and at any place. And such an unrestricted claim is certainly false. One cannot, as it were, 'make' an unrestricted statement true by finding some one place or time where it applies to certain things.

   Let's take another example.

   The Liberals (here in Canada) lost the 1988 federal election. Might they have won it? In the terminology of this course, we can put this latter question this way: is there some possible world where the Liberals (in Canada) won the 1988 federal election? Certainly there is. (We just described it: it's the world – not this one – where the Liberals, not the Progressive Conservatives, won the 1988 federal election.) But how can we be so sure that the world we have latterly described is not this very world? Perhaps at some distant place in this very world (the universe) there is a planet very like Earth, and on that planet, in the country very like Canada, the (counterparts to our own) Liberals won the 1988 federal election.

   This last example is troubling because unless it is handled carefully we would have to end up saying that it is possible that the Liberals both won and lost the last federal election.

   This latter statement is self-contradictory, and at all costs we want to avoid asserting self-contradictions.

   The repair (or 'fiddle' or 'fudge') needed to avoid the self-contradiction is obvious: The Earth Liberals lost the election; the non-Earth Liberals (perhaps) won the election. We are really talking about two different groups of persons who (accidentally) happen to share the same name and (perhaps) the same political philosophy. But for all that, the Liberals (i.e. the Liberals here in Canada, on Earth) did not win the 1988 election. By "Liberals" – unless explicitly qualified otherwise – we mean the Liberals here in Canada, on the planet Earth.

   It is not necessary for us to know whether there is another planet very like Earth; whether there is a country on a distant planet which is very like Canada; or whether there is in that country a political party very like the Canadian Liberal party. It suffices, for our purposes, that we know that the Liberal party here in Canada did not win the 1988 election for us to be able truthfully and confidently to assert "The Liberals lost the 1988 election". For when we make such a statement we are talking about our own Liberals, not some counterpart (twin or doppelganger) creatures on a distant planet.

   Similarly, when you say of yourself, "I am reading these notes", you are talking about yourself, not some counterpart creature in a distant place or future time of this world.

   But while you (and the Liberal party) do not exist anywhere in the universe but here on Earth, you (and the Liberal party) do exist in countless other, non-actual, possible worlds.

   When you muse to yourself, "I wish I had won the lottery last week", you are imagining – not a distant person or place in this universe – but you, yourself, at this very place in a non-actual, but possible, universe.

   Similarly, when you wonder what would have happened had the Liberals won the 1988 election, you are not trying to imagine a distant place in this universe, but are trying to picture this very place – with the circumstances somewhat changed – in a fictional, i.e. non-actual, possible universe. When you imagine (contrary to fact) the Liberals killing the Free Trade Bill in January 1989, you are not picturing in your imagination this actual world, but rather a non-actual, possible world. You are not picturing a place or a time in this world, but a place and a time in another possible world.

   Sometimes all of this strikes students as terribly arbitrary: when we talk of Liberals, we seem to be restricting our assertions to a political party here in Canada, yet when we talk of creatures, we seem to be talking of any creature whatever – both here on Earth and alien lifeforms on distant planets. Wherein lies the difference?

   Unfortunately, there are no hard and fast rules to follow. One must become sensitive to the context in which in the assertion occurs. If one were asserting that all creatures take in energy and produce waste products, one might – reasonably – assume that this is a claim about any creature at any time or place in the universe. But were someone to assert that all creatures evolved from one common ancestor who originally lived in a freshwater sea, it would not be unreasonable to take that claim as one being (tacitly) restricted to the planet Earth.

   As a rough rule-of-thumb, if you're talking about physics and chemistry, and you assert a statement about all such-and-such, you're likely to be talking about all such things at any time or place in the universe. For example, one never, or hardly ever, distinguishes electrons found on Earth or in this galaxy from electrons found at other places in the universe. When one talks about electrons, one is almost certainly talking about electrons anywhere and at any time in the universe. If you're talking about biology, however, the situation is likely to be trickier. You might be making a truly unrestricted statement about all times and places, but you might – as we have seen – also be making a statement tacitly restricted to certain organisms occurring in a specific place during a specific epoch. But if you're talking about politics, or history, or psychology, then it is more likely that you are making a statement tacitly restricted in both space and time.

   If these latter sorts of distinctions seem excessively arbitrary at first, they will become second-nature as we explore more examples in the first few weeks of this course. (Don't worry much about this at this early stage. You'll get the hang of it soon enough.)

Why posit other worlds? – an example from logic

The concept of possible world is used throughout philosophy: in semantics, in philosophy of science, in metaphysics, in ethics, etc. Perhaps we might have a spare lecture in this course where I might be able to survey some of these other uses with you. But for the moment, our concern lies with the use of the concept of possible world in logic.

   Consider the statement

(C)

There does not seem to be any 'necessity' to this statement; we can readily imagine that it 'might have been otherwise'. But suppose now that we add some further information:

(P1)

(P2)

Now these latter two statements – like (C) itself – are not 'necessary': any of these three statements could have been otherwise. But note one highly important fact: if the latter two statements [(P1) and (P2)] are true, then the statement (C) must also be true. While (C) is not itself 'necessary', it is nonetheless, we say, 'necessitated by' (P1) and (P2). If (P1) and (P2) are both true, then it is not possible (i.e. under those particular circumstances, it is not possible) for (C) to be false.

   This notion of one statement's (or a set of statements') necessitating another statement is one of the pivotal concepts of logic. It bears the technical name entailment or implication. And it can be intuitively explained by invoking the concept of a possible world.

   What does it mean for a set of statements to 'necessitate' (imply) another statement?

   Let's look back at our example.

   However a world may differ – pigs might fly, water might flow uphill, there might be three sexes, etc. – one thing is certain: if (P1) John left work two minutes after Alice and if (P2) Alice left work at 4:20 PM, then it must also be true that (C) John left work at 4:22 PM. Put still another way: however circumstances may have differed, just so long as John left work two minutes after Alice and just so long as Alice left work at 4:20 PM, then it must also be true that John left work at 4:22 PM.

   This crucial prefatory qualification – "however a world may differ" (or, "however circumstances may differ") – which we've just used in this example is the motivation for the entire enterprise of importing the concept of possible world into logic. For the concept however circumstances may differ is nothing but an equivalent way of invoking the very concept of another possible world. Another possible world just is a different set of circumstances. And thus we may restate the previous point this way: Any possible world in which John leaves work two minutes after Alice and in which Alice leaves work at 4:20 PM is also a possible world in which John leaves work at 4:22 PM.

   Indeed, using this concept of possible world we will be able to give a powerful and intuitive definition of implication (entailment): "A statement P implies a statement Q" means "Q is true in all possible worlds in which P is true". (And shortly, in Chapter One, we will learn how to draw possible-worlds diagrams to depict such a relation.)

   Try an example. Imagine for a moment the statement P, "Mary washed her blue Datsun on Sunday morning." Can you think of a statement that will be true in any and every possible world in which P is true? Here's one (there is in fact an infinity of others): (Q) "Mary washed something on Sunday". Every possible world in which P is true is also a possible world in which Q is true. P may be said, then, to imply Q.

   We have begun in this little exercise to 'get a handle on' one of the most fundamental, crucial, parts of our intellectual repertoire. By invoking the concept of possible world, we begin to be able to explicate and to understand many of the logical moves we routinely make (sometimes correctly, occasionally not). Once we understand what these logical moves are, we can begin to refine our use of them, to hone them so that they may be used more cogently and skillfully.

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