Copyright © Norman Swartz 1989
This revision: January 2, 1998
Department of Philosophy
Simon Fraser University
Supplementary notes for
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,
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
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
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
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
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
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,
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) John left work at 4:22 PM
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) John left work two minutes after Alice.
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
(P2) Alice left work at 4:20 PM
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
What does it mean for a set of statements to 'necessitate' (imply)
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
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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