Thomas asked:

Is what we call "outer space" infinite?

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There is a paradox from Ancient Greek philosophy which goes like this. Suppose that the universe —
what we now refer to loosely as 'outer space' — is finite, and not infinite. Imagine an archer at the
outer limit of the universe who shoots an arrow. Now we have to decide what happens to the arrow:

*If the arrow carries on flying, then obviously the archer could not have been situated at the outer limit
of the universe, contradicting the hypothesis.

*On the other hand, if the arrow hits a wall, then that too contradicts the hypothesis that we have
gone right to the outer limit of the universe. There is something beyond that limit, viz. a wall. And now
the same question arises, whether the wall is of finite thickness, or infinite thickness.

These two alternatives were regarded as exhaustive, therefore showing that the idea of a finite
universe was absurd. However, one can think of at least three other alternatives:

*The arrow ceases to exist. Or, more precisely, as the arrow passes the outer limit of the universe,
first the head, then the shaft, then the feathers go out of existence. From a purely logical point of
view, this is a neat solution. However, it raises serious problems for the possibility of physics, in the
way that it flagrantly violates conservation principles.

*The arrow reappears on the other side of the universe. A good way to imagine this is by analogy with
a piece of paper rolled into the shape of a pipe. As an arrow goes over the left hand edge of the
paper, it reappears on the right hand edge.

*If you set out looking for the edge of the universe, using the best available methods for keeping in a
straight line, you will never find it. Instead, if you keep going long enough you will return to the point
you started from. This is in fact the view of modern relativity physics, according to which the geometry
of space itself is 'curved'.

In other words, philosophical analysis shows that it is logically possible that space is finite. The idea
of a finite space is not intrinsically absurd. Modern physics leads to the conclusion that what we have
demonstrated to be logically possible is in fact the case.

Geoffrey Klempner

Second opinion:

There are two problems here, one is that we do not know what kind of universe we are living in. We
know that it is expanding but depending on certain conditions (the rate of expansion and the average
density of the universe) there are a number of different answers to your question. The second
problem is that we do not really what it means to talk about infinity, the concept is teeming with
paradox and all kinds of nasty things to give us headaches.

Further if the universe is infinite it has no centre or more specifically every point can be regarded as
the centre.

As 1 said earlier the kind of universe we live in depends on certain constants having certain values
Cosmologists have developed models to predict the fate of the universe depending on the values. If
the rate of expansion is such that the universe will continue to expand then space is infinite. If
however the universe ends up as a "big crunch" collapsing back in on itself then space is not infinite,
but neither does it have a boundary. In such a universe gravity would be so strong that space is bent
round on itself and if one could travel fast enough for long enough one would eventually come back
where one started, so in effect one could travel forever in a finite space! But it is an empirical and as
yet undecided matter as to which model this universe fits.

Brian Tee
Dept of Philosophy
University of Sheffield.

Third opinion:

In PhysicsBook III Aristotle distinguised the void from the infinite.

Outer space is a void and we cannot say anything about it since it is not part of our conceptual
scheme. Infinity, on the other hand, is part of our conceptual scheme, i.e. the ideas we have in and
about our world. Examples are infinite numbers and time.

The infinite, like a void, is not space, in that there is no top or bottom, it can't be divided in half or have
any qualities. However, Aristotle doesn't want to say there is no infinity or the consequence would be
finite numbers and time with a beginning and end. So he defines infinity in terms of finitude. This is to
say that whatever magnitude you have you have you can always have more, and any magnitude is
infinitely divisible. This is not to talk of actual magnitudes, or space as such, since Aristotle defines
infinity as potentialrather than actual.There are infinite potential operations for any magnitude.

Rachel Browne