Infinity

7. Human finitude

Problems about the infinite, we have seen, are grounded in our own finitude. On the one hand our finitude prevents us from being able to think of anything, including the whole of reality, as truly infinite. On the other hand it also prevents us from being able to think of anything finite – anything to that extent within our grasp – as the whole of reality. One way to reconcile these would be to deny that there is any such thing as the whole of reality and to argue that there are only bits of reality, each a part of some other. Here once again we see application of the Scope Distinction: every bit of reality is a part of something, but there is nothing of which every bit of reality is a part. Aristotle, Kant and even to an extent Cantor played out variations on this theme.

But one of the most pressing questions of philosophy still remains: in what exactly does our finitude consist? Some of the most striking features of that finitude are conditioned by our temporality. In particular, of course, there is the fact of our death. How are we to view death? Among the many subsidiary questions that this raises, there are two in particular which are superficially equivalent but between which it is important to distinguish. Putting them in the crudest possible terms (their refinement would be a large part of addressing them): (1) Is death a ‘bad thing’? (2) Would immortality be preferable to mortality?

It can easily look as if these questions must receive the same answer. True, no sooner does one begin refining them than one sees all sorts of ways in which a full, qualified response to one can differ from a full, qualified response to the other. But it is in any case important to see how, even at this crude level, there is scope for answering ‘yes’ and ‘no’ respectively. Putting it very roughly, death is a bad thing because it closes off possibilities, but immortality would not be preferable to mortality because mortality is what gives life its most basic structure and, therewith, the possibility of meaning.

To answer ‘yes’ to (1) and ‘no’ to (2) in this way is once again to invoke the Scope Distinction. It is to affirm that at each time there is reason to carry on living for longer, while denying that there is reason to carry on living forever. Meaning, for self-conscious beings such as us, can extend further than any given limits. But it cannot extend further than them all.

If it is true that, in some sense, at some level and with all the myriad qualifications that are called for, the answer to (1) is ‘yes’ and the answer to (2) is ‘no’, then, coherent though that is, it points to a basic conflict in us: while it would not be good never to die, it is nevertheless never good to die. That conflict is one of the tragedies of human existence. It is also a version of the original conflict which underlies all our attempts to come to terms with the infinite. In thinking about the infinite, we are thinking, at a very deep level, about ourselves.