Mark asked:

When I peer into the night sky, I can perceive infinity...Atoms are building blocks and I visualize an
infinite number of building blocks compiling the atom...I draw a line from one to the other and along
this line plot an infinite number of points with each point sprouting out into an infinite number of
directions. From each sprout et cetera, et cetera. From this I picture my grid of infinity. I don't yet
know how to label each point on this grid. If I could label one point I would allocate it as a memory
location for all that our earth, galaxies, and knowledge represent. All of the other infinite memory
locations are full of unknown infinite amounts of information.

My question is: in view of the above visualization, how can a Philosopher place so much emphasis on
an arrangement of words (formed from a finite stockpile of words) allegedly presented by an icon of a
past society (let's say Socrates for a start)?

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What a picture! I hardly know where to begin. Let us agree that philosophy, and indeed all human
knowledge and experience, is something very very small in relation to infinity. The thing is that we,
you and I - or the human race - are also very very small in relation to the whole of space or the whole
of time. So what is very very small in relation to infinity can still be big for us.

You will probably reply that the fact that the history of philosophy from the Greeks onwards looks big
to us is merely an appearance, not reality. But what is the standard of size? Does the Earth, for
example, only 'appear' big? How small would the Earth have to appear in order to appear as small as
it really is? The answer isn't, 'Very, very small'. There isno answer to that question. And that is the
point.

From a finite stock of words, it seems impossible that one could ever form an adequate concept of
infinity. The mathematical definition of an 'infinite set' as a set that can be put into a one-to-one
correspondence with a proper subset (e.g. pairing up all of the whole numbers with just the even
numbers) does not seem to capture the essence of the concept of infinity. That definition merely tells
us something aboutinfinity. Some philosophers would conclude that the idea of an actually existing
infinite - as opposed to a rule that can be indefinitely re-applied, like counting, 2, 4, 6 etc - is
incoherent. It doesn't make sense. It is just a sound that we utter, not knowing what we mean by it. I
am not saying that I agree with that hard-headed view. But how confident are you - seeing as you are
stuck with having to use words along with the rest of us - that you knowwhat thought you are
attempting to express by the words you utter?

Reason and argumentation, the arrangement of words, is important because it is the best we have
got. Forget infinity. In relation to the difficulty of the perennial problems of philosophy, the efforts of
philosophers seem puny enough. OK, so we can't hope to make giant strides. We can only
accomplish a little at a time. But there's urgent work to be done, all the same. Let's get on with it!

Geoffrey Klempner