[Abandoned Draft] Philosophy and Infinity

Number 1, by Jackson Pollock, 1949

Posted by Thomas Scarborough

The new view our world is one of infinite relations.  In the words of philosopher Mel Thompson, we see ‘a seamless web of causality that goes forwards and backward in time and outwards in space’.

This was not the case in previous ages.  While philosophers of the past indeed had some sense of ‘everything’, they typically interested themselves in more immediate things: for example, the nature of matter, the requirements of the ‘good life’, or the principles of politics.

It stands to reason then that, if we live in a world of infinite relations, the concept of infinity becomes central to (post) modern philosophy.  With this in mind, this essay briefly explores the nature of this infinity, and what it may mean to us.

Typically, we see infinity as something which is pinned somewhere.  We know the expression, ‘From here to infinity,’ which, importantly, implies not only that infinity exists, but that there is a ‘here’ to it.  It is proverbial.  That is, while infinity is open on one side, it is bounded on the other.

‘Countable’ infinities are well known to mathematicians, if not the rest of us.  These are related to the countable natural numbers: say, 1, 2, 3, 4 ... and so on.  So, too, are ‘continuum’ infinities, which are related to whole numbers—and with them, rational and irrational numbers—say, 1/1, 1/2, 1/3, 1/4 ... and so on.  All these infinities are bounded on one side, but open on the other.

An infinity of relations, however, differs from the infinity of mathematics and science.  It is unbounded on both sides—or rather, on all sides, everywhere.  This is the reality in which we live—at least, when we try to imagine it from a detached point of view, and not the point of view of my own fixed self or any other fixed origin.

Our view of infinity powerfully shapes our thinking.  If, in anything, one assumes a single bounded side to infinity, this immediately legitimises the single bound or fixed point. Without it, the entire system must collapse.  It has to be referenced to that point.  Thus infinity's bound is anchored—yet anchored, as it were, in a bottomless and endless sea.

I have a fixed point in a formula: 0 (nought).  I have a proven fact: ‘Hydrogen and oxygen makes water.’  I have a principle: ‘Do no harm.’  Or I have a philosophy: existentialism, for example, or rationalism or idealism.  But because all of these are deposited in the midst of the infinity without bounds, they exist in isolation, and can ground nothing more than themselves.

This is most palpable in the area of ethics.  If we approach ethics from the point of view of ‘is’—which is fact—we cannot reach the point of view of ‘ought’—which is value.  The problem lies not only with simple, descriptive facts.  It lies with purported facts of any kind: moral facts, social facts, political facts, religious facts.

Every one without exception cannot lead us to value.  They cannot, because they exist in an arbitrary and very specific place in an unbounded infinity, without being referenced to any fixed point except their own—while the question of ethics is what there is beyond limited scenarios.  This is what makes it such a big question in philosophy.

There is only one viable option open to us which may ‘fix’ something entirely.  That is to reference our thinking to infinity itself.  One might wonder how such a thought could be of any use to us.  An analogy might help.

If I reference the position of a buoy to the seaweed I see underneath it, or the birds which circle overhead, I have an unstable reference.  If I reference it to the sandy shore in the distance, this would seem more stable, though not completely so.  Or I may reference it to the stars—but even the stars will move.  Ideally, it would be referenced to everything.

It all suggests, in a sense, a philosophical theory of relativity, in which a static universe of thought is discarded.  Space does not allow the further development of this thought in this post, but possible applications to ethics appear in my Pi article, How Shall We Re-Establish Ethics in Our Time?