A computer simulation of a network of cosmic strings in an expanding universe, provided by Paul Shellard

The question of why there is a world at all was raised in short pamphlet by the philosopher Leibniz in 1697 entitled ‘On the Ultimate Origination of Things’. Leibeniz realized that it did not matter whether you thought the world was eternal or appeared out of nothing as maintained by orthodox Christian doctrine. All theories and beliefs still faced the problem of why there was something rather than nothing. Philosophers took little interest in this question for a long time after Leibniz. Problems like this were not part of an analytical philosophy that built up understanding of things step by step. Leibniz’s problem needed an understanding of everything step by step. Leibniz’s problem needed an understanding of everything all at once. It was too ambitious. In fact, it was as good a candidate as any for an intrinsically insoluble problem. Philosophers who considered the question, like Wittgenstein (‘Now how the world is, is a mystical, but that it is’) and Heidegger, had little to say in answer to it and appear more interested in wondering about why the question is one that we find so compelling. ~ page 283

The only novel contribution to this problem before twentieth century was the consideration of whether the well defined concept of mathematical existence had any cosmological implications. The development of axiomatic mathematical systems, in which a system of self consistent rules (‘axioms’) were laid down and consequences deduced or constructed from them, led to a ‘creation’ of mathematical statement that was logically consistent was said to ‘exist’. Mathematicians would produce what became known as ‘existence proofs’. This is clearly a far broader concept of existence than physical existence. Not all the things that are logically possible seem to be physically possible and not all of those now seem physically to exist. However, a philosopher like Henri Bergson clearly thought that this type of weak mathematical existence was a possible avenue along which to search for a satisfying solution to Leibniz’s problem:

“I want to know why the universe exists… Whence comes it, and how can it be understood, that anything exists? … Now, if I push these questions aside and go straight to what hides behind them, this is what I find: - Existence appears to me like a conquest over nought… If I ask myself my bodies or minds exist rather than nothing, I find no answer; but that a logical principle, such as A = A, should have the power of creating itself, triumphing over the nought throughout eternity, seems to be natural … Suppose, then, that the principle on which all things rest, and which all things manifest, possess an existence of the same nature as that of the definition of the circle, or as that of the axiom A = A: the mystery of existence vanishes…..”

Unfortunately, this approach to why we see what we see is doomed to failure. As the nature of axiomatic systems has become more fully appreciated it is clear that any statement can be ‘true’ in the same mathematical system. Indeed, a statement which is true in one system might be false in another. ~ Page 284 (The Book of nothing)