Math and Myth

What I like is that number does not exist, and yet nothing could exist without it.

Stand by, I have some more to add.....

Therefore I wonder if subject of mathematics is real, in a different way to the reality of ordinary objects of perception. But then, of course, number is intrinsic to the way in which everything is organised.

BUt if number was imaginary, why is it the same for everyone? Does it mean we all have a common 'imaginary realm'? Surely I can't imagine a different 7 to you?

Here I want to consider whether there is a difference between what is real and what exists.

'Exist' is derived from a root meaning to 'be apart', where 'ex' = apart from or outside, and 'ist' = be. Ex-ist then means to be a seperable object, to be 'this thing' as distinct from 'that thing'. This applies to all the existing objects of perception - chairs, tables, stars, planets, and so on - everything which we would normally call 'a thing'. So we could say that 'things exist'. No surprises there, and I don't think anyone would disagree with that proposition.

Now to introduce a metaphysical concern. I was thinking about 'God', in the sense understood by classical metaphysics and theology. Whereas the things of perception are composed of parts and have a beginning and an end in time, 'God' is, according to classical theology, 'simple' - that is, not composed of parts- and 'eternal', that is, not beginning or ending in time.

Therefore, 'God' does not 'exist', being of a diffrent nature to anything we normally perceive. Theologians would say 'God' was superior to or beyond existence (for example, Pseudo-Dionysius; Eckhardt; Tillich.) I don't think this is a controversial statement either, when the terms are defined this way (and leaving aside whether you believe in God or not, although if you don't the discussion might be irrelevant or meaningless.)

But this made me wonder whether 'what exists' and 'what is real' might, in fact, be different. For example, consider number. Obviously we all concur on what a number is, and mathematics is lawful; in other words, we can't just make up our own laws of numbers. But numbers don't 'exist' in the same sense that objects of perception do; there is no object called 'seven'. You might point at the numeral, 7, but that is just a symbol. What we concur on is a number of objects, but the number cannot be said to exist independent of its apprehension, at least, not in the same way objects apparently do. In what realm or sphere do numbers exist? 'Where' are numbers? Surely in the intellectual realm, of which perception is an irreducible part. So numbers are not 'objective' in the same way that 'things' are. Sure, mathematical laws are there to be discovered; but no-one could argue that maths existed before humans discovered it. Mathematical relationships are indubitably a function of perception; nothing is counted if there is no-one to count.

However this line of argument might indicate that what is real might be different to what exists.

I started wondering, this is perhaps related to the platonic distinction between 'intelligible objects' and 'objects of perception'. Objects of perception - ordinary things - only exist, in the Platonic view, because they conform to, and are instances of, laws. Particular things are simply ephemeral instances of the eternal forms, but in themselves, they have no actual being. Their actual being is conferred by the fact that they conform to laws (logos?). So 'existence' in this sense, and I think this is the sense it was intended by the Platonic and neo-Platonic schools, is illusory. Earthly objects of perception exist, but only in a transitory and imperfect way. They are 'mortal' - perishable, never perfect, and always transient. Whereas the archetypal forms exist in the One Mind and are apprehended by Nous: while they do not exist they provide the basis for all existing things by creating the pattern, the ratio, whereby things are formed. They are real, above and beyond the existence of wordly things; but they don't actually exist. They don't need to exist; things do the hard work of existence.

So the ordinary worldly person is caught up in 'his or her particular things', and thus is ensnared in illusory and ephemeral concerns. Whereas the Philosopher, by realising the transitory nature of ordinary objects of perception, learns to contemplate within him or herself, the eternal Law whereby things become manifest according to their ratio, and by being Disinterested, in the original sense of that word.

the material of this book is indispensable for anyone who wishes to understand the real spiritual roots of Western civilization.