Saturday, 7 October 2017

God, Mathematics & Münchhausen's Trilemma


At some point I'm going to do the final edits on my book on the question of what one might call 'is-ness' - a series of chapters that attempt to tackle mathematical and philosophical questions related to the question of why there is something rather than nothing. In the meantime, I'll try to summarise the kernel of the book's content in a short blog post. Here goes:

To attempt a philosophical stab at the big question of existence, I get about as far as I think I can get - which is roughly this. Something underpins reality - by that I mean there is a grand explanation for why existence 'is' - a reason that something exists instead of nothing. From what we've covered in previous blog posts, it's evident to me that physical reality isn't it. This leaves, I think, only two plausible contenders: God or mathematics.

Unlike our interpretations of God and mathematics, physics just doesn't seem to amount to a complexity powerful enough to contain an ultimate explanation. When we think of complexity, we think of a lower level complexity and an upper level complexity. The lowest level complexity would be something containing just a single bit of information. But once we start to think of an upper level complexity, we find that there really is no limit to how complex complexity can get. To me, such a realisation necessitates either one of the following:

A} Mathematics is the reason that existence 'is'.

B} God is the reason that existence 'is'.

Which is most likely to be true - A, B or neither? If it's neither A nor B then we are going to have to think up an alternative - and the trouble is, I don't think we humans have one, or are capable of arriving at one. It seems like it has to be God or mathematics, or possibly a concession that the mind goes blank, but where's the fun in that? So, on the question of whether it's God or mathematics, let's explore further.

Some statements can follow from other statements. If a minute is longer than a second, and an hour is longer than a minute, it naturally follows that an hour is longer than a second. Some statements are verified by having evidence to corroborate them. A 2017 Ferrari's 0-60mph time is shorter than a 2017 Nissan Micra's 0-60mph time, and it would be easy to corroborate this in a race.
 
The classic problem with general statements about ultimate existence is that neither of those qualities apply - that is, there are no further statements that can support them, and there is no evidence to corroborate them.

If there's no evidence for a statement, and that statement also follows on inferentially from any other statements, we run up against the Münchhausen trilemma - which says that we have only three options when providing proof:

1) The circular argument in which theory and proof support each other (i.e. we repeat ourselves at some point)

2) The regressive argument in which each proof requires a further proof, ad infinitum  (i.e. we just keep giving unending proof after proof)

3) The axiomatic argument, which rests on accepted precepts (i.e. we reach some bedrock assumption or certainty)

The circular argument says that X therefore Y, and Y therefore X. For example, if the Bible is the word of God it will say it is the word of God; the Bible says it's the word of God, therefore it is the word of God. If the conclusion is also one of the premises, the argument is a logical fallacy.

The regressive argument is where we have a statement P that we try to explain by P1, which needs explaining by P2, and so forth - carrying on into an infinite regress of Ps. For example, God (P) is the cause of the universe. What then caused God (P1)? What then caused the cause of God (P2)?, and so forth.

The axiomatic argument is an argument that is self-evidently true without recourse to further proof. For example, a whole orange is greater than a segment of that orange. There is no logically valid argument that says a part of something is greater than the whole of that thing.

I've thought a lot about why God or mathematics are our best two ultimate explanations for reality, and therefore our two best efforts at conceiving that which is behind the existence of nature. With God or mathematics I think we give ourselves the best chance of reaching a final theory that may avoid circularity; a final theory that may halt the regression; and a final theory that requires the least amount of difficulty in providing justification.

To see why, consider our studies of biology; we can break down biology into eukaryotes, and eukaryotes into introns and exons, and further into encoding, and further into the physics of atoms and electrons, and further all the way down to mathematics. Breaking down different elements into isotypes is not the same thing, though, as breaking down numbers into different constituents of numbers, because with the latter we never depart from mathematics. To ask what is more primary than chemistry or biology is easy; to ask what is more primary than mathematics is probably to be guilty of asking something insurmountably difficult.  

However, mathematics doesn't help us defeat the tripartite problem found in the trilemma. Regressively mathematics seems to be a self-containing system; and axiomatically it provides a bedrock on which numbers are found. It also has a degree of circularity in that at a human level of perception it is bound up in human minds interpreting our own interpretation of reality. But it doesn't seem to me to satisfy the answer to the primary question of 'is-ness' quite as well as God does, and I think there is a subtle reason why, which I'm now going to explain.

Rather than having to choose between God and mathematics, it makes better sense to me to postulate God and mathematics together, with God being primary and mathematics being a property of that primacy cause. It seems to me impossible to even conceive of the mind of God without mathematics, because mathematics is a primary property of thinking.

This is because sentience involves the concept of quantification - there is nothing thought can do without the involvement of numbers. Numbers to thinking are rather like the property of wetness is to water. By the same logic, it seems to me we can't have mathematics without an up and running sentience to think it.

Consequently, out of the two I can make more of a case for God being the primary cause and mathematics being a necessary part of God's mind than I can mathematics being the primary cause with no sentience behind it. To postulate God as the ultimate cause is not to deny that mathematics is more primary than nature - for mathematics may well be instantiated in the mind of God. As I said, it may not even make sense to talk of God's mind or consciousness without imputing some kind of mathematical framework inhered in those Divine thoughts (if God is triune in nature, as Christianity tells us, then numbers are implicit in God's tri-aspectual personality) .

If the Divine mind is the ‘is-ness’ that contains the primary Truth (capital T) that governs existence, then His is the reality from which there is no sense of beyondness. If God is the creator and the Aseity we are looking for to close down the explanatory protocols, then it would stand to reason that it is His mind that has an ontology whose non-existence would be an impossibility, and therefore the reason there is something rather than nothing.
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