[While working on an ebook containing a large number of my weblog posting, I decided this article, The Christian in the Universe of Einstein: 6. Adopting the Techniques of Negative Theology to Physics and Metaphysics, first published under that ugly title on 2007/03/09, provides a good summary of some of the fundamental, metaphysical aspects of my worldview. In the ebook, I’ve made some minor changes, but I’m republishing it here without those changes.]
I’ve argued that the human mind is shaped by its immediate environments, including social relationships starting with that between infant and mother. From there, we expand out into larger sections of those immediate environments and may begin to interact with other environments. In this expansion into other environments, we’re like other opportunistic animals — bears and wolves being my favorite examples. Those species are missing the brain structures, mostly in the prefrontal cortex, which interact with even ancient, ‘reptilian’ sections of our brains to allow us to plan ahead, keep in mind objects which aren’t present, form abstract groupings from particular objects, and even to form concepts not clearly related to anything in our experience.
Any claim for human ‘uniqueness’ — only hinted at in the above paragraph — is clearly true in a substantial sense but it’s also overly simplified. Chimpanzees have at least some raw abilities related to abstract thinking but don’t display any signs of developing skills from those raw abilities — in general. Recently, scientists were a little surprised to observe chimps in the wild making spears and using them to kill monkeys. We should learn something from the very rarity of this sort of behavior, given that chimps do show abstract thinking readily when given specific incentives. But we also need to see that we are mostly citizens of our universe. The chimpanzees are our cousins.
Already, there are hints of thought patterns akin to those of negative theology, both the deliberate and conscious formation of analogies and also the nay-saying that tries to say, “No, God is not truly this,” or “No, men are not truly this.” This sort of reasoning is, in fact, natural to disciplined human thought, But remember that this sort of thought is not purely negative except in perhaps some branches of Buddhism. The real method of negative theology, as practiced in Christianity, is based upon the realization that we creatures know our physical environments and must speak of even God in terms which are derived from our experiences and relationships. Analogies are formed and then an attempt is made to negate the most important errors which arise from applying creaturely analogies to God.
This way of thought, analogy and negation, is most applicable to our efforts to understand something that is not quite definable in explicit terms. I like to think in this way, forming analogies, sometimes drawing on knowledge far afield from the objects of my current thought. When I apply the analogy and I start seeing possible or realized problems, I start adding other analogical elements to counteract the original analogy. This can get complicated fast and all sorts of errors can eventually be hidden in a way of thought. Also, an abstract way of thought can sometimes come to be thought of as the truth rather than an attempt to deal with one part of reality or another. We should be faster to clean out our houses of thought, including those houses which contain accumulated thoughts about God Himself, the ultimate and only true reality.
Let me make a case study of sorts of some of my own thought processes behind the worldview I developed in my book, “To See a World in a Grain of Sand”. This is rough because I didn’t keep any notes as I proceeded and my ways of thought tend to be too discursive to truly accord with a systematic presentation.
1. Where do the ideas of abstract mathematics and abstract metaphysics come from if we are physical creatures who learn from the physical things and relationships of this world?
We can become dualists at this point as most do, including most who consider themselves to be materialists. As some have pointed out, concepts of software have crept into the thoughts of the materialists. Soul or software are the same if it’s something that floats above the physical entity, only accidentally attached.
Another traditional form of dualism is the belief in a realm of Ideas which are pure, not corruptible or changeable in any other way. Some accuse Plato of teaching this, but I read more nuanced and qualified views in the few dialogues I’ve read — in translation only. On the other hand, Neoplatonists did seem to teach this form of dualism and they had a great, and not always good, influence on thought in both Christian and non-Christian science, as well as other domains of knowledge.
Suppose we decide that empirical reality is sufficient for the natures of empirical entities. There is no magical extra added in, from soul-stuff or from software which can supposedly implement a ‘mind’ in the patterns of brain-cells or the patterns of insects or sunspots. There is also no realm of pure ideas which we can access.
We’re now stuck with things and relationships of things to each other as the foundation of some extraordinarily complex mathematics. It’s not clear how ideas of infinities larger than ordinary infinity can arise if all our mathematics has to arise in our physical brains formed in interactions with environments in this physical universe. There are many such abstractions in mathematics which raise such problems.
Those problems have to be considered in light of the empirical evidence that human mind-events are tied strictly to events in the brain. Since the brain is embedded in a body and that is embedded in complex environments, we’re not really forced to find all mathematics in the brain as such. But its not clear how we can use any of this to explain the power of the human mind if it is founded entirely in the physical brain.
We have ourselves a seeming conflict between scientific evidence that the brain is the foundation of our thinking activity and the fact that some human beings can imagine and analyze possibilities which seem unrealizable in this universe.
2. Cosmological astrophysics and particle physics support a narrative of our universe which begins with the entire universe compressed to densities and states of being which can be described mathematically but not well-imagined by a human mind formed to deal with trees and rocks and hamsters.
As we reverse the narratives of the so-called Big Bang model of this phase of Creation, we find a general tendency for thing-like being to melt down and even to merge in fundamental ways with energy and fields. This cosmological mush is a vaguer sort of being to us humans with our minds formed for thing-like environments.
If we extrapolate back through the Big Bang… What might lie on the other side of that extremely dense state? Is it merely a point of oscillation and what we see is what truly exists? Is there some sort of quantum vacuum on the other side of that dense state? Does thing-like being truly melt away? That is, we might wonder if there is a different sort of being on the other side of that initial point of our universe, that point of extremely high-density.
The possibility of a different sort of being underlying the thing-like being of our universe raises a faint hope of letting us at least talk about the problem of abstract mathematics without falling into one form or another of dualism.
3. Modern physics defines space and time in terms of relationships to thing-like being, things and fields and some strange entities underlying them.
Do time and space as we know them exist on the other side of that initial time of our universe? I’m assuming here it was an initial point and not just an oscillation point where a previous, similar universe had collapsed. I’m also assuming our universe isn’t just a fluctuation bubbling out of a quantum vacuum. So far as I can tell, a prior quantum vacuum would arise only in a state of thing-like being essentially the same as that of this universe.
Unlike thinkers like Kant who absolutized the nature of things in this universe, this phase of Creation as I would say, we’ve denied that the nature of things in this universe tells us what the underlying nature of things truly is. Not surprisingly, at least not to me, we’ve been led to speculate very tentatively that stuff that is not thing-like underlies thing-like being. That underlying stuff also, speculatively, doesn’t have time-like or space-like aspects. But it would have to have aspects which would allow it to be shaped into this thing-like universe and to provide the stuff to make the things of this universe.
4. Having speculatively stripped thing-like being of many of the properties we associate with substantial being in general, I add in the claim of St. Thomas: “Things are true”.
To a Christian, this should be almost trivially true because of the belief in a Creator God. If God creates from nothing, then the things He creates must be true because they’re manifestations of some of His thoughts, in a manner of speaking.
5. At this point, I’ll return again to mathematics to point out that the line of thought which runs through Cantor and Goedel and Church and Tarski and Turing, arrived at an alien station in the mid-1960s when the great Russian mathematician Kolmogorov and an American high-school student named Gregory Chaitin speculated independently that randomness is a matter of coding efficiency. Most people seem to think that randomness is some sort of mystical and irrational concept.
By 1990 or so, Chaitin’s work had culminated in a proof that all numbers are random. This is to say that a random number is an infinite stream which has no patterns at all which would allow it to be described in fewer characters than a straightforward listing of the number itself. Numbers which are clearly not random include integers and such numbers as 0.3333… or 1/3. These numbers have a measure which is 0 relative to the measure of random numbers.
Google search for Dr. Chaitin’s website if you wish. It has a number of shorter, downloadable papers and also references to his books including the undergraduate computer textbook (Cambridge U. Press) which covers his proof that ‘all’ numbers are random. It turns out that Goedel’s more famous theorem is a corollary of this theorem.
Randomness is factuality, as was pointed out by Professor Mark Kac of Cornell in the early 1970s based on the early work of Chaitin and Kolmogorov.
6. Now I ask: Is it possible that “Truths are thing-like?”. Now we’re in a fine mess from having taken modern physics and ancient theology seriously. That is, we’ve taken the narrative of the so-called Big Bang model in reverse to find that, supported by particle physics, nature herself has little respect for the opinions of man: some of the properties which many traditional metaphysicians have assumed as necessary seem to be quite contingent. They’re add-ons to some sort of being which is very abstract and strange from the human viewpoint.
When we follow the narrative of the universe in reverse, when we see it melting down into a seemingly more homogeneous stuff than we could directly imagine, can we possibly say that we are seeing hints of the truths from which this universe was shaped? That is, did God create first some very strange and abstract stuff which is the manifestation of the truths we know and perhaps many others? For example, is gravity a particularized form of a metaphysical principle of unity which holds together those truths in the Primordial Universe and holds together matter and energy and fields in this particularized universe?
This extension of the Thomistic claim that “Things are true” is a very dangerous and potentially fruitful analogy. In my book, and a few entries, I’ve already begun to use the techniques of negative theology to try to bring this analogy under control, but I like the idea because it brings all that is creaturely in any sense inside of God’s Creation and leaves the Almighty, He who is His Own Act-of-being, free to be God. Unlike the Libnizean God, one who’s sneaked into Christian thought, the God of Jesus Christ isn’t just a divine computer processing some humanly accessible set of truths which God Himself must take as absolute. This theological issue has great implications for mathematics and science, whichever way it’s settled.
Should we strip away some of our common-sense assumptions to reach a better understanding of the ‘stuff’ which is the foundation of our universe? We have guidelines from physics which point towards more general forms of physical being, lacking many thing-like properties and perhaps not having time-like or space-like aspects. Maybe we should be as brave as the negative theologians of Christian history and dare to reason towards more fundamental forms of being? To be quite honest, my Christian beliefs guided me, especially in my willingness to conjecture that truths are thing-like. There are some deep theological and metaphysical possibilities to this line of thought but I’ll not talk about those here.
The bottom-line in my worldview is:
God created a Primordial Universe which is a manifestation of abstract truths, mathematical and logical and metaphysical. From this very abstract stuff, He shaped this universe which is a world when viewed in light of His purposes. That is, the moral order which only God can truly see is what makes this universe into a coherent narrative or a world.
The bottom-line on the ‘techniques’ used to develop this worldview is:
There is a complex weaving back and forth between fields of knowledge irrationally separated over the past five or six centuries. Those complex movements are coordinated by the traditional Catholic techniques of thought: analogy is disciplined by negations of undesirable aspects of the analogies which show up as the thought proceeds.
This is a more literary style of reasoning and is in conflicts with the most fundamental attitudes of modern liberal society which would bureaucratize all of Creation and would restrict all efforts to understand Creation to those which can be stated clearly in textbooks. The very stars themselves should obey the various by-laws and regulations of those who’ve been rendered incapable of the humbling wonder which should remind us of what Aquinas claimed centuries ago;
The human mind is, in principle, capable of comprehending all of this universe but any actual human mind is, in fact, incapable of comprehending so much as a flea.