In a recent essay, What is an Explanation?: The Context of Thought and Language, I opened up a line of discussion which might provide a new view of some of my basic ideas, a view which might lead me to more fruitful explorations and perhaps others to better understandings of what I’m trying to do along with perhaps encouraging them to develop their own ideas on how this work of re-understanding God’s Creation should be done by Christians or others who see order in being. I’ve found that sometimes I can better understand my own written thoughts if I re-express them in different terms or from different viewpoints.
Let me start with an example from mathematics which I consider to be the study of a peculiar, very abstract from of being from which this concrete world was, in part, shaped. Very serious mathematicians of a philosophical bent of mind were trying in the late 1800s into the early 1900s to found mathematics upon logical bedrock, some of them intending to do so by first showing a few logical rules could generate the natural numbers. Those mathematicians set up proposed systems, the best of which developed elaborate machinery which included terms such as x(0), x(1), x(2), etc. The idea was to start with nil or zero and declare a successor element to zero, “1″, and then to declare a successor element to 1, “2″, and so forth. The problem, and it was missed at first by even such brilliant thinkers as Bertrand Russell and Alfred North Whitehead, was that the natural numbers [0, 1, 2, 3...] were used as indices for symbols meant to build up the set of natural numbers from very simple thoughts of a logical sort. They had assumed the very ordering and counting processes they were trying to prove legitimate and so ended an effort to find an easy way to build at least natural numbers from the basic building blocks of nil and a successor operation. [A minor point---mathematicians don't seem to agree as to whether or not `0' belongs in the natural numbers.]
One brilliant mathematician from that time made a particularly interesting claim, used in recent years as the title of a book written by the physicist, Stephen Hawking. The original words of Leopold Kronecker, a 19th century mathematician of great accomplishment, were: “God made the natural numbers [or integers according to some translators, but negative numbers add some complications to these efforts], all else is the work of man.” He “believed in the reduction of all mathematics to arguments involving only the integers and a finite number of steps.” Like the Pythagoreans, Kronecker didn’t even believe in the irrational numbers, let alone the likes of Cantor’s transfinite numbers.
Kronecker believed in the integers (or natural numbers) as the building blocks, along with well-defined finite operations, of all mathematics. I say that there are no building blocks as such—for what it’s worth, I’m much more open than Kronecker and his followers to non-finite operations in proofs and other mathematical activities. I even believe in Cantor’s transfinite numbers and other strange entities from abstract being.
Mathematics is the study of some types of abstract being, which types have increased greatly in the Modern Age. What is most important for this discussion is that mathematics concerns relationships and I’ll claim those relationships generate the number `9′ and those, perhaps with a few others, also generate the number pi (3.14159…). So it is that I can claim that Russell and Whitehead and their colleagues in the decades around 1900 were on the right path except that they had too impoverished a sense of relationship as they tried to generate numbers from only a successor relationship. In fact, what is needed is the entirety of the sets of relationships which are dealt with in number theory and that implies the task misunderstood by those brilliant thinkers is ultimately no more and no less than the field of mathematics in its entirely. (Stated this way, my program seems to be similar to that of the researchers working on Category theory except that I’m considering mathematics and any possible abstractions covering multiple fields to be real, if very abstract, being. Essentially, I’m trying to understand mathematics as part of a program to understand all forms of created being. I’m a metaphysician and theologian rather than a technical mathematician. Or physicist. Or historian.)
How is mathematics to be understood? By doing it.
How is life to be understood? By living it.
How is the universe to be understood? By living in it, by exploring it, by thinking clearly and exactly about it.
How is the world to be understood? By seeing the universe in light of God’s purposes or perhaps the moral order seen by many including some atheists and pagans.
This points to an answer, at least currently plausible, to the question: How can we explain created being?
I’ve denied there are fundamental building-blocks as such and the task arises to develop a new program which will be part of a new civilization or perhaps a revived Western Civilization. This program will itself help define the the intellect or communal mind of the citizens of this new or revived civilization. Furthermore, as a Christian, I’ll claim this intellect to be that of the pilgrim Body of Christ, an intellect to be completed and perfected in the world of the resurrect—as so much will be completed and perfected.
I’ll take a stab at understanding this program and can promise I’ll not yet be clear and exact. That will take years, and perhaps multiple generations, of effort.
Multiple streams of abstract created being have fed into this world:
- some abstract being shaped into matter and energy and fields,
- some remaining relatively abstract in the form of relationships which change over time and are called stories or narratives, and
- some remaining relatively abstract in the form of relationships we ourselves detect, and use, as our minds or souls.
Our universe can be defined as being made of mostly, perhaps entirely, the concrete stuff in the first item above. But our universe becomes a world when we also consider the more abstract stuff which I sometimes simplify (or perhaps oversimplify) as being the manifestation of God’s purposes or moral order or even rationality or reason to someone like Einstein.
I certainly think the above list is incomplete but I have no intention of building lists which are likely to have arbitrary elements until I can develop some more powerful tools, or at least point others to more powerful tools, to bring all of this into a more clear and more exact focus.
For now… We talk and scientists do their research as if there are building blocks of concrete entities, such as rattlesnakes and stars. And human beings and bricks. These concrete entities exist in spacetime, well described so far by Einstein’s General Theory of Relativity. These concrete entities are made of layers of successively more particular, that is—more concrete, bits of matter. (Many physicists would advocate speaking of energy in the sense of energy-matter—E=MC^2—rather than matter; make the substitution if you wish.) So far as concrete forms of being go, we can actually describe and quantify the transition from the most concrete of abstract being to truer concrete being. This description and quantification is the work of quantum physicists and all others (such as computer chip designers) who use the field. (Unfortunately, the systems of equations are not generally solvable by known techniques, but some powerful results have come from even the so-far limited successes of applying quantum physics in the real world. And, from a fundamental viewpoint, experiments can be done which prove quantum physics works to an extreme level of accuracy.)
Stars are complex entities, swirling magnetic fields and plasma encircling matter dense enough to undergo nuclear fusion—and this is a rather grotesque oversimplification. Rattlesnakes are complex entities, DNA and RNA and mitochondria and other forms of flesh and blood—all interacting in a remarkably complex metabolism which is something like a self-regulating system so long as you consider the environment of the rattlesnake to be part of the system—but this is also an oversimplification. Human beings have all the complexity of rattlesnakes plus they form minds which are complex systems of concrete and abstract relationships—this is perhaps the greatest of these oversimplifications. All of these entities come together in stories and in one great story that is the world.
Relationships. We assume that human communities form by way of relationships, though we often assume wrongly it’s the softer and more sentimental relationships—love in various forms—which are crucial in forming strong human communities. In fact, it’s something of a truism among modern sociologists that the strongest bonds in human communities are those of dependencies.
In any case, I already noted above that I consider relationships to be primary over stuff. Stuff is formed from relationships, as we are told both by the Bible and by quantum physics. (See Einstein and Bohr’s debate on the meaning of reality and Quantum Mechanics and Moral Formation: Part 1 for my early discussions of this issue.)
I’d like to speculate further but I’m trying to be cautious for now as I am not confident yet that I know how to advance to the next level of understanding. More powerful tools are needed and I’m exploring in the fields of geometry and topology, especially as used by modern physicists. Maybe I’m choosing the wrong tools. If so, someone will come along to show it can be done with some fancy group theory or just simple forms of category theory or whatever.
There is something that comes to mind which might help others to bring these claims of mine into better focus. We might be able to imagine, or at least think ourselves to imagine, particles as having the sort of existence as to be able to exist independent of a greater universe—other than perhaps some sort of spacetime. I think we fool ourselves into imagining an isolated particle, let alone an isolated human being, but I can certainly convince myself that I can do so, even when I don’t really believe myself.
The most fundamental relationships of our concrete universe, those of spacetime as described by the General Theory of Relativity and those of matter-energy as described by quantum physics, had to pretty much come into existence in their current form and to remain in existence for our concrete universe to come into existence and remain in existence. Without that full package of relationships, there couldn’t have been, couldn’t be, a single electron or neutron or electromagnetic field.
If I’m right, our ability to imagine particles existing apart from the entire universe as we know it is delusionary, though understandable. This is to say we can look at a rock and seemingly strip away all that is around it so that only the rock exists, but this is an error, perhaps useful, in our imaginative thinking. Everything gets still messier when we consider the other forms of abstract being which shape concrete entities by way of relationships, and thus do show up in physical manifestations that are explorable and maybe even quantifiable—such as brain structures.
So what could it mean to `explain’ the concrete being of this universe in terms of `elementary particles’ or the like? For the most part, it’s a good strategy for exploring the concrete stuff of this universe but it’s ultimately misleading. Such thinkers as Wittgenstein were close to the truth in proposing the search for the smallest building blocks would lead to the universe in its totality. My enhancement of this claim is, for now—merely, to point to relationships as being definitive of this concrete universe and to take all that creates or shapes concrete being as true being.
This isn’t entirely a new claim. Some scientists and philosophers and thinkers in other fields have proposed related ideas, though more than a bit cowardly in following up on the implications. The uniqueness of my claim lies in its context as part of a greater understanding of this concrete universe as a part of a Creation, the work of the God of Jesus Christ, a Creation which must be understood by hard work, investigation of empirical reality by open-minded theologians as well as poets and novelists and historians and painters and music-composers as well as physicists and chemists and geometers and evolutionary biologists and engineers and politicians responsive to reality. And so on. To a Christian such as me, this must all be understood in light of Christian revelation, that is, this universe is part of a Creation which was intended, and is intending in the Thomistic sense, to be the place of birth and growth of the Body of Christ—including the Incarnate Son of God and there is another world which will be the home for time without end of that Body when it contains all those resurrected to share the life of the Son of God.
An explanation of the world, the universe seen in its greater order even ordered to God’s purposes, can’t rely just any ideas of elementary relationships or elementary particles. Elementary relationships exist early—as a complex body of relationships—and then elementary particles come to be. Both of these are an early part of a narrative in which higher-level relationships and particles and then complex, concrete entities come into existence and begin to shape matter into complex entities, including galaxies and gorillas.
For a very preliminary discussion of some of my efforts to find more powerful tools for a more clear and more exact understanding of created being, abstract and concrete, see my recent essay: Adopting Mathematical Reasoning in Non-quantitative Fields of Thought.