In reading Richard Gregory’s Mind in Science, I find that he raises a seemingly plausible objection to those thinkers who `regress’ to seeing abstractions, including knowledge, in the objective world. He states his objection in a short and loaded way:
[The psychologist Kenneth] Craik is suggesting that human inference has its validity and logical power because and only when it shares the structure of reality. This is pushing the concept of analogue computing to its limit. But how can thinking be like the objects of thought? Craik is surely slipping back here into a `picture’ account with all its attendant difficulties. … Craik is forced to say that abstractions such as numbers exist as other objects exist; for his brain states are non-representing objects. He thus goes back on Gauss’s insights, which rescued us from the classical difficulties of mathematics, logic and language. This is surely a step backwards, which we should regard with extreme caution. [page 373]
I see various problems with Gregory’s viewpoint, not from a traditional Platonist viewpoint which — at least allegedly — follows the ancient Athenian’s view that there is an abstract realm which is more real than this concrete world. My starting point is a sophisticated-naive re-understanding of modern understandings of space, time, matter, and energy — from cosmology and particle physics and abstract mathematics, but also history and poetry and music. With this sort of re-understanding, deliberately bereft of conventional epistemological filtering of real-world information, I have come to believe that concrete forms of created being are shaped from abstract forms of created being. This wasn’t really something forced upon me, in any bad way, but ultimately a way of truly solving the problems Professor Gregory refers to. The problems weren’t caused by Platonism as such but rather by any general attempts to separate thought and object. Recently, I read about such efforts in The Meaning of Truth, a collection of Williams James’ articles on the real meaning of pragmatism. James knew quite well that man as we know him, the physical creature, doesn’t have any special access to any sort of transcendental realm of truths or thoughts or whatever, but I know of no Jamesian pragmatist who has grabbed the bull by the horns and dealt directly with the discontinuities in being caused by this separation of concrete and abstract realms though such thinkers as Walter J. Freeman and Gerd Gigerenzer have helped to establish the human mind as a set of relationships centered upon a creature of concrete being.
But I deny man is fully a concrete being and I speak not of just the fact that all concrete beings in this universe have relationships which are immaterial. Concrete being is shaped from abstract being and that more abstract realm remains in our bodies and our relationships — including our minds — as clay remains in the bricks of our buildings, as carbon and hydrogen remain in the wood of the frames of those buildings. The modern feeling that its wrong to conjecture a separate Ideal realm is valid but modern thinkers have not the guts or perhaps simply not the flexibility of mind to realize that if there is no Ideal realm but there are abstractions we can somehow access, that means those abstractions are here, in the very stuff of our bodies and in our relationships with other entities and with the entirety of various narratives.
We are still the clay as well as bricks, in a manner of speaking. Going beyond the clay, we’re also carbon and oxygen and arsenic (a small amount only, please). Still further, we find ourselves to be protons and neutrons and electrons and — very rarely — some of the strange particles mostly produced in high-energy regions such as supernovas and the accelerators at physics labs. Beyond that? I’ll skip a layer or so being actively explored by exotic empirical investigations and I’ll claim we are yet those very strangely abstract entities in the investigations of theoretical physicists and mathematicians. Or at least we’re the ones which really exist. These investigations are in an early stage and the specific directions chosen by theoreticians might not correspond to the abstract forms of being from which this universe was shaped. But it seems true for now that our universe was shaped from some relatively more abstract form of being and I’m willing to conjecture that process, in one or more additional steps, takes us back to the truths manifested by God when He called Creation into existence.
I’m going to turn to a mathematics textbook, Morton Hamermesh’s Group Theory and its Application to Physical Problems, where we read:
It must be stated at the outset that all our results [dealing with various physical problems] are obtainable without the formal methods of group theory. The alternative “simple” methods are, in fact, a physicist’s rediscovery of some group-theoretical techniques. For simple problems, the formal treatment is also simple; in complex problems, the use of powerful tools can save considerable labor. We should not deprecate formalism as such — so long as the physical ideas are not lost from sight, the formalism is valuable. [page xiii]
Professor Hamermesh is far too modest on the behalf of mathematics and other fields of abstract thought. One clue that such is the case is the dependence, shown over the history of human thought and anticipated in a general understanding — however imperfect — in the thought of Aristotle and — even more so — St. Thomas Aquinas, that abstractions of the most ethereal type often end up being used in the physical sciences and engineering. Moreover, many abstractions in both mathematics and metaphysics have been generated over the centuries in the works of physics and other fields of empirical studies and contributed back to mathematics or metaphysics. In fact, Aquinas seemed to think the second process to be dominant, understanding abstract forms of being by studying concrete forms of being, but he lived before science and mathematics had become major, self-sustaining activities.
In their deeper and not directly observable levels, cosmological physics and particle physics — I’ll ignore the overlap for now — conjecture entities which are quite abstract, that is, they have effects in the directly observable levels of concrete reality but they are radically different sorts of entities. This actually occurs even at all levels where there is a quantum effect. The wave-function of quantum mechanics has a `dual’ nature of a sort only roughly similar to the dualistic natures some conjecture for body-soul or brain-mind. Interact with that wave-function thingie as if it were a particle and — abracadabra — it is a particle with particular location. Interact with that wave-function thingie as if it were a wave and — abracadabra — it is a wave with a particular momentum. It’s possible this is telling us something — maybe there is some substantial truth and not just an analogical truth in my claim that concrete flesh-and-blood human beings are frozen soul. That’s a matter not to be settled, so far as I can tell, until we have a vocabulary and a way of using it that we can test our ways of speaking about the full spectrum of being. I certainly don’t claim to have such a vocabulary nor such a way of using it and feel strongly this will result from a multi-generational effort by a good number of explorers and thinkers.
I’m moving fast and furious rather than carefully and so I’ll move on to discuss some comments made by William James in The Meaning of Truth. First, he tells us:
Abstract concepts, such as elasticity, voluminousness, disconnectedness, are salient aspects of our concrete experiences which we find it useful to single out. Useful, because we are then reminded of other things that offer these same aspects; and, if the aspects carry consequences in those other things, we can return to our first things, expecting those same consequences to accrue. [page 246]
I have talked often about the mind’s movement from the concrete up to the abstract and back down to another, different but similar, concrete thing or relationship of concrete things. The difference is that I claim it corresponds to real being, that is, the things and the other things, as well as the relationships, at the concrete level aren’t just `thought about’ using the abstractions, they are shaped from abstract being which corresponds to those abstractions which are far from `merely’ mental. In our acts of `thinking about’, we are imitating the Creator’s acts of creating concrete things by shaping them from abstract being.
Again quoting William James from The Meaning of Truth:
Without abstract concepts to handle our perceptual particulars by, we are like men hopping on one foot. Using concepts along with the particulars, we become bipedal. [page 246]
This is true but also sticks to the view that there is being, real stuff, and then there are magical incantations which help us describe and maybe control that real stuff, but those incantations are connected to the real stuff only through the human being, our bodies and especially our perceptual organs being in contact with the real stuff and our minds being able to grab hold of the magical words which allow us to generate human abstractions about the true reality, the reality of dirt and water and flesh and blood. No.
Again, no. As I’ve said before, James and his followers came to understand deeply and truly the bottom-up processes by which we can make sense of empirical reality. James seems to have rejected the possibility that we are, in a manner of speaking, building up into an existing world, however tentatively we perceive and conceive that world, when we engage in those bottom-up processes. Both the philosopher James and the mathematician Hamermesh above see the patterns of the abstract in the concrete thing but don’t pursue the possibility that both are forms of being, different points on a spectrum of created being as I’ve claimed before. That spectrum of being is necessary for a world, a universe ordered to be a moral narrative. That spectrum is necessary for a human being to become a true person, and entity which shares the fundamental properties of a world: unity, coherence, and completeness.
Let me try to pull this line of thought together a little. In the modern world, we’ve learned lessons such as this:
- space and time can be one structure,
- the very stuff of stars and rocks and human flesh were shaped from some strange stuff in the early seconds of the expansion of the universe and that strange stuff seems to be abstract in such a way as to be describable only in terms of what might be called `demanding’ mathematics,
- the constituents of matter behave in ways that force us to give priority to relationships over stuff, and
- there are numbers far greater than what we call `infinity’.
In understanding this sort of exciting and disturbing knowledge, in understanding the narrative physicists have proposed for this universe, in understanding the evolution of life and of the human brain in particular, in understanding the appearance of the human mind in history, I’ve come to believe that created being is created being is created being. I’ve come to believe we should take quantum physics and cosmological physics and particle physics seriously — concrete, thing-like being is shaped from some more abstract sort of being.
It’s good to appreciate the ways of building knowledge of the empirical realms of being by bottom-up means. It’s good to appreciate the value of applying abstractions to extend and deepen that knowledge. Yet, we achieve the widest and deepest understanding of this universe if we avoid the easy path of “understanding empirical things, by studying those things and applying abstract thought during that study.” To be sure, there is much that can be accomplished by traveling that path, but there’s a harder path by which we seek to understand what is the relationship between the abstract and the concrete rather than thinking the abstract to be no more than a tool useful in understanding the concrete. Is abstract thought, even mathematical thought, no more and no less than magical incantations by which we gain some sort of occult control over rocks and flesh and energy? Is the abstract no more and no less than wizardly wisdom? In opposition to such ways of thought, implicit or explicit, I claim that created being lies on a spectrum going from the fully abstract, the truths God manifested as the truly raw stuff of Creation, to the fully concrete, the rocks which are frost-heaved each year through the New England soil.
Let’s have the courage and the faith to respond to created being in its deepest and widest form, the totality of created being.