[Draft as of 2016/10/03. Hoping for publication on Internet before end of 2016.]
Is a man a unity or is he a collection of warring fragments? Or is something else true, perhaps an intermediate view, or—my favorite—some sort of complex being not describable in current terms of discourse? I should qualify my statement of the last possibility, which I believe to the closest to the truth: I think mathematicians working at the most abstract regions currently accessible to the human mind have discovered tools of thought, quantitative and qualitative, which can provide us with superior ways of discussing complex forms of created being. That entire argument is one which can be carried out only by way of a program to show such is the case. This book will be the first giant step in such a program—unless this giant step sends me into a brier-patch or over a cliff.
But a giant step isn’t enough. We need to explore ahead of where we can reach; that exploration will necessarily take place by way of the human imagination as much by the more rational parts of the human mind. This is a project I’ve actually been working on for 25 years, if not always consciously so. I’ve explored in the way of a novelist and even (quite) amateur poet through novels including some in which characters were poets; I’ve explored in the way of an admirer of mathematics and science through essays; I’ve explored in the way of a philosopher and theologians through other essays often overlapping with those dealing with mathematics and science.
I’ll step back… Is being a unity or is there concrete being which can be partly understood by abstract ways of thought separate from being as such? Is it perhaps the case, as I have argued, that what we think of as abstract thought is truly a form of being which is abstract in some way poorly understood? This poor understanding would be a result of misunderstanding of being, as I would claim in a necessarily circular way.
Let’s move on to Christian claims, poorly understood even in the heyday of partially Christian civilization in Europe. Is the world a true sacramental unity of matter and something else? Is man a true sacramental unity of body and soul or mind?
Are our very questions on these issues misguided by the misunderstandings of thinkers early in the development of higher human thought and of human exploration of what lay around them? Should we be paying more attention to modern knowledge than we pay to speculations upon earlier bodies of lesser knowledge of lesser quality? Or at least differently balancing our attention to these separate bodies of speculative and empirical knowledge?
Is it possible that the divisions in views of reality that we see are the result of not understanding that “created being is created being is…” and it is so dynamic as to make early thinkers see things as inert collections of matter moved by something else, spirits or life-forces or whatever?
The problems stated in the above paragraphs, the other many problems, are not to be solved anytime soon and certainly not in a single book. Yet, what I say in this book points to an important gap in modern thought—despite the often excessive use of quantitative mathematics, mathematical thought is poorly understood and rarely used to tackle more general, more abstract, levels of understanding.
Human mathematics has grown even more complex and richer than other aspects of human being, the physical sciences and history and culture and forms of community and so on. These fields of studies are parts of the human mind which forms by way of encapsulating those parts of Creation we can explore or speculate upon, along with the very small body of revealed knowledge which comes to the human mind by some as yet mysterious process.
It would seem to me that general human worldviews, largely determined by various forms of human being perhaps best described as theology and philosophy and poetry, haven’t kept up to the advances in those other components of human being.
Years ago, I conceived the possibility of adopting the insights of the most fundamental of the sciences, mathematics, to the development of a worldview adequate to the needs of man in the 21st century. This book will be a step in that direction. Note that the epigraphs for this book are the same as my earlier book, A More Exact Understanding of Human Being. I’ll quote them again for the ease of the reader but mostly because of the importance of the issue:
My soul [in Thomas the organ for thought] is not I; and if only souls are saved, I am not saved, nor is any man. [From the Commentary to 1 Corinthians by St. Thomas Aquinas as quoted by Hannah Arendt in The Life of the Mind (page 43).]
Modernity is not simply a historically-datable cultural phenomenon; in reality it requires a new focus, a more exact understanding of the nature of man. [Pope Benedict XVI, in a speech given on 2008/06/07 to participants in the sixth European Symposium of University Professors, which was held in Rome from 2008/06/04 to 2008/06/07 on the theme: “Broadening the Horizons of Reason. Prospects for Philosophy”.]
To make one aspect of the above claim more clear, I’ll provide another quote included in the body of A More Exact Understanding of Human Being:
[J]ust as a disciple reaches an understanding of the teacher’s wisdom by the words he hears from him, so man can reach an understanding of God’s wisdom by examining the creatures [God] made… [Page 17 of Commentary to 1 Corinthians by St. Thomas Aquinas.]
It seems to me, and has seemed to me for years, that the greatest weakness we bring to the task of understanding created being is our inability to see a human community (the Body of Christ in the limit) as being one without taking away from the individuality of the members of that community. We are some sort of gathering of isolated individuals or else we are a collective with compromised or even deleted individuality. This leads us to misunderstand the nature of the human mind and to miss the fact that we have communal minds; we can’t deal well with the badness of brainwashing by peer (herd) pressure nor the mysterious goodness of difficult ideas, pioneered by creative geniuses, becoming standard material in elementary or secondary school courses and in human thought in general.
We can find better possibilities in just the introductory chapters of books on abstract algebra and differential geometry and topology and a few other areas of mathematics. We can even see some progress on this issue in more concrete form in some particular results from physics and chemistry and biology and various synthetic fields of study such as the sciences of complex or chaotic systems or—better still—the sciences of self-organizing systems.
In this book, I’ll start at the abstract but mathematically basic level of `shape’, using differential geometry and topology, “abstract or qualitative geometry” and just a hint of other ways of thought. This is inadequate to the task but I’ll be following, approximately, the path I’m taking in tackling this problem, especially in my efforts to learn or relearn the mathematics needed for this simple way of viewing human being as individuals which are points with nice properties—qualitative and quantitative, points which are members of communities considered as surfaces with nice properties (manifolds).
Let’s see if we can harness this to provide general attitudes and ways of thought sufficient to understand this unity arising out of diversity, this oneness which is actually a collection of particular individuals; this seems to be a way of reasoning which can make sense of various parts and aspects of this universe and the various complex entities it contains. More than this, to get to the oneness of abstract and concrete being, we need to take on the task of understanding what a Christian would label as `Creation’.
As a general warning: I don’t consider understanding to be some sort of textbook-friendly, closed system of thought. Understanding is the development of a good way of describing what we know and understanding reaches its peak when it becomes our very way of thinking. In other words, we have a duty to shape our minds, our basic and sophisticated levels of thought, to reality. We fail when we try to squeeze reality into a system of thought we bring to the task of understanding our world, a system of thought which is typically a rigidified version of an earlier understanding of reality as known in, say, the 13th century, or one which came out of the poorly founded metaphysical speculations of a German Idealist of the 18th century or a Liberal Idealist of the 20th century. Such understandings are inadequate and downright unreasonable in the world after Darwin and Einstein.