Our delusions about the world being subject to understanding by an out-of-the-box human mind and our allied delusions about human control over that world lead us into various specific errors. We ignore what doesn’t fit into our favorite schemes, that is, we are blind and deaf to what doesn’t fit into our delusionary schemes of understanding. We think we and our children are born with preformed minds and try to understand that world and to teach those children by pushing knowledge into those preformed minds; in the modern West and most certainly in the United States, the duty of teachers is to push knowledge into those minds rather than realizing that the mind needs to be shaped by immersion in a subject, even if the subject were the vaguely defined study of how to be a good citizen. It’s of some interest that athletic coaches and military trainers train and educate those under their charge by more penetrating techniques, even deliberately driving those under their charge into states of exhaustion to destroy their reluctance to take on their new roles. In fact, the mind shapes itself in active responses to what lies outside of itself—the true insight expressed in a strange way in the Zennish claims that there is no difference between knowledge and the knower, between subject and object.
So we have distorted out own mental development and that of our children and, most obviously, that of our communities. Rather than responding to a world of evolutionary and developmental processes, we think to be building first huts of mud and grass, then wooden huts, then stone structures right up to pyramids, then concrete coliseums and temples and aqueducts, then stone cathedrals…right up to steel and concrete skyscrapers. And we don’t get the point, at least not the bulk of human beings including most of the members of the political and economic elite. That is we don’t get the point that the minds of people who build mud and grass huts, those who build pyramids, those who build steel and glass skyscrapers, are minds suited to a world in which those were real possibilities available to and created by human animals responding actively to their environments. They were not just foreseeable stages in the progression of a species fated to build steel and glass skyscrapers from the time the first apish man learned how to use fire to light and to cook and to create grasslands; they were not just learning stages for a species set in this world to exploit it.
We fall into such errors partly because of the `intuitions’ built into our brains by the processes of evolution. Even the most brilliant of mathematical physicists first learned to count as an infant because he has a brain inclined to count due to the survival and the reproductive success of his finger-counting ancestors over the previous hundreds of thousands of years. And that great mathematical physicist named Einstein was a man born near the end of the 19th century and had a brain shaped by his active responses to a world which knew of Archimedes and Newton and Maxwell and also knew of Homer and Shakespeare and Goethe.
We also are fooled because we, as a species have learned to summarize some sorts of knowledge in axioms and rules which work with those axioms, using that axiomatic system to organize our more complex knowledge and to create various short-cuts which prevent us from having to repeat the messy trial-and-error processes which led to the physics and engineering knowledge which can build skyscrapers.
We create our own opportunities and our own problems by way of our very power to think abstractly, to set up—for example—geometric systems. We can somehow rise above our individual and communal selves to judge those selves and the world in which those selves exist—download my book, Four Kinds of Knowledge: Revealed Knowledge, Speculative Knowledge, Scientific Empirical Knowledge, Practical Empirical Knowledge, for a still preliminary account of what is involved in human `knowing’. In fact, a `world’ is a speculative construction of accessible and mundane environments, up to the entire `universe’ as defined in modern physical cosmology and beyond. Call this construction a `worldview’ and we can free the word `world’ for referring to the objective reality which we see imperfectly and incompletely—often in a downright distorted way. I go at this and other issues again and again in my writings, trying to draw out the subtleties and nuances because of the underlying complexity often masked by the view that things are really so simple. (I lightly address this issue in Enriching Our Moral World: Simple Is Digested Complexity.)
In a simple analogy: the construction of Blocks worlds led to a lot of good work in artificial intelligence research in which a very simple concrete world was abstracted so that it could be manipulated as if a well-defined mathematical system. The term `well-defined’ points to the problem. For example, once topology was seen as the study of continuities of certain types of systems, by the way of simple set operations, it could be well-defined in remarkably simple ways as the study of sets which behaved in certain ways under basic set operations; a continuous function was then defined as one which has an inverse which maps open sets to open sets. (Very roughly, an open set is a general concept whose simple manifestation is a line which doesn’t include its endpoints.) Modern mathematics is so powerful just because it has `fragmented’ into these well-defined fields of study which are interrelated but separated in important ways. It is also so powerful because mathematicians learned to live with a situation confusing to outsiders: some fields, such as number theory, are strictly quantitative while other fields, such as topology, are mostly qualitative and are often greatly concerned with existence proofs. And its also so powerful because a rich field such as topology (originally and even now dealing with continuous deformations which tell us a doughnut and a tea-cup are the same `shape’, as are a filled-in square and a filled-in circle—by some rigorous understanding of `shape’) can be reduced to some simple sets of axioms about sets. The original power of topology is retained but it can also deal with problems which weren’t even possible to imagine before those simplifications which are actually great abstractions.
Much work in trying to understand our complex world, say the genetic aspects of terrestrial life or the economic or political aspects of human being, seems to involve the implicit construction of blocks worlds and then the direct (naive?) analysis without proper understanding of the need for qualitative analysis of those assumed blocks worlds to determine if the solutions or understandings they seek even exist or—still more basically—to determine by playing out scenarios if those blocks worlds even correspond to reality in the desired ways. Reality might not be cooperative. For example, artificial intelligence researchers discovered early on that a robot which relied on pure logical reasoning could freeze for hours while trying to prove it possible to get around one or more obstacles between it and its goal. Obviously, there are better ways to plan moves even in fairly simple physical situations. A hawk won’t eat well if he takes hours of analysis to determine if he can get to a squirrel running through a field with the protection of scattered trees.
The trick, for at least those responsible for scouting out the future and forming understandings about futures suddenly become radically different todays, is to jump to a higher level of abstraction but always staying within the constraints of concrete reality. This last statement might seem contradictory but it’s not—we’ve found in recent centuries that higher level abstractions in mathematics might be found by exploring concrete reality or they might be found by developing further the abstractions already developed. In either case, there is an admittedly vague sense in which we might say that mathematics as a whole is found in concrete reality—any alternative statements will also be vague or downright false.
Let me consider a few problems seeming far from the reach of abstract mathematical reasoning:
- Is there an qualitative description of human being which is worth much?
- Can such an abstract description, if it exists, help us to provide further descriptions of our possibilities, the ways in which we can shape ourselves?
- Can such an abstract description, if it exists, help us to understand the true relationships of individual and communal human being?
- Is there a coherent understanding of personhood other than as a synonym for nature?
- If personhood is a coherent concept subject to disciplined discourse: are all human beings persons?
- What is a community, really?
Though I have my own still developing answers to some of these questions and a few ideas about all the rest, I don’t intend to propose definitive answers to any of them in the initial batch of the essays and books I can hope to write, only to explore the possibility of developing a more disciplined way to speak about these `qualitative’ issues by borrowing tools from qualitative mathematics. After I succeed, or someone else succeeds, in this initial project of providing a more complex and sophisticated framework of analysis for the complex human relationships of complex communities, then that framework can be used to express, say, Christian or Jewish moral and even theological ideas, perhaps a variety of ideas from other stances.
In any case, there are more such questions which I think can best be dealt with in an intelligent and non-ideological way by proper use of `qualitative’ forms of reasoning which have led to deep and important results in mathematics and mathematical physics and computer science and other fields of human research.
In closing, I’ll confess that my efforts in this general vein are powered by a great and optimistic faith that the qualitative forms of reasoning discovered by mathematicians and some other mathematically inclined scientists can be abstracted to provide ways of reasoning appropriate for understanding human being, individual and communal. This is a continuation of the use, for example, of paths crooked and straight in moral thought. The moral realms of this world have grown opaque to much of that thought and we have no tools to rebuild our thought. If being is one and knowledge about being is ideally one then any powerful reasoning processes developed for use in, say, moral issues might well prove useful to mathematicians and physicists and engineers and others.