In E. F. Schumacher’s book, A Guide for the Perplexed (a short book that I often recommend to people who want to dip into philosophy for the first time), there is a final chapter called “Two Types of Problems.” In it, Schumacher contrasts what he calls “convergent problems” from “divergent problems.” I am convinced of the vital importance of the distinction for the governance of our lives and politics, so let me give you a thumbnail version:
A convergent problem is one in which various solution-seekers, working independently of one another, would converge toward the same answer. An arithmetic problem is clearly an example; another is the problem of water transport, which converged on the solution of the hollow boat, types of which were independently developed all over the world. One hint to spotting a convergent problem is that its solution can be written down and be put to use without restatement of the problem that gave it rise. If an answer can be agreed upon, can be written down, and also renders worthless its correlative problem, then that problem was convergent. A convergent problem is a technical problem.
A divergent problem on the other hand does not produce the same answer among various thinkers. Solutions diverge and often produce opposite prescriptions for dealing with them. The example Schumacher gives is the education of children. One party working on this issue would emphasize the issue of the transmission of learning from one generation to the next. “Those who have (or are presumed to have) knowledge and experience teach, and those who as yet lack knowledge and experience learn. For this process to be effective, authority and discipline must be set up.” (p. 122) Another party says that the “educator is like a good gardener, whose function is to make available healthy, fertile soil in which a young plant can grow strong roots; through these it will extract the nutrients it requires. The young plant will develop in accordance to its own laws of being, which are far more subtle than any being can fathom, and will develop best when it has the greatest possible freedom to choose exactly the nutrients it needs.” (p. 122). So one faction recommends discipline, which if a little is good then more is better (in the direction of a stifling conformity), and the other represents freedom, in which the limit case is feral existence. (Other examples are nature/nurture, public/private, stability/change, tradition/innovation.) The divergent problem of education, whose “solution” requires some sort of awareness of the necessary tensional balance between these two rival poles, instead becomes a polemical shouting match between two sides who have favored one pole of the “truth” at the expense of another. Divergent problems are dialectical problems, what Schumacher calls “human problems.”
Much mischief is done in society by failing to recognize the existence of divergent problems, and to think (wrongly) that all real problems are reducible to the convergent/technical type. The Greeks (particularly Aristotle in Nicomachean Ethics, Book VI, but throughout Plato too) captured a similar distinction in their speech with a precision that is missing in English. Techne is skill that corresponds to the application of convergent solutions to convergent problems. Techne/skill is applied in the regime of poesis/making in which an end/telos is known in advance and can be specified precisely in advance of the making. Phronesis on the other hand is the practical wisdom that corresponds to the virtuous performance of right action. Phronesis/practical-wisdom is applicable to the regime of praxis/action. Phonesis must rule in those situations where there is no specifiable end/telos distinct from the specific performance/praxis. The end (or direction) of activity governed by phronesis can only be fully understood by the one engaged in the activity and attuned to its immanent norms. The “end” established by phronesis is often more an orientation than a stopping point. The dialectical problems of the divergent kinds are “solved” by the guidance of phronesis within the concrete setting of the actions themselves.
The distinction, which we have variously called convergent/divergent, technical/dialectical, techne/phronesis also has an echo in the difference that Gabriel Marcel points out between a problem and a mystery:
“A problem is something which I meet, which I find completely before me, but which I can therefore lay siege to and reduce. But a mystery is something in which I am myself involved, and it can therefore only be thought of as a sphere where the distinction between what is in me and what is before me loses its meaning and initial validity.” — Being and Having, p. 117.
The problems of philosophy are often of the divergent type, which explains the strong, polar disagreements among its proponents. Divergent problems have dialectical opposition built into them by nature and require the wisdom of phronesis to navigate. They are personally involved, existential problems. They never go away but are built into the ontological makeup of our species, informing its striving. The question of “the right way to live” is a preeminently divergent question. My hope is that my work on “defective reading” will help contribute to lived-out answers to the many divergent problems in which we swim.