Part 2. The act of learning and difficulties over the infinite.
Given what we have already said about the nature of education, it is clear that learning is not the task of the teacher. It is almost tautological to say that learning is the student's task, but we need to look at this more carefully if we are to get a real sense of how instruction, specifically catechetical instruction, needs to work.
Ordinary learning is achieved actively by the intellectual abilities of the learner. I look out onto the world and make sense of things by my own power: first, grasping only the vague outward natures of things, and gradually by means of abstraction, synthesis and experience coming to know their causes and principles and inner natures. As a child I marvel at a burning candle: its liquid wax and glowing flame seem to be a great mystery which I know only by seeing. Over time, though, I become acquainted with fire, its need for fuel, the rule that wax melts at a certain heat, etc. In coming to know a person I begin only with shallow impressions of character and appearance, but through time I come to understand how this person came to be this way, the specific qualities of his character, and most importantly the ends which motivate him. The meeting of the active mind and the world produces all this knowledge in me.
Instruction is simply a guided version of the same process. The teacher presents various data to me together so that I can more easily arrive at abstract knowledge of things. The historian teaches us the imprudence of autumnal invasions of Russia by pointing to Napoleon and Hitler. The scientist has a set of highly-coordinated experiences with matter and describes them so that other scientists can have the same experiences and derive general principles from them.
The example of science will help us move to our next point. The knowledge of the material sciences (physics, chemistry, biology, physiology, etc.) is fitted to the capacities of the human mind. It is easy for us, by nature (disregarding the variety of actual aptitudes for certain types of study among people) to know the sort of things these sciences deal with. All of them are based on abstraction from material things to general principles of their behavior.* Everyone fortunate enough to know his own limitations has, however, reached a point at which some proposition seems basically incomprehensible. More to the point, there are some things which we positively know that the human intellect cannot grasp. No one can know the actual value of π. We can define it and express it symbolically in infinite series or fractions, but we simply cannot know the true numerical ratio between a circle and its diameter. Were the human intellect infinitely powerful, it could simply apprehend π directly and know it as it is. As things stand, we can only say things like "it is greater than 3.14159" or "it is less than 22/7". Likewise, there are various physical concepts which cannot be perfectly known (the gravitational constant, for example, which expresses the strength of gravity). All of this attests the the finitude of the human intellect. No amount of abstraction or approximation will bring us to knowledge of the infinite.
*[Note: The shift from genuine principles to probabilistic conjectures in physics reflects the gradual frustration of physicists in their attempt to know the essence of mobile being — probabilities are useful, but they are a far cry from actual knowledge of causes.]
Aside from these rather unexciting examples (π and physical constants), humans run up against the infinite in much more obvious ways in everyday life. Consider the five year old who asks "why?" to everything he is told, until his parents either confess their ignorance or force the questioning to stop by some diversion. We rarely bother to ask ourselves where his questioning would finally terminate. What is the final reason for everything? This question occurs to adults in a subtle way whenever we are making a choice: why should I do this rather than that? Why should I do anything at all? What is my final goal? The ordinary, comprehensible answers to these questions (money, power, pleasure, knowledge, family, fame) — all things achievable in this life — seem inadequate to the reality of human desire. Give a man all of these things to the greatest extent and he can still be discontented. Some of the happiest people seem to have none of them, and it is difficult to believe that their happiness is some sort of self-delusion. The perfection of worldly life seems not to give us the answer to this "why?". We have vague intimations that only something infinite will do the trick, but how could one find out? Direct knowledge of things which transcend the world of finite, material reality is unreachable by man, who comes to know only by abstraction from experience.
I said in my heart, "come now, let me try you with pleasure and the enjoyment of good things." See, this too was vanity. Of laughter I said: "Mad!" and of mirth: "What good does this do?" I undertook great works; I built myself houses and planted vineyards; I made gardens and parks, and in them set out fruit trees of all sorts. I amassed for myself silver and gold, and the treasures of kings and provinces. Nothing that my eyes desired did I deny them, nor did I deprive myself of any joy; rather, my heart rejoiced in the fruit of all my toil. But when I turned to all the works that my hands had wrought, and to the fruit of the toil for which I had toiled so much, see! all was vanity and a chase after wind. There is no profit under the sun. I went on to the consideration of wisdom, madness and folly. And I saw that wisdom has as much profit over folly as light over darkness. Yet I knew that the same lot befalls both the wise man and the fool. So I said in my heart, if the fool's lot is to befall me also, why should I be wise? Where is the profit? And in my heart I decided that this too is vanity. Therefore I detested life, since for me the work that is done under the sun is bad; for all is vanity and a chase after the wind. (Ecclesiastes 2:1-17, with some omissions.)