Science does not, and can not claim that reality is limited only to what enters directly into our experience through the senses. We can see with our own eyes that water is a liquid, but the fact that each molecule of water consists of two atoms of hydrogen and one of oxygen is something which escapes us, because these atoms are not visible. But perceived facts are far from being the only facts we can know. There are facts which we can know of, rather than know. The way to arrive at them is byinference. For instance, we apprehend water by direct perception of its appearance. If I examine a drop of water through a microscope, I can have a better understanding of it. But it is only by inference, and not by direct observation that I can grasp the fact that each molecule of water is composed of two atoms of hydrogen and one of oxygen.
A.E. Mander, in his book Clearer Thinking, observes with great pertinence:
It is useful to reflect that, if we were equipped with different senses, all that we now perceive would be unknowable to us by direct perception. For example, if our eyes were as powerful as a microscope, we should be able to see bacteria. But we could not then perceive elephants. We should be obliged to infer their existence.
Similarly, we now perceive the phenomena, which, being of wavelengths lying within certain limits, are registered by our sense of sight. There are millions of facts we see. Yet if our eyes were differently constructed so that they were turned to long wavelengths instead of very short ones, then we should have direct sense perceptions of wireless waves, which now we know only by inference, but we should then have no direct perception of all that part of the universe which is now visible to our eyes. We could only infer it (p. 48).
Later, he goes on to remark:
Of all the facts in the universe of fact, we can know some, relatively few, by sense perception. But how can we come to know of others? By inference, or reasoning. Inference or reasoning is a mode of thinking by which, staring from something known, we end by forming a belief that there exists a certain fact hitherto unknown.
How can we be sure that there is any validity in this thought-process that we call ‘reasoning’? How can we be sure that the belief which we from by reasoning is true? The answer to this is that we do begin by simply assuming that our methods of reasoning are reliable, that they lead us to conclusions, which correspond with facts.
Starting from facts known by sense perception, we may reason to the conclusion that some other fact, though not yet perceived, exists. We may thus be as sure of an inferred fact as we are of any perceived fact, provided that our original data are perceived facts.
The same method of reasoning leads us to thousands of different conclusions. They are now so highly probable that we can regard them as approximate certainties (p. 49).
This basic principle may be summed up in a single sentence: The reasoning process is valid because the universe of fact is rational (p.50).