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He may honestly try to tell you what all his assumptions are, Determining an Author's Message 1 33

or he may just as honestly leave you to 6nd them out for yourself. Obviously, not everything can be proved, just as not everything can be defined. If every proposition had to be proved, there would be no beginning to any proof. Such things as axioms and assumptions or postulates are needed for the proof of other propositions. If these other propositions are proved, they can, of course, be used as premises in further proofs.

Every line of argument, in other words, must start somewhere. Basically, there are two ways or places in which it can start: with assumptions agreed on between writer and reader, or with what are called self-evident propositions, which neither the writer nor reader can deny. In the first case, the assumptions can be anything, so long as agreement exists. The second case requires some further comment here.

In recent times, it has become commonplace to refer to self-evident propositions as "tautologies"; the feeling behind the term is sometimes one of contempt for the trivial, or a suspicion of legerdemain. Rabbits are being pulled out of a hat. You put the truth in by defining your words, and then pull it out as if you were surprised to find it there. That, however, is not always the case.

For example, there is a considerable difference between a proposition such as "a father of a father is a grandfather," and a proposition such as "the whole is greater than its parts." The former statement is a tautology; the proposition is contained in the definition of the words; it only thinly conceals the verbal stipulation, "Let us call the parent of a parent a 'grandparent.' "

But that is far from being the case with the second proposition.

Let us try to see why.

The statement, "The whole is greater than its parts," expresses our understanding of things as they are and of their relationships, which would be the same no matter what words we used or how we set up our linguistic conventions. Finite quantitative wholes exist and they have definite finite parts; for example, this page can be cut in half or in quarters. Now, 1 34 HOW TO READ A BOOK

as we understand a finite whole ( that is, any finite whole ) and as we understand a definite part of a finite whole, we understand the whole to be greater than the part, or the part to be less than the whole. So far is this from being a mere verbal matter that we cannot define the meaning of the words "whole"

and "part"; these words express primitive or indefinable notions. As we are unable to define them separately, all we can do is express our understanding of whole and part by a statement of how wholes and parts are related.

The statement is axiomatic or self-evident in the sense that its opposite is immediately seen to be false. We can use the word "part" for this page, and the word "whole" for a half of this page after cutting it in two, but we cannot think that the page before it is cut is less than the half of it that we have in our hand after we have cut it. However we use language, our understanding of finite wholes and their definite parts is such that we are compelled to say that we know that the whole is greater than the part, and what we know is the relation between existent wholes and their parts, not something about the use of words or their meanings.

Such self-evident propositions, then, have the status of indemonstrable but also undeniable truths. They are based on common experience alone and are part of common-sense knowledge, for they belong to no organized body of knowledge; they do not belong to philosophy or mathematics any more than they belong to science or history. That is why, incidentally, Euclid called them "common notions." They are also instructive, despite the fact that Locke, for example, did not think they were. He could see no difference between a proposition that really does not instruct, such as the one about the grandparent, and one that does-one that teaches us something