CHAPTER ELEVEN What's the Proposition and Why not only coming to terms but making propositions occurs among traders as well as in the world of books. What a buyer or seller means by a proposition is some sort of proposal, some sort of offer or acceptance. Ip honest dealings, the man v.'ho makes a proposition in this sense is declaring his intention to act in a certain way. More than honesty is needed for successful negotiations. The proposition should be clear and, of course, attractive. Then the traders can come to terms.
A proposition in a book is also a declaration. It is an expression of the author's judgment about something. He affirms something he thinks true, or denies something he judges to be false. He asserts this or that to be a fact. A proposition of this sort is a declaration of knowledge, not intentions. The author may tell us his intentions at the beginning in a preface. In an expository book, he usually promises to instruct us about something. To find out whether he keeps those promises, we must look for his propositions.
The order of reading reverses the order of business somewhat. Businessmen come to terms after they find out what the proposition is. But the reader must usually come to terms with an author first, before he can find out what the author is proposing, what judgments he is declaring. That is why the first rule of interpretation concerns words and terms, and the second, which we are about to discuss, concerns sentences and propositions.
There is a third rule of interpretation closely related to the second. The author may be honest in declaring himself on matters of fact or knowledge. We usually proceed in that trust. But honesty is not enough. Unless we are exclusively interested in the author's personality, we should not be satisfied with knowing what his opinions are. His propositions are nothing but expressions of opinion unless there is some reason for them. If it is the subject matter of the book we are interested in, and not just the author, we want to know not merely what the propositions are, but why.
The third rule, therefore, deals with arguments of all sorts. There are many kinds of reasoning, many ways of supporting what one says. Sometimes it is possible to argue that something is true; sometimes no more than a probability can be defended. But every sort of argument consists of a number of statements related in a certain way. This is said because of that. The word "because" here signifies a reason being given.
The presence of arguments is indicated by other words which relate statements, such as: if this is so, then that; or, since this, therefore that; or, it follows from this, that that is the case. In the course of earlier chapters, such sequences occurred. If thinking, I said, is the use of our minds to gain knowledge, and if we use our minds to gain knowledge only in two ways, either in being taught or in investigating, then, I said, we must conclude that all the thinking we do occurs in the course of one or the other of these two activities.
An argument is always a set or series of statements of which some provide the grounds or reasons for what is to be concluded. It, therefore, takes a paragraph, or at least a collection of sentences, to express an argument. The premises or principles of an argument may not always be stated first, but they are the source of the conclusion, nevertheless. If the argument is valid, the conclusion follows from the premises. That does not necessarily mean that the conclusion is true, because the premises which'support it may be false, one or all.
Perhaps you have already observed something about the sequence of these three rules. We go from terms to propositions to arguments, by going from words (and phrases) to sentences to collections cf sentences or paragraphs.
When grammar was still taught in the schools, everyone was acquainted with these units. A schoolboy knew that an orderly sequence of sentences made up a paragraph. My experience with college students in the last ten years makes me doubt that this simple knowledge is common any longer. They do not seem able to write or speak sentences and paragraphs, and that has made me wonder whether they can recognize them in the books they read.
You will notice, furthermore, that we are now moving in the direction of building up from simpler to more complex units. The smallest significant element in a book is. of course, a single word. It would be true but not adequate to say that a book consists of words. It also consists of groups of words, taken as a unit, and similarly groups of sentences, taken as a unit. The reader, who is active rather than passive, is attentive not only to the words but to the sentences and paragraphs. There is no other way of discovering the author's terms, oropositions, and arguments,
The movement of this second or interpretative reading seems to be in the opposite direction to the movement of the first or structural reading. There we went from the book as a whole to its major parts, and then to their subordinate divisions. As you might suspect, the two movements meet somewhere. The major parts of a book and even their principal divisions contain many propositions and usually several arguments. But if you keep on dividing the book into its parts, you at last have to say: "In this part, the following points are made." Now each of these points is likely to be a proposition, and some of them taken together probably form an argument.
Thus, the two processes, which we have called the first and the second reading, meet. You work down to propositions and arguments by dividing the book into its parts. You work up to arguments by seeing how they are composed of propositions and ultimately of terms. When you have completed these two readings, you can really say you know the contents of a book.
There is one other thing to be noticed about the rules we are going to discuss in this chapter. As in the case of the rule about words and terms, we are here also dealing with the relation of language and thought. Sentences and paragraphs are grammatical units. They are units of language. Propositions and arguments are logical units, or units of thought and knowledge.
If you remember what our main problem was in the last chapter, you will be prepared to face a similar one here. Because language is not a perfect medium for the expression of thought, because one word can have many meanings and two or more words can have the same meaning, we saw how complicated was the relation between an author's vocabulary and his terminology. One word may represent several terms, and one term may be represented by several words.
Mathematicians describe the relation between the buttons and buttonholes on a well-made coat as a perfect one-to-one relationship. There is a button for every buttonhole, and a hole for every button. Well, the point is that words and terms do not stand in a one-to-one relation. The greatest error you can make in applying these rules is to suppose that a one-to-one relationship exists between the elements of language and those of thought or knowledge.
Let me show you this at once in the case of sentences and propositions. Not every sentence in a book expresses a proposition. For one thing, some sentences express questions. They state problems rather than answers. Propositions are the answers to questions. They are declarations of knowL edge or opinion. That is why we call sentences which express them declarative, and distinguish sentences which ask questions as interrogative. Other sentences express wishes or intentions. They may give us some knowledge of the author's purpose, but they do not convey the knowledge he is trying to expound.
Moreover, not all the declarative sentences can be read as if each expressed one proposition. There are at least two reasons for this. The first is the fact that words are ambiguous and can be used in various senses. Hence it is possible for the same sentence to express different propositions if there is a shift in the terms the words express. "Reading is learning" is certainly a simple sentence. But if at one place I mean by "learning" the acquisition of information, and at another I mean the development of understanding, the proposition is not the same, because the terms are different. Yet the sentence is verbally the.same.
The second reason is thafall sentences are not as simple as "reading is learning." You may remember from grammar school, if you belonged to a more fortunate generation, the distinction between simple sentences, on the one hand, and complex or compound sentences, on the other. When its words are used unambiguously, a simple sentence usually expresses a single proposition. But even when its words are used unambiguously, a compound sentence expresses two or more propositions. A compound sentence is really a collection of sentences, connected by such words as "and," or "if" and "then," or "not only" and "but also." You may rightly conclude that the line between a long compound sentence and a short paragraph may be difficult to draw. A compound sentence can express a number of propositions related in the form of an argument.
Complex sentences are the most difficult to interpret. There is no question that compound sentences express several propositions somehow related. But a complex sentence may express either one proposition or several. Let me take an interesting sentence from Machiavelli's The Prince to show you what I mean:
A prince ought to inspire fear in such a way mat, if he does not win love, he avoids hatred; because he can endure very well being feared whilst he is not hated, which will always be as long as he abstains from the property of his citizens and from their women.
That is grammatically a single sentence, though it is both compound and complex. The semicolon and the "because" indicate the major break which makes the sentence compound. The first proposition is that a prince ought to inspire fear in a certain way.
Beginning with the word "because," we have a complex sentence. It could be made independent by saying: "The reason for this is that he can endure," and so forth. This complex sentence expresses two propositions at least: (l) the reason why the prince ought to inspire fear in a certain way is that he can endure being feared so long as he is not hated; (a) he can avoid being hated only by abstaining from the property of his citizens and their women.
You can see why it is important to distinguish the various propositions that a long compound and complex sentence contains. In order to agree or disagree with Machiavelli, you must first understand what he is saying. But he is saying three things in this one sentence. You may disagree with one of them and agree with the others. You may think Machiavelli is wrong in recommending terrorism to a prince on any grounds; but you may acknowledge his shrewdness in saying that the prince had better not arouse hatred along with fear, and you may also agree that keeping his hands off their property and women is an indispensable condition of not being hated. Unless you recognize the distinct propositions in a complicated sentence, you cannot make a discriminating judgment on what the writer is saying.
Lawyers know this fact very well. They have to examine sentences carefully to see what is being alleged by the plaintiff or denied by the defendant. The single sentence, "John Doe signed the lease on March 24," looks simple enough, but still it says several things, one of which may be true and the other false. John Doe may have signed the lease, but not on March 24, and that fact may be important. In short, even a grammatically simple sentence sometimes expresses two or more propositions.
I have said enough to indicate what I mean by the difference between sentences and propositions. They are not related as one to one. Not only may a single sentence express several propositions, either through ambiguity or complexity, but one and the same proposition can be expressed by two or more different sentences. If you grasp my terms through the words and phrases I use synonymously, you will know that I am saying the same thing when I say, "Teaching and being taught are correlative functions," and "Initiating and receiving communication are related processes."
I am going to stop explaining the grammatical and logical points involved, and turn to the rules. The difficulty in this chapter, as in the last, is to stop explaining. Perhaps I had better assume that the school you went to taught some grammar. If it did, you may see now why all that business of syntax, of parsing and diagramming sentences, was not a meaningless routine invented by old-fashioned teachers to crush the spirit of the young. It all helps toward skill in writing and reading.
In fact, I should say it is almost indispensable. You cannot begin to deal with terms, propositions, and arguments— the elements of thought—until you can penetrate beneath the surface of language. So long as words, sentences, and paragraphs are opaque and unanalyzed, they are a barrier to, rather than a medium of, communication. You will read words but not receive knowledge.
Here are the rules. The first rule, you will recall from the last chapter, is: Find the important words and come to terms. The second rule is: Mark the most important sentences in a book and discover the propositions they contain. The third rule is: Locate or construct the basic arguments in the book by finding them in the connection of sentences. You will see later why I did not say "paragraphs" in the formulation of this rule.
You have already been introduced to the second and third rules. In the early chapters, we marked the sentence "reading is learning" as important, because it expressed a basic proposition in this discussion. We also noted several different kinds of argument: a proof that the great books are most readable, and a marshaling of evidence to show that the schools have failed to teach the arts of reading and writing.
Our task now is to get further light on how to operate according to the rules. How does one locate the most important sentences in a book? How, then, does one interpret them to discover the one or more propositions they contain?
Again, there is this emphasis on what is important. To say that there is only relatively small number of important sentences in a book does not mean that you need pay no attention to all the rest. Obviously you have to understand every sentence. But most of the sentences, like most of the words, will cause you no difficulty. From your point of view as a reader, the sentences important for you are those which require an effort of interpretation because, at first sight, they are not perfectly intelligible. You understand them just well enough to know there is more to understand. These may not be the sentences which are most important for the author, but they are likely to be, because you are likely to have the greatest difficulty with the most important things the author has to say.
From the author's point of view, the important sentences are those which express the judgments on which his whole argument rests. A book usually contains much more than the bare statement of an argument, or a series of arguments. The author may explain how he came to the point of view he now holds, or why he thinks his position has serious consequences. He may discuss the words he has to use. He may comment on the work of others. He may indulge in all sorts of supporting and surrounding discussion. But the heart of his communication lies in the major affirmations and denials he is making, and the reasons he gives for so doing. To come to grips, therefore, you have to see the main sentences as if they were raised from the page in high relief.
Some authors help you do this. They underline the sentences for you. They either tell you that this is an important point when they make it, or they use one or another typographical device to make their leading sentences stand out. Of course, nothing helps those who will not keep awake while reading. I have met many students who paid no attention to such signs. They preferred to read on rather than Stop and examine the important sentences carefully. They somehow knew unconsciously that the author was not just being helpful. He was trying to get them to do some mental work where it was most needed.
There are a few books in which the leading propositions are set forth in sentences which occupy a special place in the order and style of the exposition. Euclid, again, gives us the. most obvious example of this. He not only states his definitions, his postulates, and axioms—his principal propositions—at the beginning, but he labels every proposition to be proved. You may not understand his statements. You may not follow his arguments. But, if you have eyes in ' your head, you cannot miss the important sentences or the grouping of sentences for the statement of the proofs. That is^all done for you.
The Summa Theologica of St. Thomas Aquinas is another book whose style of exposition puts the leading sentences into high relief. It proceeds by raising questions. Each section is headed by a question. There are many indications of the answer which St. Thomas is trying to defend. A whole series of objections opposing the answer is stated. The place where St. Thomas begins to argue his point is marked by the words, "I answer that." There is no excuse tor not being able to locate the important sentences in such a book, those expressing the reasons as well as the conclusions, yet I must report that it is all a blur for students who treat everything they read as equally important. That usually means that everything is equally unimportant.
Apart from books whose style or format calls attention to what most needs interpretation by the reader, the spotting of sentences is a job the reader must perform for himself. There are several things he can do. I have already mentioned one. If he is sensitive to the difference between passages he can understand readily and those he cannot, he will probably be able to locate the sentences which carry the main burden of meaning. Perhaps you are beginning to see how essential a part of reading it is to be perplexed and know it. Wonder is the beginning of wisdom in learning from books as well as from nature. If you never ask yourself any questions about the meaning of a passage, you cannot expect the book to give you any insight you do not already possess.
Another clue to the important sentences is found in the words which compose them. If you have already marked the important words, they should lead you to the sentences which deserve further attention. Thus the first step in interpretative reading prepares for the second. But the reverse may also be the case. It may be that you will mark certain words only after you have become puzzled by the meaning of a sentence. The fact that I have stated these rules in a fixed order does not mean that you have to follow them in that order. Terms constitute propositions. Propositions contain terms. If you know the terms the words express, you have caught the proposition in the sentence. If you understand the proposition conveyed by a sentence, you have arrived at the terms also.
This suggests one further clue to the location of the principal propositions. They must belong to the main arguments of the book. They must be either premises or conclusions. Hence, if you can detect those sentences which seem to form a sequence, a sequence in which there is a beginning and an end, you probably have put your finger on sentences which are important.
I said a sequence in which there is a beginning and an end. Every argument which men can express in words takes time to state, more obviously so than a single sentence. You may speak a sentence in one breath, but there are pauses in an argument. You have to say one thing first, then another, and still another. An argument begins somewhere, goes somewhere, gets somewhere. It is a movement of thought. It may begin with what is really the conclusion and then proceed to give the reasons for it. Or it may start with the evidences and reasons and bring you to the conclusion which follows therefrom.
Of course, here as elsewhere, the clue will not work unless you know how to use it. You have to recognize an argument when you see one. Despite some disappointing experiences in teaching, I still persist in my opinion that the human mind is as naturally sensitive to arguments as the eye is to colors. The eye will not see if it is not kept open, and the mind will not follow an argument if it is not awake. I explain my disappointment with students in this connection by saying that they are mostly asleep while they read a book or listen to what goes on in class.
Several years ago, Mr. Hutchins and I began to read some books with a new group of students. They had had almost no training in reading and had read very little when we first met them. One of the first books we read was Lucretius' account of The Nature of Things. We thought this would be interesting for them. Most of our students are extreme materialists to begin with. And this work by Lucretius is a powerful exposition of the extreme materialistic position. It is the most extensive statement we have of the position of the ancient Greek atomists.
Because they were beginners in reading (though most of them were college juniors and seniors), we read the book slowly, at the rate of about thirty pages a time. Even so, they had difficulty in knowing what words to mark, what sentences to underline. Everything Lucretius said seemed to them of equal importance. Mr. Hutchins decided that it would be a good exercise for them to write out just the conclusions which Lucretius reached or tried to prove in the next part. "Don't tell us," he said, "what Lucretius thinks about the gods or women, or what you think about Lucretius. We want the argument in a nutshell, and that means finding the conclusions first."
The main argument in the section they had to read was an attempt to show that the atoms differ only in shape, size, weight, and speed of motion. They have no qualities at all, no colors or smells or textures. All the qualities we experience are entirely subjective—in us rather than in things.
The conclusions could have been written down in a few propositions. But they brought in statements of every sort. Their failure to extract conclusions from everything else was not due to lack of training in logic. They had no difficulty in following the line of an argument once it was presented to them. But they had to have the argument lifted out of the text for them. They were not good enough readers yet to do that for themselves. When Mr. Hutchins did the job, they saw how the statements written on the board formed an argument. They could see the difference between the premises—the reasons or evidences—and the conclusions they supported. In short, they had to be taught how to read, not how to reason.
I repeat, we did not have to teach them logic or explain in detail what an argument was. They could recognize one as soon as it was put on the board in a few simple statements. But they could not find arguments in a book because they had not yet learned to read actively, to disengage the important sentences from all the rest, and to observe the connections the author made. Reading Lucretius as they read the newspaper, they naturally did not make such discriminations.
Now let us suppose that you have located the leading sentences. Another step is required by the rule. You must discover the proposition or propositions each of these sentences contains. This is just another way of saying that you must know what the sentence means. You discover terms by discovering what a word means in a given usage. You discover propositions similarly by interpreting all the words that make up the sentence, and especially its principal words.
Obviously, you cannot do this unless you know a little-grammar. You must know the role which adjectives and adverbs play, how verbs function in relation to nouns, how modifying words and clauses restrict or amplify the meaning of the words they modify, and so forth. You must be able to dissect a sentence according to the rules of syntax. I said before that I was going to assume you knew this much grammar. I cannot believe you do not, though you may have grown a little rusty from lack of practice in the rudiments of the art of reading.
There are only two differences between finding the terms which words express and the propositions in sentences. One is that you employ a larger context in the latter case. You bring all the surrounding sentences to bear on the sentence in question, just as you used the surrounding words to interpret a particular word. In both cases, you proceed from what you do understand to the gradual elucidation of what is at first relatively unintelligible.
The other difference lies in the fact that complicated sentences usually express two or more propositions. You have not completed your interpretation of an important sentence until you have separated out of it all the different, though perhaps related, propositions it contains. Skill in doing this is easily exercised. Take some of the complicated sentences in this book and try to state in your own words each of the things that is being asserted. Number them and relate them.
"State in your own words!" That suggests the best test I know for telling whether you have understood the proposition or propositions in the sentence. If, when you are asked to explain what the author means by a particular sentence, all you can do is to repeat his very words, with some minor alterations in order, you had better suspect that you do not know what he means. Ideally, you should be able to say the same thing in totally different words. The ideal can, of course, be approximated in degrees. But if you cannot get away at all from the author's words, it shows that only words have passed from him to you, not thought or knowledge. You know his words, not his mind. He was trying to communicate knowledge, and all you received were words.
The process of translation from a foreign language into English is relevant to the test I have suggested. If you cannot state in an English sentence what a French sentence says, you know you do not understand the meaning of the French. Such translation is entirely on the verbal level, because even when you have formed a faithful English replica, you still may not know what the writer of the French sentence was trying to convey. I have read a lot of translations which reveal such ignorance.
The translation of one English sentence into another, however, is not merely verbal. The new sentence you have formed is not a verbal replica of the original. If accurate, it is faithful to the thought alone. That is why the making of such translations is the best test you can apply to yourself, if you want to be sure you have caught the proposition, not merely swallowed the words. I have tried it countless times on students. It never fails to detect the counterfeit of understanding. The student who says he knows what the author means, but can only repeat the author's sentence to show that he does, would not be able to recognize the author's proposition if it were presented to him in other words.
The author may himself express the same proposition in different words in the course of his writing. The reader who has not seen through the words to the proposition they convey is likely to treat the equivalent sentences as if they were statements of different propositions. Imagine a person who did not know that "24-2== 4" and "4 — 2 = 2" were different notations for the same arithmetic relationship— the relationship of four as the double of two, or two as the half of four.
You would have to conclude that that person simply did not understand the equation. The same conclusion is forced on you concerning yourself or anybody else who cannot tell when equivalent statements of the same proposition are being made, or who cannot himself offer an equivalent statement when he claims to understand the proposition a sentence contains.
These remarks have a bearing on the problem of reading two books about the same subject matter. Different authors frequently say the same thing in different words, or different things using almost the same words. The reader who cannot see through the language to the terms and propositions will never be able to compare such related works. Because of their verbal differences, he is likely to misread the authors as disagreeing, or to ignore their real differences because of verbal resemblances in their statements. I would go further and say that a person who cannot read two related books in a discriminating way cannot read either of them by itself.
There is one other test of whether you understand the proposition in a sentence you have read. Can you point to some experience you have had which the proposition describes or to which the proposition is in any way relevant? Can you exemplify the general truth which has been enunciated by referring to a particular instance of it? To imagine a possible case is often as good as reporting an actual one. If you cannot do anything at all to exemplify or illustrate the proposition, either imaginatively or by reference to actual experiences, you should suspect that you do not know what is being said.
All propositions are not equally susceptible to this test. It may be necessary to have the special experience which only a laboratory can afford to be sure you have grasped certain scientific propositions. We shall return to this point later in the discussion of reading scientific books. But here the main point is clear. Propositions do not exist in a vacuum. They refer to the world in which we live. Unless you can show some acquaintance with actual or possible facts to which the proposition refers or is relevant somehow, you are playing with words, not dealing with thought and knowledge.
Let me give you one illustration. A basic proposition in metaphysics is expressed by the following words: "Nothing acts except what is actual." I have had many students repeat these words to me with an air of satisfied wisdom. They have thought they were discharging their duty to me and to the author by so perfect a verbal repetition. But the sham was too obvious, I would first ask them to state the proposition in other words. Seldom could they say, tor instance, that if something does not exist, it cannot do anything. Yet this is an immediately apparent translation—apparent, at least, to anyone who understood the proposition in the original sentence.
Failing to get a translation, I would then ask tor an exemplification of the proposition. If any one of them told me that people do not run away from what is merely possible —that a baseball game is not postponed on account of possible showers—I would know at once that the proposition had been grasped.
The vice of "verbalism" can be defined as the bad habit of using words without regard for the thoughts they should convey and without awareness of the experiences to which they should refer. It is playing with words. As the two tests I have just suggested indicate, "verbalism" is the besetting sin of those who fail to read interpretatively. Such readers never get beyond the words. They possess what they read as a verbal memory which they can recite emptily. Strangely enough, one of the charges made by progressive educators against the liberal arts is that they tend to verbalism, when the facts clearly show that it is progressive education's neglect of the three R's which does exactly that. The failure in reading—the vicious verbalism—of those who have not been trained in the arts of grammar and logic shows how lack of such discipline results in slavery to words rather than mastery of them.
We have spent enough time on propositions. Let us now turn to the third rule, which requires the reader to deal with collections of sentences. I said before that there was a reason for not formulating this third rule by saying that the reader should find the most important paragraphs. The reason is that there are no settled conventions among writers about how to construct paragraphs. Some great writers, such as Montaigne and Locke, write extremely long paragraphs;
others, such as Machiavelli and Hobbes, write relatively short ones. In recent times, under the influence of newspaper and magazine style, most writers tend to cut their paragraphs to fit quick and easy reading. I must confess to you that in the course of writing this book I have often made two para' graphs out of what seemed to me to be naturally one, because I have been told that most readers like short paragraphs. This paragraph, for instance, is probably too long. If I had wanted to coddle my readers, I should have started a new one with the words, "Some great writers."
It is not merely a matter of length. The point that is troublesome here has to do with the relation between language and thought. The logical unit to which the third rule directs our attention is the argument—a sequence of propositions, some of which give reasons for another. This logical unit is not uniquely related to any recognizable unit of writing, as terms are related to words and phrases, and propositions to sentences. An argument, as we have seen, may be expressed in a single complicated sentence. Or it may be expressed in a number of sentences that are only part of one paragraph. Sometimes an argument may coincide with a paragraph, but it may also happen that an argument runs through several paragraphs.
There is one further difficulty. There are many paragraphs in any book which do not express an argument at all—perhaps not even part of one. They may consist of collections of sentences that detail evidence or report how the evidence has been gathered. As there are sentences that are of secondary importance, because they are merely digressions or side remarks, so also can there be paragraphs of this sort.
Because of all this, I suggest the following rule: Find if you can the paragraphs in a book which state its important arguments; but if the arguments are not thus expressed, your task is to construct thsm, by taking a sentence from this paragraph, and one from that, until you have gathered together the sequence of sentences which state the propositions that compose the argument.
After you have discovered the leading sentences, the construction of paragraphs should be relatively easy. There are various ways of doing this. You can do it by actually writing out on a pad the propositions that together form an argument. Or you can put a number in the margin to indicate the place where the sentences occur that should be tied together in a sequence.
Authors are more or less helpful to their readers in this matter of making the arguments plain. Good authors try to reveal, not conceal, their thought. Yet not even all good authors do this in the same way. Some, such as Euclid, Galileo, Newton (authors who write in a geometrical or mathematical style), come close to the ideal of making a single paragraph an argumentative unit. With the exception of Euclid, there are almost none who make every paragraph an argument. The style of most writing in non-mathematical fields of science tends to present two or more arguments in a single paragraph or to have an argument run through several.
In proportion as a book is more loosely constructed, the paragraphs tend to become more diffuse. You often have to search through all the paragraphs of a chapter to find the sentences you can construct into the statement of a single argument. I have read some books which make you search in vain, and some which do not even encourage the search.
A good book usually summarizes itself as its arguments develop. If the author summarizes his arguments for you at the end of a chapter, or at the end of an elaborate section, you should be able to look back over the preceding pages and find the materials he has brought together in the summary. In The Origin of Species, Darwin summarizes his whole argument for the reader in a last chapter, entitled "Recapitulation and Conclusion." The reader who has worked through the book deserves that help. The one who has not, cannot use it.
Another difference between a good and a bad writer is the omission of steps in an argument. Sometimes they can be omitted without damage or inconvenience, because the propositions left out can be generally supplied from the common knowledge of readers. But sometimes their omission is misleading, and may even be intended to mislead. One of the most familiar tricks of the orator or propagandist is to leave certain things unsaid, things which are highly relevant to the argument, but which might be challenged if made explicit. While we do not expect such devices in an honest author whose aim is to instruct us, it is nevertheless a sound maxim of careful reading to make every step in an argument explicit.
Whatever kind of book it is, your obligation as a reader remains the same. If the book contains arguments, you must know what they are, and in a nutshell. Any good argument can be put into a nutshell. There are, of course, arguments built upon arguments. In the course of an elaborate analysis, one thing may be proved in order to prove another, and this may be used in turn to make a still further point. The units of reasoning, however, are single arguments. If you can find these in any book you are reading, you are not likely to miss the larger sequences.
This is all very well to say, you may object, but unless one knows the structure of argument as a logician does, how can one be expected to find them in a book, or worse, to construct them when the author doesn't state them com-pactly in a single paragraph?
I can answer you by pointing out why it must be obvious that you do not have to know about arguments "as a logician does." There are relatively few logicians in the world, for better or for worse. Most of the books which convey knowledge and can instruct us contain arguments. They are intended for the general reader, not tor the specialists in logic.
I, for one, do not believe that great logical competence is needed to read these books. I repeat what I said before, that the nature of the human mind is such that if it works at all during the process of reading, if it comes to terms with the author and reaches his propositions, it will see his arguments as well.
There are, however, a few things I can say which may be helpful to you in carrying out this third rule. In the first place, remember that every argument must involve a number of statements. Of these, some give the reasons why you should accept a conclusion the author is proposing. It you find the conclusion first, then look for the reasons. If you find the reasons first, see what they lead to.
In the second place, discriminate between the kind of argument which points to one or more particular facts as evidence for some generalization and the kind which offers a series of general statements to prove some further generalization. General propositions which are called self-evident, or axioms, are propositions we know to be true as soon as we understand their terms. Such propositions are ultimately derived from our experience of particulars.
For example, when you understand what any physical whole is, and when you understand what it means for anything to be a part of such a whole, you know at once that the whole is greater than any of its parts. Through understanding three terms—whole, part, and greater than—you at once know a true proposition. The most important step in getting to that truth is restricting the meaning of the word "whole" by the qualification physical. The proposition that the whole is greater than a part is not true for every sort of whole. But when you use these words with restricted meanings, you reach terms which are evidently related in a certain way. What becomes evident in this way is a familiar axiom, a proposition which men have commonly recognized to be true for many centuries.
Sometimes such propositions are called tautologies. The name makes very little difference except to indicate how you feel about the proposition whose truth is clear without proof—a generalization which is argued directly from particulars. When in modern times self-evident truths have been called "tautologies," the feeling behind it is sometimes one of contempt for the trivial, or a suspicion of legerdemain. Rabbits are being pulled out of the hat. You put the truth in by defining your words, and then pull it out as if you were surprised to find it there. Notice, however, that that is not the case. To restrict the meaning of a word is not to define a thing. Wholes and parts are things, not words. We did not define them. In fact, we cannot. What we did do was to limit our words so that they referred to a certain type of thing with which we are acquainted. Once that was done we found we knew something that our restricted words could express.
In the literature of science, the distinction is observed between the proof of a proposition by reasoning and its establishment by experiment. Galileo, in his Two New Sciences, speaks of illustrating by experiment conclusions which had already been reached by mathematical demonstration. And in a concluding chapter, the great physiologist Harvey writes: "It has been shown by reason and experiment that blood by the beat of the ventricles flows through the lungs and heart and is pumped to the whole body." Sometimes it is possible to support a proposition both by reasoning from other general truths and by offering experimental evidence. Sometimes only one method of argument is available.
In the third place, observe what things the author says he must assume, what he says can be proved or otherwise evidenced, and what need not be proved because it is self-evident. He may honestly try to tell you what all his assumptions are, or he may just as honestly leave you to find them out for yourself. Obviously, everything cannot be proved, just as everything cannot be defined. If every proposition had to be proved, there would be no beginning to any proof. Such things as axioms, or propositions somehow drawn directly from experience, and assumptions, or postulates, are needed for the proof of other propositions. If these others are proved, they can, of course, be used as premises in further proofs.
These three rules of reading—about terms, propositions, and arguments—can be brought to a head in a fourth and final rule. This fourth rule governs the last step in the second reading of a book. More than that, it ties the second reading together with the first.
You may remember that the last step in the first reading was the discovery of the major problems which the author tried to answer in the course of his book. Now, after you have come to terms with him and grasped his propositions and arguments, you can check what you have found by answering the following questions. Which of the problems that the author tried to solve did he succeed in solving? In the course of solving these, did he get into any new ones? Of the problems he failed to solve, old or new, which did the author himself know he failed on? A good writer, like a good reader, should know whether a problem 'has been solved or not, though I can see how it might cost the reader less pain to acknowledge the failure.
When you are able to answer these questions, you can feel reasonably assured that you have managed to understand the book. If you started with a book that was above you—and one, therefore, that was able to teach you something—you have come a long way. More than that, you are now able to complete your reading of the book.
The third and last stage of the job will be relatively easy. You have been keeping your eyes and mind open and your mouth shut. Up to this point, you have been following the author. From this point on, you are going to get a chance to argue with the author and express yourself.
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