Every-day reasoning

Front matter

s

WASHINGTON

Entered, according to Act of Congress, in the year 1876, by

Preface

THIS work is offered to teachers as an aid in setting before their pupils the principles of Inductive Logic. As our reasoning is inductive rather than deductive in daily life, it is important that the young should -know at least the methods and tests. No great claim to originality is made, as no effort was put forth to attain it. Everything within reach has been examined, in order to gain additional light ; and much that was desirable was left out, in order to keep the book within such bounds that it could be easily mastered by average students in a single session. ( Some important matters, and some especially clear illustrations, have been repeated in different connections, in the belief that repetition aided the memory. The design in preparing the work was not merely to offer a text-book to schools, but also to provide a convenient manual for men and women in their professional and daily life, wherein they might find suggestions for making their experiments, reaching their conclusions, and testing the correctness of the same. Under the title Every-Day Keasoning, an outline of the thought has been very frequently delivered as a lecture; and the favorable reception accorded to the subject in that form has led to the hope that greater usefulness would be attained by its publication in this form. Of course, the difference of circumstance and aim will account for the difference of style.

Washington and Jefferson College.

Part Third. Methods Of Induction

PAGB

General Statement 51

Method of Agreement 53

Method of Difference 58

Method of Besidues 65

Method of Concomitant Variations ... 70

Classification by the Four Methods 87

Analysis 92

Questions of Inductive Logic 96

Final Causes or Design 102

Part Fourth. Steps In Induction

Stating the Question 107

Gathering the Facts Ill

Detection of Law 115

Verification — Explanation of Facts 120

Eule of Harmony 123

Eule of Simplicity 129

Eule of Concurrence 135

Eule of Sufficiency? 141

Eule of Prediction 148

Jhe Interpretation of Documents 155

The Art of Debate 162

Index 169

Introduction

THE irresistible reason for keeping arithmetic as a study in every common school is, that every person must keep all their accounts by it. If they are not able to perform its simpler operations correctly, they are not able to take care of their own rights. They are liable to be both intentionally and unintentionally cheated. In order, therefore, to fit them, in any sense, for their future lives, our children are taught these arithmetical rules. They are rightly enough compelled to learn the multiplication table, before they have any true idea of what it means, -or any conception of the many uses they will afterwards have for it.

These same things are just as true of reasoning as of arithmetic. Everything we do is done for a reason. We do not need arithmetic for every conclusion to which we come. We cannot come to a conclusion without more or less of a reasoning process. The old adage, of children learning to dread the fire, is reached by the method of agreement. The child dreads this fire, because it agrees in appearance and otherwise with the fires by which it has heretofore been burned. This is exactly inductive reasoning. The same thing will be true of the child in all its after life. It will plan its business, and seek its pleasures, by reasons which are subject to, and may be tested by, the methods of inductive logic. Every merchant at his counter, every mechanic at his trade, every farmer in his fields, every housewife at her work, every cook at the stove, in arranging each step of their daily duties, will decide on what they will do, because they either wish to attain what they have been able

X INTRODUCTION.

to accomplish in that way before, or they will try some new plan, because they want to avoid some evil, or danger, or apparently needless labor. If their reasoning is correct and their facts reliable, they may expect success; if they are mistaken as to the, facts, or incorrect as to their inductions from them, the/ will almost certainly fail. Masses of men are bankrupt, jecause they bought at the wrong time and sold at the wrong time. Their intentions were honest, but their reasonings were fallacious ; and no integrity of purpose will save a man, when he misses his facts, and reasons badly on such as he may have. When now life and its opportunities come to us but once, and a blunder, though sometimes it may be rectified in the future, irreparably loses for us the present occasion, of what supreme importance is it, that we should, as far as possible, save ourselves from mistakes ! Every day we will do what we will do, because we think, by the course we adopt, we will attain our desired ends. If in that course of reasoning we are wrong, we will fail, and ought to. By as much, therefore, as the number of times we act on our own judgment exceeds the number of times we need to employ arithmetical computation, by so much is a knowledge of inductive logic of more practical use than arithmetic.

Geography is everywhere taught, and children's minds are burdened with the names of innumerable capes and rivers they will never see, ancl of whose existence, if they should be ignorant all their lives, they would perhaps lose but little. It is not creditable either to a child's parents or teachers, that it should be allowed to grow up unable to speak its mother tongue with considerable accuracy. Many people, however, who use bad grammar, and know but little geography, succeed finely in business, because they can reason correctly. Thus they make no mistakes in trade, and waste neither time nor money on foolish projects, with all their bad grammar.

INTRODUCTION. XI

The great difficulty, however, with inductive logic is, to make it so plaiu that its application to every- day life will be obvious. If it could be so simplified and adapted to common affairs, that its relation to daily business could be seen as directly as that of arithmetic or grammar, there would be no serious obstacle in securing for it a similar place. But even if no book fully meeting the case has yet been provided, it is worthy of consideration whether it is not better to study a poor book than none at all. By no possibility can any one escape the necessity of every-day reasoning ; and the successes or failures that will come from their good or bad logic, will come upon their own heads, study or no study.

In this work, Part First is devoted to a discussion of the different kinds of truth and reasoning ; Part Second treats of the materials furnished us on which to reason ; Part Third explains the four methods and the questions inductive logic is adapted to answer ; Part Fourth gives the steps to be followed and the five tests by which true conclusions may be known to be true, and false ones detected as false. Some practical matters are then added, not immediately connected with this subject, but belonging to its field rather more than to any other included among text-books. All readers, as well as all students, are strongly advised to commit to memory the names of the four methods and the five tests, and then so study them that their names will readily suggest their application.

EVERY-DAY REASONING.

Part First. Truth

TKUTH vs. FALSEHOOD.

TRUTH is, what is, as it is. Otherwise defined, truth is the characteristics and relations of things, individually, collectively, and relatively. Truth thus includes not merely the conditions of things considered alone, but it is limited and confined by the relations of things among themselves. The opposite of truth is falsehood, which is an assertion that certain things, characteristics, or relations exist when they do not. By comparing and contrasting these two, a more exact knowledge of both will be obtained.

First Distinction. — Truth is in things. Falsehood is never in the things, but only in the conceptions of them, or the statement of those conceptions in words. There are thus three places where truth may be found, and only two for falsehood. Truth exists first in the things themselves. Then this truth may be correctly perceived by the mind. It may then be stated in words, as it is thus correctly perceived by the mind. -For example, two and two are four. We see this and say so. The ship has three masts. We count them, and state the fact. The horse is a quadruped. We notice this when we see one, and so record it. But if we say two 2 13 and two are five ; the ship is feathered ; the horse chews the cud ; these are not true. They have not, however, changed the relations of numbers, the character of the ship, or the nature of the horse. Things themselves never lie. Men may misunderstand them, and they may consciously or unconsciously state that which is not true concerning them ; but the truth is not affected either by their misapprehension or misstatement. It remains the same, regardless of the impressions men take up concerning the matter. Truth, therefore, is in things themselves, and may be perceived by the mind, and then stated in words ; but falsehood is only found in men's conception of things, or their statements in words.

Second Distinction. — Truth is true without regard to man's action, and so is true before its discovery by the human mind. Our perception of it affected us, but it did not affect it. It was just as true before, as after, men came to the knowledge of it. Gravitation was just the same before the discovery of its laws by Newton, that it has been since. It acted just as powerfully, and in just the same way. The stones fell, and stars moved, and bodies weighed, just as they did afterwa'rds. After we discover truth, we are enabled to avail ourselves of it in the accomplishment of our purposes ; but the truth was there before. Steam was as ready to do its work before the days of \Vatt as since, only we could not use it. The development of geometry in no way affected the relations of lines or angles. Falsehood, on the other hand, never exists until after men have acted. As it exists only in our conceptions or our statements, of course it could only come into being by the action of our minds. It was a great error to say that two pounds of lead would fall to the ground twice as fast as one pound; but such a thought never had any existence until some mistaken philosopher made the assertion. The indications were all the other way, until Ananias and Sapphira asserted that what they gave

TRUTH. 15

the apostles was the whole price for which they sold their land. It is thus left for the action of finite mind to bring all falsehood into being.

Third Distinction, — Truth is always consistent with itself, so that each separate truth is consistent with every other truth. There is no such self-consistency and harmony in error. Falsehoods are not only at war with truth, but they wrangle and fight with each other. Every proposition of geometry is consistent with every other proposition. Every law of nature harmonizes with every other law. Truths are not only consistent when occurring at the same time, but they are the same in all time. When we have met with them once, we always find them returning the same. Even when they seem to contradict, we are sure that further inquiry will reveal the secret of the apparent contradiction, and show that, instead of being a real contradiction, it is only a further proof of their fundamental harmony. Falsehoods and errors, however, cannot be reconciled. Their contradictions are obstinate and without remedy. They are Ishmaelites. Each one is against every other, and all the others against it. The reason of this is plain. They come from finite mind, not from nature; thus there is no uniform cause underlying their existence. They spring up out of men's mistaken notions, or their misleading words. If there is, therefore, consistency and harmony, — as there is sometimes among a few of them, — it is not the result of nature, but of design. Hence the proverb, that "liars should have good memories." Lacking this, they contradict themselves, and so disclose their falsehoods. History scarcely offers an instance of a fraud that could not be detected by its contradictions, while almost every page is marked by truths whose discovery was more or less due to search suggested by apparent inconsistencies, which were resolved by the new discoveries.

MIXED TEUTH AND FALSEHOOD.

Truth and falsehood, or error, although thus radicallydifferent, are not so opposed that they may not be mingled together. The truth in things is indeed unmixed with error, but a large part of men's observations have somewhat of truth, and somewhat of error in them ; and it is often very difficult so to state even true views, that no mixture of error shall be allowed to be hidden under our words. A witness is testifying as to what he saw of a quarrel, and affirms that he saw the prisoner strike the wounded man with a weapon. The truth was, he saw the prisoner in the melee with a knife in his hand, brandishing it over his head, and inferred that he inflicted the wound. The wound, however, was made with a dagger, sharp-pointed, but with no side edges ; and as there was but one wound, it was clear that the knife was not used at all. Both his observations and his statements had a mixture of truth and error. Many times the most difficult and delicate task is to separate this truth from falsehood, and much discipline is needful to enable us to recognize just what we do see, and limit our statements to the things thus actually seen. All falsehoods are by no means intentional, but they are just as misleading as if they were. An intention to state the truth no more makes an error true, than an intention to see correctly will remedy defective vision. An honest error may be just as fatal as a premeditated lie. A minister gave his wife poison when he intended to give her medicine. The fact that it was given in love could not save her life. No purpose, however pure, can transform error into truth. We must, therefore, inquire into the ability as well as the integrity of those who furnish us our facts, before we decide on their credibility. We cannot for ourselves verify all the facts on which we must reason, and so must take much furnished by others; and great care and ability will be required to separate the wheat of truth from the chaff of error with which it is mingled.

THE IMPORTANCE OF TRUTH. 17

THE IMPOETANCE OP TKUTH.

t It is impossible to rate at too high a value this knowledge of the truth. The successes and failures, the encouragements and disappointments of life, are mainly attributable to want of correct information, and inability to draw correct conclusions frffm the information we have. If we proceed on false grounds, we are not to hope that nature will change, to relieve our defects. Having received the endowments of mind for the very purpose of discovering the true, and separating it from the false, a neglect to use these intellectual gifts properly is a crime that deserves the failures and mistakes m by which, in the course of nature, it is punished. The experience of alh ages has taught the wisest of mankind to esteem the truth very highly. No patience or perseverance is considered in any measure unrequited, if thereby any grain of truth is added to human knowledge. The very first prerequisite to entering on investigation, therefore, is a singleness of mind that will accept any truth that may reveal itself, however it may contradict some previous notions. There is required a like readiness to discard any error, however it may have been cherished, the moment its character is detected. No error is valuable. All truth is priceless, and no man has any claim to be called a true thinker, who rebels against giving up any error at the demands of the truth. The truth always issues in the right, and error, however prosperous for a time, can only come to ultimate grief. Nature, and the God of nature, will at last be found supreme, and their truth vindicated. In all ages, scholars and philosophers have exhausted their power of language in laudation of truth, and the Son of God, as if to emphasize its importance, called himself " the way, the truth, and the life." Truth is our only guide to safety, and if, adopting error, we escape folly and peril, it is by accident.

NECESSAKY AND CAUSED TKTJTH.

Truth may be divided into two departments, according .to the character of the subjects with which it has to do. One of these divisions is called necessary truth, and the other caused truth. The essential difference is indicated by the names necessary and caused. The relations of space and number are illustrations of necessary truth. The angles made by two intersecting straight lines in the same plane are not equal to four right angles, because any will made them so. It could not be otherwise. Two and two are four, I always and everywhere. It is not so with some other things. Thus, the builders might have made a ship with four or five masts, if they had so pleased. The Creator might have made the horse to chew the cud, as well as the cow and the sheep. These last are, therefore, not necessary truths, but caused truths. This leads us to notice a second distinction between these two kinds of truths, namely, that caused truth depends on some will, while necessary truth does not. No volition could make two and two ten, or construct six right angles by any number of straight lines, intersecting each other at the same point in the same plane. Volition can have no influence on necessary truth ; it exists as it is, by its own necessity. On the other hand, all caused truth exists as the result of volition ; otherwise it would not exist at all. If the builders had not done their work, there would have been no ship ; if the Creator had so pleased, the world might have been made, and never a horse appeared on it; or the horses that were on it might all have had horns. What was, and how it was to be, depended on his determination. How long it shall be true also depends on will. I have built my house, but it depended on my will when I should build it, and it depends on my will how long it will last. I may, if I please, tear it down to-morrow. It exists, like all caused truth, as we might say, by sufferance.

NECESSATvY AND CAUSED TRUTH. 19

It was produced by causes, and causes can destroy it. The house will last so long as it is not taken down, or destroyed by fire, or tempest, or decay. So geology tells us of animals, not now extant, and other convulsions may so change the face of the earth as to destroy some kinds of animals altogether, and it may be occupied by others, as different from any now as the elephant js different from the megatherium. Caused truth is thus comparatively temporary. Its existence and present modifications are of recent origin, and will not, in any event, remain long unchanged: It is otherwise with necessary truth ; it is unchangeable. As it exists of necessity, it must, of course, be eternal. Two and two have always been four, and always will be. No cause made this so, and no cause can change it, so that two and two would be anything else than four. It is identical and invariable. We have thus three points of distinction between necessary and caused truth. The first is that from which each division takes its name. One is necessary, and the other is caused. Again, caused truth depends on volition, while the other does not. So, thirdly, necessary truth is eternal, while caused truth is temporary.

With these three points of difference, there is one point wherein there is no difference. Both are equally true. Because a thing which is true now was not true last year, and may not be true next, does not in any way invalidate its present verity. Caused truth, while it is true, is just as true as any necessary truth can be. It is no more certain that two and two are four, than that Napoleon was defeated at Waterloo, or that Washington was the first President of the United States. This is important, in view of the fact that often words and phrases are used to designate caused truth, which seem to carry under them an implication of some uncertainty. Thus the adjectives experiential, contingent, and probable, are used in speaking of it, or of the evidence by which it is proved ; and these are set over against, and contrasted with, such words as self-evident, axiomatic, and demonstrative, as applied to necessary truth, and reasoning on it. This use of terms is apt to mislead us. The name caused truth is better, for the reason that after the causes have once produced their effect, the existence of that effect is just as certain as any truth is, and may be unhesitatingly relied on, so long as it lasts. With reference to very much of this caused truth, such as the events of history, it has passed out of the reach of change, and can, therefore, be no more doubtful. No future event can destroy the fact of Napoleon's overthrow, or substitute another name for Washington's as the first President. The channel of the Mississippi may be changed by the water wearing for itself new courses, and the great cities of to-day may become ruins, as many of the great cities of the past are now in decay. Some forms of caused truths are thus liable to change. The element of time must, therefore, be carefully noted ; for while a truth may not continue to be true as a constantly present truth, yet if it ever has been true, no change can destroy the fact that it was true at that time. Attention is, therefore, to be given to this point in every ' statement, whether it makes its assertion as a present and continuing fact, or as a fact at a definite time in the past. If it is true, nothing can be more true. There may be, as we shall see, a difference in our assurance of its truth ; but even in this respect, concerning a large part of caused truth, the assurance and certainty are just as absolute and positive as they can be in regard to any necessary truth. There may be great uncertainty as to the authorship of the letters of Junius. We may assert, with pretty strong confidence, that Shakespeare wrote the plays which go by his name, although many stoutly deny it. But who doubts his own existence, or the erection of the Egyptian pyramids, or that eagles can fly ? The truth, therefore, of caused truth, is as true as any truth. Our uncertainty of it does not affect it.

REASONING ON NECESSARY TRUTH. 21

It may affect us ; but to doubt that which is sufficientlyproved is utterly unreasonable.

KEASONING ON NECESSAKY TKUTH.

In reasoning on necessary truth, we begin with axioms, whose truth we see by direct inspection. This direct perception is alsa called intuition, and is a power with which the human mind is endowed to perceive certain truths, not merely as true to the extent of its experience or observation, but as true in all time and in all space. As examples, we have such axioms as, that the whole is greater than any part ; things equal to the same thing are equal to each other. Such truths the mind perceives to be true on its first occasion of experience, as universal truths; yet all such truths must show themselves true in every case of experience or observation. They cannot, as some say, override our experience ; but they must vindicate themselves in all experience. Every case must be an illustration of their truth. This is what is meant by their being universal truths. Of course, if they are necessary, they must be universal.

Beginning, then, with these axioms, or self-evident truths, we proceed by logical steps, all of which are easily reducible to the form of the syllogism, to reach other necessary truths, which are no less true than the first, but whose truth is not equally obvious at first sight. We say that multiplying by five hundredths is the same as dividing by twenty. We may not perceive this at once, but we can easily discover that they are in effect the same. It may not be obvious at once, that if I have a table eight feet long and four feet wide, it contains thirty-two square feet ; but by examination, I can see that there must be four rows of eight square feet, and thus thirty-two square feet in all. From that instance, I know that the same is true of every surface. In all such cases, we proceed from that which is seen to be true by intuition to that which is seen, by this process of reasoning, to be just as certain as the first conceded truths. This kind of reasoning is aptly called demonstrative; and the whole process a demonstration. It carries with it the highest degree of certainty.

SEASONING ON CAUSED TEUTH.

When we come to reason on caused truth, we are not able to proceed by such easy steps, since we have no self-evident truths with which to start out. We must begin with propositions, whose truth is itself a subject of inquiry. As we have said, necessary truth, being independent of all volition, and having but one way in which it can be, this may be learned beforehand, as that all right angles are equal; Caused truth, however, was made true by the. adoption by some will of one out of the, perhaps, infinite variety of possibilities, and, therefore, it cannot be known beforehand. It can be learned only by experience. You cannot tell beforehand how many acres a farmer will sow in wheat. You can tell just how many degrees there will be in any circle he may draw. You know with certainty that, however many fields he may divide his farm into, the sum of all .the fields will be equal to the whole farm, These latter are illustrations of necessary truth. In caused truth, no such self-evident truths furnish a starting-point. We see that the sheep and cow both chew the cud, and both have cloven feet ; but we cannot thence say that all cloven-footed animals chew the cud, as we could in regard to the sum of the farmer's fields being equal to the whole farm. We can see no necessity for cloven-footed animals chewing the cud. Indeed, if we look further, we find that the hog, although cloven-footed, does not chew the cud. It is thus evident that observation is our only resource, and that it is a work requiring very great care and caution. To no error are

CLASSIFICATION. 23

inexperienced persons more liable, than this of leaping at unfounded conclusions. With such false premises, it would be strange if our reasoning did not lead us to false conclusions. That it does so lead, is evident from the blunders men are constantly making. It will not do, however, in recoiling from such mistakes, to adopt the equally unfounded conclusion that all reasoning is hopeless. It is a well-established fact that qualities are found in clusters, so that one is a sign of the others. It is on this basis that we proceed in classification.

CLASSIFICATION.

By classification is meant the division of objects into groups which are more or less alike. No two things are exactly alike in every particular; but while there are sufficient differences to distinguish even the most similar, yet there are also very great resemblances. It seems to be a natural operation of mind to simplify its labors by omitting all particulars not important to its immediate aims, and so Hold more firmly those that are of this present importance. These last become more obvious by being kept solely in view. Of the things thus under consideration, there are those which may be considered as a unit, in that they all agree in some one particular. The others agree in the absence of this one particular. This i3 the simplest form of classification, where all the things considered are divided into these two classes, namely, those which have, and those which have not, a given quality.

Observation of nature, however, shows that it is possible to carry this operation much further, because things are found which agree not merely in one quality, but in many others also. Thus, the distinction between animal and vegetable life is one that includes a great many points of difference. So eagles and robins, although both birds, differ in a great many other respects beside the beak and the claws.

The camel differs from all other animals used by man for travel or burden in a great many points, in which they are all alike among themselves. We thus find that there are groupings extant in the things themselves. Men may make divisions and classifications regardless of these natural clusters, but such are justly called arbitrary classifications. When we follow the groupings of nature, our classification is scientific. Perhaps nothing could more certainly manifest the deep conviction of the human mind that there are these groupings of nature, than the readiness with which we appreciate the ludicrousness of a fanciful classification. In " Gulliver's Travels," we are treated to a description of a race of Liliputians, who were divided into two fierce parties over the question whether, when an egg was eaten, it should be broken at the big end or -the little end. Both the Bigendians and the Little-endians asserted that there was a difference in the flavor and fitness in this practice. If, now, nature has no classifications, and the distinction between a bird and a fish has no more meaning and reality in nature than this given by Swift, then there can be nothing absurd in Gulliver's histories. The truth is, men make only arbitrary classifications. In so far as their classifications are scientific, they are only reading the classifications God has made in nature. When we are able to read the constitution of the world aright, we find all things already in their own place, classified ready to our hand. It is here, just as it is in a book. The book may be written in a language we cannot understand. It contains the thoughts of its author, but they are as yet concealed from us. When we are able to read the language, we receive and think again the author's thoughts. The task for man is, to learn to read aright the truths of nature. When we are able to do this, we think again the thoughts of God, and that is the perfection of science. The task we have in hand is to understand the correct methods for this study of nature.