An outline of logic

Front matter

m m mm i.

m

BOUGHT WITH THE INCOME FROM THE

Preface

The aim of this volume is, among other things, to give a concrete discussion of ambiguity, to simplify the study of causal connections, and to treat with greater detail than is usually done the type of inference called circumstantial evidence, the nature of proof, and the postulates of reasoning. The place assigned to the syllogism is relatively small, the subject being presented with a minimum of detail. In the distribution of emphasis, the function of logic as a guide in reasoning has been constantly borne in mind. It is partly for this reason that the illustrations are, as a rule, taken from other sources than the physical sciences, because I incline to think that in the past these latter have been relied upon more than is desirable. Finally, I have added a chapter on sense-perception, in the hope that it wiU aid in making logic a propaedeutic to philosophy.

A word or two of explanation may be in place regarding the discussion of causal connections. I have ventured to depart from the treatment made classic by J. S. Mill, because the treatment in question seems to me to be neither logically nor pedagogically justifiable. In the first place, we must distinguish between connections that are universal and connections that are causal, and also between the corresponding methods of proof. While a universal connection may be of a causal character, this is not necessarily the case. Moreover, the causes with which we habitually deal in science and in everyday life vi PREFACE

are by no means universally followed by the effects with which they are properly correlated. The proof of causal connection as such is dependent, I think, upon the Method of Difference alone. It is not necessary to show in detail that Mill's other methods introduce no new principle. The Method of Concomitant Variations, for example, is merely the Method of Difference as applied when the point of difference shows quantitative variations. The Joint Method, which Mill himself calls the Indirect Method of Difference, is the Method of Difference as applied in comparisons between units which consist of groups instead of individual cases. The Method of Agreement can show, at most, a universal connection, without determining the character of the connection. Ordinarily the cases which are assigned to this method fall more properly under the ' Indirect Method of Difference,' as when we examine the connection between water supply and typhoid fever. And the Method of Eesidues, while informing us that the causes already known are not sufficient to account for the total effect, neither furnishes a clue to the remaining cause or causes, nor enables us to test their claim when they have been discovered.

The nature of my obligations to other writers, particularly to Professor James, wiU be easily discerned by the trained reader from the citations and references. I wish, further, to express my indebtedness to my former colleagues in the University of "Wisconsin, Professors E. B. McGilvary and F. C. Sharp, who have read the book in manuscript and aided me with numerous valuable criticisms and suggestions.

B. H. B.

Chapter I Introductory Page

Reasoning or inference — The definition of logic — The awareness of likeness and difference — Concepts and judgments — Concepts and classes — The extension and intension of terms — The imperfection of classification . . 1

I

Chapter V The Nature And Interpretation Of Propositions

PAGE

Judgment and proposition — Categorical and conditional propositions — The quality and quantity of propositions — The distribution of terms — The obversion and conversion of propositions — False obversion — False" conversion 51

Chapter VI

The purpose of the syllogism — ^The definition of the syllogism — The parts of the syllogism — The inclusion and exclusion of classes — The rules of the syllogism — The figures of the syllogism — Reduction — Sorites, or chains of reasoning — Inferences in quantitative relations . . 65

Chapter VII Hypothetical And Disjunctive Syllogisms

The hypothetical syllogism — The disjunctive syllogism — The dilemma — The relation of categorical and conditional syllogisms — The function of the syllogism . . 81

Chapter VIII False Assumption Or Begging The Question

Incomplete arguments — ^The definition of false assumption — False assumption, ambiguity, and imperfect disjunction — False assumption and the syllogism — Two special forms of false assumption: (a) Reasoning in a, circle, (b) Irrelevancy, or ignoring the question . 93

CONTENTS

Chapter IX The Proof Op Universal Connections Page

Proof by enumeration — Proof by the Method of Agreement — The principle of uniformity — ^Uniformity as a postulate — ^The impossibility of varying all irrelevant circumstances — Reasonable doubt — Conversion — ^Mathematical propositions ... . ... 107

Chapter X

Causation — Group comparisons — The Method of Diflference — Plurality of points of diflference — Plurality of causes — ^Merely apparent points of difference— Inference to other cases — Proof of causation as dependent upon number of instances — Concomitant variations . . 123

Chapter XI

Judgments of probability as based upon classes — The constancy of classes — The nature of probability — ^How probability is made more accurate — The principle implied in estimates of probability — The function of numbers in estimates of probability — Probability as based upon individual resemblances — ^The nature of analogy — ^Analogy and classification — False analogy — The value of analogy — The relation of analogy to circumstantial evidence . 148

Chapter XII Circumstantial Evidence And The Test Of Truth

The nature of circumstantial evidence — Examples — The test of truth— Competing explanations — The function of reasonable doubt — Probability and certainty — ^Hypothesis, theory, and fact — The fallacies of circumstantial evidence 170

X CONTENTS

Chapter XIII Observation And Memory Page

The popular notion of observation — Difficulties of the view — ^How association is determined — ^Memory — The problem involved — The solution of the problem — Observation and explanation ... . . . . 198

Chapter XIV

The definition of reasoning — Logical necessity — Judgment and inference — ^The reasoning of animals — Why some persons reason better than others — The development of inference — Deduction, induction, and circumstantial evidence . . ... 216

Chapter XV

The argument for scepticism — Criticism of the argument — Unreasoned scepticism — ^The non-rational basis for the test of truth — To what extent our interests may properly determine belief — Belief and evidence — ^Mysticism and the test of truth . . . . . 236

Chapter XVI

The subjectivity of sense-qualities — ^Primary and secondary qualities . . . . . . 255

exebcises 269

Chapter I

Reasoning or Inference. — The special subject-matter of logic is reasoning. What is meant by reasoning is shown most simply through contrast with what is not reasoning. Some facts may be known immediately or at first hand, while others are known through certain mental processes called reasoning or inference. The former kind of knowledge is independent of any experience other than the one of the present moment, while the latter is not. Thus we need no information outside the fact itself to inform us that the ache of a decaying tooth is disagreeable, or that the flame of a lighted candle is bright. These facts are known directly, with no help from other facts. They can be experienced by the child as well as by the adult. But if we say that the ache will stop when the tooth is pulled, or that the flame will bum the hand with which it comes in contact, the situation is different. In order to know this, we must have information based upon other experiences than the experience of the ache or the bum. The knowledge that the fire before us will bum is not immediate but rnediate, i.e., it is acquired through our knowledge of other facts. As a provisional statement, therefore, we may say that reasoning or inference occurs whenever we assert something to be true on the ground that something else is true. "When the reasoning is intended to convince some one else of the truth of the assertion, it is usually called argument.

Good and Bad Reasoning. — We all know from experience that there is good reasoning and bad reasoning. If we say that B is true because A is true, A and B are supposed to be so related that the belief in A involves the belief in B. But we may be mistaken in this relation, in which ease our conclusion that B is true does not ' follow.' According to some accounts, the wise men of Spain argued with Columbus that he could not reach India by sailing west, because if the earth were round, as he asserted, he would at some time reach a point where the ship would be going down hill and ultimately fall off, just as a miniature vessel would fall, if it should attempt to travel around an artificial globe. If A is true (earth round), B must be true (circumnavigation impossible). If there is a resemblance between earth and artificial globe in contour of surface, there must be a further resemblance, so it was held, in the relation of each to the objects upon its surface. In the same way we reason that because the fire which we see resembles other fires in its general appearance, it resembles these other fires also in burning the hand that comes too near. Both arguments are based upon resemblance, but the one is correct while the other is not. In making their comparison, the wise men overlooked an important point of difference, viz., that for an object on the artificial globe the point towards which it gravitates is outside the globe,- while for objects on the earth this point is within the earth itself.

A somewhat different form of bad reasoning is the inference that certain things, such as seeing the moon over the right shoulder, will bring good luck, or that certain ' charms ' will ward off evil. Such beliefs are usually based on a coincidence that is interpreted to mean a causal relation. Here the inference is guided, not by resemblance, but by difference — by the difference in the state of affairs before and after the alleged cause made its appearance. The advertisements of patent medicines, with pictures to show the difference between before and after taking, furnish another illustration of the point. The belief in B — that the second event is the effect of the first — is based upon the belief in A — ^that the alleged cause was the only circumstance which was present to disturb the existing conditions.

It will appear more fully as we proceed, that all reasoning, both good and bad, goes back, in the end, to the awareness of resemblance or difference. As suggested by the illustrations just given, the correctness of reasoning depends upon the success with which the selection of resemblances or differences is made. The important question, therefore, is. How can we know when we have selected the points of resemblance or difference that are necessary to prove our point?

The Definition of Logic. — The reasoning by which a fact is supported, or upon which the assertion of a fact is based, is commonly called the evidence or proof for the fact. Unless otherwise specified, we shall use the words ' fact ' and ' thing ' in the widest sen^e, as inclusive of anything positive or negative about which a statement can be made. When the reasoning seems to be trustworthy but is not so in reality, it is called a fallacy. The existence of fallacy makes it necessary to reflect upon reasoning, in order to determine how fallames arise and wherein proof consists. Logic is suf5ciently defined for our purposes if we say that it is the science of proof or evidence*

If we are to learn the difference between good reasoning and bad reasoning, we must know something about reasoning in general. By ascertaining how reasoning proceeds, what methods it employs, and what assumptions it makes, we may discover what final test or standard it implies, and how fallacies occur. This final test will be stated when we have made a survey of the field. Our first concern will be to discuss actual reasoning in some of its phases, and the fallacies incident to reasoning.

The Awareness of Likeness and Difference. — The awareness of likeness and difference means that we put together things which in some respects are different from each, other, and that we discriminate between things which in some respects are alike. It means, therefore, that to some extent we resolve things mentally into their elements, because we pick out their points of likeness and of difference and set them over against each other. In the act of noticing a resemblance we also take some account of the difference, for if we did not, we should not distinguish the two resembling things at all, and hence not be aware of any resemblance. All resemblance involves differ- * Cf. J. S. Mill, System of Logic, Introduction.

ence, and all difference involves resemblance; but in reasoning it is sometimes the resemblance and sometimes the difference which is important and which becomes the object of our chief attention.

Concepts and Judgments. — We resolve things mentally into their elements by noticing their resemblances and differences when compared with other things. This process of dissection is a process that involves both analysis and abstraction. An object like a box, for example, we break up in thought into its various parts, and this phase of the process is called analysis. Then we retain one of these elements, say squareness, and discard the rest. This is called abstraction (Latin ab, and trahere, to draw away from), because the element has now been isolated from its setting. This quality we can thereafter recognize in the most diverse contexts, such as square buildings, square tables, and square, areas of land; we know that whatever things resemble each other in being square, resemble each other also in the possession of the geometrical qualities that go with squareness. This attribute of squareness in its detached form is called a concept or idea. We can have ideas of attributes, such as ' squareness,' or of individual things, such as ' this flash of lightning,' or of ' London,' etc.; or of classes, such as ' men,' ' fish, ' etc. ; all of them being formed by the process of analysis and abstraction. Owing to this abstraction, ideas possess a fixity which is not found in sense-perception. Perceptions are changeable and transitory; whereas we can refer at different times to an idea as the same idea that we had before. ' ' The function by which we mark off, discriminate, draw a line round, and identify a numerically distinct subject of discourse is called conception, ''' * and the mental product of this act of conception is called a concept, idea, or meaning. A judgment on the other hand is sufficiently defined for the present if we say that it is the affirmation or denial of an idea, i.e., the assertion of something as true or false.

Concepts and Classes. — Leaving aside individual ideas for the present, we find that all ideas imply classification, for they are all ideas of something that can find embodiment in more than one instance. They are formed by the isolation of some attribute or set of attributes that are common to a number of different cases. It is true that we often do not think of the different instances in which the attribute in question is embodied. When we say, " Honesty is the best policy, " or " Virtue is its own reward, " we do not necessarily make any conscious reference to the different instances of honesty or virtue of which these sayings hold true. But unless the existence, in some sense or other, of these different instances is taken for granted, the assertions have no meaning. "Words, therefore, which designate attributes may be taken as class names whenever it suits our purpose to do so. " By a class will here be meant any imagined group of individual cases, whether material things or immaterial, whether real or unreal, — a group in which every individual is supposed to resemble all the others in some respects, though differing in others. There are classes of actions and events just as of anything else ; ' miracle ' is a class name, for instance ; or ' coronation, ' ' battle, ' ' eclipse ' ; in fact any name * James, Psychology (Briefer Course), p. 239.

which is used so as to admit of a plural, — either simply, as ' miracles,' ' negroes,' ' battles,' or in the more circuitous form of ' pieces of gold,' ' cases of deceit,' and so on."*

As this quotation indicates, a class name may consist of more than one word. Any word or group of words which serves to point out any imaginable subject of discourse is looked upon as a name or term. If the name is one that is applicable in the same sense to a number of different cases, the name may be regarded as a class name. Nor does it matter how temporary or artificial the group may be. ' ' The men who at the risk of their lives entered the burning buildiag in order to rescue the occupants " is as much a class name as ' dog,' or ' tree,' or ' justice.' Moreover, the existence of classes is implied in adjectives and verbs as well as in nouns. To say, for example, that appearances are deceptive, means that appearances belong to the class of things which are deceptive. And in ' flowers grow ' the word ' grow ' points to a class of objects which have the common characteristic of growth. Adjectives and verbs, therefore, are class names in so far as they are names which are not confined to a single thing but applicable in the same sense to a group of things.

The Extension and Intension of Terms. — It has been shown that class names have two aspects; they apply to a certain group of objects or 'things,' and they indicate certain attributes or characters. The size of the group to which the term applies determines the extension of the name, while the qualities for which it stands represent or determine the inten- * Sidgwick, The Use of Words in Reasoning, p. 150.

sion of the name. Instead of extension and intension, th,e terms denotation and connotation are sometimes used. As one writer says, " The denotation of a name consists of the things to which it applies, the connotation consists of the properties which it mplies."*

The Importance of Classification. — We have seen that classes are formed in every case on the basis of certain attributes or characters that are common to the class. As this -world of ours is constituted, such an attribute or character may imply another, so that it serves as a sign of this other. If, therefore, we put into the same class the things that are alike in some particular quality, we may be enabled to know in advance what to expect from the entire class. To take a simple illustration, if we abstract the attribute ' fire ' from one of its special forms, whether as a lighted candle, a burning match, or a bonfire, one unpleasant experience with fire will be sufficient to put us on our guard against all the I'est. By such a process of abstraction and classification, the child learns that sugar is sweet ; that water will quench the thirst ; that crockery will break if dropped to the floor, while a rubber ball wili not ; that glass will cut the fingers, while sticks may be handled with safety; and so on throughout the whole round of its little existence. In adults we have, of course, the same sort of thing, only on a larger and more complex scale.

Classification is, in short, a device whereby we are

enabled to simplify tremendously an environment

which would otherwise be too complex for any finite

intelligence. If we were obliged to become directly

*Bosanquet, The Essentials of Logic, p- 88.

acquainted with every object and every event, i.e., if things were entirely, and not merely partly, different from each other, adjustment would be impossible, since we should be unable to forecast the behavior of anything. We can anticipate the future and construe the past because certain things behave alike in certain respects. We can prove that certain things have happened in the past because we know what kind of causes are necessary to produce the given effects; we can foretell the future because "we know what effects will be produced by the given causes; we are able to resort to proof because certain things can be depended upon to go together.

The Imperfection of Classification. — It has been stated that the awareness of likeness and difference leads to the formation of ideas and that this in turn involves classification. If the attribute in reference to which the classification was made is shown to be an invariable sign of some other attribute, we are in possession of knowledge that holds for the entire class. But in order to acquire such knowledge the classification must be made with sufQcient care to bring out the point of resemblance that is common to the class. As a matter of fact, however, this resemblance is not always clearly discriminated. We may classify without knowing clearly wherein the different cases that are put into the same class resemble each other. Whenever this happens there is danger that we may take the wrong attribute as a sign of the second attribute. Such confusion is apparently at the basis of the assertion, " Nor are we much moved by the objection that it is wrong to enter the liquor trade, which appears to us just as legitimate as any other." * The line of reasoning by which the writer apparently reaches his conclusion is as follows: (1) Whatever is (morally) right is blameless. (2) A man has a good (legal) right to engage in the liquor business; and therefore (3) The liquor business is (morally) blameless. Persons who charge exorbitant rates of interest are apt to reason in a similar way. Moral right and legal right are classed together, and no distinction is made between the two. The fact that they are classed together indicates that they are alike in certain respects, viz., in the conformity to a standard. The standard differs, however, in the two cases. We cannot say that whatever is in conformity to a standard is blameless, but only what is in conformity with the moral standard. This distinction is not made, because in classing moral right and legal right together we do indeed recognize a resemblance, but we do not take the pains to discover wherein they are alike and wherein they are different, with the result that the undefined resemblance is taken as a reliable sign of the second attribute, ' blameless.' If our ideas always involved suflScient analysis, such errors would not occur. But if these fallacies are to be properly appreciated we must know how classifications are actually made and how the shortcomings of our classifications are intensified by the names that are applied to them. The consideration of these topics, therefore, will be our next undertaking. * Fortnightly Review, Vol. 27, p. 2.

Chapter II

It has been pointed out that by means of classification we are enabled to simplify an environment which would otherwise be much too complex for rational conduct. Things that are found to be alike are called by the same name, and we ordinarily proceed on the assumption that the point of resemblance which we have discovered and on the strength of which the name has been applied, is invariably related to some other quality, so that we know beforehand the nature of the entire class. Since classification is so important, it is not a matter of accident that we apply the same name to things which resemble each other in certain respects. Now if names were perfect instruments, they would indicate wherein the different things are alike. They would be names for the common points of resemblance and nothing more. The point of resemblance being known, we could ascertain what quality or attribute goes with it, if any. But this ideal is not often realized. In the case of simple attributes such as squareness, straightness, duration, etc., the point of resemblance is sufficiently well understood for most purposes. Then there are certain ' natural ' groups, which for all ordinary purposes can be indicated by a class name with little danger of error, even though we do not know very precisely what the

n nature of the resemblance may be. It is usually safe to speak of ' men,' ' horses,' ' trees,' and similar objects and to draw certain inferences concerning I them, in spite of the fact that we are unable to define these terms. But even if we grant that terms like the above are not likely to cause trouble, there is still a large group of terms such as ' capital,' ' labor,' ' religion,' ' education,' ' government,' etc., which, owing to their vagueness, are the source of endless confusion. When the nature of the resembling qualities is not known, the terms are almost sure to mean different things on different occasions, with the result that what is true of some members of the class only, is taken to be- true of all.

Undefined Similarity and Metaphor. — ^A study of language soon reveals the fact that clearly defined ideas and correspondingly definite class names are not to be found in the early stages of thought and language, but presuppose development and effort. In order to understand the development of ideas and language, it is necessary to realize that a resemblance may be ' felt ' before we know wherein it consists. The fact that the nature of the resemblance which underlies the extension of a name need not at the outset be clearly apprehended, is both curious and significant. It is possible to see a resemblance among different things, and yet be utterly at a loss to know just wherein the resemblance consists. Thus a person may be a good judge of faces and be able to classify them with considerable sk|ll as good or bad, but his ability to give reasons for his opinions may lag woefully behind. He does not know just why he judges as he does. There is something iu the criminal type of face, for example, which he somehow detects at once and which fills him with aversion, and yet he is unable to point out what it is. The common attribute or point of resemblance is ' felt ' rather than distinctly conceived. Physiognomy is a study that attempts to analyze out those common characteristics which enable us to classify faces as we do. We classify them, not through blind instinct, but on the basis of an unanalyzed resemblance.

Whenever the similarity is so intangible that we are unable to specify the point of resemblance, we can only indicate the resemblance by describing one thing in terms of another, i.e., by means of a metaphor. The use of a metaphor, so far as we are at present concerned, means the application of a name that stands for a complex of attributes to some object or thing which possesses only a portion of these attributes, without specifying which of the attributes are possessed by the object or thing in question. To take a familiar illustration, the statement that the camel is the ship of the desert is metaphorical, for while the camel is a ship in some respects, it is not a ship in every respect. The word ' ship ' includes a complex of attributes, and the statement does not make clear which of these attributes it means to ascribe to the camel. In a similar way, we speak of a person as being ' metallic ' ; or, to borrow an illustration from Professor James, we may describe a family as having ' blotting-paper ' voices. Such terms are universally recognized as metaphors.

' ' The mode in which words are learnt and extended may be studied most simply in the Mu-sery. A child, say, has learnt to say mambro wheifft sees its nurse.

The nurse works a hand-turned sewing machine, and sings to it as she works. In the street the child sees an organ-grinder singing: it calls mambro: the nurse catches the meaning and the child is overjoyed. The organ-grinder has a monkey: the child has an india-rubber toy ; it calls this also mambro. The name is extended to a monkey in a picture-book. It has a toy musical box with a handle; this also becomes mambro, the word being extended along another line of resemblance. A stroller with a French fiddle comes within the denotation of the word: a towel-rail is also called mambro from some fancied resemblance to the fiddle. A very swarthy hunchback mambro frightens the child: this leads to the transference of the word to a terrific coalman with a bag of coals on his back. In a short time the word has become a name for a great variety of objects that have nothing whatever in common to all of them, though each is strikingly like in some point to a predecessor in the series. When the application becomes too heterogeneous, the word ceases to be of use and is gradually abandoned, the most impressive being the last to go. In a child's vocabulary where the word mambro had a run of nearly two years, its last use was an adjective signifying ugly or horrible." *

The history of the child, as just exemplified, merely epitomizes the history of the race. ' ' The first words are probably names of entire things and entire actions, of extensive coherent groups. A new experience in the primitive man can only be talked about by him in terms of the old experiences which have received names. It reminds him J|| certain ones from among them, but * Minto, 'Logic, p. 83.