A Class Manual in Formal Logic By PAUL J. GLENN, Ph.D., S.T.D. PROFESSOR OF PHILOSOPHY AND HISTORY OF PHILOSOPHY IN THE COLLEGE OF ST. CHARLES BORROMEO, COLUMBUS i! 15 & 17 SOUTH BROADWAY, ST. LOUIS, MO.. AND 33 QUEEN SQUARE, LONDON, W.C 1929 ■ Kââ···· ALL RIGHTS RESERVED Printed in U. S. A. NIHIL OBSTAT Msgr. Joseph A. Weigand, LL.D., Censor Librorum IMPRIMATUR Jacobus Joseph Episcopus Columbensis NIHIL OBSTAT Sti. Ludovici, die 16. Sept., 1929, Joannes Rothcnsteiner, Censor Librorum IMPRIMATUR Sti. Ludovici, die 17. Sept., 1929, * Joannes J. Glennon, A rchiepiscopus Copyright 1929 BY B. HERDER BOOK CO. Vail-Ballou Press, Inc., Binghamton and New York 69591 •. .i This little book is dedicated with reverence and regard To The Very Reverend Michael Andrew Lambing, V.F., P.R., of Scottdale, Pennsylvania, a Master of the Divine Dialectic, whose Ideas, Judg­ ments, and Reasoning have, for more than Fifty Priestly Years, found expression in his Doc­ trine and Practice, and have taught unnumbered Souls the Logic of Life in the Love of the Lord. PREFACE There are several excellent manuals in Formal Logic now available, and a new textbook in the sub­ ject ought to justify its appearance by clear and compelling reasons. Such reasons, however, are not far to seek. The curriculum of the modern college is much crowded. Formal Logic has a place in it indeed, but a minor place. A single semester, or, at the most, a single school-year, is the period of time usually al­ lowed for the mastering of this fine science. Quite obviously, the splendid texts of Crumley, Joyce, Clarke, and others of similar scope, cannot be got through satisfactorily in five months—or in ten. On the other hand, the outlines of Logic, like Shallo’s or Coppens’, are of real value only to the student who wishes to make a rapid review of matter already studied and well grasped. The fact emerges that there is need of a new textbook in this subject. There is need of a textbook that will be more than an outline, and yet not too ambitious in scope ; a textbook that will avoid the more ponderous termi­ nology (but not the traditional nomenclature) of the scientific logician, while expressing dialectical s νί PREFACE doctrine in language both clear and precise. There is need of a text that will combine moderate brevity with relative completeness, concise expression with exactness, interest with directness. This manual seeks to supply what is here de­ scribed as requisite. It is designed to serve the young collegian who has need of the splendid training of a course in Dialectics, or Formal Logic, but who has all too little time to give to the subject. The book is a serious attempt to present the essentials of a noble science. It is no cheap or flippant attempt to enter­ tain those who study it; it is not a statement of doc­ trine in words of one syllable; it is no brief for the patent falsehood that Dialectics may be mastered with small effort. Nor is the book in any sense a manual of self-instruction. It is purely the result of an attempt to supply a class-text that teacher and pupil alike will find usable in the difficult curricular conditions of the present time. This book is not documented, for it is the writer’s conviction that documentation in an undergraduate class-manual is not only a useless bit of ornamenta­ tion but a positive distraction to the average student. Besides, it is the teacher’s work to direct the reading of his class—when reading is found possible or op­ portune—and the textbook which interferes in this matter may be described, not without justice, as pre­ sumptuous. A short bibliography, as a concession to convention, is all that can be reasonably asked in the PREFACE vii way of documentation in a book intended primarily for undergraduates. It is the writer’s earnest hope that this book may be found useful, and that it may be accounted as “teachable” a textbook as he and others have found it in its manuscript form. The writer is indebted to the V. Rev. Justin FI. McManus, O.P., S.T.D., President of Aquinas College, Columbus, for a critical reading of the manuscript ; and to the Rev. Herman E. Mattingly, A.M., of the Faculty of Saint Charles Col­ lege, for a careful checking of the proofs. P. J. G. College of Saint Charles Borromeo, Columbus, Ohio. J : i i ■ I>; Î! CONTENTS Afl^ Preface....................................................................... Introduction.................................................. · xi * * Art. I. Description and Definition of tpe Idea................................................... Art. 2. Classification of the Idea Art. 3. The Universal Idea I * BOOK FIRST TPIE IDEA CHAPTER I. The Idea Itself.................................... T 2I 27 II. The Idea Expressed...................................... 41 Art. i. Definition and Classification of the Term..................................................... 41 Art. 2. The Use of the Term ... 49 III. The Idea Explained...................................... 54 Art. I. Definition............................................ 55 Art. 2. Logical Division............................... 59 BOOK SECOND THE JUDGMENT I. The Judgment Itself..................................... 69 ix CONTENTS x £ PAGE CHAPTER IL The Judgment Expressed........................... 73 Art. I. Definition of the Proposition 73 Art. 2. Classification of the Proposition 76 Art. 3. Relative Properties of Proposi­ tions ..................................................... 9’ I. Definition BOOK THIRD REASONING I. II. HI. 109 Reasoning Expressed 117 117 Fallacies to Avoid.......................................... 123 146 153 166 Appendix. On the Reduction of Syl­ 176 logisms ............................................... ■A 4$ M 2. Object 3. Importance 4· Division I. DEFINITION Reasoning Itself Art. I. The Syllogism and Its Kinds Art. 2. Laws of the Syllogism Art. 3. Figures and Moods of the Syl­ logism ..................................................... Art. 4. Imperfect Syllogisms INTRODUCTION Bibliography 181 Index 183 Dialectics is the practical science of correct think­ ing. a) Dialectics is a science. A science is a relatively complete and systematically arranged body of re­ lated facts (truths or laws) together with their hows and whys, their causes or reasons. Dialectics is a science because it sets forth, in an orderly, systematic, and complete manner, the laws which govern correct thinking, and it shows how knowl­ edge of these laws is achieved, and why these laws must be accepted as valid. b) Dialectics is a practical science. A science that presents facts which enrich knowledge, but which do not directly imply laws or norms for the guid­ ance of thought or action, is called a speculative science. A science that presents facts from which directive norms or laws are immediately derived is called a practical science. The function of a specu­ lative science is primarily cultural ; that of a practical science is primarily directive. Dialectics is a practical xi xiii DIALECTICS INTRODUCTION science because the study of its data causes to emerge a body of laws by which the mind must be directed in order to think consistently and correctly. These laws are called the Laws of Thought; hence Dia­ lectics is sometimes defined as the Science of the Laws of Thought. c) Dialectics is a science of thinking. By thinking we mean reasoning, working out an implication, drawing a conclusion, inferring a consequence. Sometimes the word think is used in the sense of “have an opinion,” as when we say, “I think you are right.” Again, the word is often used in the sense of “remember” or “call up to pensive rec­ ollection,” as when we say, “To think the old days over is a luxury divine.” The word thinking is used in no such senses here. Nor do we confuse the word thinking with knowing. Thinking is only one of the processes by which knowing is achieved. We may know a thing by direct sensation (that is, by direct use of the senses), as, for instance, we know that it is raining, or that we have toothache. And we may know a thing by direct grasp of the understanding (that is, of the mind, or the intellect) without having to “think it out,” as, for example, we know that a totality is greater than any of its parts. But when we come to know a thing by think­ ing we have worked the thing out by studious and progressive steps of mental activity. When, for in­ stance, one has worked out the demonstration of the theorem which states that the sum of the angles of any triangle is i8o°, one has been thinking. Such thinking is called reasoning or discursive thought; it connects up data and moves from point to point in order to reach a final conclusion. It is of such reasoning or discursive thought that we speak when we use the term thinking in our definition of Dia­ lectics. d) Dialectics is the science of correct thinking. Correctness means right order, consistency, legiti­ macy of procedure, justifiability of inference. It does not mean truth. Take a piece of reasoning in illustration : All animals are rational A lion is an animal Therefore a lion is rational. At once you object: “The first statement is not true; as a matter of fact, all animals are not rational.” This is not the point of the matter for Dialectics. ..Take the statement as it stands; accept it as given. Ask only whether the last statement (the conclusion) is necessarily drawn from the first two statements (the premisses'). Dialectics asks but a single question: “Is the conclusion necessarily in­ ferred from the premisses as given?” If the answer to this question is affirmative, then the reasoning -—the thinking—is correct. The sole function of ■ηϋ DIALECTICS INTRODUCTION Dialectics is to see that the thinking process is justifiably employed upon data supplied to it. Dia·· lectics does not investigate the truth of such data nor the certainty with which such data are known. remembered that the mind is no mere machine—a man who is to use his mind in complicated and in­ volved thinking must first of all know how the mind operates. He must know how to make the mental process consistent, orderly, legitimate, justi­ fiable—in a word, he must know how to make this process correct. Afterwards he will learn the tests for truth and certainty in the things about which he reasons, even as the miller will presently learn the tests for good grain. Ultimately, of course, Dialectics aims at achieving truth and certainty, just as the inexpert miller aims ultimately at good flour when he is studying the milling machinery and not thinking directly about flour. But the special and immediate aim of Dialectics is correctness in the process of thinking. xiv AÏ * . F Dialectics then is the science of correct thinking, not of true and certain thinking. The science of true and certain thinking is called Epistemology or, more accurately, Criteriology. We see at once that Dialectics (which looks to correctness in thinking) and Criteriology (which looks to truth and certainty in thinking) are supplementary : together they make up the Science of Logic. Sometimes Dialectics is called Formal Logic, and Criteriology is called Material Logic. In modern usage the simple term Logic ordinarily means Formal Logic or Dialec­ tics» The differences as well as the positive relations that exist between these two sub-sciences or parts of Logic (viz., Dialectics and Criteriology) may be made clear by an illustration : A man who is to operate a mill must first of all understand the mill­ ing machinery. He must know the action of each mechanical part of the mill ; he must understand how the motor force is applied ; he must see that the belts run true. Only after he has mastered the mechanical operation of the mill need he concern himself about the quality of grain that goes into its hoppers. Similarly—although it must alwa^ ; be .Φ ; 2. OBJECT Now the special and immediate aim of a science is called its Formal Object. The Formal Object of Dialectics is, therefore, correctness in thinking. The thing or things with which a science deals in order to achieve its Formal Object constitute the Material Object of that science. The Material Object of Dialectics is the various mental acts that go to make up the thinking process. Dialectics studies these (the Material Object) in order to achieve correct­ ness (its Formal Object). Several sciences may deal with the same subject­ XVI DIALECTICS matter; in other words, several sciences may have the same Material Object. But no two sciences can have the same Formal Object. Anatomy and Hygiene, for example, have the same Material Object ; each deals with the organs of the human body. But these two sciences have distinct Formal Objects, for Anatomy studies the bodily organs with the view of learning their structure, while Hygiene studies the same organs with the view of knowing their proper functions and the means by which proper functioning may be conserved. Similarly, Dialectics and Criteriology both study the mental operations. These sciences have, therefore, the same Material Object. But in studying the mental oper­ ations Dialectics looks to correctness therein, while Criteriology looks to truth and certainty to be achieved thereby. Thus these sciences have distinct Formal Objects. We draw the line of demarcation between sciences that deal with the same subject-matter (Material Object) and discern the proper limits and scope of each in the light of the famous axiom : “Sciences are distinguished one from another by their Formal Objects.” .3. IMPORTANCE '.; You may say : “This science of Dialectics appears useless to me. I am equipped by nature for thinking INTRODUCTION xvii things out with clearness and consistency. Did I not use my reasoning powers correctly when I mastered my very first lessons in elementary arithmetic? Did I not perform with great exactness some very complicated pieces of reasoning when I worked out, step by step, the proofs of the various theo­ rems of geometry? Why should I study Dialectics when I already possess what it proposes to give me?” It is true that you do possess a natural power for reasoning things out, and your natural capacity and aptitude for such reasoning is called Natural Logic. But Natural Logic is not sufficient for all the requirements of an educated person. You have, doubtless, a taste for things beautiful; but you would hot set yourself up for an art critic without some special study. You may have a fine ear for music, you may play admirably “by air” ; still, it woutd~take 'âTông têrtn of study and diligent prac­ tice to entitle you to the naffiê Of rïiüàîCtâm.“Similarly, you may have a keen and quick mind ; your endow­ ment of Natural Logic may be large; but you re­ quire, none'■“the less, the training of Dialectics to enable you to make ready and just analyses of com­ plicated argument, or to penetrate easily and surely to the exact point of fallacy in a.n unjustified in­ ference. Dialectics tends to perfect your gift of Natural Logic, to make it more smooth, more orderly xviii DIALECTICS , and consistent, more keen and penetrating, more graceful and artistic in its functioning. Of course, a knowledge of the mere rules of Dialectics will not make a keen reasoner any more than a theoretical knowledge of the names and uses of tools will make a good mechanician. But Dia, lectics furnishes the technique of keen reasoning to anyone who will make use of it and diligently practise ‘ it. Dialectics may be said to offer its rules with the i scriptural admonition, “He that can take it, let him take it.” Now any person of diligence and good will can “take it” and make the most splendid use ΐ of it. '— How much harm is done in the world by faulty reasoning! How many are convinced by fallacies in matters of mind, of religion, of morals, of politics, of education values ! A knowledge of Dialectics, made usable and useful by unfailing practice, will enable * one to analyze such fallacies, and not only to de­ clare them fallacies but to show where and how , and why they are fallacious. Now any science that can equip a mind for such a service as this is a very important science indeed. 4. DIVISION Dialectics seeks correctness (Formal Object) in the mental operations (Material Object), and thus it must study the latter in order to achieve the INTRODUCTION χίχ former. The plan of study in this science is, there­ fore, determined by the mental operations them­ selves.1 The mental operations may be reduced to three major processes, viz., simple apprehension, judg­ ment, and reasoning. a) The first mental process is the act by which the mind grasps or apprehends a reality and knows it essentially. This operation is called Simple Appre­ hension, and its product is the Idea. Therefore the study of the first mental operation is the study of the idea in its formation and nature. b) The second mental operation is the act by which the mind, comparing two ideas, notices their re­ lation, and pronounces (judges) them in agreement or in disagreement. This operation of the mind is called Judgment. c) The third mental operation is the act by which the mind infers or draws out an explicit judgment that is implicity contained in other judgments. This act of the mind is called Inference or Reasoning. These three mental operations make up the Material Object of Dialectics, and by studying them we learn the mode of the mind’s functioning, and are enabled to state the laws which must govern the mind if it is to act correctly. 1 Throughout this manual the words, mental and intellectual, are used as synonyms. The three nouns, mind, intellect, and understanding, are also taken as perfectly synonymous. ί DIALECTICS XX Our study will deal with the Idea, Judgment, and Reasoning in three Books, as follows : Book Second Book First The Idea Chap. I. The Idea Itself Chap. II. The Idea Expressed Chap. III. The Idea Explained Judgment Chap. I. Judgment: Itself Chap. II. Judgment Expressed Book Third Reasoning Chap. I. Reasoning Itself Chap. II. Reasoning Expressed Chap. III. Fallacies to Avoid BOOK FIRST THE IDEA This Book first discusses the idea as it is in the mind, briefly describing its formation and constituents, and offer­ ing a definition and classification of ideas. Next, the idea is considered as expressed by the Term. Finally, the idea is studied as explained by Definition and Logical Division. The Book is therefore divided into three Chapters, as follows : Chapter I. The Idea Itself Chapter II. The Idea Expressed Chapter III. The Idea Explained CHAPTER I THE IDEA ITSELF This Chapter describes the idea, studies its formation and constituents, and offers a definition of idea in the light of such study. A list or classification of ideas is then set forth. Finally, after the general classification, a special study is made of the most important class of ideas, viz., the universal idea. The Chapter is accordingly divided into the following Articles : Article I. Description and Definition of the Idea Article 2. Classification of the Idea Article 3. The Universal Idea Description and Definition of the Idea a)Description b)Formation c)Constituents d)Definition Article a) i. DESCRIPTION OF THE IDEA Let ten circles of varying diameter be drawn on a blackboard with chalks of different colors. Here we have ten pictures that differ in size, in color, and in position or location on the blackboard. Yet, different as they are, the ten pictures represent an identical thing, and we say that each is “a circle.” Now this is a remarkable thing—ten pictures that I 2 DIALECTICS are different and yet represent the same thing. Studying the matter, we discern that the pictures are different only in points that do not necessarily belong to the identical thing that is expressed or represented in each of them. We find that the size of the pictured circle has nothing to do with its being a circle—it might be larger or smaller and still be a circle. Similarly, we understand that the color and location of the pictures might be changed without destroying them as representations of an identical thing. Now these points that may be altered without affecting the representative character of the pictures are nonessential points, they are accidental in the represen­ tations—that is to say, they happen to be this partic­ ular size, color, etc., but might just as well be an­ other size, color, etc., as far as their effect upon the representative value of the pictures is concerned. Yet these accidental points serve some purpose. They serve to distinguish each individual picture from the others. The accidental points of size, color, and location do not indeed affect the circle, for all the ten varying pictures represent the circle equally. But these points do serve to distinguish and identify each picture as this picture. These accidentals mark the individual picture, and they are called individu­ ating marks. Inasmuch as the individuating marks are marks by which the individual picture is noted or known, they are called individuating notes. We THE IDEA ITSELF 9| 3 say therefore: these ten pictures differ in individuating notes, but they represent an identical thing, viz., the circle. The identical thing which the pictures represent is an essence; it is the essence circle. But we do not grasp or apprehend this essence by our senses. Sensation (that is, the action of the senses) does not perceive the essence which the pictures express or represent. The eye does not see the essence circle. What the eye sees is the individual pictures, the individuating notes. It is the mind in us, the intellect or understanding, that peers beneath the individuating notes and apprehends the single identical thing represented in the ten varying pictures. The mind grasps or apprehends the essence circle, separating it out, so to speak, from the individuating notes that represent it. Now the mind’s grasp of an essence is an idea. The essence of a thing is that which makes the thing what it is in its basic reality. When the mind has a clear grasp of an essence, it can express that essence in a 'definition. Thus when one knows that the circle is “A closed curved line, alike in all particulars, every point of which is equidistant from a point within or centre,” one has the idea of circle clearly and distinctly formed in one’s mind. One knows an essence; one has grasped an essence; and the mind’s grasp of an essence is an idea. 9| 9 9 9 9 9 9 9 9 9 ■ m M II || il I η ® I I J I | j 4 b) DIALECTICS FORMATION OF THE IDEA Ideas are formed by the mental operation called Simple Apprehension, and this means separating out an essence from its individuating notes and grasping it. This operation involves two or more acts of the mind. The chief acts that can enter into the opera­ tion of Simple Apprehension are : attention, abstrac­ tion, reflection, comparison, analysis, and synthesis. Before defining these acts, we shall study two illus­ trations in which some of them are exemplified. i. First Illustration A boy who has never seen a representation of circle nor heard it described is shown such a repre­ sentation drawn in white in the upper left corner of a blackboard. First, sensation (that is, the action of the senses, —here, of sight) beholds the picture as a sensible (here, visible) object. Next, the mind attends to what the sense per­ ceives; it focuses, with more or less intensity, upon the picture and knows it as this thing. Then the mind discerns that, while the color, the location, and the size of the picture are essential to it as this picture, these points are not essential to it as a picture of that which it represents. The mind of the boy adverts to the fact that the picture might ' be larger or smaller, or drawn in another place, or ■KW. THE IDEA ITSELF with a different color of crayon, and still be a pic­ ture of the thing which is pictured here. In a word, the mind sees that the individuating notes do not count in the actual thing which is here represented. Therefore the mind leaves the individuating notes out of account, neglects to consider them, and lays hold of the thing which these notes happen to clothe and express in the present instance. Now the leav­ ing individuating notes out of account is called abstraction. We say that the mind, in forming ideas, abstracts from individuating notes. The mind of the observant boy has thus formed an idea by acts of attention and abstraction follow­ ing upon sensation. ii. Second Illustration A little boy goes walking in the wood with his father. He is told to notice various things: grass, moss, vines, bushes, trees, weeds, wild flowers. He is told that all these things are plants. Slowly, and at the first obscurely, he forms the idea plant. First, sensation presents the various objects to his perception. He sees the various things called plants, and touches them with his hands. Secondly, he elicits an act of mental attention, knowing the objects thereby as these objects. Thirdly, attention continuing, there comes a men- 6 w ■4 DIALECTICS tai comparison in which likenesses and differences in the objects are noticed. Fourthly, there comes the act of abstraction by which all differences of size, shape, color, location, qualities of hardness and softness, roughness and smoothness, etc., are left out of account as non­ significant (that is, as individuating notes) since all the objects under consideration differ in these points and yet are equally plants. Thus through sensation and the mental acts of attention, comparison, and abstraction, the boy forms the idea plant. At first, of course, it is obscure in his mind; but if he could express in words what his intellect has really grasped, he would say some­ thing like this : “A plant is a bodily thing that lives and grows, but it cannot feel nor move about from place to place as an animal can.” The boy has, therefore, the grasp of an essence; he knows what a plant is, what any plant is, no mat­ ter how different (in accidentals, in individuating marks) individual plants may be. And : the mind's grasp of an essence is an idea. In these illustrations we see exemplified the men­ tal acts of attention, abstraction, comparison. There are yet others to be considered. Suppose the lad mentioned in the Second Illustra­ tion were to turn over in mind the matter of plant. In the words attributed to him we discover the fact THE IDEA ITSELF 1 : i 1 7 that he has already formed the idea animal and that he uses this as a point of comparison in forming the idea plant. This is comparison again ; but notice that it is the comparison of ideas in the mind, not of external objects of attention. The comparison of the ideas plant and animal, indicated in the words of the boy, is achieved by “thinking them over,” and is therefore not only an act of comparison, but also an act of reflection. Now reflection, or reflex mental activity, is the turning of the mind upon it­ self, its acts, or its states. Suppose again that the boy should investigate the make-up of his idea plant. lie finds that it is made up of two notes, not individuating notes (for these are the known marks of external individual things) but essential notes (that is, ideas that come together to form a single idea). These essential notes are bodily thing and living thing. These are the notes that the boy discovers in his new idea, for he says: *‘A plant is a bodily thing that lives, etc.” Now the reflex advertence of the mind to the essential notes of an idea is called analysis. The converse of analysis is synthesis. When the boy puts together again (by reflex action of the mind) the notes that make up his idea, he elicits a mental act of synthesis. Another example of syn­ thesis is found in the putting together of the ideas of gold and mountain to form the idea golden mountain. Notice that this is a real idea; one who has b. .· 8 DIALECTICS formed it does not merely imagine (that is, form a phantasm of) what a certain golden mountain would ' look like, but one knows what a golden mountain, any golden mountain, would be if there were such a thing. One grasps an essence, one understands what such a mountain is or would be. Now we list and define the various mental acts that may be involved in the process of Simple Ap­ prehension or idea-forming. The first two mentioned must always be present in that process : 1. Attention is an act by which the mind fixes its consideration upon one object or group of objects to the complete or partial exclusion of all others. 2. Abstraction is an act by which the mind singles out for separate consideration a thing naturally bound up with other things and inseparable from them. Thus, for example, in any given representa­ tion of the circle, the size, color, and position of the picture are inseparable from that which they here and now represent. Yet the mind by abstraction can consider one accident apart from the others, and can consider the essence apart from all the accidents or individuating notes that clothe it. 3. Reflection (or reflex act) is an act by which the mind turns, so to speak, upon itself, becomes ad­ vertently aware of itself, of its act, or of its state, and considers or studies these things objectively. 4. Analysis is an act by which the mind resolves THE IDEA ITSELF 9 an idea into the essential notes, the other ideas, that make it up. 5. Synthesis is an act by which the mind com­ pounds two or more ideas into one, making these the essential notes of a single idea. 6. Comparison is an act by which the mind di­ rectly notices likenesses and unlikenesses in the ob­ jects of attention, or reflexly notices such likenesses and unlikenesses in ideas. Thus comparison is dis­ tinguished as direct and reflex comparison. Before taking up the next point of our study, viz., the Constituents of the Idea, we must notice a few important matters that belong to the subject of the Formation of the Idea. I. All ideas have their beginnings, immediately or remotely, in sense perception, that is to say, in sen­ sation. No ideas are inborn (innate) in the mind. The senses present their findings to the mind through the imagination or fancy (which is itself a sense­ faculty), and these are elaborated by attention, ab­ straction, etc., into ideas. This elaboration of sense­ findings into ideas is not a groundless or gratuitous or arbitrary function of the mind: the mind does not “make up” its ideas without reference to real­ ity. The process is a real working out of the essence of the realities perceived by the senses. The phrase “forming ideas” does not, therefore, indicate a turn­ ing out of a mental product by the grinding of men- ίο DIALECTICS tai machinery; it indicates the function of getting at and knowing the objective essences of things. 2. Ideas of sensible things (that is, of things per­ ceivable by the senses) are formed by the immediate activity of the mind upon sense-findings. Ideas of supersensible things (that is, of things above the reach of sense) are formed by justified derivation from directly formed ideas. Thus the ideas of man, hill, tree, fire, are formed directly; while the ideas of spirit, angel, soul, God, honesty, malice, are formed derivatively—that is to say, by derivation from other ideas which were formed directly upon sensation. Hence it is clear that all ideas have their first beginnings in sensation. 3. There are Qire£ grades of ideas : i. Ideas of sensible things are are called physical ideas, and the abstraction by which such ideas are formed is called physical abstraction. Physical ab­ straction prescinds from the individuating notes of sensible objects. Ideas derived from physical ideas are still called physical if they represent concrete realities that are beyond the reach of the senses, such as, for example, the ideas of soul, angel, God. For the rest, derived ideas are mathematical or meta­ physical ideas ; and these we consider in the follow­ ing paragraphs. ii. Ideas of merely understandable quantity are called mathematical ideas, and the abstraction by P i THE IDEA ITSELF 11 which such ideas are formed is called mathematical abstraction. Ideas of weights, numbers, measures, geometrical figures, etc., are mathematical ideas. The idea line, for example, is a mathematical idea, an idea of understandable quantity, not of sensible quantity. For the thing which we understand as the line cannot be perceived by any of the senses. A line cannot really be drawn ; it can only be under­ stood. To “draw a line’’ means to make a mark which, however fine and tenuous, has always two dimensions, viz., length and width ; whereas a line has only one dimension, viz., length. Again, the idea two represents an understandable quantity, not a sensible one. We understand what “two” means quite apart from any numbered reality. We understand that “two and two make four” without having to inquire, “Two what?” It makes no difference whether the two be ap­ plied to men or angels, to thoughts or bricks ; it is a quantity understandable in itself ; it is a mathematical idea. iii. Ideas applicable to material and immaterial things alike are called metaphysical ideas, and the abstraction by which such ideas are formed is called metaphysical abstraction. The idea of being is such I an idea. A body is being, a spirit is being, the distinc­ tion between body and spirit is being, a creature is be­ ing, the Creator is being,—everything and anything that can be thought of as existing must be conceived 12 DIALECTICS as some thing, that is to say, as being. Other meta­ physical ideas are those of unity, goodness, truth, sub­ stance, accident, etc. These classes of ideas and the corresponding classes of abstraction (viz., physical, mathematical, meta­ physical) are called grades because there is an ascend­ ing scale in their process ; each presupposes the fore­ going, like steps in a stairway. Thus mathematical abstraction is physical abstraction plus a further abstraction ; and metaphysical abstraction is the other two plus a still further abstraction. Physical abstrac­ tion prescinds from individuating notes. Mathemat­ ical abstraction prescinds from individuating notes and from everything except understandable quantity. Metaphysical abstraction prescinds from individuat­ ing notes, from quantity, and refines the idea into the most general representation of reality, material and immaterial. 4. When we form an idea of a thing we apprehend it, we get it into the mind’s grasp. Now we cannot get things literally into the mind ; we can only get repre­ sentations of likenesses of things into the mind. Such likenesses must conform to the nature of the mind (which is immaterial') to be intelligible. When ab­ straction has set aside individuating notes, there re­ mains the understandable essence of a thing ; this essence is suited for the grasp of the mind for it is not a material or bodily thing in itself ; it is called the intelligible species. We may describe abstraction by THE IDEA ITSELF 13 calling it the act by which the mind discerns the in­ telligible species (the understandable essence) of a thing. This species the mind actively impresses upon itself (this is the species impressa), and, in reacting to the impression, the mind, so to speak, images and expresses the species or essence (this is the species expressa). The species expressa is the idea. 5. Notice the following names, synonyms for idea: i. Inasmuch as the mind is, so to say, impregnated by the species impressa and conceives the species ex­ pressa, the idea is called the concept. This name is ac­ curately used in contradistinction to the percept or sense-image. ii. Inasmuch as the mind is said to grasp or appre­ hend the species or understandable essence, the idea is called apprehension. And since the mind in appre­ hending does not affirm or deny anything of the es­ sence apprehended, but simply grasps it, the idea is called simple apprehension. The same name is used for the process of forming the idea; here we use the name to designate, not the process, but its fruit, the idea. iii. Inasmuch as the idea is that in which and by which an essence is noted or known, the idea is called the notion. iv. Inasmuch as the idea is an essential representa­ tion or likeness of an essence, the idea is called the mental image. (The name idea itself is a form of the Greek word eidos, which means image.) 14 DIALECTICS v. Inasmuch as the mind, reacting to the species impressa, expresses the essential likeness or repre­ sentation of an essence, the idea is called species expressa. vi. Inasmuch as the mind in eliciting the species ex­ pressa expresses or names the essence, the idea is called the mental term or verbum mentis. vii. Inasmuch as the mind in apprehending tends to its object to grasp it, the idea is called the intention —a term which must not be confused with the inclina­ tion or determination of the will which we call by the same name. As the mind in-tends (tends to) its ob­ ject in apprehending, and may afterwards view it or study it reflexly, we distinguish first intentions and second intentions, or direct and reflex intentions. A first intention is the apprehension of an understand­ able essence, the forming of an idea. A second inten­ tion is the act of advertence of the mind to its idea. c) CONSTITUENTS OF THE IDEA Most ideas are the product of synthesis, although the mind does not become aware of this until it re­ flects, and analyzes its ideas. Such analysis will show that most ideas are made up of other ideas com­ pounded together. The component ideas are called the essential notes of the idea because they are that by which an essence is noted or known. We shall analyze the idea man (that is, human THE IDEA ITSELF 15 being) in order to find what essential notes make it up: 1. The idea man first of all represents a thing, a being. The idea being is the first essential note in all ideas made up or compounded of other ideas. The idea being is simple ; it cannot be analyzed. The first essential note, then, in the idea man is “being.” 2. We do not conceive man as a being such as wis­ dom or whiteness, but as a substance, as a subsistent being. Therefore, the second essential note in the idea man is “subsistent.” 3. We do not conceive man as a spiritual substance but as a bodily one. The third essential note in the idea man is “bodily.” 4. We do not conceive man as an inert body like a stone, but as a living being. The fourth essential note in the idea man is “living.” 5. We do not conceive man as having mere plant­ life like a flower or tree, but as endowed with sense and sensation. The fifth essential note in the idea man is “sentient.” 6. We do not conceive man as merely sentient like a brute animal, but as thinking and willing, that is to say, as rational. The sixth and final essential note in the idea man is “rational.” Summing up these essential notes which are com­ pounded together in the single idea man, we find that this idea is the representation of an essence that is a ι6 DIALECTICS “subsistent, bodily, living, sentient, rational being." Now the sum-total of essential notes that make up an idea is called the Comprehension of that idea. Com­ prehension is sometimes called Connotation. Notice an important matter here: the notes that compose the Comprehension of an idea arc distin­ guishable in the mind, but they do not signify sepa­ rate parts in the extramental object of the idea, that is, in the object outside the mind which the idea represents. The parts which make up an objective nature or physis are called physical parts; such, for example, are body and soul in physical man. The es­ sential notes comprised in the Comprehension of an idea are called metaphysical parts because they repre­ sent a distinction which lies beyond (meta-) mere physical partition. Thus body and soul, although united substantially in physical man, are really sepatable parts of man ; they are essential physical parts, not essential notes. So also hands, feet, arms, trunk, are physical parts of man. But the idea man com­ prises notes which the mind can distinguisn, but which do not imply a corresponding distinction of parts in physical man. Thus sentiency and rationality are not separable in physical man, as soul and body are separable. Notice further : the essential notes that make up the Comprehension of an idea are called metaphysical grades, because one presupposes the foregoing. Thus in the idea man “bodily” presupposes “subsistent”; THE IDEA ITSELF 17 “living” (in this instance) presupposes “bodily sub­ stance”; “sentient” presupposes “living bodily sub­ stance," etc. Hence the metaphysical parts or essential notes of an idea are also called metaphysical grades. After studying the idea in its Comprehension or in­ trinsic constitution, we turn to the consideration of the idea in extrinsic application. We ask, “What ob­ jects can the idea represent essentially in the mind?” The sum-total of the objects that the idea can repre­ sent in the mind is called the Extension of the idea. Extension is sometimes called Denotation. The “constituents” of the idea are Comprehension and Extension. Every idea has its intrinsic make-up, and this is its Comprehension. Every idea represents a thing or things, and this is its Extension. The reason for the names Comprehension (Con­ notation) and Extension (Denotation) is seen in the following two statements : 1. Comprehension or Connotation is the sum-total of the essential notes which the idea comprehends or co-notes in itself, in its own intrinsic make-up. 2. Extension or Denotation is the sum-total of objects, extrinsic to the idea itself, which the idea represents or denotes, or to which its application ex­ tends. Example : The Comprehension of the idea man is a sum-total of six essential notes, viz., being, sub­ sistent, bodily, living, sentient, rational. 18 DIALECTICS The Extension of the idea man is the sum-total of all human beings. There is an important axiom to be learned here, viz., “As Comprehension increases (in number of es­ sential notes), Extension decreases (in objects de­ noted), and vice versa.” The reason for this axiom is obvious. The more essential notes there are in the Comprehension of an idea, the more definite it is, and the more limited the field in which it is applicable. Conversely, the more objects and classes of objects there are in the Ex­ tension of an idea, the less definite and precise that idea must be.; Similarly, the more lines an artist puts into a portrait, the more definite and limited the por­ trait becomes. In the mere outline of a few strokes, the portrait might represent man, woman, or child; but as the lines are filled in the portrait becomes less and less general ; it becomes particular, and finally individual. The so-called “inverse ratio” of Com­ prehension and Extension is graphically repre­ sented in Bishop Turner’s “Lessons in Logic” as fol­ lows : Comprehension Body Body Body Body Extension minerals, plants, animals, men. .................. ...................... ............ plants, animals, men. with life........................ • . .............. - · - animals, men. with life and sentiency with life, sentiency, and reason men. THE IDEA ITSELF 19 d) DEFINITION OF THE IDEA An idea is the representation of the essence of a thingjn the mind. 1. It is a representation. It is not a picture. A pic­ ture is a material likeness of an individual bodily reality. Thus a portrait of a man is a material repre­ sentation of the external appearance of one man, at one moment of time, in a certain place, attired in a certain manner, etc. The idea man is the living grasp of what a man is. It is a living apprehension in a liv­ ing mind ; it is therefore a vital representation. It is sometimes called an intentional image or intentional representation to indicate that it is the vital grasp (apprehension or “intention”) of an essence by the mind. Notice that the idea is not limited like the por­ trait. The idea represents what a Qian is, what any man (male, female, infant, adult) is, at any time, in any place, irrespective of dress, nationality, manner, posture, etc. Nor is the idea like a picture in imagina-, tioii. Such a picture we call a fancy or a phantasm. A phantasm has all the limitations of a portrait or a moving picture : it represents an individual in a mate­ rial way; but the idea represents the essence of a thing in an immaterial way. 2. The idea is the representation of an essence. The essence of a thing is that which makes the thing what it is. The essence is sometimes called the quiddity or whatness because it is the answer to the penetrating question, “What is the thing?” And the answer to 20 DIALECTICS that question must be no mere description, no acci­ dental or individual characterization, but it must be the actual definition of what the thing is in its basic reality. If one should ask, “What is the circle5'’ the answer would not be, “It is on the blackboard,’’ or “The circle is drawn in white,” or “The circle is ten inches in diameter.” The answer is that a circle is a closed curved line, alike in all particulars, every point of which is equidistant from a point within or centre. This is the definition of circle, and it expresses what the mind knows the circle is and must be if it is to be a circle at all. This expresses that which makes a cir­ cle what it is, viz., the essence of circle. 3. The idea is a representation of an essence in the mind. The representation is not in the senses nor in the imagination ; it is in the mind, the understand­ ing, the intellect. The senses can perceive only indi­ vidual bodily things; but the idea is the grasp of an essence abstracted from any and all individual and bodily limitations. The imagination forms phantasms which also represent individual bodily reality and are in themselves as limited as a portrait or moving pic­ ture ; but the idea has not these limitations. The idea is a representation beyond the capacity of the senses and the imagination; it is necessarily in the mind. SUMMARY OF THE ARTICLE We have covered four important points in this Article : THE IDEA ITSELF 2I 1. We have studied the description of the idea, learning to understand it as the mind’s grasp of an essence. We learned to distinguish individuating notes from the essence accidentally clothed in such notes. 2. We have investigated the formation of the idea, learning to define sensation, and the intellec­ tual acts of attention, abstraction, comparison, re­ flection, analysis, synthesis. We have learned the three grades of abstraction and the corresponding grades of ideas. We have studied synonyms for idea. 3. We have studied the constituents of the idea, learning to define Comprehension and Extension, to notice their inverse ratio, and to understand what is meant by “essential notes” or “metaphysical grades” of the idea. 4. We have studied the definition of the idea, and hâve subjected each phrase of the definition to de­ tailed examination. Article 2. Classification of the Idea This Article groups or classifies ideas according to various aspects in which ideas may be viewed. These as­ pects,—the bases of our classification,—are as follows : a) , origin b) perfection in representing ç) Comprehension d) Extension e) relations 22 {intuitive-derivative) I. Intuitive ideas are those which originate in the direct grasp of that which they represent. Such are the ideas that are formed immediately upon sensa­ tion. Thus the ideas of sensible things, and the ideas one forms of one’s own feelings (and even thoughts) are intuitive ideas. 2. Derivative ideas are derived from intuitive ideas. Such are the ideas of supersensible things like soul, spirit, God, unity, truth. Such also are the ideas that originate in arbitrary synthesis of intuitive ideas—ideas like a sea of fire, a golden mountain, a talking tree. a) origin perfection {clear-obscure; distinct-vague; complete-incomplete ) I. An idea which represents its object as discern­ ible from all other objects is clear; otherwise it is obscure. If, for instance, I know the circle merely as a plane figure, I have some sort of idea of it ( for the circle is a plane figure) but my idea is obscure, because the circle as a plane figure is not discernible from the triangle, the quadrilateral, etc. When I come to know the circle as discernible from all other plane figures, my idea ceases to be obscure and be­ comes clear. 2. A clear idea that presents its object in such wise that the more important essential notes are dis­ tinguishable one from another is distinct; otherwise b) THE IDEA ITSELF DIALECTICS it is vague or confused. If, for example, I am able to distinguish what the circle is in itself as well as to know it from other plane figures, my idea of the circle is clear and distinct; if, however, I merely know it as discernible from other plane figures, with­ out being able to give any sort of definition of it in itself, my idea of the circle is clear but vague. 3. When an idea is so perfectly distinct that all its essential notes can be distinguished and enumer­ ated, the idea is complete; otherwise, although clear and distinct, it is incomplete. If, for example, I know that man is a rational animal, my idea is distinct; but it is not complete unless I can enumerate the essential notes comprised in the idea animal (viz., bodily, living, sentient substance). comprehension {simple-compound; concrete­ abstract) 1. Ideas that have but one note in their compre­ hension are simple; ideas that have more than one such note are compound. The idea of being (and its synonyms and equivalents) is simple. The idea of man—although it represents a single essence—is compound, for it has six essential notes in its Com­ prehension, as we have already seen. 2. An idea that represents something as a substrate or subject together with its determinant is concrete; an idea that represents a determinant as separated from a subject is abstract. The idea man is concrete, c) 24 DIALECTICS for it represents some thing with the determinant humanity. The idea humanity is abstract, for it represents a determinant apart from its subject. Examples of the concrete idea : body, spirit, object, white horse, pious man. Examples of the abstract idea : bodiliness, objectivity, whiteness, piety. extension (singular, universal, particular, transcendental} 1. An idea that has only one object in its Exten­ sion is singular. Such are the ideas of this circle, my father, Herbert Hoover, Pittsburgh, Ohio. 2. An idea which represents an essence that many objects may have is universal. Such are the ideas of circle, father, president, city, state. 3. A universal idea taken partially and inde­ terminately is particular. Such are the ideas of some circles, many fathers, certain presidents, a few cities, numerous states. 4. An idea that is so general or universal that it transcends -the bounds of class and applies to all classes and individuals (though not in precisely the same manner and sense to each) is transcendental. Such an idea is that of being. Notice that the universal idea differs from the collective idea. A collective idea signifies a number of individuals taken as a unit, but does not represent an essence common to the individuals, but only to the units. Thus the ideas of army, jury, family, com- d) THE IDEA ITSELF 25 mittee, etc., are collective ideas. The collective idea may be singular (as, this army), universal (as, all juries), or particular (as, some families). The universal idea is a subject of supreme im­ portance in Dialectics. We devote to its study the next Article of this Chapter. e) (identical-different; associable-opposed) 1. Ideas that have the same Comprehension or Extension are identical. Those that have the same Comprehension are formally identical. Such are the ideas man and rational animal. Ideas that have the same Extension are materially identical. Such are the ideas John Brown and this sealot, or Herbert Hoover and our president. Non-identical ideas are different. 2. Different ideas that are not mutually exclusive arid may be harmoniously joined or compounded in the same idea are associable or congruotis. Such are the ideas living and sentient. Ideas that are not as­ sociable are repugnant or opposed. i. Two opposed ideas are contrary when they ex­ clude each other but leave a ground between them ; they do not exhaust the possibilities. Thus the ideas black and white are contrary ideas. They exclude each other but do not exhaust the possibilities, for there are many things neither black nor white. ii. Two opposed ideas are contradictory when relations 20 DIALECTICS they exclude each other and leave no common ground between them; they exhaust the possibilities. Such arc the ideas white and not-whitc. They exhaust the possibilities, for there is nothing conceivable which is neither white nor not-white. iii. Two opposed ideas are relative when one im­ plies the other as a different object. Thus the ideas parent and child are relative. The idea parent in­ volves the idea child, but indicates that the object which is parent is not at the same time child. John cannot be at once the parent and the child of George. The idea involved in another is an implicit idea. Thus we say that the idea child is involved in the idea parent, and parent is the explicit idea while child is an implicit idea. Conversely, considering the idea child directly (explicitly) we find implicit in it the idea parent. Examples of ideas between which the opposition of relation exists; husband-wife; superior-inferior ; ruler-subject. iv. Between two opposed ideas there exists the op­ position called privation when one is the idea of a perfection that should be present in a given subject, and the other is a negation or denial of that perfec­ tion. Thus between the ideas sight and blindness (when used with reference to man, for example) there exists the opposition called privation. The idea which negatives or denies the perfection is called privative. Such an idea is merely negative, and not privative, when it denotes the absence of a perfection ' i , ‘ % i'.1 ϊ ■ „4 sf A £ Γ THE IDEA ITSELF T J: ? Z rTy*^' Ü Î4 t iT fr/ r ■$ * s: 27 in a subject that could not have that perfection in any case, Thus blindness used with reference to a stone is negative but not privative. SUMMARY OF THE ARTICLE In this Article we have learned to classify ideas as follows : a) By Origin : intuitive and derivative obscure b) By Perfection : vague clear fincomplete distinct·] complete c) By Comprehension: simple & compound; concrete & abstract d) By Extension : singular, universal, particular, trans­ cendental . i materially ( formally Cal e) By Relations : · differ- f associable _ ent [by contrariety opposed J by contradiction 1 by privation [by relation Article 3. The Universal Idea a) The Reflex Universal b) The Direct Universal The universal idea, or, as it is often called, simply The Universal, is an idea that represents an essence which can be common to many things and is predi- ; 28 DIALECTICS cable of each of these things in the same manner. Thus the idea metal represents an essence common to gold, silver, copper, lead, zinc, brass, aluminum, etc., and the idea can be predicated of all these to­ gether, and of each of them singly, in the same man­ ner. All are metals ; each is equally a metal. Thus also the idea virtue represents an essence common to honesty, purity, benevolence, charity, etc., and the idea can be predicated of all and each of these things in precisely the same manner : all come together in the class virtue, and each is equally a virtue. Thus again the idea man represents an essence common to Tom, Dick, Harry, Mary, Rose, Jane, etc., that is to say, an essence common to each and every human individual ; and the idea is predicable of all mankind together, and of each human individual taken singly. Notice such predications in the following : “Man is mortal” ; “John is a man.” The ideas metal, virtue, man are therefore Universals. Most of our ideas are Universals. Even many singular ideas are Universals in themselves, but are made singular by the use of some qualifier like this. Thus the idea father is itself a Universal : it is predicable of all fathers (thus the Christmas ads say: “Gifts for father.”) and of each father. It is made singular by the use of qualifiers in “this father,” “my father,” etc. The word universal is derived from the Latin unum versus alia (one in relation to other things). II THE IDEA ITSELF 29 For the Universal is one, that is, it is a single idea in the mind and represents a single essence. But this essence may be found in a plurality of things other than the idea itself; and so the Universal stands representatively related to other things. Now the “other things,” the things or objects that have the essence which is represented in the mind by the Universal, are called the subjects or the inferiors of the Universal. These inferiors are, first of ally ideas contained in the scope of the Universal. In a further sense, the inferiors are the extramental things represented by the Universal. Thus the Uni­ versal body is an idea that includes in its scope the ideas of living-body and non-living body inasmuch as these are bodies. The ideas living-body and non­ living body are Universals themselves, but they are lesser Universals than the greater Universal body. Hence these lesser Universals are inferiors of the greater Universal in which they are included. Here we see that when a Universal is applied to its in­ ferior the process in an application or predication of ; idea, to idea. This is, as we have learned, a reflex process. Therefore the Universal considered in appli­ cability or predicability to its inferior ideas is called the Reflex Universal. In studying the Reflex Univer­ sal we ask : “In how many ways may a Universal be predicated of its inferior ideas?” In other words the question is : “In how many ways,—with what vary­ ing measure of exactness, necessity, completeness, or «Τι, 30 DIALECTICS possibility,—may a Universal be predicated of its inferior ideas?” We sec from the above that the Reflex Universal is the Universal adverted to as such. But before the mind adverts to its Universal as such, it is already a Universal and can represent a plurality of things understandable, as they are in nature, apart from the consideration of the mind. In this aspect, the in­ feriors of the Universal are the extramental things which have the essence represented in the Universal. The Universal as a representation of these things is called the Direct Universal. In studying the Direct Universal we ask : “In how many classes do things (as understandable) exist in nature, apart from the consideration of the mind?” The Reflex Universal is, therefore, the Universal viewed in relation to its inferior ideas. The Direct Universal is the Universal considered as directly representative of an essence which can be common to extramental things. a) THE REFLEX UNIVERSAL “In what modes or ways may the Universal be predicated of its inferior ideas?” In five ways. These ways or modes are called The Five Predicables, or simply The Predicables. Aristotle called them Categoremata. The Predicables are the five ways in one or another of which every Universal is predicable of its inferiors. The Predicables are modes of predica- THE IDEA ITSELF tion, not classes of extramental reality. They are the following: 1. Species. When a Universal is predicable of its inferior as one and coextensive with it in content, as completely defining it, then the Universal is the Species of its inferior idea. Thus the Universal rational animal is the Species of its inferior idea man. In the predication, “Man is a rational animal,” the Universal rational animal completely defines the es­ sence man. If you represent these Universals (viz., rational animal and man) by concentric circles, the circumferences will fall exactly one upon the other; the circles will coincide. 2. Genus. When a Universal is predicable of its inferior idea as defining that part of its essence which it has in common with another Species, then the Universa! is the Genus of its inferior idea. Thus the Universal animal is the Genus of its inferior idea man. In the predication, “Man is an animal,” the Universal animal defines that part of the essence of its inferior mcm which man has in common with an­ other Species contained in the scope of animal, viz., .brute. If you draw a circle to represent the Universal animal and another to represent man, the circles will overlap in part. The field of their overlapping will indicate the Genus of the two Universals (inferiors of animal), rational animal and non-rational animàl, or simply man and brute. A Genus always includes two Species, not completely, but according to their ’ | | J . . 32 DIALECTICS common part. In their parts which are not common these will be contradictories, and so will exhaust the possibilities; thus there will only be two. 3. Specific Difference. T he common part of the two Species included under any Universal is their Genus. The part which is not common is their re­ spective Specific Difference, viz., that by which Species is distinguished from Species under a com­ mon Genus. Therefore, when a Universal is predicable of its inferior idea as defining that part of its essence (or Species) by which it is distinguished from the other Species of the same Genus,- the Universal is the Specific Difference of its inferior idea. Thus the Universal rational (i. e., rational being) is the Specific Difference of its inferior man. In the predication, “Man is rational,” the Universal rational defines that part of the essence (or Species) of its inferior man which marks it off as distinct from the other Species with which it has a common Genus, viz., non-rational animal. In the circles just drawn to illustrate Genus, the overlapping area may be marked “animal” to indicate the Genus. Then the non-overlapping areas may be marked “rational” on the one hand, and “non-rational” on the other to indicate the respective Specific Difference of rational animal and irrational animal, that is, man and brute. Notice here that Genus plus Specific Difference gives the complete essence or Species. 4. Attribute or Property. When a Universal is THE IDEA ITSELF i ■ \ ' I ' 33 predicate of its inferior idea as defining no part of its Species or essence but as indicating something that belongs by natural necessity to that essence, then the Universal is the Property or Attribute of its in­ ferior idea. Thus the Universal risible (that is, risible being, being that can laugh) is the Attribute of its inferior man. In the predication, “Man is risible,” the Universal risible defines no part of the Species or essence man, but indicates something that man (when his nature is fully and integrally constituted) must have by natural necessity. 5. Accident. When a Universal is predicable of its inferior idea as defining no part of its Species (or essence) and as belonging to it by no natural neces­ sity, but simply as happening to belong to it, or as being capable of belonging to it, then the Universal is the Accident of its inferior idea. The Accident in­ dicates what may be or may not be present to the inferior idea. Thus the Universal reading being is the Accident of its inferior man. In the predication, ; “Man is a reading being,” the Universal reading being defines no part of the Species or essence man; nor does it indicate something which belongs to that Species or essence by natural necessity ; it merely indicates what may happen to be predicable of its inferior, what may or may not be present to its inferior. The Predicables are to be studied with the closest attention and application until they are thoroughly JI “fr- ii LI ■JJ? 1 Ti J DIALECTICS 34 and ineradicably impressed upon understanding and memory. In studying them the pupil must keep con­ stantly in mind the cardinal principle : The Pred­ icables are not classifications of things; they are modes of predication, modes according to which the mind applies idea to inferior idea. Of course, the process is not a mere arbitrary one ; for the ideas do represent real essences, and the Universal is verified in each and every one of the extramental realities that have the essence which it represents. An important matter to be studied after mastering the Predicables, is the so-called “Subordination of Genera and Species.” This is graphically expressed in a scheme called the Porphyrian Tree, a drawing first made by Porphyry, a philosopher of the third century. We reproduce it here : , CORPOREAL^" A- NON-CORPOREAL LIVING NON-LIVING ORG ANJS SENTIENT; NON-SENTIENT ■RATIONAL, non-rational ■*-·> MAN t lnrlividualt : Tom. John» Mary, Jane, etc3 THE IDEA ITSELF 35 The Porphyrian Tree shows how a Universal may be a Genus with respect to its inferiors, and at the same time a Species with respect to a higher Genus. Study the tree well. Notice the following points : 1, Substance is called the highest genus, for it is not itself a species of a higher genus. All the other genera (body, organism, animal) are themselves species of higher genera. Body and organism are in­ termediate genera, having gênera above and below them. Animal is the lowest genus, for it contains species which are not themselves genera of further species. 2, Corporeal substance and non-corporeal sub­ stance are called the highest species, for there is no species in a higher order. Rational animal (or man) is the lowest species for it is not in turn a genus of its inferiors, but is predicable only of individuals. All other species are intermediate species, since they have species above and below them, or, in other words, since each of them is a species of one genus, and in turn a genus of yet lower species. 3, Each genus considered in reference to the species immediately contained in it is called the Prox­ imate Genus ; other genera, higher up the “tree” than the Proximate Genus, are called Remote Genera. Thus organism is the Proximate Genus of sentient organism and non-sentient organism, but is the Re­ mote Genus of man. 36 ’· t'l a EMU DIALECTICS 4. The lists on the right and left hand, that is, the “branches” of the tree on either side of the trunk, indicate Specific Difference. Notice that each species is constituted by Proximate Genus plus Specific Dif­ ference. Thus the species living body (or organism) is constituted by the Proximate Genus body plus the Specific Difference living. 5. Each genus (except the highest) is itself a species of a higher genus. Each species (except the lowest) becomes in turn a genus of a lower species. b) THE DIRECT UNIVERSAL “In what classes do things, as understandable, exist in nature?” In ten classes or Predicamentals. Aris­ totle called them The Categories. The Predica­ mentals are substance, and nine accidents. substance is a being, bodily or spiritual, that is fitted for existence in its own right, not merely as a determination or qualifier of something else. Ex­ amples of substance : animal, man, body, soul, spirit, God, hill, tree. accident is a being that is not fitted for existence in its own right, but regularly requires a substrate or subject in which to inhere. Action, for example, is a predicamental accident: we do not find action in bulk, so to speak, or independently existing, but only in an acting thing. Color is another example of ac­ cident; it is a quality; and color is not a thing fitted THE IDEA ITSELF 37 for independent existence but only as the determina­ tion or qualifier of a body. There are nine accidents and only nine. Anything that can be conceived of as existing must be con­ ceived as a substance or as one of the nine accidents. We shall list the accidents in a moment. Here we offer a reminder and a warning : the predicamental accidents are classes of understandable reality; the other Accident that we have learned about in the last few pages, that is to say the predicable Accident, is quite a different matter. The predicable Accident is not a classification of understandable reality ; it is a mode of applying a Universal to its inferiors. Let the student make sure that he understands quite clearly the difference between the Predicamental Ac­ cident which is here studied in its nine branches, and the Predicable Accident which he has learned as a mode of predication in the mind. The predicamental accidents are : 1. Quantity: the spatial extension of bodily sub­ stance. 2. Quality: determination of the character of a substance, bodily or spiritual : i. dispositions or habits, such as prudence or health; ii. capacity or lack of it, such as rationality or blindness; DIALECTICS iii. determination of passive character, such as a color, temperature, age. iv. bodily outline or figure, such as round­ ness, angularity. 3. Relation: the order or standing of one thing with reference to another, such as likeness or unlikeness, identity or difference, paternity, servitude. 4. Place: position in reference to surrounding space. Place is indicated in such expressions as, in the street, at Rome, on the housetops, in the corner. 5. Posture: position in reference to parts of the same body. Posture is indicated in such ex­ pressions as, standing, sitting, lying down, huddled up, lolling, outstretched, sprawled out. 6. Time: position with reference to past, pres­ ent, or future events. Time is indicated in such expressions as, at two o’clock, in the evening, after the ball, in five minutes, to-day, before noon. 7. Habit: determination of externals such as dress, equipment. Habit is indicated in such expressions as, armed, dressed, well ca­ parisoned. (N. B. Habit of mind or soul or body—like studiousness, virtue, health—is Quality. ) 8. Action: the production of change, the affect­ THE IDEA ITSELF 39 ing of an object. Action is indicated in ex­ pressions like, heating, striking, wounding. 9. Passion: the receiving or suffering of change, being affected. Passion is indicated in ex­ pressions like, being heated, being struck, being wounded. There is an ancient Latin couplet,—used to ex­ emplify the Predicamentals or Categories and at the same time to fix them in memory,—which may be loosely translated as follows : The tree cools the six slaves worn out by sum­ mer’s heat ; To-morrow 1’11 stand in the country in garments clean and neat. Notice the manner in which the couplet exemplifies the Predicamentals : tree: Substance cools : Action six: Quantity slaves : Relation (indicates reference to master) worn out : Passion heat : Quality to-morrow : Time I’ll stand: Posture m the country : Place in garments, etc. : Habit 40 y SUMMARY OF THE ARTICLE We have defined the Universal and learned what is meant by its inferiors. We have viewed the Universal in its reflex and direct aspects. We have seen that the Reflex Universal is predicable of its inferiors as their Genus, Species, Spe­ cific Difference, Property or Attribute, or Accident. We have learned that these modes of predication are called Predicables or Categoremata. We have studied the classification of things as they are in nature with reference to the understand­ ing of the mind. We have thus learned that the mind grasps objective reality either as substance or as one of the nine accidents. These ten classifications of un­ derstandable reality we have learned to call The Predicanientals or The Categories. Mï fi M $: il DIALECTICS T I CHAPTER II i THE IDEA EXPRESSED | This Chapter studies the idea as exteriorly expressed by the term. The term is defined and classified, and then viewed in its use in the expression of ideas. The Chapter is accordingly divided into the following Articles : Article I. Definition and Classification of the Term Article 2. The Use of the Term | f B ? ; Article i. Definition and Classification of the Term a) Definition b) Classification a) DEFINITION OF THE TERM A term is a sensible, arbitrary sign which mani­ fests an idea and the reality which that idea repre­ sents in the mind. I. A term is a sensible, arbitrary sign. A sign is anything that gives knowledge of something other than itself. Thus smoke is a sign of fire; a red flag is the sign of danger; a portrait is a sign of the person it represents. A sign gives knowledge of some­ thing other than itself, and this is called the thing signified. We distinguish various types or kinds of signs : 41 42 ; f •i $ ï ■ i fi J’ ! ' fc* DIALECTICS i. If the sign resembles the thing signified, it is a formal sign. Otherwise it is an instrumental sign. A portrait is a formal sign of the person represented; smoke is an instrumental sign of fire. ii. If there is a connection or relation based on the nature of things between an instrumental sign and the thing signified, the instrumental sign is called natural; otherwise it is arbitrary (or conven­ tional). Smoke is a natural instrumental sign of fire ; a red flag is an arbitrary instrumental sign of danger. A term must be a sensible sign, that is, it must be perceivable by one or more of the senses. A sign perceivable by the sense of hearing is an audible sign. Such a sign may manifest an emotion (such as pleasure, pain, surprise) ; thus laughter, sobbing, a groan, a sigh, a gasp, are audible signs of emotion. Again, an audible sign may manifest an idea, and then it is an oral term. An oral term is a word or group of words expressing, through articulate sounds of the voice, an idea and the reality which that idea represents in the mind. Notice that an oral term is a word or group of words. Single words that can manifest ideas are called categorematic words. Every categorematic word is a term. Words that must be grouped with others to express an idea are called syncategorematic words; and such words, taken by themselves, are never terms. Examples of categor­ ematic words : house, home, hill, beauty, truth. Ex- THE IDEA EXPRESSED amples of syncategorematic words : of, because, very, etc. (prepositions, articles, adverbs, interjections). A sign perceivable by the sense of sight is a visible sign. Such a sign may manifest an emotion (pleasure, pain, surprise); thus a start, trembling, pallor, flushed cheeks, etc., are visible signs of emotion. Again, a visible sign may manifest an idea, and then it is either a gesticular term (as in the finger­ language of the deaf and mute) or a written term. 2. A term manifests an idea. As we have just seen, there are signs which manifest emotion ; these are not terms; nor are any signs that manifest mere qualities or affective states called terms. Thus a de­ vout attitude is a sign of attentive prayer fulness, but it is not a term. Thus the teeth of an animal and the compact consistency of a bit of beef are (each in its own way) signs of age; but these things are not terms. A. term to justify its name must manifest an idea. 3. A term manifests an idea and the reality which that idea represents in the mind. In other words, a term manifests an idea and the thing, the object, of which the idea is an essential representation. The term sun, for example, does not merely manifest the presence of the idea sun in the mind of the speaker; it also expresses (that is, conveys to the attention and knowledge of the hearer) the heavenly 44 DIALECTICS body, the objective sun; and this is its first and direct function. It is to be noticed here that while terms serve us most notably in conveying ideas to other minds, they also serve us in expressing ideas to ourselves. A little reflection will convince anyone that a man does his thinking in, or to the accompaniment of, a kind of internal speech. One cannot express ideas clearly to . ; others unless one has expressed these ideas with clearness to oneself. b) CLASSIFICATION OF THE TERM Terms are classified according to three aspects which their study presents to consideration, viz., 1. the exactness with which they manifest ideas; 2. the Comprehension of the idea expressed (called also Comprehension of the Term), and 3. the Ex­ tension of the idea expressed (called also the Extension of the Term). I. Exactness. A term used throughout a given context in precisely the same sense is called univocal. If a term be used in two or more utterly different senses in the same context, it is called equivocal. If a term be used in different but related senses, so that its use is not identical nor yet entirely different in any two instances in the same context, the term is called analogous, and between the uses analogy is Hi !i ; i ΐ i THE IDEA EXPRESSED said to exist. To illustrate: In the sentence: “Man is mortal, man must die,” the term man is univocal. In the sentence: “There is a bank (that, is, savings bank) on the bank of the stream,” the term bank is equivocal. In the sentence, “O cruel slave, O cruel sword, that wrought so foul a death!” the term cruel is analogous. Analogy may also occur when only one term is used, its sense being metaphorical and therefore related to the normal and natural and ordinary sense of the same term. Thus there is analogy in the expression. “O cruel spear that pierced the Saviour’s side !” The term cruel is used in a figurative or metaphorical sense, the cruelty of the user of the spear being thus attributed to the weapon itself. We distinguish two kinds of analogy : i. Analogy of Proportion. When the relation between the normal and ordinary sense of a term and its figurative or metaphorical sense is based on likeness or resemblance, the analogy is one of proportion. Thus the term “smiling meadowlands” contains an analogy of proportion: for there is a conceivable resemblance between a smiling human face and bright sunlight on green fields. Other examples of this analogy: “frowning skies,” “the running sea,” “the rude, imperious surge.” ii. Analogy of Attribution. When the relation be­ tween the proper and ordinary sense of a term and the figurative sense of it is based on something other than likeness or resemblance, the analogy is one of Hjl '1|| H M ya ;9 S H q| |l a .3 I 1 1 | ! I I I - WÎSW 46 * DIALECTICS attribution. Thus the term “cruel spear” involves an analogy of attribution ; for cruelty, which, in proper sense, can only be attributed to a person, is here attributed to a weapon which a person can use; and there is no relation of resemblance here, but one of instrumentality—that is, the spear serves as the instrument of cruelty. Another example of such analogy is the term “a healthy climate.” 2. Comprehension. Terms are divided under this head into positive, negative, and privative terms; into simple and complex terms; and into concrete and abstract terms. A positive term expresses a thing, an affirmation; a negative term expresses the absence of a thing; a negative term becomes privative when it denotes the absence of a perfection that ought to be present. Examples : positive terms: man, game, wealth, love of God, loyalty to the country's cause; negative terms: non-living, the not-self, unmindfulness, indis­ position, immensity, infinity ; privative terms : ig­ norance (in one who could and should know), blind­ ness (in one who could and should have the perfec­ tion of sight). Notice carefully that negative terms denote the ab­ sence of something, whether this be a perfection or an imperfection. Thus infinity denotes the absence of limitation ; the term expresses the greatest per­ fection thinkable ; and yet it is a negative term. An­ THE IDEA EXPRESSED 47 other negative term is immensity ; it denotes per­ fection by denying limitation or measurability, but it is still a negative term. Thus it will be seen that terms are positive or negative by reason of their form or make-up; if they have a negative or privative particle as prefix (such as in-, un-, non-, il-, im-, etc.) or suffix (like -lessness) they are negative terms. A simple term consists of a single word ; a com­ plex term has more than one word. Examples : simple terms: man, brother, humanity, blindness; complex terms: love of God, a sin against Faith, the President of these United States, something of im­ portance. A complex term always has a principal member and an incidental member, the former expressing the leading idea, and the latter qualifying that idea. Thus in the complex term, “The love of God,” the principal member is “love,” and the incidental mem­ ber is the adjective phrase “of God.” Again, in the term, “The books on your table,” the principal mem­ ber is “books,” and the incidental member is “on your table.” It is important to learn this matter well, for we shall recur to it presently. A concrete term expresses a concrete idea. Ex­ amples : man, wood, animal, wise and prudent leader. An abstract term expresses an abstract idea. Ex­ amples : humanity, woodiness, animality, wisdom, prudence, leadership. 48 DIALECTICS 3. Extension. Terms are divided under this head into singular, universal, indefinite, particular, and collective terms, according as they express ideas of the same names. Examples of singular tenus: this circle, my father, Alfred E. Smith. Examples of universal terms: all circles, every father, each can­ didate. Examples of indefinite terms (that is, of terms in which there is no word to indicate the scope of their extension) : circles, fathers, candidates. Ex­ amples of particular terms: some circles, many fathers, several candidates. Examples of collective terms (that is of terms expressing “groups.” These terms are singular, universal, particular, or in­ definite) : this family; all juries; some armies; com­ mittee, delegation, crowd. A singular term is proper or common according as it is a singular and individual name or a general name limited to an individual by a restrictive par­ ticle. Thus the following singular terms are proper: Al Smith, St. Charles College, Nevada. The fol­ lowing singular terms are common: this candidate, one college, that state. SUMMARY OF THE ARTICLE In this Article we have studied the term as the expression of an idea and the reality represented by the idea. We have learned that the term is the sign of an idea. We have distinguished signs as formal and instrumental, and the latter we have sub- THE IDEA EXPRESSED 49 divided into natural and arbitrary signs. We have discussed signs as audible and visible, and terms as oral, gesticular, and written. In classifying terms we have listed them as uni­ vocal, equivocal, and analogous. We have studied analogy, and have learned what is meant by “an­ alogy of proportion” and “analogy of attribution.” We have learned the following further classification of terms: positive, negative, privative, simple, com­ plex, concrete, abstract, singular, universal, indefi­ nite, particular, collective. Singular terms we have distinguished as proper and common. Article 2. The Use of the Term a) Supposition b) Appellation A term may be used in two ways, viz., a) to sig­ nify a definite reality, and b) to modify or qualify the signification of another term. The first use is called Supposition ; the second use is called Appella­ tion. a) supposition of terms If you look up a term in the dictionary you are likely to find a list of meanings. Suppose you look up the word “body,” a common term. You will find a long litany of definitions. Among others you will notice : 50 DIALECTICS 1. the total organized substance of an animal or plant, living or dead ; 2. the trunk or main part as distinguished from limbs and head ; 3. a person, a human being—often in composi­ tion, as anybody, ^everybody ; 4. a kind or form of matter; a material sub­ stance ; 5. a number of things or individuals col­ lectively, as “a body of troops” ; 6. that part of a garment designed to cover the body; /. a distinct mass of matter, as “a body of water” ; 8. consistency, substance, thickness, as “a paint of good body”; 9. a corpse. Now when you use the term “body” in a given con­ text, you select one definite sense of that term. That selection is your supposition or taking of the term. For example, if you say, “The body rested in state in the Cathedral,” your supposition of the term body is in the sense of “corpse.” The whole list of senses in which it is possible to use a term constitutes its meaning or significa­ tion ; or, more accurately, its general meaning or general signification. Supposition is special; it is the taking of a term in a special meaning, a definite 1« 'I t THE IDEA EXPRESSED 51 and restricted signification. We distinguish different kinds of supposition : i. Material Supposition. When a term is taken to signify itself as a group of words, letters, or sounds, its supposition is material. In the statement “Man is a monosyllable,” the supposition of the term “man” is material. Other examples of material supposition : “Jones is a proper name” ; “Mankind is accented on the last syllable” ; “Good name is not hyphenated.” ii. Formal Supposition. When a term is used to signify a reality other than itself, it is formal in supposition. Formal supposition may express a mode of being which a reality has in the mind, or accord­ ing to one’s understanding of the reality, and then its formal supposition is logical. Examples of log­ ical supposition: “Man is a species” (that is, an in­ ferior of the Universal animal; not a material or biological class).—When formal supposition ex­ presses a mode of being which a thing has in nature apart from the consideration of the mind, the sup­ position is real or ontological. Examples: “Man is ■ mortal” ; “Man wants but little here below.” When a collective term is used, its real supposition may be collective or distributive, according as it signifies a group as a unit or as individuals. Example of col­ lective supposition: “The jury reached a verdict” . (that is, as a unit). Example of distributive sup­ position : “The jury went home” (that is, the mem­ bers of the jury went to their several homes). 52 b) DIALECTICS appellation of terms Appellation is the application of the idea ex­ pressed in one term to a reality expressed in another term. When one says, for example, “a good philoso­ pher,” the idea expressed in the term “good” is applied to the reality expressed in the term “philoso­ pher.” The appellation of terms amounts to the ap­ plication of one term to another. The term applied is the appellant; the term to which application is made is the appellate. Thus in the term, ‘‘a good philosopher,” the appellant is “good,” and the appel­ late is “philosopher.” When an appellant is applied to a concrete term, two senses are possible. For a concrete term means two things, viz., a subject reality, and a determinant or modification. Thus the concrete term “man” means “something” (subject) which has the determi­ nant of “humanity.” Again, the term “philosopher” means “somebody” (subject) who has the determi­ nant “knowledge of philosophy.” Now the subject or substrate reality involved in the concrete expres­ sion is called the matter-signified, while the de­ terminant or qualifier is the form-signified. This leads us to the following classification of appella­ tion : i. Material Appellation. When the appellant is applied to the matter-signified, the appellation is material. Thus if the term, “a good philosopher” is taken to mean a good man who knows philosophy, THE IDEA EXPRESSED 53 the appellation is material. If the term, “a truthful artist” means a truth-telling individual who hap­ pens to know how to paint, the appellation is ma­ terial. ii. Formal Appellation. When the appellant is ap­ plied to the form-signified, the appellation is formal. Thus if the term “a good philosopher” is taken to mean a man who has a good understanding of phil­ osophy, the appellation is formal. Again, if the term, “a truthful artist” is taken to mean an artist whose work expresses truth, the appellation is formal. SUMMARY OF THE ARTICLE In this Article we have learned carefully to dis­ tinguish between the general meaning of a term and its use, or supposition, in a special instance. We have divided supposition into two classes, material and formal, and the latter we distinguished as logical and real ; real supposition of collective terms we dis­ tinguished as collective and distributive.—We also studied the application of terms to terms, or Appella­ tion, and this again we distinguished as Material and Formal Appellation. CHAPTER III THE IDEA EXPLAINED a f?» ft By This Chapter sets forth the method of explaining ideas. Ideas, as we have seen, may be obscure or vague, and explanation is needed to render them clear and distinct. Such explanation is required not only for the proper con­ veying of ideas to others, but also for the clarifying of ideas in our own minds. Now ideas are explained by analyzing them and setting forth the results of the analysis. We may analyze the Com­ prehension of an idea and show the essential notes that make it up; and we express the results of such analysis in an essential Definition. And we may analyze the Extension of an idea and group its inferiors into classes convenient for the purpose we have in hand ; and such grouping or classification is called Logical Division. That Definition and Logical Division may serve their purpose of clarifying ideas and rendering them distinct and complete, it is neces­ sary that these explanations be developed according to well defined laws or rules. This Chapter therefore discusses the matters of Definition and Logical Division and the rules by which these are rendered serviceable in the work of explaining ideas. The Chapter is accordingly divided into two Articles, as follows : Article x. Definition Article 2. Logical Division 54 THE IDEA EXPLAINED 55 Article i. Definition a) Doctrine of Definition b) Rules of Definition a) DOCTRINE OF DEFINITION In the widest sense, definition is the explanation of an idea or term according to its content or use. Varieties of definition may be set forth, beginning with this general description, and thus we may ar­ rive at a precise knowledge of the nature of real essential definition with which alone Dialectics is con­ cerned. We distinguish the following types of defi­ nition : I. Nominal Definition. Nominal definition ex­ plains a term by telling something about it con­ sidered as a name. Nominal definition may be con­ structed : 1. according to etymology, as, “ ‘Hippopotamus’ is derived from two Greek words, hippos (horse) and potamos (river)” ; ii. by translation, as “ ‘Hippopotamus’ means ‘river horse’ ” ; iii. by substitution, as, “Theodicy is Natural Theology.” 2. Real Definition. Real definition tells the content of an idea with more or less completeness and ac­ curacy. It tells something about the thing for which the idea (and term) stands. It is : i. Essential, when it declares exactly what the 56 DIALECTICS essence of a thing is. Essential definition is either physical or metaphysical according as it expresses the essential objective elements that make tip a reality, or the essential notes that make up an idea in the mind. Thus, “Adan is a creature made of body and soul” is a physical definition ; while “Alan is a rational animal” is a metaphysical definition. In simpler language, a physical definition explains an essence by naming its parts ; while a metaphysical definition explains an idea by naming its essential notes. ii. Descriptive definition (or simply Description'), when it tells something about an essence in itself, or its properties or accidents, but does not adequately express what that essence is. Description may be ac­ cidental, as, “Man is a biped without feathers” ; it may be proper or attributiz>e, as, “Man is a walking and talking being”; it may be genetic (showing origins), as, “Man is formed of the slime of the earth” ; it may be causal, as “Man is made by God (efficient cause) to know and love God (final cause) Dialectics, as we have remarked, has to do only with real essential definition. b) RULES OF DEFINITION The following rules are most important. Remem­ ber that Dialectics is the science of correct thinking. Now no one can think correctly—in matters intri- THE IDEA EXPLAINED 57 cate and involved—without a clear grasp of the ele­ ments of thought (ideas), and such clear knowledge depends largely upon adequate essential definition. Thus one must know what a definition is and should be. The test of definition, as well as the manner of constructing it, is contained in the following set of four rules. Rule I. The definition must be exact The rule means that the definition must square precisely with the idea (term) defined, not falling short or extending beyond the limits of the latter. Another way of expressing this rule is: Let the definition be neither wider nor narrower than the term defined. The following definitions offend against this rule : Cats are domestic animals ; Charity is that which covers a multitude of sins ; Man is an animal ; A circle is a plane figure. Rule II. The definition must be clear The purpose of definition is to clarify ideas. That purpose is defeated if the definition be as obscure as what it should clarify. This rule is violated by the use of ambiguous, metaphorical, or indefinite ter­ minology, and sometimes by the use of complex technical expressions. The following definitions vio­ late this rule: 58 DIALECTICS A window is an orifice in an edifice for the exclusion of elemental disturbances, and the admission of illumination through translu­ cent substances ; Evolution is the transit from the homogeneous to the heterogeneous ; A biological species is a class marked by mor­ phological discontinuity and interspecific sterility. Rule HI. The definition must not contain the term defined, even implicitly The definition is meant to clarify, but we do not clarify or explain a thing by repeating its name. I do not clarify the idea of circle by defining it as “a circular line.” The following violate this rule: A metal is a metallic substance; A body is any substance of bodily character; Psychology is the scientific study of psychic activities ; “The duties of an archdeacon are purely archidiaconal.” Rule IV. Essential definition consists of proximate genus and specific difference The Proximate Genus sums up all the essential notes that enter into the Comprehension of an idea save the last. And the Specific Difference gives this ultimate note. Hence Proximate Genus plus Specific THE IDEA EXPLAINED 59 Difference equals the sum of essential notes—the entire essence. The student is referred to the study of The Porphyrian Tree, page 34. Definitions that violate this rule are exampled above in the para­ graph on Description. The following jingle, wretched as doggerel may be, is yet a valuable mnemonic, and sums up the Four Rules of Definition in proper order : Defining, be exact and clear; Don’t let the term defined come near ; Essential Definition mocks All but Spec. Diff. and Genus Prox. SUMMARY OF THE ARTICLE In this Article we have learned what is meant by nominal definition, which is only the explanation of the sense of a term. We have also learned what real definition is, and this we have subdistinguished as essential definition and description. We have studied and exemplified the Four Rules of Definition. Article 2. Logical Division a) Doctrine of Logical Division b) Rules of Logical Division a) DOCTRINE OF LOGICAL DIVISION Logical Division is the orderly and systematic grouping or classification of the inferiors of a Uni­ versal. If one divides the inferiors of the Universal 6o DIALECTICS man thus : white men, red men, yellow men, black men, one has made a Logical Division. Thus Logical Division explains ideas by exem­ plifying them in classes. Logical Division differs from Real Division. Real Division is the division of a reality into its com­ ponent parts. Real Division is physical when actual objective parts of a reality are distinguished; thus man is physically divided into body and soul ; thus a tree is divided into trunk, roots, and branches. Real Division is metaphysical when it is the distinction of essential notes in an idea. Thus when the idea man is divided into the ideas rational and animal we have metaphysical division. It will be seen from the above that Definition de­ pends upon metaphysical division; for an idea must be analyzed or divided into its essential notes before these can be summed up in an essential definition. Thus Real Division looks (as does definition) to content ; but Logical Division looks to Extension or application of an idea. In every Logical Division three elements are dis­ tinguished : i. The Principle of Division. This is the base, the aspect, the point of view, from which the divi­ sion is made. If I divide “Books” into Books on Theology, Books on Philosophy, Books on History, etc., the Principle of Division is “Nature of Con­ tents.” If I divide “Books” into red books, blue THE IDEA EXPLAINED 61 books, green books, brown books, etc., the Principle of Division is “Color of Binding.” If I divide “Books” into Latin Books, Greek Books, Hebrew Books, German Books, English Books, etc., the Principle of Division is “Language in which books are written.” 2. A Totality Divided. This is a universal idea considered as applied in Extension. In examples given above, the “Totality Divided” is the Universal book taken in extension. 3. Dividing Members. These are the groups ef­ fected by the Logical Division. Thus if I divide the Universal man (taken in Extension as all human beings'), into white men, black men, yellow men, red men, each of these classifications or groups is a “dividing member” of the Logical Division. To illustrate the elements of Logical Division : 1. Totality Divided: man 2. Principle of Division : race 3. Dividing Members: men of the white race, men of the black race, men of the yellow race, men of the red race. b) RULES OF LOGICAL DIVISION Logical Division, like Definition, is a means of clarifying ideas (and terms). Now if it be not regular, consistent, systematic, and complete, it will defeat its purpose, and will only muddle and ob- THE IDEA EXPLAINED 62 V *?> DIALECTICS 63 scure idea (terms) instead of clarifying them. Hence the following rules must be carefully learned and faithfully observed. The reason for each rule will be made apparent by examples. Dividing Members : Useful chairs, ornamental chairs. The list of Dividing Members is incomplete; for there are chairs which serve neither use nor orna­ ment. Rule I. In each Logical Division there must be only one Principle of Division If there is a shift of base, a change of principle, the Division cannot be otherwise than confusing; hence it will be rather a hindrance than a help in the matter of clarifying ideas. The following example offends against this rule : Rule III. Let no single Dividing Member be Co­ extensive with The Totality Divided To propose as a Dividing Member what is equal in Extension with the Totality Divided is to fail to divide; hence, in such instances, the supposed Log­ ical Division is inane and useless. The following example offends against this rule : Totality Divided : Americans Principle of Division : Religion Dividing Members : Catholics, Democrats, Quakers, etc. Totality Divided : Animals Principle of Division : Cognitive capacity Dividing Members: Sentient animals, rational animals. Protestants, Rule II. The sum of The Dividing Members must equal The Totality Divided This rule means that the Division must be com­ plete—no Dividing Members omitted. If the rule is not observed, the Division can serve no purpose of clarifying, for it will lack definiteness because it is incomplete. The following example of Division of­ fends against this rule : Totality Divided : chairs Principle of Division : service Notice that “sentient animals” is not a proper classification or group of animals, for all animals are sentient. t I Rule IV. The Dividing Members must be properly arranged To fail in proper arrangement—coordination and subordination—of Dividing Members is to make the Division a confusing jumble, and hence to defeat its purpose, which is to clarify. The following Division offends against this rule: DIALECTICS 64 Totality Divided: Americans Principle of Division: Place of Residence Dividing Members: North Americans, South Americans, Central Americans, Mexicans. “Mexicans,” a national group, should not be co­ ordinated with the continental groups. Its place is one of subordination to “North Americans.” The following is a correct Logical Division : Totality Divided : Americans Principle of Division: Place of Residence Dividing Members: North Americans, South Americans, j Central Americans' Canadians ; Inhabitants of U. S. A. ; Mexicans, Alaskans (States:) Pennsylvanians, Ohioans, New Yorkers, etc., etc. (Counties:) Westmoreland (Towns & Cities:) People of Latrobe, Scottdale, etc., etc. County residents; Fayette County, etc. (Townships:) People of Unity Township, East Huntington Township, etc., etc. (Wards.) First Ward residents; Second Ward etc., etc. The Rules of Logical Division are summed up in the following jingle: THE IDEA EXPLAINED 65 f 1 * One principle; all members call ; And let no member equal all; Arrange—with due deliberation— Coordinate subordination. SUMMARY OF THE ARTICLE ·, In this Article we have learned what is meant by Logical Division. We have contrasted Logical with Real Division, physical and metaphysical. We have learned the use of Logical Division, studying its essential elements, and exemplifying the rules which must be observed in order to make Logical Division serve its purpose of clarifying ideas (or terms). i ; BOOK SECOND ? THE JUDGMENT i i , j., ? I This Book discusses the second operation of the mind, viz., Judgment. It describes, defines and classifies the Judg­ ment. It then considers the Judgment as expressed in the Proposition. The Book is therefore divided into two Chapters, as follows: Chapter I. The Judgment Itself Chapter II. The Judgment Expressed CHAPTER I THE JUDGMENT ITSELF a) Description b) Definition c) Elements This Chapter describes and defines the second mental operation, viz., the Judgment, and analyzes it in order to study its constituent elements. The Chapter is not divided into Articles. a) DESCRIPTION OF THE JUDGMENT The mind not only forms ideas ; it also compares one idea with another and notices and enunciates their relation as agreement or disagreement. This operation of the mind is the Judgment. Now how can ideas agree or disagree ? Obviously, in their essential make-up, their Comprehension. If the essential notes (Comprehension) of two ideas are precisely the same, these ideas are identical, and are in full agreement. If two ideas are identical up to a certain point, they are in so far in agreement, and beyond that point they are in disagreement. Thus the ideas man and animal agree inasmuch as all the essential notes in the Comprehension of animal (viz., being, subsistent, bodily, living, sentient) are also in the Comprehension of the idea man (which is, being, subsistent, bodily, living, sentient, rational). 69 70 DIALECTICS The agreement of these two ideas can be enunciated by the mind in the judgment, “Man is an animal.” Inasmuch, however, as the ideas also disagree in point of rationality, the mind can enunciate the judgment, “Man is not an irrational animal.” b) J‘i « d 11 definition of the judgment Judgment is the pronouncement of the mind upon the agreement or disagreement of two ideas. When agreement is enunciated, the judgment is positive or affirmative. When disagreement is enunciated, the judgment is negative. The judgment is a pronouncement of the mind ; it is a mental enunciation, a predication. When one idea is enunciated of another as its inferior {subject}, the idea so enunciated is called the predicate. Thus, judgment may be called the pronouncement of the mind in which a predicate-idea is enunciated of a subject-idea. All this will make clear the following somewhat difficult statement: Judgment is the pro­ nouncement of the mind that one idea (subject) is or is not contained in the Extension of another idea (predicate) as an inferior. You may illustrate the matter by circles. Draw a circle to indicate the idea animal. Draw another circle, partially overlapping the first, to indicate the idea man. The overlapping area indicates the point in which man and animal agree, and we may say— in so far—that man is an animal, and enunciate this THE JUDGMENT ITSELF 71 mentally in the judgment, “Man is an animal.” The part of the man-circle which does not overlap, justi­ fies the judgment, “Man is not a brute.” On the other hand, the part of the animal-circle which does not overlap, justifies the judgment, “A brute is not a man.” c) ELEMENTS OF THE JUDGMENT Three elements enter into every judgment : 1. two ideas in the mind ; 2. comparison of the two ideas by the mind ; 3. pronouncement by the mind (predication) on the agreement or disagreement of the two ideas. The first two of these elements are taken together to constitute the material element of the judgment ; the last is the formal element, the judgment proper. We may mention here in passing that there are such things as sense-judgments. With these Dialect­ ics has nothing to do, for this science treats of intel­ lectual judgments wherein pronouncement is made upon ideas. Sense-judgments may be elicited by brutes, by those of undeveloped mind, and by normal adults acting without intellectual advertence. Thus the judgment that such a being is friendly or un­ friendly (that is, is one to be sought after or avoided), that one sound is a summons and another a dismissal, are sense judgments. So also are judg- ; i 72 i n ffeV. ■; iîF r* DIALECTICS ments upon bodily things formed immediately upon sensation, such as “It is raining,” “I feel cold.” SUMMARY OF THE CHAPTER In this brief Chapter we have learned what is meant by judgment, by the terms subject and pred­ icate, by the term predication or pronouncement of judgment. We have distinguished positive and nega­ tive judgments, and have listed the elements of judg­ ment, classifying these as material and formal. 1 A ',f CHAPTER II THE JUDGMENT EXPRESSED •V 1 Just as the idea is expressed exteriorly by the term, so the judgment is expressed exteriorly by the Proposition. This Chapter studies the nature of the Proposition, de­ fines and classifies it, and sets forth the relative proper­ ties of Propositions. The Chapter is accordingly divided into the following Articles : Article I. Definition of the Proposition Article 2. Classification of the Proposition Article 3. Relative Properties of Propositions ' Article i. Definition of the Proposition = I ? I. Categoricals Obviously Compound.—There are four types in this group : i. C opidative propositions. These have more than one subject, more than one predicate, or more than one of each; and these are joined by conjunctions such as and, or, nor, etc. Examples : ‘‘Teter and James were Apostles”; “Simon and Jude were Apos­ tles and martyrs” ; “John was an Apostle and Evan­ gelist.” The truth of copulative propositions depends upon the truth of the several simple propositions to which they may easily be reduced.1 ii. Adversative propositions. These express op­ posed judgments, and show the opposition by par1 The student may be puzzled here to find mention of the truth of the propositions discussed. He may say, “What has : Dialectics to do with truth? Its aim is correctness.” We answer; We study nothing of the nature of truth here, nor of tests for truth as such. But we must take account of the fact that propositions are necessarily true or false, and this property sometimes determines them as veritable specimens of a given type of proposition or excludes them from such type. There- Ί 1 THE JUDGMENT EXPRESSED 85 tides like but, however, nevertheless, yet, still, etc. Examples : “Happiness lies not in the possession of earthly but of eternal goods” ; “Now you are clean, yet not all”; Samson was strong; nevertheless he fell through the power of one weaker than himself.” The truth of adversative propositions depends upon the truth of the simple propositions to which they may be reduced, and also upon the fact of true op­ position existing between these component simple propositions. Thus we have a false adversative in, “Peter was a martyr ; nevertheless he went to heaven.” Here the component simple propositions are true, but the opposition expressed in “nevertheless” does not exist between them. iii. Relative propositions. These are made up of partial propositions connected by correlative particles like when—then, so—as, as—as, whoever—he, where—there, etc. Examples : “Where a man’s treasure is, there is his heart also” ; “Where two or three are gathered together in my name, there am I in the midst of them” ; “As the shepherd is, so is the flock” ; “Like father, like son” ; “Whoever doth the will of my Father, he shall enter the kingdom of heaven.” The truth of relative propositions de­ pends upon the truth of the component simple propo­ sitions and also upon the existence of a true relation obtaining between or among them. fore in determining the limits of types, mention must be made of truth and falsity. Here the questions of truth and correct­ ness have something in common. II ί H 86 DIALECTICS iv. Causal propositions. These consist of proposi­ tions united by causal particles such as because, since, as, for, etc. Examples : “Man is free because he is rational” ; “You will be sick, for you have eaten tainted food”; “Since Simon has no penny, he shall have no pie.” The truth of causal propositions depends upon the truth of the component simple propo- II. Categoricals Not Obviously Compound.— Since these propositions need to be drawn out of the obscurity of their composition and shown to be compound, they are called exponible propositions. The simple propositions into which they may be re­ solved are called their exponents.—There are four types of propositions not obviously compound : i. Exclusive propositions. These have attached to subject or predicate an exclusive particle like only, alone, etc. Examples : “Patrick alone stood up for me”; “God only knows.” The exponents of the sec­ ond example are : “God knows” and “Others do not know.” ii. Exceptive propositions. These include the ex­ pression of a limited predication, that is, they show that some inferiors of the subject do not receive the predication, or that some inferiors of the predicate THE JUDGMENT EXPRESSED 87 are not enunciated of the subject. This exception is indicated by particles such as except, but, save, omit­ ting, etc. Examples: “All save John had gone’’; “Mary likes all her studies except history’’; “The class, omitting the consistent idlers, passed a bril­ liant examination.” The exponents of the first ex­ ample may be stated as follows: “John had not gone”; “All others had gone.” iii. Comparative propositions. These declare that a predicate is to be enunciated of one subject equally with another ; or more or less truly, extensively, em­ phatically, of one than of another. Comparative particles are used, such as more, less, better, worse, equally, etc. Examples : “Good name is better than great riches” ; “Kind hearts are more than cor­ onets” ; “John and Jim are equally enthusiastic” ; “Mary is less diligent than Alice.” iv. Reduplicative propositions. These view a sub­ ject from different angles, and make partial predica­ tions about it, using such words as inasmuch, as, in as far as, etc. Examples : “Shakespeare as a man was of upright character, as a poet he was supreme, as a philosopher he was notable, as a dramatist he was unexcelled, as an actor he was indifferent.” “The physician, inasmuch as he is a physician, treats hu­ man ailments ; inasmuch as he is a man, he thinks and wills ; inasmuch as he is an animal, he eats and sleeps.” If the reduplicative particle is equivalent to because, the proposition is to be first reduced to the 88 DIALECTICS causal type, and then resolved into its simple com­ ponents. If the reduplicative particle merely indicates a changed point of view, the proposition is called specificative, and is to be reduced to the copulative type, and then into its simple exponents. The first example given above is specificative; the second is implicitly causal. Hi. Hypothetical Propositions A hypothetical proposition is conditioned : it makes no absolute predication, but expresses a dependency existing between two or more propositions. The matter is made clear by an example: “If a fast day falls upon Sunday, the fast is not observed.” Notice that the proposition does not say simply, “The fast is not observed,” but makes that proposition depend upon the fulfillment of a condition. There are three types of hypotheticals to be considered : I. Connective (or simply. conditional') proposi­ tions. These always have a member introduced by the particle if. The member so introduced is called the condition or antecedent; the other member is called the consequent. We may define a connective hy­ pothetical as a proposition in which the consequent depends in such wise upon the antecedent that if the antecedent be true, the consequent must be true. Ex­ amples : “If you go, I shall not remain here”; “If the storm comes before we reach home, we are in for a wetting.” The truth of connective hypotheticals THE JUDGMENT EXPRESSED 89 depends solely upon the relation of dependence enunciated as existing between antecedent and con­ sequent. Thus the following is not a true connective hypothetical: “If you vote the Republican ticket, you will go to heaven.” Now you may actually vote the Republican ticket, and you will (one hopes) actually go to heaven by and by ; but there is obvi­ ously no relation of dependency between these things. II. Conjunctive propositions. These enunciate the impossibility of two things occurring simultane­ ously, or of two facts being true at one and the same time. Examples : “Socrates is not at once a philoso­ pher and an ignoramus” ; “One cannot stand and sit at the same time” ; “Oscar Skavinsky cannot be sim­ ultaneously a Republican and a Free-Stater.” The truth of such propositions depends solely upon a true exclusive opposition existing between their com­ ponent parts. Propositions of this type are easily re­ duced to two connective hypotheticals. Thus the first example may be reduced as follows : “If Socrates is a philosopher, he is not an ignoramus” ; “If Socrates is an ignoramus, he is not a philosopher.” III. Disjunctive propositions. These enumerate exhaustive lists of possibilities no two of which can be simultaneously true, nor can all be simultaneously false, but one must be true and the rest false. Ex­ ample : “It is either day or night”; “It is spring, summer, autumn, or winter” ; “The thing is possible or it is not possible.” For a proposition to be a true 90 DIALECTICS disjunctive hypothetical two things are required: I. The enumeration of possibilities must be complete ; and 2. There must be an exclusive opposition between or among the enumerated possibilities. The following is therefore no true disjunctive: “It is spring, or autumn, or winter.” The following also fails of the character of a true disjunctive: “It is either white or sweet.” iv. Complex Propositions A complex proposition has a complex term as subject. A complex term, as we have learned, is one that consists of two or more simple terms. Such a term has always a principal member and an incidental member. In the term, “the love of God,” the princi­ pal member is “love” and the incidental member is “of God.” Now complex propositions may be reduced to their exponents, and these will always be two, one containing the principal member of the complex term, and the other containing the incidental member. Ex­ ample of the complex proposition : “The fear of God is the beginning of wisdom.” v. Multiple Propositions A multiple proposition formally expresses more than one predication. Now a compound proposition may contain many simple propositions as exponents, and still not be multiple. Thus, “Peter, James, and John beheld the Transfiguration” is a compound r THE JUDGMENT EXPRESSED 91 proposition, and may be reduced to three simple propositions; yet it is not multiple, for it has only one predication, viz., “beheld the Transfiguration.” On the other hand, “John runs and jumps” is a compound and a multiple proposition ; even though it has only one subject, there are two distinct predica­ tions concerning that subject. Let the student de­ termine whether the following are compound and not multiple, or compound and multiple : Brothers and sisters I have none; Peter believed and was baptized ; I hope and pray that you are well ; The army, the navy, and the marines took part in the battle ; Gold and silver I have not and desire not. Learn the axiom : A multiple proposition is always compound, but a compound proposition is not neces­ sarily multiple. SUMMARY OF THE ARTICLE In this Article we have studied in detail the various types of propositions. This study will be well repaid when we come to the consideration of reasoning and the syllogism. Accurate thinking, correct reasoning, demands a clear knowledge of the values of terms and propositions, and of the principles immediately detived from such knowledge. We have learned to classify propositions as follows : DIALECTICS 92 I. In Quantity and Quality: A—propositions E—propositions i—propositions O—propositions (Universal (Universal (Particular (Particular affirmative) negative) affirmative) negative) U. In Structure : I. SIMPLE. a) Modal 'necessary contingent possible impossible 'copulative obviously com­ J adversative relative pounded causal b) Categorical 2. COMPOUND.- not obviously compounded comparative reduplicative connective c) Hypothetical' conjunctive disj unctive d) Complex e) Multiple Article 3. Relative Properties of Propositions a) Opposition b) Equipollence c) Conversion We have hitherto considered propositions in them­ selves. Now we are to consider them in relation to THE JUDGMENT EXPRESSED 93 other propositions made up of the same terms. This consideration will show certain relative properties that exist among propositions, and these properties serve as a means of direct or immediate inference. By immediate inference through the relative prop­ erties of propositions we may conclude to other propositions, or to a knowledge of the truth or falsity of other propositions. We are to study three relative properties of propositions. The first of these is opposition which exists between propositions that have the same sub­ ject and predicate, but which differ in quantity or quality or both. The second relative property is equtpollence, or “equivalence,” which exists between two propositions that have the same subject and predicate and the same force of meaning (“equiva­ lent propositions”) yet differ in the number of nega­ tions they contain. The third relative property is conversion which exists between a proposition and itself transposed (that is, subject and predicate hav­ ing changed places), the truth of the proposition be­ ing conserved. a) opposition of propositions Opposition is a relative property which exists be­ tween two propositions that have the same subject and the same predicate but differ in quantity or 94 DIALECTICS quality or both. Example : “All men are wise”— “Some man is not wise.” There can be no opposition without a basis of agreement; indeed, there can be no disagreement without agreement,—a point where divergence be­ gins. Thus we cannot discern any opposition between the propositions, “The snow is deep” and “This book is tiresome.” These are simply independent and unrelated propositions. They are in no sense op­ posed. For opposition to exist between two proposi­ tions, these must have the same subject and the same predicate. Thus we see that there is opposition be­ tween these propositions : “The snow is deep” and “The snow is not deep.” There are two kinds or types of opposition, viz., opposition properly so called, and opposition improp­ erly so called. Of the first type we have two sorts, viz., contradiction and contrariety. Of the second type we have also two sorts : subcontrariety and subalternity. A word on each of these follows : I. Contradiction exists between an affirmative and a negative proposition (which have the same subject and predicate) when one expresses precisely that which is requisite and sufficient to overthrow the other. Such propositions leave no middle ground between them; they exhaust the possibilities. There­ fore we say: Of contradictories, one is necessarily true, the other necessarily false. Example: “Every man is wise”—“Some man is not wise.” These THE JUDGMENT EXPRESSED 95 propositions cover the whole ground. Study will show that they verify the description and definition of contradictories, and that they justify the principle enunciated about the truth and falsity of such propositions. 2. Contrariety exists between a universal affirma­ tive and a universal negative proposition, each hav­ ing the same subject and predicate. Such proposi­ tions leave a middle ground between them. They do not exhaust the possibilities. Thus, although con­ traries are sweeping denials of each other, they are not in such complete and accurate opposition as con­ tradictories. Examples : “Every man is wise”— “No man is wise.” The principle concerning truth and falsity here is : Of contraries, both cannot be simultaneously true, although both may be false. 3. Subcontrariety exists between two particular propositions, one affirmative and one negative, both of which have the same subject and predicate. Ex­ ample: “Some man is wise”—“Some man is not wise.” Obviously, the “some man” need not be the same individual, and hence there is no proper op­ position between the propositions. They have an opposition improperly so called. Yet such proposi­ tions have a definite relation, and of them we enunci­ ate the following principle : Of sub contraries, both may be true, but both cannot be false. If it could be false that “some man is wise,” and also false that “some man is not wise”—then thought is annihilated. 96 DIALECTICS 4. Subalternity exists between a universal affirma­ tive proposition and a particular affirmative hav­ ing the same subject and predicate. It also exists between a universal negative proposition and a par­ ticular negative having the same subject and pred­ icate. Examples : “Every man is wise”—“Some man is wise”; “No man is wise”—“Some man is not wise.” Here again the opposition is improper. Yet such propositions have a definite relation and we may enunciate a relative principle about them. First, how­ ever, we must name the subalterns : the universal proposition is called the subalternant and the par­ ticular proposition (which differs only in quantity from the universal proposition) is called the sub­ alternate. The principle is : Of subalterns, the truth of the subalternant involves the truth of the sub­ alternate, but not vice versa; and the falsity of the subalternate involves the falsity of the subalternant, but not vice versa. In other words, if subalternant is true—subalternate true ; if subalternate is true—subalternant true or false; if subalternate is false—subalternant if subalternant is false—subalternate true or false. Apply the principle in these examples : must be may be is false; may be THE JUDGMENT EXPRESSED subalternant : subalternate : subalternant: subalternate: subalternant : subalternate : 97 “Every man is wise” “Some man is wise” “All men are mortal” “Some men are mortal” “No man is a spirit” “Some man is not a spirit.” All the principles enunciated above may be studied and justified in the “Logical Square” which graph­ ically illustrates the opposition of propositions. We give the Logical Square here, reminding the student of the letter-symbols of propositions, viz., A-pr©posi­ tion is universal affirmative; E-proposition is uni­ versal negative; I-proposition is particular affirma­ tive; O-proposition is particular negative: THE LOGICAL SQUARE Principles I. Of contradictories, one is necessarily true, the 2. Of contraries, both cannot be simultaneously true, although both may be false. 3. Of subcontraries, both may be true; both cannot be false. 4. Of subalterns, if the subalternant is true, the subalternate must be true, but not vice versa; and if the subalternate is false, the subalternant must be false, but not vice versa. NOTE : The practical value of opposition ap­ pears in argument or debate. From this relative property we gain important points of knowledge, such as : I. Not to make general and sweeping state­ ments (A or E propositions), lest our whole argu­ ment be blown to pieces by the proof of the con­ tradictory—a single opposed instance; 2. Not to try to prove the contrary of a general statement, but the contradictory. To try to prove the contrary would be mountainous labor, and even if we should succeed, the argument would not be settled, or “both contraries may be false.” Hence we see the justice of the adage : “He who proves too much, proves nothing”; 3. To recognize the contradictory as the most valuable, and the thoroughly invincible argu­ ment; 4. To be on guard lest an opponent try to J THE JUDGMENT EXPRESSED 99 disprove our position by establishing the subcontrary, for “both subcontraries may be true.” 5. To avoid concluding to the truth of a subalternant from the truth of a subalternate, and to watch for this illog­ ical proceeding on the part of an opponent. The Logical Square also reveals Opposition of Propositions as a means of immediate inference. We can infer from any true A- or E-proposition the truth of its subalternate, the falsity of its contrary and contradictory. From any false I- or O-proposition we can infer the falsity of its subalternant and the truth of its contradictory. Let the student de­ termine what can be inferred from any false A- or E-proposition, and from any true I- or O-proposition. b) EQUIPOLLENCE OF PROPOSITIONS Equipollence (or “equivalence”) is the relative property existing between two propositions that have the same subject and predicate and mean the same thing, but which differ in point of one or more negations. Example : “All men are animals”—“No man is not an animal.” The practical value of equipollence appears in the following facts: 1. The study of equipollence makes for accuracy of thought and expression; 2. Some­ times a seeming denial may be shown by equipol­ lence to be in reality an affirmation ; 3. Equipollence affords a means of direct inference by which an ob­ scure or vague proposition may often be expressed in clear and distinct form. By équipollence, then, we infer the equivalent of a proposition or of its opposites from the proposi­ tion itself, To form the equivalent of the opposites, the following rules are to be followed: I. To form the equivalent of the contradictory of any simple proposition, place a negative particle before the subject. “All men are wise”—“Not all men are wise.” “Not all men are wise” equals “Some men are not wise,” the contradictory of the original proposition. 2. To form the equivalent of the contrary of any simple proposition, place a negative particle before the predicate. “All men are wise”—“All men are not-wise.” The latter proposition equals, “No man is wise,” the contrary of the original proposition. 3. To form the equivalent of the subaltern (sub­ alternant, if the original proposition is I- or 0-; subalternate, if the original proposition is A- or E-), place a negative particle before both subject and predicate. “All men are wise”—“Not all men are not-wise.” The latter proposition equals, “Some man is wise,” the subalternate of the original Aproposition. Again, “Some man is not wise”—“Not some (i. e., any) man is not not-wise.” the latter proposition equals, “No man is wise,” the subalternant of the original O-proposition. The equipollence of compound propositions need THE JUDGMENT EXPRESSED ιοί not be discussed in detail in this manual. As a general rule, let such propositions be reduced to the simple propositions that they contain, and equipollence be shown as indicated in the foregoing rules. c) CONVERSION OF PROPOSITIONS Conversion is that process by which one proposi­ tion is immediately inferred from another by trans­ posing the subject and predicate and keeping the resultant proposition as true as the original proposi­ tion. The original proposition is called the conver­ tend, and the resultant proposition is the converse. Between convertend and converse there exists, there­ fore, a definite relation, which we call the relative property of conversion. Example: “Some man is wise”—“Some wise (being) is a man.” Conversion is a very serviceable means of im­ mediate inference. By its use the dialectician may draw true and valid propositions from other proposi­ tions. But there are rules that must be carefully fol­ lowed, else this sort of immediate inference is un­ warranted. The rules are: 1. The converse must be of the same quality as the convertend. This rule means: if the convertend is affirmative, the converse will be affirmative; and if the convertend is negative, the converse must be negative. 2. No term in the converse can have a wider Ex­ tension than it had in the convertend. Else the in- 102 THE JUDGMENT EXPRESSED DIALECTICS ference would be unwarranted as stating more than the proposition whence it was inferred. 3. Special rules : An E- or an I-proposition is con­ verted simply, that is, II- will be converted to E-, and I- to I-. An A-proposition is converted accidentally, that is, A- will not convert to A-, but to I. An 0proposition cannot be converted directly. In other words : A converts to I (accidental conversion) E converts to E (simple conversion) I converts to I (simple conversion) O is not convertible Let us study some examples of conversion. Suppose the A-proposition, “All men are wise” is to be converted. We first look at the terms of the proposi­ tion to make sure of their extension. “All men” is universal; “wise (beings)” is particular, being the predicate of an affirmative proposition. Therefore, when the proposition is converted we cannot make the subject “All wise beings” but “some wise beings.” Can we use “men” in a narrower, more retricted Extension in the converse than in the con­ vertend? Yes, the rule forbids only the expanding of the Extension of terms. Certainly, if we have something stated as true of all men we may infer it as true of some men: for the principle is, “If a sub­ alternant is true, the subalternate is true.” Now we ! ! ' ’ | 1 ■ 5 j ·. 103 proceed to the conversion of “All men are wise.” The converse is, “Some wise beings are men.” Notice that this justifies the dictum, “A converts to I.” Take the E-proposition “No man is wise.” This is a negative proposition. Now in negative proposi­ tions the negation affects the copula, even if it be expressed in a particle prefixed to the subject. The accurate expression of “No man is wise” is “All men are-not wise.” Now examine the Extension of the terms of this proposition. The subject is univer­ sal; the predicate is also universal, being the predi­ cate of a negative proposition. Therefore we may use both terms in full Extension (i. e., as universal terms) in the converse. We proceed to convert “No man is wise.” The converse is, “No wise (being) is a man.” Notice that this justifies the dictum, “E converts to E.” Take the proposition “Some men are wise.” Both terms are particular : the subject, because it is quali­ fied by the limiting “some” ; and the predicate, be­ cause it is the predicate of an affirmative proposi­ tion. Therefore the converse will have both subject and predicate particular. And since the quality may not change, the converse will be a particular af­ firmative, that is, an I-proposition. Hence we see that “I converts to I.” The converse, therefore, of “Some men are wise” is “Some wise beings are men.” Take the O-proposition “Some men are not wise.” 104 THE JUDGMENT EXPRESSED DIALECTICS The subject is particular, and the predicate—being predicate of a negative proposition—is universal or in full Extension. Now the converse will have to be negative by the first rule of conversion: "The converse must be of the same quality as the convertend.” Therefore when the particular “some men” becomes the predicate of the converse it will have to be changed to “all men.” But this conflicts with the second rule of conversion : “No term can have a wider Extension in the converse than it had in the convertend.” Therefore in the case of the O-proposition direct conversion is impossible. / 1 ! ρ 1 i SUMMARY OF THE ARTICLE In this Article we have learned what is meant by Opposition, Equipollence, and Conversion of prop­ ositions. We have learned these as properties of propositions and as processes of immediate inference. They are valuable processes of such inference, for they enable the dialectician to see the faulty and illogical nature of statements unwarrantedly made in virtue of other statements, and they equip him for the task of forming clear and valid infer­ ences. Suppose the student, after mastering this Artide, should hear a lecturer remark : “I have been for many months a close observer of the life of the Catholics of French Canada. These people are intensely religious. Yet their life is barren of those ) f \ 1 1 'i >' ί 105 little comforts and conveniences that modern science has made available to us here in America. Can any­ one, seeing this, doubt the well-known fact that the Catholic religion stands in spirit and in fact against the progress of science?” The words may be “boiled down” to the following: “French Canadian Cath­ olics are unprogressive.” This proposition is then converted into “All Catholics are unprogressive.” The dialectician sees at once the point of fallacy in the whole argument : the speaker has inferred the truth of a subalternant from the truth of its sub­ alternate,—an unwarranted procedure. We have learned that Equipollence and Opposi­ tion of propositions also serve as means of infer­ ence and as “checks” or bases of criticism upon un­ warranted inference. In all the matter studied in this Article there is much that can be put to practical use, much that makes for clear thinking, even though the student must pay for this service by hard study of dry rules and tedious explanations of principles. Let the student put his knowledge to immediate service in daily reading of books and newspapers. He will be amazed at the number of instances of unwarranted inference he will discover. Let him in each instance reduce the inference to a proposition in logical form, and then criticize it according to the rules learned in this Article for the relative proper­ ties of propositions. He will find the work interest­ ing, and he will be stirred to greater effort by the ιο6 DIALECTICS consideration of the fact that the inferences he sees as unwarranted (and sees how and why and where they are illogical) convince a great many people— even educated people—who accept them as sound reasoning and correct thinking. nd fa ■Π! I 1W BOOK THIRD REASONING This Book discusses the third and most complex of the mental operations, viz., reasoning. First, reasoning is studied as it goes on in the mind; then as expressed in argumentation, the most perfect form of which is the syllogism. The laws of the syllogism are stated and justified. Finally, the Book discusses some examples of fallacious reasoning so that the student may have practical warning of the pitfalls that lie in wait for him, and may be wary in his evaluation of argument. The Book is therefore divided into the following Chap­ ters : Chapter I. Reasoning Itself Chapter II. Reasoning Expressed Chapter III. Fallacies to Avoid ■ CHAPTER I REASONING ITSELF a) Description b) Definition c) Methods This Chapter describes and defines the operation called reasoning, and discusses two methods of using it. The Chapter is not divided into Articles. a) DESCRIPTION OF REASONING In the last Chapter of the foregoing Book we learned that propositions may imply other proposi­ tions, and that these may be immediately inferred by the aid of Opposition, Equipollence, and Conver­ sion. Such immediate inference is, indeed, a kind of reasoning, for it is “thinking things out.” But reasoning ordinarily means mediate inference, and it is in that sense that we understand the term reasoning in the present Book. When two ideas are compared, their relation of agreement or disagreement is enunciated by the mind in a judgment. But sometimes the mind, be­ cause of obscurity in the ideas, cannot tell whether they agree or disagree. Direct judgment is therefore impossible. Judgment must be reached in an indirect, log ho DIALECTICS roundabout, mediate way. When such a judgment is worked out, we have mediate inference or reasoning proper. Now the roundabout or mediate process of arriv­ ing at judgment may be illustrated as follows: The mind compares ideas A and B, but because of their ' obscurity, finds immediate judgment impossible. However the mind sees that idea A agrees with idea C; it also sees that idea C agrees with idea B. Thus, by using idea C as the medium it arrives at the judg­ ment “A agrees with B.” This is mediate inference; this is reasoning. To illustrate further : Suppose the mind com­ pares the two ideas oak and plant. Let it be further ? supposed that the ideas are obscure or vague, so that oak is associated in the mind chiefly with rugged sturdiness and strength, and plant with green and tender growth. The mind, comparing the two ideas, i, is not inclined to pronounce the judgment, “The oak is a plant.” Still, in spite of vagueness, there is in the idea oak the partly grasped note of growth. For this reason the mind is not inclined to enunciate the judgment, “The oak is not a plant.” Judgment is baulked ; the mind cannot pronounce upon the agree< ment or disagreement of the two ideas. Suppose, however, that the mind knows clearly that the oak is a tree. Suppose further that it understands that all trees are plants. Thereupon, using as medium the idea tree, the mind can work out the judgment conk REASONING ITSELF in cerning oak and plant in the following manner : All trees are plants; the oak is a tree ; therefore, the oak is a plant. The two examples given may be graphically illus­ trated as follows : * *T From the foregoing we see that reasoning is a roundabout way of arriving at judgment. We also see that the judgment is worked out of two other judgments, thus : All trees are plants The oak is a tree Therefore, the oak is a plant The two judgments from which the judgment sought is worked out are called premisses. The judg­ ment worked out is the consequent or conclusion. Notice that the conclusion is worked out of the premisses by the mind. It must therefore be in the premisses. From this we learn that the conclusion is nothing more than an explicit enunciation of what is implicitly contained in the premisses. Analyzing the premisses we see that they involve three ideas. The mind seeks to pronounce judgment 112 DIALECTICS upon two ideas ; for the purpose it calls in a third idea known in relation to the other two. Now the idea which the mind seeks to predicate of another is the major idea, and the idea about which predica­ tion is to be made is the minor idea. In other words, the mind in reasoning seeks to know whether one idea is or is not contained in the Extension of an­ other idea as its inferior or subject. Technically, the mind seeks to know whether the minor idea is or is not included in the Extension of the major idea. The mind seeks to make a predication, to predicate the major of the minor idea, affirmatively or nega­ tively. Therefore the major idea will always be the predicate of the conclusion, and the minor idea will always be the subject of the conclusion. In the illus­ tration given above, the major idea is the idea plant ; the minor idea is the idea oak, and judgment upon these ideas is rendered possible by using a middle idea viz., the idea tree. Summing up, we find that the reasoning process involves three judgments and three ideas. The judg­ ments are two premisses and a conclusion. The ideas are the major, middle, and minor ideas. In the next Chapter we shall learn that these elements of reason­ ing find respective expression in three propositions and three terms, which have the names here ascribed to the mental elements of reasoning, viz., premisses and conclusion ; major, middle, and minor terms. REASONING ITSELF b) 113 DEFINITION OF REASONING Since reasoning has as its elements three judg­ ments and three ideas, we may define it on the basis of its ideas, and on that of its judgments : 1. Reasoning is an operation of the mind by which the agreement or disagreement of two ideas is inferred from their known relation to a common third idea. 2. Reasoning is an operation of the mind by which a judgment is explicitly inferred from two other judgments in which it is implicitly contained. A little study will show that the two definitions are identical in meaning. The first definition tells us that the thing to be accomplished by reasoning is the inference of “the agreement or disagreement of two ideas,” and this is judgment. The second definition simply tells us that judgment is sought. c) METHODS OF REASONING. The two methods of reasoning are inductive and deductive reasoning, and these are usually called simply Induction and Deduction. I. Induction reasons from individual and par­ ticular data to a general or universal conclusion. Thus if one experiments with a specimen of each of the known metals, and finds that every one of them is heavier than water taken in equal bulk, one must conclude : “All the known metals are heavier than a 114 DIALECTICS water.” This is induction, and complete induction. Again, suppose one observes that various bodies, in all circumstances of time, place, temperature, etc., tend to fall towards the center of the earth. One may (although experiment has by no means been made with each and every existing body) assert as a conclusion : “All earthly bodies tend towards the center of the earth.” This is incomplete (but suf­ ficient) induction. Again, suppose one perforins the experiment reported as follows in a newspaper : “An English scientist hitched a fly to a tiny wagon, and discovered that it could pull seventy times its own weight over smooth surfaces.” If one concluded from such an experiment : “All flies can pull seventy times their own weight over smooth surfaces,” one would give evidence of incomplete and insufficient induction. Induction is the only method available to the ex­ perimental sciences. Its conclusions are known as scientific facts and scientific laws. It is valid when complete (a thing hardly possible) and also when incomplete but sufficient, that is, when its con­ clusions are drawn from representative data, thoroughly and exhaustively investigated. Induction when incomplete and. insufficient has no scientific value, although it may indicate to the investigator a line of experiment that will eventually result in valid and scientific conclusions. But induction, how­ ever valuable, is not of first importance in rational REASONING ITSELF * > ) / t \ ί 1 * • . 115 science. Dialectics is concerned with deduction, not with induction. In passing, however, let us notice that the two methods are not opposed, one to the other, but are supplementary. Deduction starts with a general or universal datum ; and induction seeks to establish a universal truth so that particular truths can be deduced therefrom. 2. Deduction reasons from the universal to the particular and individual. The example of mediate inference (reasoning) given above illustrates the fact. Let us repeat it here : All trees are plants (a universal datum) The oak is a tree Therefore the oak is a plant (i. e., one kind of plant—a particular datum). Deduction proceeds from two important principles, called the Dictum de Omni and the Dictum de Nullo. These are : i. Dictum de Omni: Whatever is affirmed of a class as a whole, is thereby affirmed of each and every member of that class. To illustrate: All trees are plants (plant affirmed of whole class tree ) The oak is a tree (member of the class) The oak is a plant (plant affirmed of that member) DIALECTICS ii. Dictum de Nullo: Whatever is denied of a class as a whole, is thereby denied of each and every member of that class. To illustrate: No tree is a spirit (spirit denied of whole class tree ) The oak is a tree (member of the class) The oak is not a spirit (spirit denied of that member) Deduction is the perfect method of reasoning. Its conclusions are, when rightly drawn, inevitable in view of the premisses. SUMMARY OF THE CHAPTER In this Chapter we have learned what is meant by reasoning, and have marked a line of distinction between immediate inference and reasoning proper. We have noted the elements of the reasoning process as three ideas and three judgments, and have learned to name these elements accurately. We have defined reasoning, and have discussed its two methods. CHAPTER II REASONING EXPRESSED Just as the idea is expressed in the term, and the judg­ ment in the proposition, so the reasoning process is ex­ pressed in argumentation. Argumentation (or argument) may be defined as a process of speech in which one proposi­ tion is explicitly inferred from other propositions in which it is implicitly contained. The most perfect form of argumentation is the syllogism. This Chapter deals with the syllogism. The Chapter treats of the nature and classification of the syllogism, the laws by which it is governed, the moods and figures in which it may be constructed, and the imperfect, but valid, forms in which the syllogism may be found. The Chapter is therefore divided into the following Articles : Article I. The Syllogism and its Kinds Article 2. Laws of the Syllogism Article 3. Figures and Moods of the Syllogism Article 4. Imperfect Syllogisms. Article I. The Syllogism and its Kinds a) The Syllogism b) Correctness and Truth of the Syllogism c) Kinds of Syllogisms a) THE SYLLOGISM The syllogism is an argument consisting of three propositions so related that when the first two 117 118 DIALECTICS are posited the third necessarily follows. Example : Every man is mortal John Smith is a man Therefore John Smith is mortal The first two propositions of the syllogism are called the premisses. The third proposition (which is implied in the premisses) is the conclusion or con­ sequent. The logical connection existing between the premisses and the conclusion is called con­ sequence; and if a conclusion is not legitimately drawn from given premisses, the syllogism is said to lack consecpience. The terms used in the simple syllogism are three in number. These are called the major term, the middle term, and the minor term, according as they express respectively the major, the middle, and the minor idea of the reasoning process. A practical rule for distinguishing the terms is the following : The major term is the predicate of the conclusion; the minor term is the subject of the conclusion ; the mid­ dle term occurs in each premiss but not in the con­ clusion. This rule is not a scientific one for the Dialectician, for it presupposes a perfect syllogism to begin with ; but it is a good handy rule in practice. The reason for it will appear upon recollection or review of what we have learned about the major, middle, and minor ideas of the reasoning process, and the place of these ideas and their function in REASONING EXPRESSED k 119 that process. In the syllogism given above, the major term is mortal; the minor term is John Smith, and the middle term is man. The major and minor terms are called extremes as contrasted with the mean, or middle term. The premisses are called the major premiss and the minor premiss. This distinction of premisses was originally based upon the distinction of terms, so that the major premiss was that premiss which contained the major term, and the minor premiss was that which contained the minor term. But usage has brought a change, and now the distinction of premisses as major and minor amounts simply to first and second premiss respectively. The three propositions and the three terms that enter into the construction of the syllogism consti­ tute its matter or material element. The logical structure, which makes clear the connection of the premisses and the consequence of the syllogism, is the form or formal element of the syllogism. b) CORRECTNESS AND TRUTH OF THE SYLLOGISM r The syllogism is correct when its material and formal elements are both present in integrity; in other words, it is correct when the conclusion fol­ lows necessarily from the premisses as given. The syllogism is true when its conclusion states a true fact, regardless of the truth of the premisses, and regardless of the consequence, that is, the necessary ■K ! 20 DIALECTICS inference of the conclusion from the premisses as given. The following syllogism is correct but not true: Every tree is a spirit The oak is a tree Therefore the oak is a spirit The following syllogism is true but not correct: Every spiritual being is immortal The soul is immortal Therefore the soul is a spiritual being Notice in the latter example that the conclusion expresses a truth, viz., “the soul is a spiritual being.” But this conclusion is not legitimately drawn from the premisses ; the syllogism lacks consequence ; therefore the syllogism is incorrect. Now Dialectics looks only to correctness in syl­ logisms. While it is evident that the syllogism can serve no worthy or valuable purpose unless it is both correct and true, we must learn first how to make it correct. The science of Dialectics has cor­ rectness of reasoning as its Formal Object, and in all that follows we look to correctness of syllogisms and not to their truth. Nevertheless, Dialectics finds a stable relation existing between truth and correct- REASONING EXPRESSED ° I 3 ( 121 ness in syllogisms, and the following practical prin­ ciples are discerned : 1. The correctness of the syllogism being sup­ posed, it follows that if the premisses are true the conclusion will be true; but if the premisses are false, the conclusion may be false or true. 2. The correctness of the syllogism being sup­ posed, it follows that if the conclusion is false, one or both of the premisses must be false; but if the · · conclusion is true, the premisses may be true or false. To state the principles in a somewhat more di­ rect form : True premisses—true conclusion True conclusion—false or true premisses False premisses—false or true conclusion False conclusion—false premisses (one or both) \ c) KINDS OF SYLLOGISMS J ’ ' i • Here we speak only of the perfect syllogism, that is, the syllogism which squares precisely with the definition of syllogism given above. Of imperfect syllogisms we shall speak in Article 4 of this Chapter. The perfect syllogism is : I. Categorical when all three of its propositions are categorical, that is absolute and unconditioned propositions. The categorical syllogism is simple or compovmd, according as its propositions are sim­ ple or compound propositions. 122 DIALECTICS 2. Hypothetical when the major (first') premiss is a hypothetical proposition. This syllogism is con­ nective (or simply conditional'), con junctive, or dis­ junctive, according as its major proposition is a connective, conjunctive, or disjunctive proposition. Examples : 1. Simple categorical syllogism: Every man is mortal John Smith is a man Therefore, John Smith is mortal 2. Compound categorical syllogism : Whatever is infinitely perfect is necessarily eternal God is infinitely perfect Therefore, God is necessarily eternal 3. Conditional syllogism : If it rains, there will be no game It rains Therefore, there will be no game 4. Conjunctive syllogism : The milk cannot be at once sweet and sour It is sweet Therefore, it is not sour 5. Disjunctive syllogism : Either Smith won, or he was defeated He was defeated Therefore, he did not win. r REASONING EXPRESSED 123 SUMMARY OF THE ARTICLE In this Article we have learned that the syllogism is the most perfect form of argumentation, which is the expression in speech of the reasoning process. We have also defined it, have studied its elements, nttd hn-irZl 1ΧΊ Ά Λ z4 4-1-1 λ *-i ·-» λ r' Γ « 4-π p’s β-ν *. Λ β-χ* OBM 124 DIALECTICS Terms,” and the second group being the “Laws of Propositions.” Laws of Terms Three terms there must be, neither more nor less, No wider in Conclusion than in Premiss; Conclusion never dares the Middle mention; The Middle, once or twice, has full Extension. Laws of Propositions Affirmatives can never breed negation ; Two negatives end ever in frustration; Conclusion follows e’er the weaker part; Particulars no argument can start. To explain these laws in detail : i. Laws of Terms first law of terms: Three terms there must be, neither more nor less. This law expresses a require­ ment of the very nature of the syllogism. For the syllogism is a process of reasoning to the agreement or disagreement of two terms through their relation to a third term. The syllogism exists for its con­ clusion; it is framed to reach the conclusion, to reason to the conclusion. Now the conclusion will express the relation (agreement or disagreement) of a subject and predicate. The predicate is the major term ; the subject is the minor term. The third term, used only in reasoning to the conclusion, is compared REASONING EXPRESSED 125 in the premisses with the major and the minor term, and is called the middle term. Every perfect cate­ gorical syllogism must have, in consequence, a major, a minor, and a middle term. It must not have more than these, else the relation of major and minor term will not be apparent; for these must be studied in their relation to a common third term (the middle term) so that their relation to each other may be discerned thereby. Notice that three terms are re­ quired, not merely three names or words. A name or word might be used in two senses, and hence, while remaining the same word, would be two terms. To introduce such ambiguity or equivocation into the syllogism would cause it to violate this First Law of Terms, for, in the case supposed, there would be four terms and not three. An example of such equivocation is the following : A bank is a place in which money is deposited This mound of earth is a bank Therefore this mound of earth is a place in which money is deposited. The term bank is one word, but is used in two ut­ terly different “suppositions,” and hence the argu­ ment contains four terms and is no true syllogism. Let the student test the following by the First Law of terms : 126 DIALECTICS Every man is God’s image Judas was a man Therefore, Judas was God’s image. A wait is a short stop A short-stop is a ball-player Therefore, a wait is a ball-player. No effect is causeless This is an effect Therefore, this is not causeless. second law of terms : No wider in Conclusion than in Premiss. That is to say : the terms must not have a larger Extension in the conclusion than they have in the premisses. If the terms should have a larger Extension in the conclusion than in the premisses, then the conclusion says more than the premisses warrant. Remember that the conclusion is only the explicit statement of what is implicitly contained in the premisses. How is one to judge of the Extension of the terms in the premisses? The subject of the premisses will always be universal or particular, and this will be indicated by qualifier or obvious sense; and the predicate of the premisses is judged by the two principles already learned, viz., I. The predicate of an affirmative proposition is undistributed (that is, is particular), and 2. The irrîsii f REASONING EXPRESSED 127 predicate of a negative proposition is distributed (that is, is universal or in full Extension). To illus­ trate : Every tiger is a living being A man is not a tiger Therefore a man is not a living being. Notice the following facts : living being in the premiss is particular—predicate of an affirmative proposition. But the same term in the conclusion is general or universal (in full Extension)—predicate of a negative proposition. Thus the conclusion says more than the premisses warrant, and the syllogism is incorrect because it violates the Second Law of Terms. Let the student criticize the following in the light of the First and Second Law of Terms. War is hell Hell is a place Therefore, war is a place. A game is a play A dramatic performance is not a game Therefore, a dramatic performance is not a play. Î 128 DIALECTICS Brass is not precious metal This ring is brass Therefore, this ring is not precious metal Gold is precious metal This ring is not gold Therefore, this ring is not precious metal. third law of terms : Conclusion never dares the Middle mention. That is to say, the middle term, which occurs in both premisses, must never occur in the conclusion. The reason is obvious. The middle term is the medium used to reach the pronounce­ ment which the mind seeks to make about the major and the minor term. The conclusion is the otie thing sought for; it is the sole reason for the existence of the syllogism; the mind knows its elements (subject and predicate—or, minor and major terms) from the start, and uses the middle term only to enable it to make pronouncement on the relation of these. There­ fore, by the very nature of the syllogism, the middle term is the means of reaching the conclusion, but has no place in the conclusion. Should the middle term occur in the conclusion, the argument is vitiated and is no true syllogism. To illustrate : John is lazy John is a student Therefore John is a lazy student. REASONING EXPRESSED 129 This is merely the compounding of terms ; it is not reasoning. The last statement merely combines the other two; it does not draw out a proposition latent in them. The last statement is only a more compact form of the other two statements. Let the student criticize the following in the light of the first three Laws of Terms : Galahad was a knight A night is dark Therefore, Galahad was dark. No cat has two tails My dog is no cat Therefore, my dog has two tails. Bread is a staple food Potatoes are a staple food Therefore, bread and potatoes are staple foods. Flattery is not good Foolish praise is flattery Therefore, foolish praise is not good. fourth law of terms: The Middle, once or twice, has ftdl Extension. That is to say, the middle term, in at least one of the premisses, must be dis- 130 DIALECTICS REASONING EXPRESSED statements without logical sequence, implying no conclusion. The following example makes the mat­ ter clear : A revolution is a war Therefore, a revolution brings misery. Some preternatural events are deceptions But this event is a preternatural event Therefore, this event is a deception. Wine is an intoxicant Whiskey is an intoxicant Therefore, whiskey is wine. The middle term, an intoxicant, is undistributed in both premisses (being in each instance the predicate of an affirmative proposition). The premisses are seen to be independent statements. Draw a circle to indicate the Extension of the term intoxicant. Within the circle make two smaller circles, marking one wine and the other zvhiskey. Thus you perceive that, while the two statements (premisses) assign both whiskey and wine to the class intoxicant, they say nothing about the full relation of whiskey to wine. Hence the conclusion set down is altogether unwar­ ranted. The argument is no syllogism ; it offends against the Fourth Law of Terms. Let the student criticize the following in the light of the four Laws of Terms : i3i # i ' \ ( ' Some birds sing melodiously All ducks are birds Therefore, all ducks sing melodiously. Î All wars bring misery ’ Diogenes sought an honest man An honest man is John Jones Therefore, Diogenes sought John Jones. All Caucasians have inviolable rights Negroes are not Caucasians Therefore, negroes do not have inviolable rights. No earthly benefit is lasting Filial love is an earthly benefit Therefore, filial love is not lasting. All typhus is dangerous This disease is not typhus Therefore, this disease is not dangerous. Sam sings songs Sam sings sweetly Therefore, songs are sweetly sung by Sam. 132 DIALECTICS No news is good news All history is no news Therefore, all history is good news. Some airplanes are biplanes That big monoplane is some airplane Therefore, that big monoplane is a biplane. ii. Laws of Propositions first law of propositions: Affirmatives can never breed negation. That is to say, two affirmative premisses can never lead to a negative conclusion. In other words, if both premisses are affirmative, the conclusion will necessarily be affirmative, The con­ clusion expresses explicitly only what is implied in the premisses. Now, two affirmative premisses imply no negation whatever. Therefore no negation can be expressed in the conclusion. Let the student criticize the following: Oranges are a tropical fruit Tropical fruits are expensive Therefore, oranges are not cheap. second law of propositions : Two negatives end ever in frustration. That is to say, no conclusion can be drawn from two negative premisses. The syl- REASONING EXPRESSED 133 logism by its nature requires the positive assertion of the relation of at least one of the extreme terms (that is, major and minor terms) to the middle term. If both premisses are negatives, they are independ­ ent denials, and nothing can be drawn from them about the relation of the major and minor term to each other. The following example makes this ob­ vious : Man is not a spirit An angel is not a man (no conclusion possible) Nothing is said in these premisses to justify an in­ ference concerning angel in relation to spirit. The result—for all the premisses tell us—might be what is illustrated in either of the following figures : third law of propositions: Conclusion follows e’er the weaker part. This law requires a somewhat lengthy and involved justification. The student is 134 REASONING EXPRESSED DIALECTICS asked to master each step in the argument before proceeding to the next. By the "weaker part” we mean negation (in quality) and particularity (in quantitj·) as opposed to the “stronger part,” that is, affirmation and uni­ versality. The law means: “If one premiss is negative and the other affirmative, the conclusion will necessarily be negative; and if one premiss is par­ ticular and the other universal, the conclusion will necessarily be particular.” I. If one premiss is negative and the other af­ firmative, the conclusion will be negative. The affirmative premiss will assert the agreement oi one of the extremes (major and minor terms) with the middle term. The negative premiss will assert the disagreement of the other extreme with the middle term. Hence, the extremes will stand in disagreement with each other—and this means that the conclusion will be negative. To illustrate: Take A and B as the extreme terms, and C as the middle term. Let the affirmative premiss be “A is C.” Let the negative premiss be “B is not C.” There is no conclusion possible except “A is not B,”—a negative conclusion. Thus, “Conclusion follows e’er the weaker part.” 2. If one premiss is particular and the other uni­ versal, the conclusion will be particular. Here the possibilities are as follows: i. both premisses may be affirmative ; or ii. one premiss may be affirmative Ί ! ■ [ ! ‘ ) ? j \ i 135 and one negative. In either case the conclusion must be particular, as we see from the following: i. If both premisses are affirmative, there will be only one universal term (that is, term taken in full Extension) in the premisses, viz., the subject of the universal premiss. Both being affirmative proposi­ tions, the two predicates will be undistributed, that is, particular; and the subject of the particular premiss will be particular : hence only the subject of the universal premiss can be universal. Now, this one universal term must be the middle term by the Fourth Law of Terms : “The Middle, once or twice, has full Extension.” Nor can this middle term ap­ pear in the conclusion, by the Third Law of Terms : “Conclusion never dares the Middle mention.” It follows, that there are no terms for the conclusion but particular terms. Hence the conclusion must be particular. Q.E.D. ii. If one premiss is affirmative and the other nega­ tive, there will be only two universal terms in the premisses, viz., the subject of the universal premiss/ and the predicate of the negative premiss. But for the conclusion to be universal, there would have to be three universal terms in the premisses. For in the present hypothesis the conclusion must be negative (as we have proved in the first part of the explana­ tion of this law), and if this conclusion were uni­ versal it would involve two universal terms—the 136 DIALECTICS subject, because it would be the subject of a universal proposition ; and the predicate, because it would be the predicate of a negative proposil ion. Now these terms could not be universal in the conclusion unless they were universal in the premisses, for the Second Law of Terms is : “No wider in Conclusion than in Premiss.” Hence the premisses would have to contain two universal terms for the conclusion; and, in ad­ dition, the premisses would have to contain the mid­ dle term in full Extension (i. e., universal) at least once. Therefore the premisses would have to con­ tain three universal terms if the conclusion were to be universal. But, as stated above, the premisses do not contain three universal terms, but only two. Therefore the conclusion cannot be a universal proposition. It remains that it must be a particular proposition. Q.E.D. ir fourth law of propositions : Particulars no argument can start. That is to say, if both premisses are particular propositions, no conclusion is possible. Such premisses will necessarily be independent state­ ments without strict logical connection. We may prove the law as follows : I. If both premisses (particulars) are affirmative, they will contain no universal term whatever. Their subjects will both be particular terms, because they are subjects of particular propositions. And their predicates will both be particular terms, because they REASONING EXPRESSED 137 are predicates of affirmative propositions. Now the premisses of every real syllogism must contain at least one universal term for, “The Middle, once or twice, has full Extension.” Hence, from particular affirmative premisses we can conclude nothing, since there is no comparison of major or minor term with the middle term in full Extension. 2. If both premisses (particulars) are negative, no conclusion is possible by the Second Law of Propositions: “Two negatives end ever in frustra­ tion.” 3. If one particular premiss is affirmative and the other particular premiss is negative, then the con­ clusion will be negative, for “Conclusion follows e’er the weaker part.” This conclusion will require a universal term for its predicate, for “In a negative proposition, the predicate is distributed.” Hence, this universal term must occur in the premisses ; and the middle term must also occur in the premisses as a universal at least once. Two universal terms must therefore occur in the premisses. But, as a matter of fact, in such premisses as we consider here, two uni­ versal terms cannot occur. Both premisses being particular propositions, it follows that only the predicate of the negative premiss can be a universal term. It is obvious, therefore, that no conclusion can be drawn from such premisses. note: For compound categorical syllogisms, the 138 DIALECTICS general rule is as follows : Reduce the syllogism to the simple categorical syllogisms contained in it, and frame or criticize these according to the Eight Laws already explained. Ordinarily, however, the Eight Laws may be applied directly, without reduction if the student will be very careful to avoid the ever­ present danger of saying more in the conclusion than the premisses warrant. Here, for example, is an unjustified inference which comes from ignoring this warning : An infinitely perfect Being is eternal God alone is an infinitely perfect Being Therefore, God alone is eternal. In the second (or minor) premiss, the force of the exclusive particle alone centers upon in finitely perfect Being. In the conclusion alone centers upon the term eternal. Thus the conclusion is unwarranted. In other words, the premisses say that God is the only infinitely perfect Being, but they do not say that only an infinitely perfect Being is eternal : yet the con­ clusion indicates that the premisses do say this, and hence the conclusion is unwarranted. This fact is shown in the following restatement of the syllogism : An infinitely perfect Being is eternal (Maybe other beings are too) God alone is an infinitely perfect Being (No ' }t) REASONING EXPRESSED 139 other Being is infinitely perfect, but maybe other beings are eternal) Therefore, God is eternal (It must not be stated, in view of the premisses, that no other beings are eternal ). It appears then that the term alone in the second (or minor) premiss merely adds a bit of information which is alien to the general progress of the argu­ ment in hand. Leaving aside this alien matter, we have the syllogism as follows : An infinitely perfect Being is eternal God is an infinitely perfect Being Therefore, God is eternal. “God is eternal” is the only conclusion that can be justified. Let the student grapple with the difficulties pre­ sented in the following syllogisms : All diligent students will receive a prize All but John are diligent students Therefore, all but John will receive a prize. Brute animals are not what men are Men are rational Therefore, brute animals are not rational. 140 DIALECTICS We are not what brutes are Brutes are animals Therefore, we are not animals. Everyone who says that Peter is baptized, says the truth Everyone who says that Peter is a Christian, says Peter is baptized Therefore, everyone who says that Peter is a Christian, says the truth. (Suggestion : There is such a thing as non-Christian baptism—that of St. John the Baptist, for instance.) The king awards honors to all who serve the state John Johnson does not serve the state Therefore the king does not award honors to John Johnson. b) LAWS FOR THE HYPOTHETICAL SYLLOGISM As we have seen, there are three types of hypo­ thetical syllogisms, the conditional, the conjunctive, and the distinctive. We deal with each of these singly. i. The Conditional Syllogism. Law: From the truth of the antecedent follows the truth of the consequent, but not vice versa; and from the falsity REASONING EXPRESSED 141 of the consequent follows the falsity of the ante­ cedent, but not vice versa. In other words : if antecedent is true—consequent is true; if antecedent is false—consequent is true or false ; if consequent is true—antecedent is true or false ; if consequent is false—antecedent is false. From these four facts we deduce two “put and take” methods for forming the minor premiss of the conditional syllogism : i. The “put”-method affirms the truth of the antecedent. Example : If God is just, the soul will survive death God is just Therefore, the soul will survive death. ii. The “take”-method denies the truth of the consequent. Example : If the soul does not survive death, God is cruel God is not cruel Therefore, the soul survives death. Notice here that we should violate the law of con­ ditional syllogisms if we made the minor of the first syllogism, “The soul will survive death,” and 142 DIALECTICS then conclude, “God is just.” This would be con­ cluding to the truth of the antecedent from the truth of the consc< 1 tient, which is an unwarranted pro­ cedure. Nor, in the second example, could we put as minor premiss, “The soul survives death,” and con­ clude, “Therefore, God is not cruel.” This would be concluding to the falsity of the consequent from the falsity of the antecedent—an unjustified procedure. 2. The Conjunctive Syllogism. Law: From the truth of one component follows the falsity of the other, but from the falsity of one component it does not follow that the other is true. In other words : if one component is true—the other is false; if one component is false—the other may be true or false. From these two facts we deduce the one method of reaching a conclusion in the conjunctive syllogism. It is the “put-take,” that is, one member of the con­ junctive premiss is affirmed (“put”) in the minor premiss, and the other is denied (“take”) in the conclusion. Example : Feter does not sit and stand at the same time Peter stands (“put”) Therefore Peter does not sit (“take”) We could not use the “take-put” method and reach a conclusion, for the members of the conjunctive V. REASONING EXPRESSED 143 premiss (the major premiss) do not exhaust the possibilities, and hence to deny one is not to affirm the other. Thus the following syllogism is incorrect, and its conclusion unwarranted : Peter does not sit and stand at the same time But he is not sitting Therefore he stands (He may be lying down!) 3. The Disjunctive Syllogism. Law : From the truth of one member follows the falsity of all the others, and from the falsity of one member follows the truth of one of the others. In other words : if one member of the disjunction is true—other or others are false; if one member of the disjunction is false—one of the others is true. From these two facts we deduce two methods of reaching a conclusion in the disjunctive syllogism. These are the “take-put” and the “put-take” methods. Examples : Either it is day or it is night It is not day (“take”) Therefore, it is night (“put”) Either it is day or it is night It is night (“put”) Therefore, it is not day (“take”) 144 DIALECTICS The student must be sure that the major premiss is a complete disjunction, else he may ( and probably will) reach an unjustified conclusion. The following example shows such a conclusion : It is spring, summer, or autumn It is not autumn Therefore, it is spring or summer (It may be winter !) Let the student criticize the following syllogisms in the light of the Laws for Hypothetical Syllogisms: If it rains the game will be postponed The game will be postponed Therefore, it rains If you are a fool, you will not study You will not study Therefore, you are a fool If you are not a fool, you will study You will study Therefore, you are not a fool If the ring is solid gold, I want it The ring is not solid gold Therefore, I do not want it We do not have rain and fair weather simul­ taneously REASONING EXPRESSED HS We have not fair weather to-day Therefore, we have rain to-day John cannot be at once studious and lazy He is not lazy Therefore, he is studious You do not weep and rejoice at the same time You are not rejoicing Therefore, you are weeping Either it rains or it does not rain It does not rain Therefore, it rains Either he is a silly fellow or he is shrewd He is not a silly fellow Therefore, he is shrewd The color of the cloth is either black or brown It is black Therefore, it is not brown Either Betsy or I killed the bear I did not kill it Therefore, Betsy killed it If John is at home, I shall visit him He is not at home Therefore, I shall not visit him 146 DIALECTICS SUMMARY OF THE ARTICLE In this lengthy Article we have learned the. laws for constructing and criticizing syllogisms. These laws are of supreme importance ; they are “Laws of Thought.” We have studied the reasons for each law, and, if we have been diligent, we have accepted no single law on faith, but have mastered the hows and whys of each, and have discovered clearly just why it must be so. The study of the Laws for Syl­ logisms and their reasons is splendid mental train­ ing, and, in addition, it gives the student the practical equipment for analyzing and evaluating argument. The student will practice the art of reducing argu­ ment to syllogistic form* before attempting to judge its validity. Article 3. Figures and Moods of the Syllogism a) Figures of the Syllogism b) Moods of the Syllogism a) FIGURES OF THE SYLLOGISM The position of the middle term in the premisses determines what is called the figure oi the syllogism. The middle term can occupy the following positions : subject of both premisses; predicate of both premisses; subject of first, predicate of second premiss; predicate of first, subject of second premiss. REASONING EXPRESSED i47 Thus there are Four Figures of the Syllogism. Ar­ ranging these according to their perfection (that is, the clarity with which they show the consequence of the argument), we determine the figures according to the position of the middle term in the premisses, as follows : First Figure: middle term is subject of first premiss, predicate of second; Second Figure : middle term is predicate of both premisses ; Third Figure: middle term is subject of both premisses ; Fourth Figure : middle term is predicate of first premiss, subject of second. Taking S for the subject of the conclusion (minor term), and P for the predicate of the conclusion, (major term), and M for the middle term, we may illustrate the Four Figures as follows: Fig. I Μ - P Fig. II S -M P - M S - M S - P S - P Fig. III M - P M - s S - P Fig. IV P - M M - S S - P A good way of fixing the Figures in memory is to liken them to the four lines that make up the letter “M ” drawing the lines as indicated here : I i; 148 REASONING EXPRESSED DIALECTICS 149 Figure III : The minor premiss must be affirma­ tive; the conclusion will be particular. Let the student determine the Figure of the fol­ lowing syllogisms, and test them by the laws just given and by the Eight General Laws : All men are rational All men are animals Therefore, some animals are rational. The meaning of this mnemonic “M” is made clear in the following schema : Fig. ΠΙ Fig. I Fig. IV Tedious tales tire Tommy “Tom Thumb” is a tedious tale Therefore, “Tom Thumb” tires Tommy. Fig. Il All metals are heavier than water Ivory is not heavier than water Therefore, ivory is not a metal. The most perfect Figure is the First. The Second and Third are of value; the Fourth is negligible, be­ ing an inversion of the First. • The Laws for the Four Figures are derived from the eight general laws of the categorical syllogism which we studied in the last Article. Without pausing to explain the derivation we state the following particular laws for the three valuable Figures : Figure I: The major premiss must be universal; the minor must be affirmative. Figure II : The major premiss must be universal; one premiss must be negative. Some judges are unjust men All judges have authority Therefore, some unjust men have authority. No creature is infinite God is infinite Therefore, God is not a creature. b) MOODS OF THE SYLLOGISM 150 DIALECTICS rangement of its propositions with respect to their quantity and quality is called its mood. Thus, for example, a syllogism may have three universal affirmative propositions, or. as we have learned to call them, “A-propositions,” like the following: All animals are sentient All men are animals Therefore, all men are sentient; and since all the propositions are A-propositions, the mood of this syllogism is indicated thus : '‘AAA.” Take another example : Some soldiers are cowards All cowards are despicable Therefore, some soldiers are despicable. It will be obvious to the student that this is an IAI syllogism in mood. Take a final example : Some animals are rational No animals are spirits Therefore, some rational beings are not spirits. Again, it is obvious that the mood of this syllogism is IEO. Now there are, absolutely speaking, as many moods of the syllogism as there are arrangements of I REASONING EXPRESSED 151 three propositions with respect to their quantity (ex­ tension of subject) and quality (affirmation or denial in the copula). In other words, there are four types ' of propositions (A, E, I, O) to be arranged in groups of three; and by the laws of mathematics we see that the possible arrangements total to four .y, in the third power, that is, sixty-four. But fifty-two of these arrangements will be found to conflict with Λ,, the laws of the syllogism, for they involve conclusion ! from negative premisses, general conclusion when ; unwarranted, conclusion from particular premisses, or negative conclusion from affirmative premisses. Casting out the fifty-two invalid moods, we have the following twelve : 1 AAA, AAI, AEE, (AEO), All, AOO, EAE, EAO, EIO, IAI, IEO, OAO. Since AEO is contained in AEE (for O is subal­ ternate of E) it may be omitted. The Eleven Moods cannot all be used validly in all Four Figures, for the propositions of the syl­ logism must conform to the special laws of figures. The absolute number of valid moods would seem to be eleven times four, or forty-four, but the special laws of figures eliminate twenty-five of these, and there remain nineteen valid moods, of which 152 DIALECTICS four are in the First Figure ( AAA, EAE, All, EIO) four are in the Second Figure ( EAE, AEE, EIO, AOO) six are in the Third Figure. (AAI, IAI, All, EAO, OAO, EIO) five are in the Fourth Figure (AAI, AEE, IAI, EAO, EIO) The First Figure, as we have said before, is the most perfect figure, for it shows most clearly the connection or consequence of the premisses and con­ clusion. For this reason Dialecticians have formu­ lated an elaborate system of rules for the reduction of syllogisms to the First Figure. To “reduce” a syl­ logism to the First Figure, is to restate it in the shape of the First Figure. The reduction of syl­ logisms is an intricate process. Doubtless it is of great value as mental training for students that can master its complexities and spare time for the ex­ ercise. But, as Keinstadler says, its practical value is inconsiderable, and, to quote no less an authority than Lepidi, “if this matter (reduction of syllo­ gisms) is found difficult for beginners, let it be omitted; their loss will not be great.” This manual of Dialectics offers here no more on the subject of reduction of syllogisms than a passing description of what it means. The subject is, however, discussed with some completeness in the Appendix. REASONING EXPRESSED 153 SUMMARY OF THE ARTICLE In this Article we have learned what is meant by the Figures and the Moods of the Syllogism. We have studied the special laws—derivations from the Eight General Laws for Categorical Syllogisms—by which each Figure is regulated, and have seen these laws applied in several examples. We have sifted out the valid Moods of the syllogism from the number of possible arrangements of the premisses of the syllogism with respect to quality and quantity, and have assigned to each Figure the Moods that may occur in it validly. We have studied what is meant by “reduction” of syllogisms. Article 4. Imperfect Syllogisms An imperfect syllogism is a shortened or length­ ened syllogism. It usually has less or more than three propositions, or has an explanatory clause attached to one or both premisses. Important types of imper­ fect syllogisms are the following : I. The Enthymeme. This is an abbreviated syllo­ gism, one of the premisses being unexpressed but clearly understood. Example : God is holy ; therefore, He hates sin. 154 DIALECTICS As a syllogism fully expressed, this argument would be : hie who is holy, hates sin God is holy Therefore God hates sin. Other examples of the Enthymeme : It rains ; therefore, my friend will not come. John is a good son ; therefore, he will take care of his aged parents. Prudent men praise this method of business; therefore, it is a sound one. Law for the Enthymeme: Supply the missing premiss, and judge by the Laws of Syllogisms. It is important that this law be carefully observed. Precipitation often leads to false conclusions through failure to observe the law. A faulty Enthymeme is usually the result of error in the unexpressed mem­ ber. Therefore, always supply the missing premiss before evaluating this form of argument. Criticize the following: I don’t understand this ; therefore, it isn’t true. This method of doing business is praised ; there­ fore, it is a good one. I saw it in the paper ; hence it must be true. REASONING EXPRESSED 155 2. The Epichirema. This is a syllogism which adds an explanation or justification to one or both of the premisses. Example : Man has a spiritual soul, for he can reason ; A spiritual soul is immortal, since what is spir­ itual cannot corrupt ; Therefore, man has an immortal soul. a, We see at once that there are Enthymemes involved in the premisses of the Epichirema. In the illustration we find the following : Man can reason; therefore he has a spiritual soul. (Full syllogism : If man can reason, he has a spiritual soul; Man can reason ; Therefore, he has a spiritual soul.) A spiritual being cannot corrupt ; therefore, it is immortal. (Full syllogism : Whatever is spiritual can­ not corrupt; Man’s soul is spiritual ; Therefore, man’s soul cannot corrupt.) The Epichirema may be made into a simple syllo­ gism by lopping off the explanatory clauses from the premisses. Thus the example here given, minus its explanations or justifications, is the following: B ■«! fci 156 DIALECTICS Man has a spiritual soul A spiritual soul is immortal Therefore, man has an immortal soul. This simple syllogism, plus the syllogisms developed from the Enthymeme-premisses, must all meet with the requirements of the Laws of Syllogisms to in­ sure correctness in the Epichirema. Therefore we state the following law: Law for the Epichirema: Reduce the Epichirema to the simple syllogisms involved in it and criticize these by the Laws of Syllogisms. 3. The Polysyllogism. This is a series of syllo­ gisms so connected as to form an unbroken chain of argument. The conclusion of one syllogism becomes the major premiss of the next. Example: He who is prudent is temperate He who is temperate is constant Therefore, he who is prudent is constant; He who is constant is imperturbable Therefore, he who is prudent is imperturbable; He who is imperturbable is without sadness Therefore, he who is prudent is without sad­ ness ; He who is without sadness is happy Therefore, he who is prudent is happy. REASONING EXPRESSED 157 Law for the Poly syllogism: Reduce the Polysyllogism to syllogisms fully expressed, and judge by the laws of Syllogisms. 4. The Sorites. This is a shortened form of Poly­ syllogism. It consists of a number of propositions so connected that the predicate of one becomes the subject of the next, and so on to the last premiss inclusive ; then the conclusion connects the predicate of the last premiss with the subject of the first. Example : He who is prudent is temperate He who is temperate is constant He who is constant is imperturbable He who is imperturbable is without sadness He who is without sadness is happy Therefore, he who is prudent is happy. Law for the Sorites: No premiss may be particular but the first, and no premiss may be negative but the last. In other words : The first premiss may be an A- or I-proposition ; The last premiss may be an O- or an E-proposi­ tion ; All other premisses must be A-propositions. i58 DIALECTICS The reason for this rule is found in the Laws of Syllogisms, for two negatives or two particulars in the premisses would make conclusion impossible. Examples for criticism : A ton of hay is a weight A wait is a short stop A short-stop is a ball-player Therefore, a ton of hay is a ball-player. A good man has a good conscience Lie who has a good conscience enjoys peace He who enjoys peace is happy Therefore, a good man is happy Three dogs are more than two dogs Two dogs are more than one dog One dog is more than no dog No dog is more than seven dogs Therefore, three dogs are more than seven dogs. 5. The Dilemma. This is a form of argument consisting of a disjunctive proposition and two con­ ditional propositions (connective type), each of which leads to the same practical conclusion. It is sometimes called “the horned syllogism,” and the two conditionals are the “horns” designed to gore an adversary. Yet the Dilemma must be constructed REASONING EXPRESSED 159 in the most accurately correct manner, else it may easily be retorted upon the person who uses it. Ex­ amples : The skeptical doctrine that we can have no certainty of anything is either true or false; If it is true, we cannot accept the skeptical doctrine itself as certain ; If it is false, then we cannot accept it; Therefore, in no case can we accept the skep­ tical doctrine. The Catholic Religion was propagated either with the aid of miracles, or without miracles ; If propagated with the aid of miracles, it is true; for miracles are a certain evidence of truth in that which they are performed to support ; If propagated without miracles, then its rapid spread in the face of superhuman difficulties and furious opposition is the greatest miracle ; Therefore, in any case, the Catholic Religion is true. Law for the Dilemma: Let the major premiss be a complete disjunction, and let the consequents of the conditional premisses be strictly drawn. Examples for criticism : i6o DIALECTICS Eualthus studied law under Protagoras, agree­ ing to pay for the teaching when he should win his first case. After finishing his studies, b.ualthus took up a business other than law, and so defended no cases. Protagoras brought suit to recover his fees. Then came the following exchange of Dilemmas: Protagoras : ‘Judges, you will presently decide this case. Eualthus will be told that he has won or lost it. If he loses it, he must pay me by your order; and if he wins it, he must pay me by the terms of our agreement. Therefore, in any case, he must pay me.” Eualthus: “Judges, if I win the case, I am ab­ solved from obligation to pay by your order; if I lose, I am absolved by the terms of our agreement. Therefore, in no case must I pay Protagoras.” The judges dismissed the case. How' would you decide it? Why? An Athenian was dissuaded from seeking office by the following argument : “Do not seek for this office. If you achieve it and rule well, you will dis­ please the bad citizens; and if you rule ill, you will displease the good citizens. Therefore, in any case, your rule will occasion displeasure, and you should not seek the place.” Let the student construct this argument in strict Dilemma-form. Then let him criticize it by the Law for the Dilemma, and con­ struct its “retort.” f REASONING EXPRESSED 161 The Calif Omar justified the burning of the Li­ brary of Alexandria in the following manner : “Either these books agree with our Koran or they are in opposition to it. If they agree, they arc use­ less; if they are in opposition to it, they are danger­ ous. Therefore, in any case, they should be de­ stroyed.” Let the student criticize this dilemma, and “retort” it. If there is such a thing as a cause, it cannot be known as such. For a cause would have to occur at one of three possible points of time, viz., before its effect, after its effect, or simultaneously with its ef­ fect. But if it occur before its effect, it is a cause before it is a cause! If it occur after its effect, it is no cause at all, since that which it supposedly pro­ duced existed before the so-called cause. If it occur simultaneously with its effect, it is impossible to know which of the concurring events is cause, and which is effect. Therefore, in no case can a cause be known as such. The last example should be called a “Trilemma,” since its disjunctive premiss involves three possibil­ ities. One with four possibilities should be called a “Quadrilemma,” and so on. But the term “Dilemma” is generally used to indicate any argument of this character. Here, at the end of our study of Imperfect Syl- -i 102 DIALECTICS logisms, it may be well to add a note concerning two forms of Argument which the .Dialectician must notice, viz., Argument from Analogy, and Argu­ ment from Hypothesis. 1. Argument from Analogy. An .Argument from Analogy is one in which a fact is deduced from an­ other because of resemblance that exists or appears to exist between them. Pathology, for example, em­ ploys analogy in tracing the causes of various dis­ eases, concluding from the like character of certain diseases to their common nature. The principle of analogy is : “Whatever prevails in one member of a class of similar things probably prevails in the other members also.” Analogy often opens the way for valid induc­ tion, but in itself it affords mere probability, not certainty, in its conclusions. Arguments from analogy are called similitude, ex­ ample, and parable. To illustrate : i. Similitude : “When a man builds a temple, he clears away the loose surface soil and lays his foun­ dation upon the solid rock beneath. Now every Christian must make his soul the temple of God. Hence he must clear away the loose soil of the pas­ sions, the mere emotions, and base the structure solidly upon faith and love.” ii. Example: “Be patient, brave, and hopeful, as the great Father of his Country was.” Example is regularly historical, never a fiction. REASONING EXPRESSED 163 iii. Parable is a fiction constructed to point a moral, or illustrate a truth. 2. Argument from Plypothesis. Hypothesis is the assuming of an unproved proposition as the pro­ visional explanation of facts investigated. It af­ fords the investigator a starting-point and a working-basis. Suppose an investigator wishes to know whether steam has motive-power. He assumes that it has such power; and this is his hypothesis. Then he tries to upset his own hypothesis, not to find justification for it. It is his starting-point, his working-basis, and if it cannot stand assault, it is to be abandoned. Suppose the hypothesis that steam has motive-power stands up under all the tests and experiments. It looks more and more like the right explanation of observed facts. It is now a theory. If the theory stands the careful and sufficient tests to which it is then subjected, if it be found to ex­ plain all the facts that the investigator assumes it to explain, then it becomes a scientific fact, a scien­ tific law. The hypothesis of the motive-power of steam may be subjected to this process, and it emerges a scientific fact and law. Suppose evolution is assumed as a hypothesis for explaining the data of geology and biology. It looks like a probable explanation of the gradation ob­ served in the life-forms on earth, in the earth’s strata, and in the fact that certain species of plant and animal life are now extinct, and that other j- h'J 1 Wai T' 164 DIALECTICS species now exist which did not exist formerly. Thus it is a hypothesis. It is subjected to test. If it tries to explain development of the earth and life as gradual and continuous, it faces the fact that there is not a trace of true intermediate forms, of stages of passage from one species of life-form to another ; it has not one Missing Link to find, but ten million. This fact prevents the hypothesis from developing into a theory. But if evolution is con­ tent to explain development by “jumps,” sudden changes, it need not look for intermediate forms; still, this explanation seems contrary to the ordinary development of individuals and of classes of life­ forms as we know them. Analogy at least is against this assumption. Therefore, the evolution hypothesis remains a hypothesis. In our day, many teachers and writers assert it as a theory, and some even assert it as scientific fact. The honest scientist, however, never makes unsupported claims—and such a claim as we have mentioned is absolutely without support. Still, it is a hypothesis. As regards man, the Catholic finds it in conflict with truth which he knouts by Divine Science, and he is right to reject it. But in the lower life-forms, it may be found true; and so it is still the working-basis, the hypothesis of many scientists. For a hypothesis to be worthy of its name it should have probability to begin with ; it should look like the explanation of data investigated. In the REASONING EXPRESSED 165 second place, it must be found to explain all the data, else it is to be rejected as inadequate, and useless scientifically. SUMMARY OF THE ARTICLE In this Article we have learned how to construct and to criticize the arguments known as the Enthymeme, the Epichirema, the Polysyllogism, the So­ rites, and the Dilemma. We have studied the matter of argument from analogy and from hypothesis. CHAPTER III FALLACIES TO AVOID When a fact has been proved by clear-cut and justified reasoning, deductive or inductive, it is said to be demon­ strated. When one (or more) of the premisses of an argu­ ment is not certainly true, but only probably so, the conclu­ sion reached is not demonstrated but shown to be probable. When one (or more) of the premisses is certainly false, although it bears the attractive appearance of truth; or when the conclusion is not justified in view of the premisses, although it seems, at first sight, to be so; then the argument is called a sophistry or a fallacy. The con­ clusion of a fallacy may express a truth, and then the conclusion is called illogical; or it may express a falsehood, and then it is called erroneous, or simply an error. This Chapter discusses some of the more commonly used fallacies. Its purpose is to equip the student for the ready recognition of unjustified reasoning and ordinary logical error, and to relieve him of the necessity of making a laborious analysis of every seemingly valid argument that he may be called upon to criticize. The Chapter is not divided into Articles. It lists and dis­ cusses the following fallacies : 1. Equivocation 2. Composition and Division 3. Evading the Point 4. Begging the Question 5. False Cause 166 FALLACIES TO AVOID j ‘ ί J j ( ; J ; 5 167 1. Equivocation. This fallacy employs equivocal or vague terms that cause the argument, when reduced to the form of a syllogism, to offend against the First Law : “Three terms there must be, neither more nor less.” Example : : r A box is a wooden case A blow on the ear is a box Therefore, a blow on the ear is a wooden case. This absurd example is a very obvious fallacy; but itis of profit to notice that it contains four terms, not three, and that the syllogism is therefore unjustified. More intriguing is the equivocation which comes from the use of vague words and am­ biguous terms like: democracy, brotherhood, hu­ manitarianism, materialism, optimism, pessimism, prosperity, progress, education, dogmatism, higher planes, contacts, values, higher life, broader vision, etc. The use of such terms as these is very common in our day, and many people employ them constantly who could not, under direst penalties, frame an ade­ quate definition of any one of them. From this fact the student should take two points for practical guid­ ance: 1) Never use vague terminology; use terms in a clear and precise sense, and define them when necessary; 2) Never allow an opponent to “get away” with a vague argument : make him define his terms. $8 fl ph Μ B 168 I DIALECTICS An example of equivocation through the use of vague terms : Prosperity promotes progress Active commerce is prosperity Therefore, active commerce promotes progress. What is meant by progress? Does it mean the in­ crease of wealth and power in the hands of those already wealthy and powerful? Does it mean the in­ tellectual illumination of mankind ? Does it mean the triumph of those who war against human justice and the dignity of the citizen as a man and the image of God? IVhat does it mean? To one thousand men the term progress conveys a thousand shades of meaning,----nay more : it conveys to nine hundred of the thousand men a meaning somewhat constant, but variously shaded; and to the other hundred it conveys a meaning that is opposed to the more gen­ eral and constant interpretation of the term. The same may be said of the term prosperity. There­ fore, the syllogism here given is valueless unless its terms be accurately explained; as it stands it is a fallacy. And how many minds, even educated minds, are content with such fallacies ! Content to accept them as evidences of truth, content to assimilate them as the embodiment of wisdom, content to make them the practical norms and principles of conduct, and even of life! FALLACIES TO AVOID 169 2. Composition and Division. This fallacy attributes a predicate to a qualified subject when that predicate is applicable to the subject only when i unqualified; or it attributes a predicate to an unI qualified subject when that predicate is applicable to ! the subject only when qualified. In other words, this fallacy compounds subject and qualifier in one, and then attributes a predicate which belongs to the sub­ ject alone without the qualifier (Fallacy of Com­ position) ; or it divides a subject from its qualifier, and then attributes a predicate which belongs to that subject only when compounded with its qualifier (Fallacy of Division). Example : I 1 Sinners cannot get to heaven St. Augustine was a sinner Therefore, St. Augustine could not get to heaven. Here we have the Fallacy of Division. The subject to which the predicate “those who cannot get to heaven” really applies is “unconverted sinners.” The fallacy divides the subject “sinners” from its quali­ fier “unconverted,” and then applies a predicate only applicable when the subject is undivided. Supplying the lacking qualifier, we have: Unconverted sinners cannot get to heaven St. Augustine was a (converted) sinner 170 DIALECTICS .Therefore— (four terms in frémisses ; no con­ clusion· possible). A further example: To make blind men see is to do a contradictory thing Our Lord made blind men see Therefore, Our Lord did a contradictory thing. This is the Fallacy of Composition. The term blind men is properly kept in compounded sense in the major premiss, which means “blind men as such cannot see, and to say that they can remain blind and yet see is a contradiction.” But in the minor premiss, the term ought to be understood in divided sense, as “those whom the Lord caused to cease to be blind and to see.” Our fallacy, however, holds it compounded or composed. To controvert this fal­ lacy, we point out the fact that blind men in the major premiss is compounded or composed, and the same term in the minor premiss is or ought to be divided; hence we see that the syllogism involves equivocation, presents four terms, and baulks the drawing of any conclusion. The example given here is made obviously false so that the student may go whole-heartedly into the task of finding out where its point of fallacy lies. But there are thousands of intriguing arguments,— FALLACIES TO AVOID 171 not obviously false but which involve the Fallacy of Composition or that of Division,—seen in books and heard in lecture-halls and university class-rooms every day and every hour. The student will do well to be on guard against this very deceiving fallacy. Let him find the point of fallacy in the following: The Mosaic Law is abrogated The Ten Commandments are part of the Mo­ saic Law Therefore, the Ten Commandments are abro­ gated. I will not join a Church whose members are rascals Many members of the Catholic Church are rascals Therefore, I will not join the Catholic Church. r Γγ’*Μ i S 3. Evading the Point. This is a fallacy which of­ fers argument or proof for something other than the point at issue. An example of this fallacy is found in the arguments of those zealots who set out to prove that Catholics are idolatrous, and spend their entire effort in proving that images are not to be adored,—a matter in which every Catholic will thoroughly agree. Another example is found in the usual type of argument offered in defense of the hy­ pothesis of evolution. When the evolutionist is ;.hj i '1 172 DIALECTICS asked : “How did human life come into being from lower life-forms?” he is very likely to reply: ‘“Well, you see, it took ages and ages, æons and æons, for the process of development to unfold to that stage which we behold in human life. Lower life-forms gradually developed variations, these became fixed, and were transmitted, and after the lapse of millions of years there emerged new species of a higher type than the originals. And so the process has gradually worked up to human life.” This is the fallacy of Evading the Point. It amounts to this : Inquirer: “How did you get here?” Traveller : “It took me a long time to arrive.” Another example of this fallacy is found in the natural philosophy of those who explain the bodily universe by declaring it made up of atoms; and who, if pressed, explain the atoms by saying that they are made up of nucleus and electrons, and so on. This is Evading the Point at issue. One does not explain a body as such by saying that it is made up of smaller bodies. This may be true, but it is not the point at issue; the point is clearly raised in the question, “What is a body?” It is not answered by saying, “It is a thing made up of smaller bodies.” The small body presents the same problem as the large body of which it is a tiny part. All this is evi­ dent in the following dialogue : FALLACIES TO AVOID 173 Inquirer: “What is a board” Pseudo-Scientist : “It is a thing made up of many grains of sawdust.” Inquirer: “But what is a grain of sawdust?” Pseudo-Scientist: “It is a small body com­ posed of numerous tiny particles.” Inquirer : “But, hang it man ! what are those particles?” Pseudo-Scientist : “Ah, you have no respect for science !” The dialogue must be offered, of course, with an apology to true scientists. But true scientists are rari­ ties; and pseudo-scientists are multitudinous, and they preach at us, and write at us, and shout at us from rostrum and stage and pressroom and even pulpit! The fallacy of Evading the Point is one of the most common, and one of the most deceiving sophistries of modern times. Many educated minds accept this fallacy as valid argument. The student must be on his guard against it, and, for his guid­ ance, he should keep two principles ever in mind : 1) Be perfectly clear about the exact point at issue; 2) Hold the adversary strictly to that point; do not permit him to wander off and prove something else,—and then claim victory. 4. Begging the Question. This fallacy assumes as proved the very point at issue, and draws from it arguments to establish its own truth. Of course, the 4*j hik 174 FALLACIES TO AVOID DIALECTICS assumption is usually covert—otherwise, the fallacy would be open error. In its most evident form this fallacy is “the vicious circle,” a good name, for it involves reasoning in a ring·, proving A by B, and 13 by A. Thus Descartes proved the existence of God by the testimony of our reason ; and then he proved reason valid by the perfection of God, Who could not give us deceiving faculties! Let the student consider the following and see if he can find in it the fallacy of Begging the Ques­ tion : “. . . we must assume natural selection to be the principle of the metamorphoses, because all other apparent principles of explanation fail us, and it is inconceivable that there should be another capable of explaining the adaptation of organisms without assuming the help of a prin­ ciple of design.” As a suggestion to the student, let it be said that the question here is the existence or non-existence of a designer of the universe, and particularly of life in. its varied forms. We offer no apologies to the scientist here, for the quotation is from a contro­ versial article by August Weismann, German biol­ ogist and zoologist of note, who died in 1914. (Cf. The Contemporary Review, Sept. 1893.) 5. False Cause. This fallacy presents as the cause I I I I J i 175 of a fact what has merely preceded it or accompanied it Thus the fall of the Roman Empire was attributed by the pagans (and by Gibbon!) to the rise of Christianity. This fallacy is often called, “Post hoc, ergo propter hoc,” that is, “After this, therefore because of this.” Other fallacies, the names of which are selfexplanatory, are : False Analogy, Defective Induc­ tion, Incomplete Enumeration, False Assumption. i, i SUMMARY OF THE CHAPTER This Chapter has taught us to be on our guard against the more common forms of logical error. This lesson has a twofold value : it makes us care< ful in constructing our own arguments and reason­ ings, and it enables us to brand illogicality in the arguments of others. The Chapter contains valuable principles for the guidance of the student, notably in the paragraphs which deal with Equivocation and Evading the Point—two of the most common and, at the same time, most powerful enemies of correct thinking. Ή i4 ; > W wd ΑΤί ■Ai 51 AT ■ Kii 'APPENDIX On the Reduction of the Syllogism To “reduce” a syllogism means to restate it in the shape of the First Figure. Hence only syllogisms of the Second, Third, and Fourth Figure are reducible. The First Figure has the following four moods: AAA EAE AII EIO Examples : I. 2. (AAA) All men are mortal John is a man Therefore, John is mortal. (EAE) No man is a spirit John is a man Therefore, John is not a spirit. 3- (AH) All men are mortal Some rational beings are men Therefore some rational beings are mortal. 4. (EIO) No man is a spirit Some rational beings are men Therefore, some rational beings are not spirits. 176 APPENDIX 177 / (note: It will be recalled from the Chapter on the i classification of propositions that the singular proposition ) is equivalated to the universal proposition since the defii nition of the universal proposition is that it takes its stibI ject in full Extension ; and the singular proposition meets , this requirement. This note is added, lest the student be | surprised to find such a proposition as “John is a man” . listed as an A-proposition.) I ii ' if: Now, the AAA mood of the First Figure is indicated by a proper name which contains all these vowels. It is called “Barbara.” The EAE mood of the First Figure is called, for like reason, “Celarent.” The All mood of the First Figure is called “Darii.” The EIO mood of the First Figure is called “Ferio.” In like manner all the moods of the other Figures (Second, Third, Fourth) are given proper names, and the whole is set forth in a Latin mnemonic stanza. Many of the consonants in the names have meanings which we shall presently explain. The mnemonic is : Barbara, Celarent, Darii, Ferio, sunt prioris; (I Figure) Cesare, Camestres, Festino, Baroco, secundœ; (II Fig­ ure) Tertia: Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison, habet; (III Figure). Quarta insuper add it : Bramantip, Camenes, (IV Figure.) Dimaris, Fesapo, Fresison. Now all the moods of the Second, Third, and Fourth Figures cannot be indiscriminately reduced to any desired mood of the First ; but in each case the mood of the First Figure to which reduction is to be made, will be determined η 1 'Cd 178 DIALECTICS by the mood and figure of the syllogism to be reduced. Therefore, in taking up any syllogism with the purpose of reducing it, the first thing to flcterminc is the figure and the mood of this syllogism as it stands. To identify the figure of a, syllogism look to the position of the middle term in the premisses, ff middle term is 1. subject of major premiss, predicate of minor— syllogism is in the First Figure; 2. predicate of both premisses—syllogism is in the Second Figure; 3. subject of both premisses—syllogism is in the Third Figure; 4. predicate of major premiss, subject of minor— syllogism is in the Fourth Figure. To identify the mood look for the valid moods in the mnemonic line which indicates the figure already identified. Find the word (proper name) which has in order the vowels which stand for the propositions of the syllogism to be reduced. Suppose we have this syllogism to reduce; All men are mortal beings (A-proposition) Some men are wise beings (I-proposition) Therefore some wise beings are mortal beings (I-proposition) First, we find that the middle term men is subject of both premisses. Thus we know that the syllogism is in the Third Figure. Next, we take up the mnemonic line for the Third Figure: Tertia: Darapti, Disamis, Datisi, Felapton, Bocardo, Feri son, and we look for the word which has the vowels (All) which stand for the propositions of the syllogism to be APPENDIX / I I I j I ' 179 reduced. These vowels must tbe found in order, i. e., A-I-1. The word “Datisi” contains these vowels in order. Thus we discover that our syllogism is in the Third Figure in Datisi. Now, to reduce it : I. The syllogism is in Datisi, a name with the initial D. This means that it can be reduced only to that mood of the First Figure which begins in D, that is, to Darii. 2. Next we look for the consonants in the name Datisi. For in the mnemonic names certain consonants have value : s means that the premiss designated by the vowel preceding is to be converted simply; p means that the premiss designated by the vowel preceding is to be converted per accidens, or acci­ dentally ; m means that the major and minor premisses are to change places ; c means that conversion is to be indirect. i Now, in Datisi we find the letter “s: following the vowel which indicates the minor premiss. This premiss then is to be converted simply. No other change is indicated. We make the reduction as follows : All men are mortal beings Some wise beings are men Therefore, some wise beings are mortal beings. Take another example : (A) All men are mortal beings (A) All mortal beings are bodily beings (I) Therefore, some bodily beings are men. To reduce: I. The figure is the Fourth, for the middle term is the predicate of the major premiss and the subject of the minor. i8o DIALECTICS 2. The mood is Bramantip, for this is the word in the mnemonic iine for the Fourth Figure, which contains in order the vowels which designate the propositions of the syllogism (AAl). We conclude that reduction must be made to Barbara since Bramantip begins with H. 3. We find the significant, consonants “m” and “p” in Bramantip, 'Die consonant “m” tells us to transpose the premisses, making them “change places.” “p” since it refers to conclusion and not to a premiss may be ignored. 4. Making the reduction we have : (A) All mortal beings are bodily beings (A) All men are mortal beings (A) Therefore, all men are bodily beings. The student is to note that syllogisms of the Second Figure in Baroco, and those in the Third Figure in Bocardo, cannot be reduced directly, since they contain O-propositions and, as we have learned, these are not directly convertible. BIBLIOGRAPHY Î Coffey, P., The Science of Logic, Longmans Green & Co., 1918. Crumley, Thomas, C.S.C., Logic, Deductive and Inductive, Macmillan, 1926. Donat, Joseph, S.J., Logica, Felician Rauch, Innsbruck, 1922. Frick, Charles, S.J., Logica, Herder, 1921. Gredt, Joseph, O.S.B., Elementa Philosophiae AristotelicoThomisticae, Herder, 1921. Jevons, W. J., Elementary Lessons in Logic, Macmillan, 1923. Joseph, H. W. B., Introduction to Logic, Oxford Uni­ versity Press, 1916. Joyce, George Hayward, S.J., Principles of Logic, Long­ mans Green & Co., 1920. Lortie, Stanislaus, Elementa Philosophiae Christianae, L'Action Social, Quebec, 1921. Pesch, Tilmann, S.J., Institutiones Logicales, Herder, 1914. Reinstàdler, Sebastian, Elementa Philosophiae Scholasticae, Herder, 1923. Turner, William, Lessons in Logic, Catholic Education Press, Washington, 1911. ι8ι