Easy lessons on reasoning

Preface

hafnot 8 ^ 8 ^?^- '" the f ° ll0Wing ^ s is one ^ich

studies for young persons of all classes.

and t a i l S n UPP ° Sed ^ T'' that the difference bet - e - a better

or on that combined with practice, or on each man's greater or less proficiency in the subjects he is treating of.

cipfe n s d of°Rr,o again COnS - der a SJStematic Stud ? of the Principles of Reasoning as sultable on] t f *

endowments and of a peculiar turn of mindf and o tho only m an advanced stage of their education.

b/aT Ind tTf f ^"^ " feqUiSite f ° r aH " and is «*-W* by all and presents not, necessarily, any greater difficulties

than .the radim^t. of Arithmetic, G«»«4f^ G»™^" all this cannot be so well evinced in an„ .*«. 1 '

merit. If the perusal of th Z T * W&7 ** by **"*

IV PREFACE

discovery, strictly so called, of anything previously altogether unknown, it is possible — since "discovery" is a relative word — to be, practically a discoverer, by bringing within the reach of thousands some important branch of knowledge of which they would otherwise have remained destitute all their lives.

And in regard to the present subject, a familiar introduction to the study is precisely what has been hitherto wanting. The existing treatises upon it may be compared to ships well freighted, but which can only unlade at a few wharfs, carefully constructed, in advantageous situations. The want is of small boats drawing very little water, which can carry ashore small parcels of the cargo on every part of the coast, and run up into every little creek.

Should the attempt to supply this deficiency prove as successful, as there is reason, from the trial that has been already made (in the Saturday Magazine), to hope, an addition by no means unimportant will have been made to the ordinary course of elementary education.

To frame, indeed, a system of rules that should equalize persons of all varieties of capacity, would be a project no less chimerical in this than in other departments of learning. But it would certainly be a great point gained, if all persons were taught to exercise the reasoning faculty, as well as the natural capacity of each would permit; for there is good reason to suspect, that, in this point, men fail quite as often from want of attention, and of systematic cultivation of their powers, as from natural deficiency. And it is at least worth trying the experiment, whether all may not be, in some degree, trained in the right exercise of a faculty which all in some degree, possess, and which all mast, more or less, exercise, whether thoy exercise it well or ill.

It was at one time contemplated to subjoin an Index of the technical terms, with brief definitions of them, and references to the Lessons and Sections. But, on second thoughts, it has been judged best to omit this, and to recommend each student

PREFACE. V

to draw up such an index for himself. It is for students, strictly so called, — -that is, persons employed in acquiring an elementary knowledge of the subject, — that the work is chiefly designed : and for these no exercise could be devised more calculated to facilitate their study than that of carefully compiling an Index, and also expanding the Table of Contents, so as to give a brief summary of the matter of each Lesson. And this being the case, it would not be any real saving of labor to the learner, to place before him such an Index and Table of Contents already drawn up.

It may be worth while to suggest to the Teacher to put before his pupils, previously to their reading each Lesson, some questions pertaining to the matter of it, requiring of them answers, oral or written, the best they can think of without consulting the book. Next let them read the Lessons, having other questions, such as may lead to any needful explanations, put before them as they proceed. And afterwards let them be examined (introducing numerous examples framed by themselves and by the teacher), as to the portion they have learned, in order to judge how far they remember it.

Of these three kinds of questions, — which may be called, i. Preliminary questions; ii. questions of instruction ; and iii. questions of examination, — the last alone are, by a considerable portion of Instructors, commonly employed. And the elementary books commonly known as "catechisms," or "books in question and answer," consist in reality of questions of this description.

But the second kind — what is properly to be ealled instructive questioning — is employed by all who deserve to be reckoned good teachers.

The first kind — the preliminary questioning — is employed (systematically and constantly) but by few. And at first sight it might be supposed by those who have not had experience of it, that it would be likely to increase the learner's difficulties. But if any well-qualified instructor will but carefully and

VI PREFACE,

judiciously try the experiment (in teaching any kind of science), he will be surprised to find to how great a degree this exercise of the student's mind on the subject will contribute to his advancement. He will find, that what has been taught in the mode above suggested, will have been learnt in a shorter time, will have been far the more thoroughly understood, and will be fixed incomparably the better in the memory.

Contents

[To be filled up by the Student] Part T. ANALYTICAL INTRODUCTION.

Lesson I., p. 13.

Lesson IL, p. 17.

Part I. Analytical Introduction

LESSON I.

N.B. — In these Lessons, whenever two equivalent "words or phrases are employed, one of them is enclosed in angular [brackets], instead of the common mark of a (parenthesis).

§ 1. Every one is accustomed more or less to employ Reasoning. There is no one that does not occasionally attempt, well or ill, to give a Reason for any opinion he entertains; — to draw Conclusions from what he sees around him, — to support those conclusions by some kind of Arguments, good or bad, — and to answer the arguments brought against him.

Now all these expressions, — " giving a reason" — "drawing a conclusion" — "bringing forward an argument" — relate to one and the same process in the mind, that which is properly called " Reasoning." And the same may be said of several other expressions also ; such as " inferring" or "drawing an inference," — "proving a point," — "establishing a conclusion," — "refuting an argument," &c. All these expressions, and some others besides, have reference, as we have said, to the process of Reasoning.

§ 2. And this process, it is important to observe, is, in itself, universally the same; however different the subject-matter of our reasoning may be, on different occasions.

The same is the case with Arithmetic. "We may have to add or sub ti act, multiply or divide certain numbers, either of Pounds-sterling, or of men, or of bushels of corn, &c, but though these are very different things, the arithmetical-process itself, in each of the operations, respectively, is always the same. For instance, to "multiply" always means to take one number a certain number of times ; whether it be men or miles, or days, that we are numbering.

So it is also with Grammar. The Nouns and Verbs and other Parts of Speech that Grammar treats of, may relate to very different subjects, and may be found in various kinds of Compositions ; such as works of Science, History, Poetry, &c, but the rules of Grammar are the same in all.

So also the art of Writing (and the same may be said of Printing) is in itself the same, however different may be the kinds of subject-matter it is employed on.

Now the same is the case (as has been above said) with Reasoning. We may be employed in reasoning on human affairs, or on Mathematics, or on Natural-history or Chemistry, or other subjects widely different from each other. But in every case the Reasoning-process is, in itself, the same.

§ 3. Any Debate [or Disputation,] when you are endeavouring to bring others over to your opinion, is one of the occasions on which Reasoning is employed ; and the word " arguing" is by some persons understood as having reference only to cases where there is a dispute between those who are maintaining opposite opinions. But this is a mistake. At least, it is a mistake to suppose that the use of " Arguments" — if we understand by that, the use of Reasoning — is confined to the case of disputes; or even that this is the principal employment of it. There is no set of men less engaged in dispute and controversy than Mathematicians ; who are the most constantly occupied in Reasoning. They establish all their propositions by the most exact proofs ; so complete as not even to admit of any dispute.

And in all other subjects likewise, a sensible man, when he wishes to make up his mind on any question will always seek for some sufficient " Reason" [or " Argument"] on which to found his conclusion.

Thus, a Judge, before whom any case is tried is occupied in weighing the Arguments on both sides, that are Drought forward by the respective Advocates. He (no less than they) is engaged in Reasoning; though the Advocates are disputing and the Judge is not.

Lesson i.] the reasoning-process. 15

A Physician, again, reasons from what he has read, and heard, and seen, in order to draw his conclusions on medical questions; — a Statesman, in political questions; — a Merchant, in mercantile matters ; and so, of the rest.

§ 4. But when any dispute does take place, between persons of opposed opinions, it may be observed that the worst educated — those who are the most unskilful in reasoning, or in clearly expressing their reasons, — are almost always the most apt to grow angry, and to revile each other, and quarrel.

And even when they do not give way to anger, they usually, after a long discussion, part, without distinctly understanding what the difference between them really consists in ; neither of them having clearly expressed his own meaning, or fully understood the other's.

Indeed it often happens that two persons who are disputing, do, in reality, disagree much less in their opinions, than they themselves imagine : or, perhaps not at all. And hence it is that the word "misunderstanding" has come to signify, a quarrel ; because quarrels so often arise from men's not clearly understanding each other's meaning.

Again, it often happens that a person not without good sense, will give such weak and absurd reasons for his opinion, even when it is a right one, that instead of convincing others, he will even produce an opposite effect.

§ 5. In order to avoid such inconveniences, and to conduct the process of Reasoning as clearly, as correctly, and as easily, as is possible, it is a great advantage to lay down accurate explanations of the principles on which Reasoning proceeds, and to employ for the purpose a technical language ; that is, a regularly-formed set of expressions, distinctly, defined, and agreed on ; and to establish certain plain simple rules, founded on, and expressed in, this technical language.

Even in the common mechanical arts, something of a technical language is found needful for those who are learning or exercising them. It would be a very great inconvenience, even to a common carpenter, not to have a precise, well-understood name for each of the several psrations he p3rf:>rm'4 ; su^li a^ chiseling, sawing, planing,

<fcc, and for the several tools [or instruments] lie works with. And if we had not such words as Addition, Subtraction, Multiplication, Division, etc., employed in an exactly denned sense, and also fixed rules for conducting these and other arithmetical processes, it would be a tedious and uncertain work, to go through even such simple calculations as a child very soon learns to perform with perfect ease. And after all, there would be a fresh difficulty in making other persons understand clearly the correctness of the calculations made.

You are to observe, however, that technical language and rules, if you would make them really useful, must be not only distinctly understood, but also learnt, and remembered as familiarly as the Alphabet; and employed constantly, and with scrupulous exactness. Otherwise, technical language will prove an encumbrance instead of an advantage \ just as a suit of clothes would be, if, instead of putting them on and wearing them, you were to carry them about in your hand.

g 6. It has been accordingly found advantageous, in what relates to the Reasoning-process, (as well as in. the case of mechanical operations, and of calculations,) to lay down explanations, and rules, and technical terms ; answering to those of Arithmetic, Grammar, and other branches of study.

Amd the technical terms and rules of Grammar, are not at all shorter, or easier to be understood and remembered, than those pertaining to the present subject.

You may perhaps meet with treatises professing much more than what we here propose; — with works pretending to teach the right use of "Reason;" (not Reasom'/i^r or "Argumentation" merely, but the whole of the Human Intellect;) and giving rules for forming a judgment on every question than can arise, and for arriving at all truths in any subject whatever. But such pretensions, however high-sounding and attractive, are fanciful and empty. One might as well profess to teach the "right use of the bodilyorgans," and to lay down a system of rules that should instruct a man in all manual arts and bodily exercises at once.

If you do but teach a person to ride, or to draw, or to spin, <fcc, something is gained ; but if you should profess

Lesson ii.] the reasoning-process. 17

to lav down a system of rules to teach all these at once, and also the business of a shipwright, and a musician, and a watchmaker, and everything else that is done by means of the bodily organs, you would teach, in reality, nothing at all.

And so it is on all subjects. It is better to undertake even a little, that it is possible to accomplish, than to make splendid professions, which can only lead to disappointment.

After all. indeed, it cannot be expected, that, in Reasoning, any more than in other mental exercises, men of very unequal degrees of intelligence should be brought to the same level. Nor is it to be expected, that men will always be brought to an agreement in their conclusions. Different men will have received different information respecting facts ; or will be variously biassed, more or less, by their early prejudices, their interests, or their feelings.

But still, there is something gained, if they are taught in respect of the Eleasoning-process itself, how to proceed rightly and to express themselves clearly ; and if when they do not agree, they can be brought at least to understand wherein they differ, and to state distinctly, what is "the point at issue" (as it is called) between them; that is, what is the real question to be decided.

And it is just so, in the case of Arithmetic also. Two persons may differ in their statements of an Account, from their setting out with some difference in the numbers each puts down; — in the Items (as it is called) of the Account. And no rules of Arithmetic can prevent such a difference as this. But it is something gained if they are guarded (as arithmetical rules do guard us) against differences arising out of errors in the calculation itself.

LESSOR ir.

§ 1. We have said that in all subjects, and on all occasions, the Reasoning-process is in itself the same Whether you are occupied in refuting an opponent, or in conveying instruction, or in satisfying your own niind on any point, — and again, whatever kind of subject-matter it is that you are engaged on, in all cases, as far as you are (in the strict sense of the word) reasoning, — that is, employing Argument — it is one and the same process (as far as it is correctly conducted) that is going on in your own mind.

And what this process is, must be the next point to be inquired into.

Although (as has been said) all men do occasionally reason, they are often, at the time, as unconscious of it as of the circulation of their blood, and of the various other processes that may be going on within the body. And even when they do, knowingly and designedly, use arguments, or are listening to those of another, they will often be as much at a loss to explain why one argument appears to them strong, and another less strong, and another utterly worthless, as if the whole were merely a matter of taste ; like their preference of one prospect, or one piece of music to another.

In order, then, to obtain correct rules for forming a judgment on this subject, and clear expressions for explaining such judgment to others, it is necessary to analyse, — as it is called, — that is, take to pieces) the Reasoning-process. And for that purpose, we should begin by examining the most plain, short, and simple arguments, and enquiring on what it is that their validity [or conclusiveness] depends ; examining also, some of those apparent-arguments which are not valid, and therefore not, in reality, arguments at all ; though they are often passed off for them, as counterfeit coin is for genuine.

§ 2. You will perceive, on examination, that what is called a " Conclusion," — that is, a proposition proved by Argument, — is drawn, in reality, from two other Propositions. And these are called its "Premises;" from their being (in natural order) "premised" or put before it.

At first sight, indeed, some might suppose that a Conclusion may follow from one Premise alone. For it happens, oftener than not, that only one is expressed. But in this case, there is always another Premise understood, and which is suppressed, from its being supposed to be fully admitted.

Lesson ii.J the reasoning-process. 19

That this is the case, may easily be made evident by supposing that suppressed Premise to be denied ; which will at one destroy the force of the Argument. For instance, if any one, from perceiving that "the World exhibits marks of design," infers [or concludes] that " it had an intelligent Maker," he will easily perceive, on reflection, that he must have had in his mind another Premise also, namely, that " whatever exhibits marks of design had an intelligent maker:" since if this last proposition were denied, the other would prove nothing. It is true, that in some cases one proposition implies another by the very signification of the words, to every one that understands those words ; as "negroes are men ; therefore they are rational-beings," now, "rational-being" is implied in the very name "man." And such examples as this have led some people into the idea that we reason — or that we may reason — from a single Premise. But take such a case as this ; some fossil-animal is discovered, which Naturalists conclude to have been a "'ruminant," from its "ha vino* horns on the skull." Now the laborers wmo duo: up the skeleton could not draw this inference, supposing they were ignorant of the general law, that "all horned animals are ruminant :" — and they might be thus ignorant, though using the name "horned animal," in the same sense as the Naturalist : for the name itself does not imply " ruminant," as a part of its signification ; and again, a Naturalist at a distance, who knew the general law, but who had heard only an imperfect account of the skeleton, and did not know whether it was horned or not, would be equally unable to draw the inference. In all cases of what is properly called "Argument," there must be two premises assumed, whether they are both expressed or not.

§ 3. Such an argument as the above, when all the three propositions are stated at full length, and in their natural order, is called a "Syllogism." And this is the form in which all correct reasoning, on whatever subject, may be exhibited.

When one of the Premises is suppressed [or understood^, which, for brevity's sake, is usually the case, the argument is called, in technical language, an " Enthymeme;" a name derived from the Greek, and denoting that there is something left out, which is to be supposed [or understood] as being well-known.

It is to be observed, that, when an argument, stated in this last form, is met by opponents, their objection will sometimes lie against the assertion itself that is made ; sometimes, against its force as an argument. They will say either, "I deny what you assume" or "I admit, indeed, what you say, but I deny that it proves your conclusion.' ' For instance, in the example above, an atheist may be conceived either denying* that the World does exhibit marks of design, or again, denyingt that it follows from thence that it must have had an intelligent Maker.

Now you are to observe, that these are not in reality objections of different kinds. The only difference is, that, in the one case, the expressed Premise is denied ; in the other, the suppressed Premise. For the force as an argumen, of either Premise, depends on the other Premise. If either be denied, the other proves nothing. If both be admitted, the Conclusion regularly drawn from them, must be admitted.

§ 4. It makes no difference in respect of the sense of an argument, whether the Conclusion be placed last or first ; provided you do but clearly mark out what is the Conclusion.

When it is placed last (which is accounted the natural order), it is designated by one of those conjunctions called "illative" such as "therefore," — "thence," — "consequently."

When the Conclusion is put first, the Premise is usually called the "Reason;" and this is designated (whether it come last or first) by one of the conjunctions called "causal" such as "since," — "because," &e.

And here it is to be observed, that each of these sets of conjunctions have also another sense; being used to denote, respectively, sometimes " Premise and Conclusion," — sometimes " Cause and Effect." And much error und perplexity have often been occasioned by not attending to this distinction.

* As many of the ancient atheists did. f As most of the modern atheists do.

Lesson ii.] the reasoning-process, 21

When I say "this ground is rich; because the trees on it are nourishing;" or again, when I express the same sense in a different form, saving, "the trees on this ground are nourishing, and therefore it must be rich," it is plain that I am employing these conjunctions to denote merely the connexion of Premise and Conclusion ; or (in other words) I am implying that the one maybe inferred from the other. For it is evident, that the flourishing of the trees is not the cause of the ground's fertility, but only the cause of my believing it. The richness of the soil follows as an inference from the luxuriance of the trees ; which luxuriance follows as an effect [or, natural consequence] from the richness of the soil.

But, if again, I say, " the trees flourish because the ground is rich," or (which is the same in sense) "the ground is rich, and consequently [or therefore] the trees flourish,' I am using the very same conjunction in a different sense; namely, to denote, the Connexion of Cause and Effect. For in this case, the luxuriance of the trees being a thing evident to the eye, would not need to be proved', and every one would understand that I was only accounting for it.

§ 5. But again, there are many cases also in which the Cause is employed as an Argument, to prove the existence of its effect. So that; the Conclusion which follows, as an Inference, from the Premise is also an Effect which follows naturally from that same Premise as its Cause.

This is the kind of argument which is chiefly employed when we are reasoning about the future : as for instance when, from favorable or unfavorable weather, any one infers that the crops are likely to be abundant, or to be scanty.

In such cases, the Cause and the Reason [or Proof] coincide ; the favorable weather being at once the cause of the good harvest, and the cause of our expecting it.

And this circumstance contributes to men's often confounding together "Cause" and — what is strictly called — "Reason;" and to their overlooking the different senses If such words as "therefore," "thence," "consequently," &c., and again, of such words as "because," "'inasmuch as/ &c., and also, of the words "follow," "consequence,"

and several others ; which have all of them that double meaning which has just been explained.

LESSON I1L

§ 1. In such an argument as that in the example above given, (in § 2, Lesson ii.) it is clearly impossible for any one who admits both Premises to avoid admitting the Conclusion. If you admit that " Whatever exhibits marks of design had an intelligent Maker," and also that "the world exhibits marks of design," you cannot escape the Conclusion that "the world had an intelligent Maker."

Or again, if I say "All animals with horns on the head are ruminant; the Elk has horns on the head; therefore it is ruminant;" it is impossible to conceive any one's doubting the truth of the Conclusion, supposing he does but allow the truth of each Premise.

A man may perhaps deny, or doubt, and require proof, that all animals thus horned do ruminate. Nay it is conceivable that he may even not clearly understand what "ruminant" means, or he may have never heard of an "Elk;" but still it will not be the less clear to him that supposing these Premises granted, the Conclusion must be admitted.

And even if you suppose a case where one or both of the Premises shall be manifestly false and absurd, this will not alter the conclusiveness of the Reasoning; though the conclusion itself may perhaps be absurd also. For instance, "All the Ape-tribe are originally descended from Reptiles or insects : Mankind are of the Ape-tribe ; therefore Mankind are originally descended from Reptiles or Insects ; here, every one* would perceive the falsity of all three of these propositions. But it is not the less true that the conclusion follows from those premises, and that if they were true, it would be true also.

§ 2. But it oftens happen that there will be a seeming

* Except certain French Naturalists.

Lesson iii.] fallacies. 23

connexion of certain premises with a conclusion which does not really follow from them, although, to the inattentive or unskilful, the argument will appear to be valid. And this is most especially likely to occur when such a seeming argument [or Fallacy] is dressed up in a great quantity of line-sounding words, and is accompanied with much vehemence of assertion, and perhaps with expressions of contempt for anyone who presumes to entertain a doubt on the matter. In a long declamatory speech, especially, it will often happen that almost any proposition at all will be passed off as a proof of any other that does but contain some of the same words, by means of strenuous assurances that the proof is complete.

Sometimes again, sound arguments will be distrusted as fallacious ; especially if they are not clearly expressed ; and the more if the conclusions are such as men are not willing to admit.

And frequently also, when there really is no sound argument, the reader or hearer, though he believes or suspects that there is some fallacy, does not know how to detect and explain it.

§ 3. Suppose, for instance, such seeming-arguments as the following to be proposed: — (1.) " Every criminal is deserving of punishment ; this man is not a criminal \ therefore he is not deserving of punishment :" or again, (2.) "All wise rulers endeavor to civilize the People; Alfred endeavored to civilize the People; therefore he was a wise ruler." There are perhaps some few persons who would not perceive any fallacy in such arguments, even when thus briefly and distinctly stated. And there are probably many who would fail to perceive such a fallacy, if the arguments were enveloped in a cloud of words, and conveyed at great length, in a style of vague indistinct declamation ; especially if the conclusions were such as they were disposed to admit. And others again, might perceive, indeed, that there is a fallacy, but might be at a loss to explain and expose it.

Now the above examples exactly correspond respectively, with the following; in which the absurdity is manifest : — (1.) " Every tree is a vegetable ; grass is not a tree; therefore it is not a vegetable;" and (2.) "all vegetables grow ; an animal grows ; therefore it is a vegetable." These last examples, I say, correspond exactly (considered in respect of the reasoning) with the former ones ; the conclusions of which, however true, no more follow from the premises than those of the last.

This way of exposing a fallacy by bringing forward a similar one where a manifestly absurd conclusion professes to be drawn from premises that are true, is one which we may often find it needful to employ when addressing persons who have no knowledge of technical rules ; and to whom, consequently, we could not speak so as to be understood concerning the principles of Reasoning.