CHAPTER XVIII.
REASONING BY a.n.a.lOGY
What is called Reasoning by a.n.a.logy is one of the most elementary forms of reasoning, and the one which the majority of us most frequently employ. It is a primitive form of hasty generalization evidencing in the natural expectation that "things will happen as they have happened before in like circ.u.mstances." The term as used in logic has been defined as "Resemblance of relations; Resemblances of any kind on which an argument falling short of induction may be founded." Brooks says: "a.n.a.logy is that process of thought by which we infer that if two things resemble each other in one or more particulars, they will resemble each other in some other particular."
Jevons states the _Rule for Reasoning by a.n.a.logy_, as follows: "If two or more things resemble each other in many points, they will probably resemble each other also in more points." Others have stated the same principle as follows: "When one thing resembles another in known particulars, it will resemble it also in the unknown;" and "If two things agree in several particulars, they will also agree in other particulars."
There is a difference between generalization by induction, and by a.n.a.logy. In inductive generalization the rule is: "What is true of the many is true of all;" while the rule of a.n.a.logy is: "things that have some things in common have other things in common." As Jevons aptly remarks: "Reasoning by a.n.a.logy differs only in degree from that kind of reasoning called "Generalization." When _many things_ resemble each other in a _few properties_, we argue about them by Generalization. When a _few things_ resemble each other in _many properties_, it is a case of a.n.a.logy." Ill.u.s.trating a.n.a.logy, we may say that if in A we find the qualities, attributes or properties called _a_, _b_, _c_, _d_, _e_, _f_, _g_, respectively, and if we find that in B the qualities, etc., called _a_, _b_, _c_, _d_, _e_, respectively, are present, then we may reason by a.n.a.logy that the qualities _f_ and _g_ must also belong to B.
Brooks says of this form of reasoning: "This principle is in constant application in ordinary life and in science. A physician, in visiting a patient, says this disease corresponds in several particulars with typhoid fever, hence it will correspond in _all_ particulars, and _is_ typhoid fever. So, when the geologist discovers a fossil animal with large, strong, blunt claws, he infers that it procured its food by scratching or burrowing in the earth. It was by a.n.a.logy that Dr.
Buckland constructed an animal from a few fossil bones, and when subsequently the bones of the entire animal were discovered, his construction was found to be correct." Halleck says: "In argument or reasoning we are much aided by the habit of searching for hidden resemblances.... The detection of such a relation cultivates thought. If we are to succeed in argument, we must develop what some call a sixth sense of such relations.... The study of poetry may be made very serviceable in detecting a.n.a.logies and cultivating the reasoning powers.
When the poet brings clearly to mind the change due to death, using as an ill.u.s.tration the caterpillar body transformed into the b.u.t.terfly spirit, moving with winged ease over flowering meadows, he is cultivating our apprehension of relations, none the less valuable because they are beautiful."
But the student must be on guard against the deceptive conclusions sometimes arising from Reasoning by a.n.a.logy. As Jevons says: "In many cases Reasoning by a.n.a.logy is found to be a very uncertain guide. In some cases unfortunate mistakes are made. Children are sometimes killed by gathering and eating poisonous berries, wrongly inferring that they can be eaten, because other berries, of a somewhat similar appearance, have been found agreeable and harmless. Poisonous toadstools are occasionally mistaken for mushrooms, especially by people not accustomed to gathering them. In Norway mushrooms are seldom seen, and are not eaten; but when I once found a few there and had them cooked at an inn, I was amused by the people of the inn, who went and collected toadstools and wanted me to eat them also. This was clearly a case of mistaken reasoning by a.n.a.logy. Even brute animals reason in the same way in some degree. The beaten dog fears every stick, and there are few dogs which will not run away when you pretend to pick up a stone, even if there be no stone to pick up." Halleck says: "Many false a.n.a.logies are manufactured, and it is excellent thought training to expose them. The majority of people think so little that they swallow these false a.n.a.logies just as newly fledged robins swallow small stones dropped into their open mouths.... This tendency to think as others do must be resisted somewhere along the line, or there can be no progress." Brooks says: "The argument from a.n.a.logy is plausible, but often deceptive. Thus to infer that since American swans are white, the Australian swan is white, gives a false conclusion, for it is really black. So to infer that because John Smith has a red nose and is a drunkard, then Henry Jones who also has a red nose is also a drunkard, would be a dangerous inference.... Conclusions of this kind drawn from a.n.a.logy are frequently fallacious."
Regarding the _Rule for Reasoning from a.n.a.logy_, Jevons says: "There is no way in which we can really a.s.sure ourselves that we are arguing safely by a.n.a.logy. The only rule that can be given is this; that the more closely two things resemble each other, the more likely it is that they are the same in other respects, especially in points closely connected with those observed.... In order to be clear about our conclusions, we ought in fact never to rest satisfied with mere a.n.a.logy, but ought to try to discover the general laws governing the case. In a.n.a.logy we seem to reason from one fact to another fact without troubling ourselves either with deduction or induction. But it is only by a kind of guess that we do so; it is not really conclusive reasoning.
We ought properly to ascertain what general laws of nature are shown to exist by the facts observed, and then infer what will happen according to these laws.... We find that reasoning by a.n.a.logy is not to be depended upon, unless we make such an inquiry into the causes and laws of the things in question, that we really employ inductive and deductive reasoning."
Along the same lines, Brooks says: "The inference from a.n.a.logy, like that from induction, should be used with caution. Its conclusion must not be regarded as certain, but merely as reaching a high degree of probability. The inference from a part to a part, no more than from a part to the whole, is attended with any rational necessity. To attain certainty, we must show that the principles which lie at the root of the process are either necessary laws of thought or necessary laws of nature; both of which are impossible. Hence a.n.a.logy can pretend to only a high degree of probability. It may even reach a large degree of certainty, but it never reaches necessity. We must, therefore, be careful not to accept any inference from a.n.a.logy as true until it is proved to be true by actual observation and experiment, or by such an application of induction as to remove all reasonable doubt."
CHAPTER XIX.
FALLACIES
A _Fallacy_ is: "An unsound argument or mode of arguing, which, while appearing to be decisive of a question, is in reality not so; an argument or proposition apparently sound, but really fallacious; a fallacious statement or proposition, in which the error is not apparent, and which is therefore likely to mislead or deceive; sophistry."
In Deductive Reasoning, we meet with two cla.s.ses of Fallacies; namely, (1) Fallacious Premise; and (2) Fallacious Conclusion. We shall now consider each of these in turn.
_Fallacious Premise_ is in effect _an unwarranted a.s.sumption of premises_. One of the most common forms of this kind of Fallacy is known as "_Begging the Question_," the principle of which is the a.s.sumption of a fundamental premise which is not conceded; the unwarrantable a.s.sumption of that which is to be proved; or the a.s.sumption of that by which it is to be proved, without proving it. Its most common form is that of boldly stating some unproven fact, authoritatively and positively, and then proceeding to use the statement as the major premise of the argument, proceeding logically from that point. The hearer perceiving the argument proceeding logically often fails to remember that _the premise has been merely a.s.sumed_, without warrant and without proof and omitting the hypothetical "_if_." One may proceed to argue logically from the premise that "The moon is made of green cheese," but the whole argument is invalid and fallacious because of the fact that the person making it has "begged the question" upon an unwarranted premise. Hyslop gives a good example of this form of fallacy in the case of the proposition "Church and State should be united."
Proof being demanded the advocate proceeds to "beg the question" as follows: "Good inst.i.tutions should be united; Church and State are good inst.i.tutions; therefore, Church and State should be united." The proposition that "Good inst.i.tutions should be united" is fallacious, being merely a.s.sumed and not proven. The proposition sounds reasonable, and few will feel disposed to dispute it at first, but a little consideration will show that while _some_ good inst.i.tutions may well be united, it is _not_ a general truth that _all_ should be so.
"Begging the Question" also often arises from _giving a name to a thing_, and then a.s.suming that we have _explained_ the thing. This is a very frequent practice with many people--they try to _explain_ by merely applying names. An example of this kind is had in the case of the person who tried to explain why one could see through a pane of gla.s.s by saying "because it is transparent." Or when one explains that the reason a certain substance breaks easily is "because it is brittle." Moliere makes the father of a dumb girl ask why his daughter is dumb. The physician answers: "Nothing is more easy than to explain it; it comes from her having lost the power of speech." "Yes, yes," objects the father, "but the cause, if you please, why she has lost the power of speech." The physician gravely replies: "All our best authors will tell you that it is the impeding of the action of the tongue."
Jevons says: "The most frequent way, perhaps, in which we commit this kind of fallacy is to employ names which imply that we disapprove of something, and then argue that because it is such and such, it must be condemned. When two sportsmen fall out in some manner relating to the subject of game, one will, in all probability, argue that the act of the other was "unsportsmanlike," and therefore should not have been done.
Here is to all appearance a correct syllogism:
"No unsportsmanlike act should be done; John Robinson"s act was unsportsmanlike: Therefore, John Robinson"s act should not have been done.
"This is quite correct in form; but it is evidently the mere semblance of an argument. "Unsportsmanlike" means _what a sportsman should not do_. The point to be argued was whether the act fell within the customary definition of _what was unsportsmanlike_."
Arising from "Begging the Question," and in fact a cla.s.s of the latter, is what is called "Reasoning in a Circle." In this form of fallacy one a.s.sumes as proof of a proposition the proposition itself; or, uses the conclusion to prove the premise. For instance: "This man is a rascal because he is a rogue; and he is a rogue because he is a rascal." Or, "It is warm because it is summer; and it is summer because it is warm."
Or "He never drinks to excess, because he is never intemperate in drinking."
Brooks says: "Thus to argue that a party is good because it advocates good measures, and that certain measures are good because they are advocated by so excellent a party, is to reason in a circle. So when persons argue that their church is the true one, because it was established by G.o.d, and then argue that since it is the true church it must have been founded by G.o.d, they fall into this fallacy. To argue that "the will is determined by the strongest motive" and to define the strongest motive as "that which influences the will," is to revolve in a circle of thought and prove nothing. Plato commits this error when he argues the immortality of the soul from its simplicity, and afterwards attempts to prove its simplicity from its immortality." It needs care to avoid this error, for it is surprising how easily one falls into it.
Hyslop says: "The fallacy of Reasoning in a Circle occurs mostly in long arguments where it can be committed without ready detection....
When it occurs in a long discourse it may be committed without easy discovery. It is likely to be occasioned by the use of synonyms which are taken to express more than the conception involved when they do not." What is called a Vicious Circle is caused when the conclusion of one syllogism is used for a proposition in another syllogism, which in its turn comes to be used as a basis for the first or _original syllogism_.
_Fallacious Conclusion_ is in effect _an unwarranted or irrelevant a.s.sumption of a logical conclusion_. There are many forms of this fallacy among which are the following:
_Shifting ground_, which consists in the pretence of proving one thing while in reality merely a similar or related thing is being proved. In this cla.s.s is the argument that because a man is profane he must necessarily be dishonest; or that because a man denies the inspiration of the Scriptures he must be an atheist.
_Fallacious Questioning_, in which two or more related questions are asked, and the answer of one is then applied to the other. For instance: "You a.s.sert that the more civilized a community, the more silk-hats are to be found in it?" "Yes." "Then, you state that silk-hats are the promoters and cause of civilization in a community?" A question of this kind is often so arranged that an answer either in the affirmative or the negative will lead to a false or fallacious inference. For instance, the question once asked a respectable citizen on the witness stand: "Have you stopped beating your mother?" An answer of either "Yes" or "No," was out of the question, for it would have placed the witness in a false position, for he had never beaten his mother, nor been accused of the same.
_Partial Proof_, in which the proof of a partial or related fact is used to infer a proof of the whole fact or a related one. For instance, it is fallacious to argue that a man has been guilty of drunkenness by merely proving that he was seen entering a saloon.
_Appeal to Public Opinion_, in which the prejudices of the public are appealed to rather than its judgment or reason. In politics and theological argument this fallacy is frequent. It is no argument, and is reprehensible.
_Appeal to Authority, or Reverence_, in which the reverence and respect of the public for certain persons is used to influence their feelings in place of their judgment or reason. For instance: "Washington thought so-and-so, and therefore it must be right;" or "It is foolish to affirm that Aristotle erred;" or "It has been believed by men for two thousand years, that, etc;" or "What our fathers believed must be true." Appeals of this kind may have their proper place, but they are fallacies nevertheless, and not real argument.
_Appeal to Profession_, in which an appeal is made to practices, principles or professions of the opponent, rather than to reason or judgment. Thus we may argue that a certain philosophy or religion cannot be sound or good, because certain people who hold it are not consistent, or not worthy, moral or sober. This argument is often used effectively against an opponent, and is valid against him personally. But it is no valid argument against his philosophy or belief, because he may act in violation of them, or he may change his practices and still adhere to his beliefs--the two are not joined.
_Appeal to General Belief_, in which an appeal is made to general or universal belief, although the same may be unsupported by proof. This is quite common, but is no real argument. The common opinion may be erroneous, as history proves. A few centuries ago this argument could have been used in favor of the earth being flat, etc. A half-century ago it was used against Darwin. Today it is being used against other new ideas. It is a fallacy by its very nature.
_Appeal to Ignorance_, in which an appeal is made to the ignorance of the opponent that his conviction may follow from his inability to prove the contrary. It is virtually no argument that: "So-and-so must be true, _because you cannot prove that it is not_." As Brooks says: "To argue that there is no material world, because we cannot explain how the mind knows it to exist, is the celebrated fallacy of Hume in philosophy. The fact that we cannot find a needle in a haystack is no proof that it is not there."
_Introduction of New Matter_, also called _Non Sequitur_, in which matter is introduced into the conclusion that is not in the premises.
Hyslop gives the following example of it: "All men are _rational_; Socrates is a man; therefore, Socrates is _n.o.ble_." De Morgan gives the following more complex example: "Episcopacy is of Scripture origin; The Church of England is the only Episcopal church in England; therefore, the church established is the church that ought to be supported."
Other fallacies, resembling in some respects those above mentioned, are as follows:
_Fallacy of Ambiguous Terms_, in which different meanings of the same word are used to produce the fallacious argument. As Jevons says: "A word with two distinct meanings _is really two words_."
_Confusion between Collective and General Meanings of a Term_, of which Jevons says: "It would be obviously absurd to argue that because _all_ the books in the British Museum Library are sure to give information about King Alfred, therefore any particular book will be sure to give it. By "_all_ the books in the British Museum Library," we mean all _taken together_. There are many other cases where the confusion is not so evident, and where great numbers of people are unable to see the exact difference."
_Arguing from the Collective to the General_, in which the fallacy consists of arguing that because something is true of the whole of a group of things, therefore it is true of any of those things. Jevons says: "_All_ the soldiers in a regiment may be able to capture a town, but it is absurd to suppose that therefore _every_ soldier in the regiment could capture the town single handed. White sheep eat a great deal more than black sheep; but that is because there are so many more of them."
_Uncertain Meaning of a Sentence_, from which confusion arises and fallacious argument may spring. Jevons says: "There is a humorous way of proving that a cat must have three tails: Because a cat has one tail more than _no_ cat; and _no cat_ has two tails; therefore, _any_ cat has three tails." Here the fallacy rests upon a _punning_ interpretation of "no."
_Proving the Wrong Conclusion_, in which the attempt to confuse conclusions is made, with the result that some people will imagine that the case is established. Jevons says: "This was the device of the Irishman, who was charged with theft on the evidence of three witnesses, who had seen him do it; he proposed to call _thirty_ witnesses who had _not_ seen him do it. Equally logical was the defense of the man who was called a materialist, and who replied, "I am not a materialist; I am a barber.""
_Fallacy of Unsuccessful Argument_, in which is attempted the illogical conclusion that _because a certain argument has failed the opposite conclusion is proven_. This fallacy is quite common, especially in cases of juries. One side fails to prove certain contentions, and the jury leaps to the conclusion that the opposite contention must be correct.
This is clearly fallacious, for there is always the possibility of a _third_ explanation. In the case of a claim of _alibi_ juries are apt to fall into this fallacy. The failure of the attempt to establish an _alibi_ is often held to be in the nature of proof of the guilt of the accused. Old trial lawyers a.s.sert that a failure to establish a claimed _alibi_ tends to injure the chance of the accused more than direct evidence against him. Yet, as all logical reasoners will see, there is no logical validity in any such inference. As Jevons has well said: "_No number of failures in attempting to prove a proposition really disprove it_." At the end of each failure the case simply stands in the same position as before the attempt; _i.e._, "not proven."
_All Violations of the Rules of the Syllogism_ const.i.tute fallacies, as may be seen by forming a syllogism in violation of one or more of the rules.
The logicians, particularly those of ancient times, took great pains to discover and _name_ new variations of fallacies, many of which were hair-splitting in nature, and not worthy of being considered seriously.
Some of those which we have enumerated may possibly be open to the same criticism, but we have omitted many of the worst offenders against practical common sense. An understanding of the fundamental Laws of Reasoning is sufficient to expose and unmask all fallacies, and such understanding is far more valuable than the memorizing of the _names_ of hair-splitting fallacies which would not deceive a child.
In addition to the above stated fallacies of Deductive Reasoning, there are other fallacies which are met with in _Inductive Reasoning_. Let us briefly consider them.
_Hasty and False Generalization_ is a common fallacy of this cla.s.s.
Persons sometimes see certain qualities in a few individuals of a cla.s.s, and mistakenly infer that _all_ the individuals in that cla.s.s must possess these same qualities. Travelers frequently commit this fallacy.
Englishmen visiting the United States for a few weeks have been known to publish books upon their return home making the most ridiculous generalizations regarding the American people, their a.s.sertions being based upon the observation of a few scattered individuals, often not at all representative. Americans traveling abroad commit similar errors. A flying trip through a country does not afford the proper opportunity for correct generalization. As Brooks says: "No hypothesis should be accepted as true until the facts are so numerous that there can be no doubt of its being proved."