: The Art of Logical Thinking; Or The Laws of Reasoning by Atkinson William Walker - Logic; Reasoning

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propositions when joined in a particular order of arrangement will make sound and valid syllogisms. We shall not set forth these tables here, as they are too technical for a popular presentation of the subject before us, and because they are not necessary to the student who will thoroughly familiarize himself with the above stated Laws of the Syllogism and who will therefore be able to determine in every case whether any given argument is a correct syllogism, or otherwise.

The forms of reasoning based upon these three several classes of propositions bear the same names as the latter. And, accordingly the respective syllogisms expressing these forms of reasoning also bear the class name or term. Thus, a Categorical Syllogism is one containing only categorical propositions; a Hypothetical Syllogism is one containing one or more hypothetical propositions; a Disjunctive Syllogism is one containing a disjunctive proposition in the major premise.

Jevons says: "To affirm the consequent and then to infer that we can affirm the antecedent, is as bad as breaking the third rule of the syllogism, and allowing an undistributed middle term.... To deny the antecedent is really to break the fourth rule of the syllogism, and to take a term as distributed in the conclusion which was not so in the premises."

REASONING BY ANALOGY

What is called Reasoning by Analogy 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 circumstances." 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: "Analogy 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."

But the student must be on guard against the deceptive conclusions sometimes arising from Reasoning by Analogy. As Jevons says: "In many cases Reasoning by Analogy 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 analogy. 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 analogies are manufactured, and it is excellent thought training to expose them. The majority of people think so little that they swallow these false analogies 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 Analogy 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 analogy are frequently fallacious."

Along the same lines, Brooks says: "The inference from analogy, 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 analogy 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 analogy 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."

FALLACIES

In Deductive Reasoning, we meet with two classes of Fallacies; namely, Fallacious Premise; and Fallacious Conclusion. We shall now consider each of these in turn.

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.

Arising from "Begging the Question," and in fact a class of the latter, is what is called "Reasoning in a Circle." In this form of fallacy one assumes 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."

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