Deductive Reasoning is, as we have seen, dependent upon the process of deriving a particular truth from a general law, principle or truth, upon the fundamental axiom that: "What is true of the whole is true of its parts." It is an analytical process, just as Inductive Reasoning is synthetical. It is a descending process, just as Inductive Reasoning is ascending.
Halleck says of Deductive Reasoning: "After induction has classified certain phenomena and thus given us a major premise, we proceed deductively to apply the inference to any new specimen that can be shown to belong to that class. Induction hands over to deduction a ready-made major premise, e.g. 'All scorpions are dangerous.' Deduction takes this as a fact, making no inquiry about its truth. When a new object is presented, say a possible scorpion, the only troublesome step is to decide whether the object is really a scorpion. This may be a severe task on judgment. The average inhabitant of the temperate zone would probably not care to risk a hundred dollars on his ability to distinguish a scorpion from a centipede, or from twenty or thirty other creatures bearing some resemblance to a scorpion. Here there must be accurately formed concepts and sound judgment must be used in comparing them. As soon as we decide that the object is really a scorpion, we complete the deduction in this way:—'All scorpions are dangerous; this creature is a scorpion; this creature is dangerous.' The reasoning of early life must be necessarily inductive. The mind is then forming general conclusions from the examination of individual phenomena. Only after general laws have been laid down, after objects have been classified, after major premises have been formed, can deduction be employed."
What is called Reasoning by Analogy is really but a higher degree of Generalization. It is based upon the idea that if two or more things resemble each other in many particulars, they are apt to resemble each other in other particulars. Some have expressed the principle as follows: "Things that have some things in common have other things in common." Or as Jevons states it: "The rule for reasoning by analogy is that if two or more things resemble each other in many points, they will probably resemble each other also in more points."
This form of reasoning, while quite common and quite convenient, is also very dangerous. It affords many opportunities for making false inferences. As Jevons says: "In many cases Reasoning by Analogy is found to be a very uncertain guide. In some cases unfortunate mistakes are committed. 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 gather them.... There is no way in which we can really assure ourselves that we are arguing safely by analogy. The only rule that can be given is this, that the more things resemble each other, the more likely is it that they are the same in other respects, especially in points closely connected with those observed."
Halleck says: "In argument or reasoning we are much aided by the habit of searching for hidden resemblances. We may here use the term analogy in the narrower sense as a resemblance of ratios. There is analogical relation between autumnal frosts and vegetation on the one hand, and death and human life on the other. Frosts stand in the same relation to vegetation that death does to life. The detection of such a relation cultivates thought. If we are to succeed in argument, we must develop what some call a sixth sense for the detection of such relations.... Many false analogies are manufactured and it is excellent thought training to expose them. The majority of people think so little that they swallow false analogies just as newly-fledged robins swallow small stones dropped into their open mouths.... The study of poetry may be made very serviceable in detecting analogies and cultivating the reasoning powers. When the poet brings clearly to mind the change due to death, using as an illustration the caterpillar body transformed into the butterfly spirit, moving with winged ease over flowing meadows, he is cultivating our apprehension of relations, none the less valuable because they are beautiful."
There are certain studies which tend to develop the power or faculty of Inductive Reasoning. Any study which leads the mind to consider classification and general principles, laws or truth, will tend to develop the faculty of deduction. Physics, Chemistry, Astronomy, Biology and Natural History are particularly adapted to develop the mind in this particular direction. Moreover, the mind should be directed to an inquiry into the causes of things. Facts and phenomena should be observed and an attempt should be made not only to classify them, but also to discover general principles moving them. Tentative or provisional hypotheses should be erected and then the facts re-examined in order to see whether they support the hypotheses or theory. Study of the processes whereby the great scientific theories were erected, and the proofs then adduced in support of them, will give the mind the habit of thinking along the lines of logical induction. The question ever in the mind in Inductive Reasoning is "Why?" The dominant idea in Inductive Reasoning is the Search for Causes.
In regard to the pitfalls of Inductive Reasoning—the fallacies, so-called, Hyslop says: "It is not easy to indicate the inductive fallacies, if it be even possible, in the formal process of induction.... It is certain, however, that in respect to the subject-matter of the conclusion in inductive reasoning there are some very definite limitations upon the right to transcend the premises. We cannot infer anything we please from any premises we please. We must conform to certain definite rules or principles. Any violation of them will be a fallacy. These rules are the same as those for material fallacies in deduction, so that the fallacies of induction, whether they are ever formal or not, are at least material; that is they occur whenever equivocation and presumption are committed. There are, then, two simple rules which should not be violated. (1) The subject-matter in the conclusion should be of the same general kind as in the premises. (2) The facts constituting the premises must be accepted and must not be fictitious."
One may develop his faculty or power of Deductive Reasoning by pursuing certain lines of study. The study of Mathematics, particularly in its branch of Mental Arithmetic is especially valuable in this direction. Algebra and Geometry have long been known to exercise an influence over the mind which gives to it a logical trend and cast. The processes involved in Geometry are akin to those employed in Logical reasoning, and must necessarily train the mind in this special direction. As Brooks says: "So valuable is geometry as a discipline that many lawyers and others review their geometry every year in order to keep the mind drilled to logical habits of thinking." The study of Grammar, Rhetoric and the Languages, are also valuable in the culture and development of the faculty of Deductive Reasoning. The study of Psychology and Philosophy have value in this connection. The study of Law is very valuable in creating logical habits of thinking deductively.
But in the study of Logic we have possibly the best exercise in the development and culture of this particular faculty. As Brooks well says: "The study of Logic will aid in the development of the power of deductive reasoning. It does this first by showing the method by which we reason. To know how we reason, to see the laws which govern the reasoning process, to analyze the syllogism and see its conformity to the laws of thought, is not only an exercise of reasoning, but gives that knowledge of the process that will be both a stimulus and a guide to thought. No one can trace the principles and processes of thought without receiving thereby an impetus to thought. In the second place, the study of logic is probably even more valuable because it gives practice in deductive thinking. This, perhaps, is its principal value, since the mind reasons instinctively without knowing how it reasons. One can think without the knowledge of the science of thinking, just as one can use language correctly without a knowledge of grammar; yet as the study of grammar improves one's speech, so the study of logic cannot but improve one's thought."