Inductive reasoning

“ Logicians generally distinguish between two branches of their science, inductive and deductive reasoning. In inductive reasoning we pass from individual facts to general principles; in deductive reasoning we pass from general principles to conclusions about individual facts. ”

“ But it may not suit our purpose thus to restrict the conclusion. We may wish to make use of it in its broad general significance. Every day we are compelled to act upon imperfect inductions, as in the case of the street car. In such cases we must resort to certain rules or tests whereby we can determine the probability of the truth of the imperfect induction. We shall consider these rules or tests after we have discussed the application of inductive reasoning to inductive argument. ”

“ There are two general ways of obtaining our basis for the process of Inductive Reasoning. One of these is called Perfect Induction and the other Imperfect Induction. Perfect Induction is possible only when we have had the opportunity of examining every particular object or thing of which the general idea is expressed. For instance, if we could examine every fish in the universe we would have the basis of Perfect Induction for asserting the general truth that "all fishes are cold-blooded." ”

“ It follows that without the experience of oneself or of others in the direction of observing and remembering particular facts, objects, persons and things, we cannot hope to acquire the preliminary facts for the generalization and inductive inference necessary in Inductive Reasoning. It is necessary for us to form a variety of clear Concepts or ideas of facts, objects, persons and things, before we may hope to generalize from these particulars. ”

“ Now, this is precisely the sort of process in which residual phenomena (such as spoken of in art. 158.) may be expected to occur. If our induction be really a valid and a comprehensive one, whatever remains unexplained in the comparison of its conclusion with particular cases, under all their circumstances, is such a phenomenon, and comes in its turn to be a subject of inductive reasoning to discover its cause or laws. It is thus that we may be said to witness facts with the eyes of reason ”

“ It might seem to follow, if all reasoning be induction, that the difficulties of philosophical investigation must lie in the inductions exclusively, and that when these were easy, and susceptible of no doubt or hesitation, there could be no science, or, at least, no difficulties in science. ”

“ The sun may not rise to-morrow, though it has never failed up to this time. Still it is by this observation of many individual cases that the truth of the propositions that men do believe has been established. We realize that our inductions are often imperfect, but the general truths so established will be found to underlie every process of reasoning, and will be either directly or indirectly the basis upon which we build up all argument.
We may then redefine inductive reasoning as the process by which from many individual cases we establish the probable truth of a general proposition. ”

“ Trains of reasoning exist only for the sake of extending an induction, founded, as all inductions must be, on observed cases, to other cases in which we not only cannot directly observe what is to be proved, but cannot directly observe even the mark which is to prove it. ”

“ Or, as from experience we know that the various kinds of metals expand when subjected to heat, we infer that all metals are subject to this law, and that consequently we may arrive by inductive reasoning at the conclusion that: "All metals expand when subjected to heat." It will be noticed that the conclusion arrived at in this way by Inductive Reasoning forms the fundamental premise in the process of Deductive Reasoning. ”

“ Induction as a mode of inference is the process of reasoning from less general premises to a more general conclusion; whereas induction as a method is a procedure from the observation of individual facts to a realization of a universal truth. In either case the conclusion of an inductive process always implies more than is contained in the premises. This gives to the conclusion an uncertainty. No induction is absolutely free from doubt except the so-called perfect induction, which form will receive attention in a later section. ”

“ This work of inductive investigation cannot be guided by any system of precise and infallible rules, like those of deductive reasoning. There is, in fact, nothing to which we can apply rules of method, because the laws of nature must be in our possession before we can treat them. If there were any rule of inductive method, it would direct us to make an exhaustive arrangement of facts in all possible orders. ”

“ The nearest approach which human theories can make to perfection is to diminish this residue, this caput mortuum of observation, as it may be considered, as much as practicable, and, if possible, to reduce it to nothing, either by showing that something has been neglected in our estimation of known causes, or by reasoning upon it as a new fact, and on the principle of the inductive philosophy ascending from the effect to its cause or causes. ”

“ The assertion, that our inductive processes assume the law of causation, while the law of causation is itself a case of induction, is a paradox, only on the old theory of reasoning, which supposes the universal truth, or major premise, in a ratiocination, to be the real proof of the particular truths which are ostensibly inferred from it. ”

“ Reason, it might be objected, is the faculty of arguing, of drawing conclusions from premises. But a little consideration will show us that, though this is so, yet all reasoning is employed upon concepts. All reasoning is either deductive or inductive. Induction consists in the formulation of general principles from particular cases. A general principle is always a statement made, not about a particular thing, but about a whole class of things, that is, about a concept. Concepts are formed inductively by comparing numerous examples of a class. ”

“ The second element in the technique necessary in reasoning is the use of either the inductive or the deductive method in the process. Induction requires--a problem, search for facts with which to solve it, comparison and analysis of those facts, abstraction of the essential likenesses, and conclusion. Deduction requires--a problem, the analysis of the situation and abstraction of its essential elements, search for generals under which to classify it, comparison of it with each general found, and conclusion. ”

“ If they are only probably correct, the conclusion is a mere presumption; if either one is false, the conclusion is probably false. But if the syllogism is correctly framed, and if both premises are true, the conclusion is irrefutable. As premises are facts that have first been established by induction, the relation between inductive and deductive reasoning is very close. In fact, deduction depends on induction for its very existence. To overthrow a deductive argument all that is necessary is to show the error in the inductive process that built up either one or both of the premises. ”

“ When the conclusion is reached as the effect of many particular experiences, the reasoning is called inductive. When some principle already established leads to another principle or to a conclusion about some particular fact, the reasoning is called deductive. ”

“ Natural uniformities are presupposed in all our reasoning about our natural surroundings, and without this presupposition things could not be reasoned about or formed into science. All our knowledge of natural events, beyond original perceptions of sense, consists in interpretation of the phenomena of which the senses make us aware. Upon this judgment of the common sense our inductions are all grounded, so that it may be called the inductive principle. ”

“ Since Reasoning, or Inference, the principal subject of logic, is an operation which usually takes place by means of words, and in complicated cases can take place in no other way; those who have not a thorough insight into the signification and purposes of words, will be under chances, amounting almost to certainty, of reasoning or inferring incorrectly. ”

“ For valid reasoning there must be parallel cases, according to substance and attribute, or cause and effect, or proportion: e.g. As cattle and deer are to herbivorousness, so are camels; As bodies near the earth fall toward it, so does the moon; As 2 is to 3 so is 4 to 6.
(2) Analogy is discussed in Logic as a kind of probable proof based upon imperfect similarity (as the best that can be discovered) between the data of comparison and the subject of our inference. Like Deduction and Induction, it assumes that things which are alike in some respects are also alike in others ”

“ You should carefully study the Art of Reasoning, as it is what most people are very deficient in, and I know few things more disagreeable than to argue, or even converse with a man who has no idea of inductive and deductive philosophy. ”

“ The philosophy of reasoning, to be complete, ought to comprise the theory of bad as well as of good reasoning. ”

“ Most inductions require no conception but what was present in every one of the particular instances on which the induction is grounded. That all men are mortal is surely an inductive conclusion; yet no new conception is introduced by it. ”

“ The notion of Cause being the root of the whole theory of Induction, it is indispensable that this idea should, at the very outset of our inquiry, be, with the utmost practicable degree of precision, fixed and determined. If, indeed, it were necessary for the purpose of inductive logic that the strife should be quelled, which has so long raged among the different schools of metaphysicians, respecting the origin and analysis of our idea of causation; the promulgation, or at least the general reception, of a true theory of induction, might be considered desperate for a long time to come. ”

“ And one of the commonest forms of fallacious reasoning arising from ambiguity, is that of arguing from a metaphorical expression as if it were literal; that is, as if a word, when applied metaphorically, were the same name as when taken in its original sense: which will be seen more particularly in its place. ”

“ Why it is that the substitution of this circuitous mode of proceeding for a process apparently much easier and more natural, is held, and justly, to be the greatest triumph of the investigation of nature, we are not, in this stage of our inquiry, prepared to examine. But it is necessary to remark, that although, by this progressive transformation, all sciences tend to become more and more Deductive, they are not, therefore, the less Inductive; every step in the Deduction is still an Induction. ”

“ By common experience, and more precisely by experiment, it is found possible to select from among the antecedents of an event a certain number upon which, so far as can be perceived, it is dependent, and to neglect the rest: to purge the cause of all irrelevant antecedents is the great art of inductive method. Remote or minute conditions may indeed modify the event in ways so refined as to escape our notice. Subject to the limitations of our human faculties, however, we are able in many cases to secure an unconditional antecedent upon which a certain event invariably follows. ”

“ Hence also induction is a real process, because, when we know that this individual magnet attracts iron, we are very far from knowing that all alike do so similarly; and the question of inductive logic, how we get from some similars to all similars, remains, as before, a difficulty, but not to be solved by the fallacy that inference is identification. ”

“ Whether we are inquiring into a scientific principle or into an individual fact, and whether we proceed by experiment or by ratiocination, every step in the train of inferences is essentially inductive, and the legitimacy of the induction depends in both cases on the same conditions. ”

“ Why is a single instance, in some cases, sufficient for a complete induction, while in others, myriads of concurring instances, without a single exception known or presumed, go such a very little way towards establishing an universal proposition? Whoever can answer this question knows more of the philosophy of logic than the wisest of the ancients, and has solved the problem of induction. ”

“ Thus, that all life depends on the presence of oxygen is (1) an universal proposition; (2) a real one, since the 'presence of oxygen' is not connoted by 'life'; (3) it is based on observation; (4) it relies on the uniformity of Nature, since all cases of life have not been examined.
Such a proposition is here called 'an induction,' when it is inductively proved; that is, proved by facts, not merely deduced from more general premises (except the premise of Nature's uniformity) : and by the 'process of induction' is meant the method of inductive proof. ”

“ In every way, therefore, it is evident that to explain induction as the colligation of facts by means of appropriate conceptions, that is, conceptions which will really express them, is to confound mere description of the observed facts with inference from those facts, and ascribe to the latter what is a characteristic property of the former. ”

“ Scientist, inventor, mathematician, man of letters, alike are not quite true to fact when they claim that pure reason and an exclusive process of induction control their mental operations. I would raise the question whether there is any such thing as the exclusively inductive method. Is it not truer to speak of the deductive-inductive than of the inductive? The Mystic Sense, with its adventurous and sometimes blundering progress, holds so important a place that without it logic and induction would be as grist without a mill. ”