Funk & WagnalFs Dictionary defines inductive reasoning as follows :
The Inductive Method in Reasoning is the scientific method that proceeds by induction. It requires exact observation : correct interpretation of the observed facts with a view to understanding them in relation to each other and their causes : rational explanation of the tacts by referring them to their real cause or law: and scientific construction: putting the facts in such co-ordination that the system reached shall agree with the reality.
Let us examine the earliest steps taken by Hahnemann in his development of the scientific approach toward the healing of the sick through the reasonable application of natural laws.
His childhood training in logical thinking crystallized his keen mind and made him peculiarly fitted for the task he assumed. In other words, he was early trained in inductive reasoning, and he was able to scientifically construct hitherto unknown principles in the care of the sick.
Exact observation : Hahnemann's honest disappointment with the practice of medicine as manifested in the eighteenth century was the direct result of his faculties of observation and reasoning. His early training demanded of him that he find logical reasons for the administration of medicinal substances, and that once given, favourable results were to be expected.
The chaotic prescriptions of that day left little reasonable grounds for clear-cut results, and his observations of the frequent failure of the physician to help sick patients toward cure, or worse still, the rapid decline of the patient in seemingly simple and uncomplicated cases under the best medical care procurable, led Hahnemann to renounce the practice of medicine. He turned to chemistry and the translation of medical literature as a means of livelihood. In one of these translations an item on the use of cinchona bark for intermittent fever arrested his attention, since he himself had recently suffered such a malady. His interest was aroused, and his experiments with medicinal substances (which he later called provings) were begun.
Here he first caught the gleam of light that led him to an understanding of the reasonable application of remedies, based on the exact observation of the ability of the drug to produce symptoms, on the one hand, and of the symptoms of the patient on the other. This problem he simplified to a logical basis.
Correct interpretation of the phenomena produced by the experiments or provings was provided by close study of series of these experiments on groups of people. Thus the probability of error was reduced through the accumulation of more data, with increasingly exact observation not only of results produced, but of possible interposing conditions which varied the results.
Hahnemann was soon convinced that the rational explanation of the phenomena was the thought, hinted at in the time of the ancient Hindu sages, by Hippocrates, Paracelsus, Stahl and others throughout the course of medical history, that "diseases are cured by medicines that have the power to excite a similar affection."
While this thought had been applied occasionally, Hahnemann was the first to insist on the importance of this premise in every case where a true cure was achieved, as he was the first to test remedial substances and classify the results with this purpose in mind.
With true scientific construction he applied the principles evolved from his inductive reasoning and the correlating experiments he had conducted.
Briefly, then, we find that these experiments had led Hahnemann to give a medicinal substance to healthy persons, to carefully record the effects which were the production of symptoms of (artificial) disease for the purpose of making these substances available for people suffering from like symptoms in (natural) disease syndromes. Thus developed his thorough work in proving as we know it.
This hypothesis, a process of inductive reasoning, proved to be a triumph through the discovery of scientific principles based on natural laws.
So, too, the principles of inductive reasoning led Hahnemann, through his observation of the effects of remedies administered on the basis of symptom similarity, to the gradual decrease of the dose, because of the consequent drug effects (as differentiated from the remedial effects) of the substances administered. This decrease of the dose was developed according to a definitely scaled formula, and this in turn led to a discovery of the principle of potentiation, or release of energy.