Early Schools of Medicine

In his "Etymologiae", Isidore of Seville (c. 560-636) wrote:
Medicine is that which preserves or restores the health of the body. Its sphere is diseases and wounds. With it are associated not only matters involving the practice of those who are properly called physicians, but also food, drink, clothing and shelter; in short, every protective defense that serves to ensure the body against external impacts and hazards.
The founder and inventor of medicine is called among the Greeks Apollo. His son Aesculapius glorified and enlarged the art. But after Aesculapius was struck by lightening and perished, the art of healing is said to have been prohibited. The practice lapsed with its founder, and for almost five hundred years it was in abeyance until the time of Artaxerxes, King of the Persians. Then Hippocrates, son of Asclepius, brought it back into use on the island of Cos.
The three individuals mentioned originated the three schools. The first, the Methodical school, began with Apollo. It adheres to incantations and remedies. The second, the Empirical school, that is the most experimental school, springs from Aesculapius. It is founded not on diagnostic symptoms but solely on experience. The third, the Logical school, that is the rational school, was due to Hippocrates. The Empiricists adhere to experience alone. The Logicians add reasoning to experience. The Methodics observe neither the rationale of the elements, nor time age or cause, but merely the incidence of the disease,

Experimental Philosophy

In his Principia, Isaac Newton (1642-1727) wrote:
...and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy...

[Newton's "hypotheses non fingo" is alternatively translated "I do not frame hypotheses."]

The Principle of Induction

Summarizing David Hume's (1711-1776) demolition of purely empirical inference, Bertrand Russell wrote:
Hume's scepticism rests entirely upon his rejection of the principle of induction. The principle of induction, as applied to causality, says that, if A has been found very often accompanied or followed by B, and no instance is known of A not being accompanied or followed by B, then it is probable that on the next occasion on which A is observed it will be accompanied or followed by B. If the principle is to be adequate, a sufficient number of instances must make the probability not far short of certainty. If the principle, or any other from which it can be deduced, is true, then the causal inferences which Hume rejects are valid, not indeed as giving certainty, but as giving a sufficient probability for practical purposes. If this principle is not true, every attempt to arrive at general scientific laws from particular observations is fallacious, and Hume's scepticism is inescapable for an empiricist.
The principle itself cannot, of course, without circularity, be inferred from observed uniformities, since it is required to justify any such inference. It must therefore be, or be deduced from, an independent principle not based on experience. To this extent, Hume has proved that pure empiricism is not a sufficient basis for science. But if this one principle is admitted, everything else can proceed in accordance with the theory that all our knowledge is based on experience. It must be granted that this is a serious departure from pure empiricism, and that those who are not empiricists may ask why, if one departure is allowed, others are to be forbidden.
These, however, are questions not directly raised by Hume's arguments. What these arguments prove--and I do not think the proof can be controverted--is, that induction is an independent logical principle, incapable of being inferred either from experience or from other logical principles, and that without this principle science is impossible.

Inductive Behavior

In discussing his theory of confidence intervals, Jerzy Neyman (1994-1981) wrote:
The word "stating" above is put in italics to emphasize that it is not suggested that we "conclude" that qL q qU, nor that we should "believe" that q is actually between qL and qU. In the author's opinion, the word "conclude" has been wrongly used in that part of the statistical literature dealing with what has been termed "inductive reasoning". Moreover, the expression "inductive reasoning" itself seems to involve a contradictory adjective. The word "reasoning" generally seems to denote the mental process leading to knowledge. As such, it can only be deductive. Therefore, the description "inductive" seems to exclude both "reasoning" and also its final step, the "conclusion". If we wish to use the work "inductive" to describe the result of statistical inquiries, then we should apply it to "behavior" and not to "reasoning".... The reasoning ended when the functions qL and qU were calculated. The above process is also devoid of any "belief" concerning the value of q. Occasionally we do not behave in accordance with our beliefs. Such, for example, is the case when we take out an accident insurance policy while preparing for a vacation trip. In doing so, we surely act against our firm belief that there will be no accident; otherwise we would probably stay at home. This is an example of inductive behavior.