History of scientific method
The history of scientific method is inseparable from the history of science itself.  The development and elaboration of rules for scientific reasoning and investigation has not been straightforward; scientific method has been the subject of intense and recurring debate throughout the history of science, and many eminent natural philosophers and scientists have argued for the primacy of one or another approach to establishing scientific knowledge.
Some of the most important debates in the history of scientific method center on: rationalism, especially as advocated by Rene Descartes; inductivism, which rose to particular prominence with Isaac Newton and his followers; and hypothetico-deductivism, which came to the fore in the early 19th century.  In the late 19th and early 20th centuries, a debate over realism vs. antirealism was central to discussions scientific method as powerful scientific theories extended beyond the realm of the observable, while in the mid-20th century some prominent philosophers argued against any universal rules of science at all.

# Early method
There are few explicit discussions of scientific methodologies in surviving records from early cultures.  The most we can infer about the approaches to undertaking science in this period stems from descriptions of early investigations into nature, in the surviving records.  An Egyptian medical textbook, the Edwin Smith papyrus, (circa 1600 BC), applies the basic components of scientific method: examination, diagnosis, treatment and prognosis, to the treatment of disease.  The Ebers papyrus (circa 1550 BC) also contains evidence of traditional empiricism.
However, although the Babylonians and Egyptians developed much technical knowledge, crafts, and mathematics used in practical tasks of divination, as well as a knowledge of medicine (and made lists or various kinds), it is the ancient Greeks who engage in the earliest forms of what we recognize as modern science.  Even for the early Greeks, geometry was a practical skill like shoemaking, relegated to what its etymology suggests: geo-metrics, or measuring the earth.  That is all Xenophon claims Socrates advises one know about geometrywhat is practically needed to measure the land correctly so as to inherit it, divide it, or use it (Memorabilia, VII.4.vii.2).  In Plato's Theatetus, Theatetus defines science  for Socrates as "what we can learn...geometry and the other sciences you just mentioned like shoemaking, and the techniques of other artisans all together, or considered separately," (Plato 1.146c-d).
However, in Ancient Greece, towards the middle of the 5th century BC, some of the components of a scientific tradition were already heavily established. Plato is an important contributor to this emerging tradition.  In Protagoras (318d-f), Plato mentions the teaching of arithmetic, astronomy and geometry in schools. The philosophical ideas of this time were mostly freed from the constraints of everyday phenomena and common sense. This denial of reality as we experience it reaches an extreme in Parmenides who argued that the world is one and that change and subdivision do not exist.

# Aristotelian science and empiricism
Aristotle provided another of the ingredients of scientific tradition: empiricism. For Aristotle, universal truths can be known from particular things via induction. To some extent then, Aristotle reconciles abstract thought with observation, although it would be misleading to imply that Aristotelian science is empirical in form.  Indeed, Aristotle did not accept that knowledge acquired by induction could rightly be counted as scientific knowledge. Nevertheless, induction was a necessary preliminary to the main business of scientific enquiry, providing the primary premises required for scientific demonstrations.
Aristotle largely ignored inductive reasoning in his treatment of scientific enquiry. To make it clear why this is so, consider his statement in Posterior Analytics,
It was therefore the work of the philosopher to demonstrate universal truths and to discover their causes. While induction was sufficient for discovering universals by generalization, it did not succeed in identifying causes. The tool Aristotle chose for this was deductive reasoning in the form of syllogisms. Using the syllogism, scientists could infer new universal truths from those already established.
Aristotle developed a complete normative approach to scientific enquiry involving the syllogism which is discussed at length in his Posterior Analytics. Perhaps most striking today, where the use of mathematics is common place in the physical sciences, would be the admonition that theorems of any one science not be demonstrated by means of another science.
A difficulty with this scheme lay in showing that derived truths have solid primary premises.  Aristotle would not allow that demonstrations could be circular; supporting the conclusion by the premises, and the premises by the conclusion. Nor would he allow an infinite number of middle terms between the primary premises and the conclusion. This leads to the question of how the primary premises are arrived at, and as we have already mentioned, Aristotle allowed that induction would be required for this task.
Towards the end of Posterior Analytics, Aristotle discusses knowledge imparted by induction.
The account leaves room for doubt regarding the nature and extent of his empiricism. In particular, it seems that Aristotle considers sense-perception only as a vehicle for knowledge through intuition. Induction is not afforded the status of scientific reasoning, and so it is left to intuition to provide a solid foundation for Aristotles science. With that said, Aristotle brings us somewhat closer to an empirical science than his predecessors.

# Emergence of inductive experimental method

## Ibn al-Haytham
During the Middle Ages (or Islamic Golden Age), early Islamic philosophy developed and was often pivotal in scientific debates. Muslim scientists used experiment and quantification to distinguish between competing scientific theories, set within a generially empirical orientation.
The prominent Iraqi Arab Muslim scientist Ibn al-Haytham (Alhacen) used experiment to obtain the results in his Book of Optics (1021).
In particular, he combined observations, experiments and rational arguments to support his intromission theory of vision, where rays of light are emitted from objects rather than from the eyes. He used similar arguments to show that the ancient emission theory of vision supported by Ptolemy and Euclid (where the eyes emit rays of light), and the ancient intromission theory supported by Aristotle (where objects emit physical particles to the eyes), were both wrong. 
Ibn al-Haytham's scientific method was similar to the modern scientific method and consisted of the following procedures:
- Explicit statement of a problem, tied to observation and to proof by experiment
- Testing and/or criticism of a hypothesis using experimentation
- Interpretation of data and formulation of a conclusion using mathematics
- The publication of the findings

## Robert Grosseteste
During the European Renaissance of the 12th century, ideas on scientific methodology, including those of Aristotle's empiricism and especially Alhacen's experimental scientific method, were introduced to medieval Europe through Latin translations of Arabic and Greek texts and commentaries. Robert Grosseteste's commentary on the Posterior Analytics places Grosseteste among the first scholastic thinkers in Europe to fully understand Aristotle's vision of the dual path of scientific reasoning. Concluding from particular observations into a universal law, and then back again: from universal laws to prediction of particulars. Grosseteste called this "resolution and composition". Further, Grosseteste said that both paths should be verified through experimentation in order to verify the principals.

## Roger Bacon
Roger Bacon was inspired by the writings of Grosseteste who had built upon Aristotle's portrait of induction and pioneered the experimental scientific method. In his enunciation of a method, Bacon described a repeating cycle of observation, hypothesis, experimentation, and the need for independent verification. He recorded the manner in which he conducted his experiments in precise detail so that others could reproduce and independently test his results.
Sometime about 1256 he joined the Franciscan Order and became subect to the Franciscan statute forbidding Friars from publishing books or pamphlets without specific approval.  After the accession of Pope Clement IV in 1265, the Pope granted Bacon a special commission to write to him on scientific matters.  In eighteen months he completed three large treatises, the Opus Majus, Opus Minus, and Opus Tertium which he sent to the Pope. William Whewell has called Opus Majus at once the Encyclopaedia and Organon of the thirteenth century.
- Part I (pp. 1-22) treats of the four causes of error: authority, custom, the opinion of the unskilled many, and the concealment of real ignorance with the pretence of knowledge.
- Part VI (pp. 445-477) treats of experimental science, domina omnium scientiarum. There are two methods of knowledge: the one by argument, the other by experience. Mere argument is never sufficient; it may decide a question, but gives no satisfaction or certainty to the mind, which can only be convinced by immediate inspection or intuition. Now this is what experience gives.
- Experimental science, which in the Opus Tertium (p. 46) is distinguished from the speculative sciences and the operative arts, is said to have three great prerogatives over all sciences:
It verifies their conclusions by direct experiment;
It discovers truths which they could never reach;
It investigates the secrets of nature, and opens to us a knowledge of past and future.
- It verifies their conclusions by direct experiment;
- It discovers truths which they could never reach;
- It investigates the secrets of nature, and opens to us a knowledge of past and future.
- Roger Bacon then illustrates his method by an investigation into the nature and cause of the rainbow, as a specimen of inductive research.

# Early modern methodologists
Despite being initially seen as a possible threat to Christian orthodoxy, Aristotles ideas became a framework for critical debate beginning with absorption of the Aristotelian texts into the university curriculum in the first half of the thirteenth century.  Contributing to this was the success of medieval theologians in reconciling Aristotelian philosophy with Christian theology. Within the sciences, medieval philosophers were not afraid of disagreeing with Aristotle on many specific issues, although their disagreements were stated within the language of Aristotelian philosophy. All medieval natural philosophers were Aristotelians, but "Aristotelianism" had become a somewhat broad and flexible concept.  With the end of Middle Ages, the Renaissance rejection of medieval traditions coupled with an extreme reverence for classical sources led to a recovery of other ancient philosophical traditions, especially the teachings of Plato.  By the seventeenth century, those who clung dogmatically to Aristotle's teachings were faced with several competing approaches to nature.
Francis Bacon (1561-1626) entered Trinity College, Cambridge in April, 1573, where he applied himself diligently to the several sciences as then taught, and came to the conclusion that the methods employed and the results attained were alike erroneous; he learned to despise the current Aristotelian philosophy. Philosophy must be taught its true purpose, and for this purpose a new method must be devised. With the first germs of this great conception in his mind, Bacon left the university.

## Galileo Galilei
While some authors trace the scientific method back to the Ancient Greeks and even to ancient artisans, Galileo Galilei (1564-1642) is generally given credit for being the father of the scientific method.
During the period of religious conservativism brought about by the Reformation and Counter-Reformation, Galileo Galilei unveiled his new science of motion. Neither the contents of Galileos science, nor the methods of study he selected were in keeping with Aristotelian teachings.  Whereas Aristotle thought that a science should be demonstrated from first principles, Galileo had used experiments as a research tool. Galileo nevertheless presented his treatise in the form of mathematical demonstrations without reference to experimental results. It is important to understand that this in itself was a bold and innovative step in terms of scientific method. The usefulness of mathematics in obtaining scientific results was far from obvious. This is because mathematics did not lend itself to the primary pursuit of Aristotelian science: the discovery of causes.
Whether it is because Galileo was realistic about the acceptability of presenting experimental results as evidence or because he himself had doubts about the epistemological status of experimental findings is not known. Nevertheless, it is not in his Latin treatise on motion that we find reference to experiments, but in his supplementary dialogues written in the Italian vernacular. In these dialogues experimental results are given, although Galileo may have found them inadequate for persuading his audience. Thought experiments showing logical contradictions in Aristotelian thinking, presented in the skilled rhetoric of Galileo's dialogue were further enticements for the reader.
As an example, in the dramatic dialogue entitled Third Day from his Two New Sciences, Galileo has the characters of the dialogue discuss an experiment involving two free falling objects of differing weight. An outline of the Aristotelian view is offered by the character Simplicio. For this experiment he expects that "a body which is ten times as heavy as another will move ten times as rapidly as the other". The character Salviati, representing Galileo's persona in the dialogue, replies by voicing his doubt that Aristotle ever attempted the experiment. Salviati then asks the two other characters of the dialogue to consider a thought experiment whereby two stones of differing weights are tied together before being released. Following Aristotle, Salviati reasons that "the more rapid one will be partly retarded by the slower, and the slower will be somewhat hastened by the swifter". But this leads to a contradiction, since the two stones together make a heavier object than either stone apart, the heavier object should in fact fall with a speed greater than that of either stone. From this contradiction, Salviati concludes that Aristotle must in fact be wrong and the objects will fall at the same speed regardless of their weight, a conclusion that is borne out by experiment.

## Francis Bacon's eliminative induction
If Galileo had shied away from the role of experimenter, the opposite can be said for his English contemporary Francis Bacon. Bacon attempted to describe a rational procedure for establishing causation between phenomena based on induction. It was, however, a radically different form of induction to that employed by the Aristotelians. As Bacon put it,
Bacon's method relied on experimental histories to eliminate alternative theories. In this sense it is a precursor to Popper's falsificationism. However, Bacon believed his method would produce certain knowledge rather than tentatively justify adherence to knowledge claims. Bacon explains how his method is applied in his Novum Organum (published 1620). In an example he gives on the examination of the nature of heat, Bacon creates two tables, the first of which he names "Table of Essence and Presence", enumerating the many various circumstances under which we find heat. In the other table, labelled "Table of Deviation, or of Absence in Proximity", he lists circumstances which bear resemblance to those of the first table except for the absence of heat. From an analysis of, what he calls, the natures (light emitting, heavy, colored etc.) of the items in these lists we are brought to conclusions about the form nature, or cause, of heat. Those natures which are always present in the first table, but never in the second are deemed to be the cause of heat.
The role experimentation played in this process was twofold. The most laborious job of the scientist would be to gather the facts, or 'histories', required to create the tables of presence and absence. Such histories would document a mixture of common knowledge and experimental results. Secondly, experiments of light, or, as we might say, crucial experiments would be needed to resolve any remaining ambiguities over causes.
Bacon showed an uncompromising commitment to experimentation. Despite this he did not make any great scientific discoveries during his lifetime. This may be because he was not the most able experimenter. It may also be because hypothesising plays only a small role in Bacon's method compared to modern science. Hypotheses, in Bacon's method, are supposed to emerge during the process of investigation with little room left for guess work and creativity. Neither did he attribute much importance to mathematical speculation "which ought only to give definiteness to natural philosophy, not to generate or give it birth" (Novum Organum XCVI).

## Descartes' Aristotelian ambitions
In 1619, Rene Descartes began writing his first major treatise on proper scientific and philosophical thinking, the unfinished Rules for the Direction of the Mind.  His aim was to create a complete science that he hoped would overthrow the Aristotelian system and establish himself as the sole architect of a new system of guiding principles for scientific research.
This work was continued and clarified in his 1637 treatise, Discourse on Method and in his 1641 Meditations. Descartes describes the intriguing and disciplined thought experiments he used to arrive at the idea we instantly associate with him: I think therefore I am (cogito ergo sum).
From this foundational thought, Descartes finds proof of the existence of a God who, possessing all possible perfections, will not deceive him provided he resolves " never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgment than what was presented to my mind so clearly and distinctly as to exclude all ground of methodic doubt."
This rule allowed Descartes to progress beyond his own thoughts and judge that there exist extended bodies outside of his own thoughts. Descartes published seven sets of objections to the Meditations from various sources along with his replies to them. Despite his apparent departure from the Aristotelian system, a number of his critics felt that Descartes had done little more than replace the primary premises of Aristotle with those of his own. Descartes says as much himself in a letter written in 1647 to the translator of Principles of Philosophy,
And again, some years earlier, speaking of Galileo's physics in a letter to his friend and critic Mersenne from 1638,
Descartes failed to produce scientific results comparable to those of his contemporaries, and so it is not here that we find Descartes primary contribution to science. His work in analytic geometry however, was a necessary precedent to differential calculus and instrumental in bringing mathematical analysis to bear on scientific matters.

## Newton's rules of reasoning
Both Bacon and Descartes wanted to provide a firm foundation for scientific thought that avoided the deceptions of the mind and senses. Bacon envisaged that foundation as essentially empirical, whereas Descartes' provides a metaphysical foundation for knowledge.  If there were any doubts about the direction in which scientific method would develop, they were set to rest by the success of Isaac Newton. Implicitly rejecting Descartes' emphasis on rationalism in favor of Bacon's empirical approach, he outlines his four "rules of reasoning" in the Principia,
- We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.
- Therefore to the same natural effects we must, as far as possible, assign the same causes.
- The qualities of bodies, which admit neither intension nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.
- In experimental philosophy we are to look upon propositions collected by general induction from phnomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phnomena occur, by which they may either be made more accurate, or liable to exceptions.
But Newton also left an admonition about a theory of everything:
Newton's work became a model that other sciences sought to emulate, and his inductive approach formed the basis for much of natural philosophy through the 18th and early nineteenth centuries.  His methods of reasoning were later systematized by Mill's Methods (or Mill's canon), which are five explicit statements of what can be discarded and what can be kept while building a hypothesis. George Boole and William Stanley Jevons also wrote on the principles of reasoning.

# Integrating deductive and inductive method
Attempts to systematize a scientific method were confronted in the mid-18th century by the problem of induction, a positivist logic formulation which, in short, asserts that nothing can be known with certainty except what is actually observed.  David Hume took empiricism to the  skeptical extreme; among his positions was that there is no logical necessity that the future should resemble the past, thus we are unable to justify inductive reasoning itself by appealing to its past success. Hume's arguments, of course, came on the heels of many, many centuries of excessive speculation upon excessive speculation not grounded in empirical observation and testing.  Many of Hume's radically skeptical arguments were argued against, but not resolutely refuted, by  Immanuel Kant's Critique of Pure Reason in the late 18th century, Hume's brilliantly formatted arguments continue to hold a strong lingering influence and certainly on the consciousness of the educated classes for the better part of the 19th century when the argument at the time became the focus on whether or not the inductive method was valid.
Hans Christian rsted, (rsted is the Danish spelling; Oersted in other languages) (1777-1851) was heavily influenced by Kant, in particular, Kant's Metaphysische Anfangsgrunde der Naturwissenschaft (Metaphysical Foundations of Natural Science). The following sections on rsted encapsulate our current, common view of scientific method. His work appeared in Danish, most accessibly in public lectures, which he translated into German, French, English, and occasionally  Latin. But some of his views go beyond Kant:
rsted's "First Introduction to General Physics" (1811) exemplified the steps of observation, hypothesis, deduction and experiment.  In 1805, based on his researches on electromagnetism rsted came to believe that electricity is propagated by undulatory action (i.e., fluctuation). By 1820, he felt confident enough in his beliefs that he resolved to demonstrate them in a public lecture, and in fact observed a small magnetic effect from a galvanic circuit (i.e., voltaic circuit), without rehearsal;
William Whewell (1794-1866) regarded his History of the Inductive Sciences, from the Earliest to the Present Time (1837) to be an introduction to the Philosophy of the Inductive Sciences (1840) which analyzes the method exemplified in the formation of ideas. Whewell attempts to follow Bacon's plan for discovery of an effectual art of discovery. He named the hypothetico-deductive method (which Encyclopdia Britannica credits to Newton); Whewell also coined the term scientist. Whewell examines ideas and attempts to construct science by uniting ideas to facts. He analyses induction into three steps:
- the selection of the fundamental idea, such as space, number, cause, or likeness
- a more special modification of those ideas, such as a circle, a uniform force, etc.
- the determination of magnitudes
Upon these follow special techniques applicable for quantity, such as the method of least squares, curves, means, and special methods depending on resemblance (such as search), the method of gradation, and the method of natural classification (such as cladistics).
But no art of discovery, such as Bacon anticipated, follows, for "invention, sagacity, genius" are needed at every step.
John Stuart Mill (18061873) was stimulated to publish A System of Logic (1843) upon reading Whewell's History of the Inductive Sciences. Mill may be regarded as the final exponent of the empirical school of philosophy begun by John Locke, whose fundamental characteristic is the duty incumbent upon all thinkers to investigate for themselves rather than to accept the authority of others. Knowledge must be based on experience.
William Stanley Jevons' The Principles of Science: a treatise on logic and scientific method (1873, 1877) Chapter XII "The Inductive or Inverse Method", Summary of the Theory of Inductive Inference, states "Thus there are but three steps in the process of induction :-
- Framing some hypothesis as to the character of the general law.
- Deducing some consequences of that law.
- Observing whether the consequences agree with the particular tasks under consideration."
Jevons then frames those steps in terms of probability, which he then applied to economic laws. Ernest Nagel notes that Jevons and Whewell were not the first writers to argue for the centrality of the hypothetico-deductive method in the logic of science.
In the late 19th century, Charles Sanders Peirce proposed a schema that would turn out to have considerable influence in the further development of scientific method generally.  Peirce's work quickly accelerated the progress on several fronts. Firstly, speaking in broader context in "How to Make Our Ideas Clear" (1878), Peirce outlined an objectively verifiable method to test the truth of putative knowledge on a way that goes beyond mere foundational alternatives, focusing upon both Deduction and Induction.  He thus placed induction and deduction in a complimentary rather than competitive context (the latter of which had been the primary trend at least since David Hume a century before).  Secondly, and of more direct importance to scientific method, Peirce put forth the basic schema for hypothesis-testing that continues to prevail today.  Extracting the theory of inquiry from its raw materials in classical logic, he refined it in parallel with the early development of symbolic logic to address the then-current problems in scientific reasoning. Peirce examined and articulated the three fundamental modes of reasoning that play a role in scientific inquiry today, the processes that are currently known as abductive, deductive, and inductive inference.  Thirdly, he played a major role in the progress of symbolic logic itself  indeed this was his primary specialty.

## Popper and Kuhn
Karl Popper (1902-1994) is generally credited with providing a context for major improvements in scientific method in the mid-to-late 20th century.  In 1934 Popper published The Logic of Scientific Discovery which repudiated the classical observationalist-inductivist account of scientific method 
and advanced empirical falsifiability as the criterion for distinguishing scientific theory from non-science. According to Popper, scientific theory should make predictions (preferably predictions 
that are not made by a competing theory) which can be tested and the theory rejected if these predictions are shown not to be correct. Following Peirce and others, he argued that science would best progress using deductive reasoning as its primary emphasis, known as critical rationalism.  His astute formulations of logical procedure helped to reign in the excessive use of inductive speculation upon inductive speculation, and also helped to strengthen the conceptual foundation for today's peer review procedures.
Critics of Popper, chiefly Thomas Kuhn, Paul Feyerabend and Imre Lakatos, rejected the idea that there exists a single method that applies to all science and could account for its progress. In 1962 Kuhn published the influential book The Structure of Scientific Revolutions which suggested that scientists worked in a series of paradigms, and argued that there was little evidence of scientists actually following a falsificationist methodology. As Kuhn put it "a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it."
Most scientists would agree that there is no single "scientific method".  There remain, nonetheless, certain core principles that are the foundation of scientific inquiry today. (see also: Scientific Method)

# Mention of the topic
The Eleventh Edition of Encyclopdia Britannica did not include an article on scientific method; the  Thirteenth Edition listed scientific management, but not method. By the Fifteenth Edition, a 1-inch article in the Micropdia of  Britannica was part of the 1975 printing, while a fuller treatment (extending across multiple articles, and accessible mostly via the index volumes of Britannica) was available in later printings.

# Current issues
In the past few centuries, some statistical methods have been developed, for reasoning in the face of uncertainty, as an outgrowth of methods for eliminating error. This was an echo of the program of Francis Bacon's Novum Organum. Bayesian inference acknowledges one's ability to alter one's beliefs in the face of evidence. This has been called belief revision, or defeasible reasoning: the models in play during the phases of scientific method can be reviewed, revisited and revised, in the light of further evidence. This arose from the work of Frank P. Ramsey, John Maynard Keynes, and earlier, William Stanley Jevons' work in economics.
Later in the 20th century, methodological naturalism came to be accepted as central to the scientific method, partly in response to rise of creation science.

# Science and pseudoscience
The question of how science operates and therefore how to distinguish genuine science from pseudoscience has importance well beyond scientific circles or the academic community. In the judicial system and in public policy controversies, for example, a study's deviation from accepted scientific practice is grounds for rejecting it as junk science or pseudoscience. However, the high public perception of science means that pseuodoscience is widespread. An advertisement in which an actor wears a white coat and product ingredients are given Greek or Latin sounding names is intended to give the impression of scientific endorsement. Richard Feynman has likened pseudoscience to cargo cults in which many of the external forms are followed, but the underlying basis is missing. Fringe or alternative theories often present themselves with a pseudoscientific appearance.