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Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering observable, empirical and measurable evidence subject to specific principles of reasoning.^[1] A scientific method consists of the collection of data through observation and experimentation, and the formulation and testing of hypotheses.^[2]

Although procedures vary from one field of inquiry to another, identifiable features distinguish scientific inquiry from other methodologies of knowledge. Scientific researchers propose hypotheses as explanations of phenomena, and design experimental studies to test these hypotheses. These steps must be repeatable in order to dependably predict any future results. Theories that encompass wider domains of inquiry may bind many independently-derived hypotheses together in a coherent, supportive structure. This in turn may help form new hypotheses or place groups of hypotheses into context.

Among other facets shared by the various fields of inquiry is the conviction that the process be objective to reduce biased interpretations of the results. Another basic expectation is to document, archive and share all data and methodology so they are available for careful scrutiny by other scientists, thereby allowing other researchers the opportunity to verify results by attempting to reproduce them. This practice, called full disclosure, also allows statistical measures of the reliability of these data to be established.

Introduction to scientific method

Ibn al-Haytham (Alhazen), 965–1039, Basra.

Since Ibn al-Haytham (Alhazen, 965–1039), one of the key figures in the development of scientific method, the emphasis has been on seeking truth:

Truth is sought for its own sake. And those who are engaged upon the quest for anything for its own sake are not interested in other things. Finding the truth is difficult, and the road to it is rough.^[3]

How does light travel through transparent bodies? Light travels through transparent bodies in straight lines only.... We have explained this exhaustively in our Book of Optics. But let us now mention something to prove this convincingly: the fact that light travels in straight lines is clearly observed in the lights which enter into dark rooms through holes.... [T]he entering light will be clearly observable in the dust which fills the air.^[4]

"Light travels through transparent bodies in straight lines only" — Alhazen in Book of Optics (1021).

The conjecture that "light travels through transparent bodies in straight lines only" was corroborated by Alhazen only after years of effort. His demonstration of the conjecture was to place a straight stick or a taut thread next to the light beam,^[5] to prove that light travels in a straight line.

Scientific methodology has been practiced in some form for at least one thousand years. There are difficulties in a formulaic statement of method, however. As William Whewell (1794–1866) noted in his History of Inductive Science (1837) and in Philosophy of Inductive Science (1840), "invention, sagacity, genius" are required at every step in scientific method. It is not enough to base scientific method on experience alone^[6]; multiple steps are needed in scientific method, ranging from our experience to our imagination, back and forth.

In the twentieth century, a hypothetico-deductive model for scientific method was formulated (for a more formal discussion, see below):

1. Use your experience: Consider the problem and try to make sense of it. Look for previous explanations. If this is a new problem to you, then move to step 2.

2. Form a conjecture: When nothing else is yet known, try to state an explanation, to someone else, or to your notebook.

3. Deduce a prediction from that explanation: If you assume 2 is true, what consequences follow?

4. Test: Look for the opposite of each consequence in order to disprove 2. It is a logical error to seek 3 directly as proof of 2. This error is called affirming the consequent.^[7]

This model underlies the scientific revolution. One thousand years ago, Alhazen demonstrated the importance of steps 1 and 4. Galileo (1638) also showed the importance of step 4 (also called Experiment) in Two New Sciences. One possible sequence in this model would be 1, 2, 3, 4. If the outcome of 4 holds, and 3 is not yet disproven, you may continue with 3, 4, 1, and so forth; but if the outcome of 4 shows 3 to be false, you will have go back to 2 and try to invent a new 2, deduce a new 3, look for 4, and so forth.

Note that this method can never absolutely verify (prove the truth of) 2. It can only falsify 2.^[8] (This is what Einstein meant when he said "No amount of experimentation can ever prove me right; a single experiment can prove me wrong."^[9]) However, as pointed out by Carl Hempel (1905-1997) this simple Popperian view of scientific method is incomplete; the formulation of the conjecture might itself be the result of inductive reasoning. Thus the likelihood of the prior observation being true is statistical in nature ^[10] and would strictly require a Bayesian analysis. To overcome this uncertainty, experimental scientists must formulate a crucial experiment, in order for it to corroborate a more likely hypothesis.

In the twentieth century, Ludwik Fleck (1896–1961) and others found that we need to consider our experiences more carefully, because our experience may be biased, and that we need to be more exact when describing our experiences.^[11] These considerations are discussed below.

DNA example

The Keystones of Science project, sponsored by the journal Science, has selected a number of scientific articles from that journal and annotated them, illustrating how different parts of each article embody scientific method. Here is an annotated example of this scientific method example titled Microbial Genes in the Human Genome: Lateral Transfer or Gene Loss?.

Four basic elements of scientific method are illustrated below, by example from the discovery of the structure of DNA:

• DNA-characterizations: in this case, although the significance of the gene had been established, the mechanism was unclear to anyone, as of 1950.
• DNA-hypotheses: Crick and Watson hypothesized that the gene had a physical basis - it was helical.^[12]
• DNA-predictions: from earlier work on tobacco mosaic virus,^[13] Watson was aware of the significance of Crick's formulation of the transform of a helix.^[14] Thus he was primed for the significance of the X-shape in photo 51.
• DNA-experiments: Watson sees photo 51.^[15]

The examples are continued in "Evaluations and iterations" with DNA-iterations.^[16]

Truth and belief

Flying horse depiction: disproven; see below.

Belief can alter observations; those with a particular belief will often see things as reinforcing their belief, even if to another observer they would appear not to do so. Even researchers admit that the first observation may have been a little imprecise, whereas the second and third were "adjusted to the facts," until tradition, education, and familiarity produce a readiness for new perception. ^[17]

Eadweard Muybridge's studies of a horse galloping

Needham's Science and Civilization in China uses the 'flying horse' image as an example of observation: in it, the legs of a galloping horse are depicted as splayed, when the stop-action pictures of a horse's gallop by Eadweard Muybridge shows otherwise. Note that at the moment that no hoof is touching the ground, the horse's legs are gathered together and are not splayed, in a gallop. Earlier paintings depict the incorrect flying horse observation (this is an example of observer bias).

This demonstrates Ludwik Fleck's caution that people observe what they expect to observe, until shown otherwise; our beliefs will affect our observations (and therefore our subsequent actions). The purpose of a scientific method is to test a hypothesis, a proposed explanation about how things are, via repeatable experimental observations which can definitively contradict the hypothesis.

Elements of scientific method

There are different ways of outlining the basic method used for scientific inquiry. The scientific community and philosophers of science generally agree on the following classification of method components. These methodological elements and organization of procedures tend to be more characteristic of natural sciences than social sciences. Nonetheless, the cycle of formulating hypotheses, testing and analyzing the results, and formulating new hypotheses, will resemble the cycle described below. This is also the expected format and outline of a scientific report:

Each element of a scientific method is subject to peer review for possible mistakes. These activities do not describe all that scientists do (see below) but apply mostly to experimental sciences (e.g., physics, chemistry). The elements above are often taught in the educational system.^[31]

Scientific method is not a recipe: it requires intelligence, imagination, and creativity.^[32] It is also an ongoing cycle, constantly developing more useful, accurate and comprehensive models and methods. For example, when Einstein developed the Special and General Theories of Relativity, he did not in any way refute or discount Newton's Principia. On the contrary, if the astronomically large, the vanishingly small, and the extremely fast are reduced out from Einstein's theories — all phenomena that Newton could not have observed — Newton's equations remain. Einstein's theories are expansions and refinements of Newton's theories and, thus, increase our confidence in Newton's work.

A linearized, pragmatic scheme of the four points above is sometimes offered as a guideline for proceeding:^[33]

The iterative cycle inherent in this step-by-step methodology goes from point 3 to 6 back to 3 again.

While this schema outlines a typical hypothesis/testing method,^[34] it should also be noted that a number of philosophers, historians and sociologists of science (perhaps most notably Paul Feyerabend) claim that such descriptions of scientific method have little relation to the ways science is actually practiced.

The "operational" paradigm combines the concepts of operational definition, instrumentalism, and utility:

Characterizations

Scientific method depends upon increasingly more sophisticated characterizations of the subjects of investigation. (The subjects can also be called unsolved problems or the unknowns.) For example, Benjamin Franklin correctly characterized St. Elmo's fire as electrical in nature, but it has taken a long series of experiments and theory to establish this. While seeking the pertinent properties of the subjects, this careful thought may also entail some definitions and observations; the observations often demand careful measurements and/or counting.

The systematic, careful collection of measurements or counts of relevant quantities is often the critical difference between pseudo-sciences, such as alchemy, and a science, such as chemistry or biology. Scientific measurements taken are usually tabulated, graphed, or mapped, and statistical manipulations, such as correlation and regression, performed on them. The measurements might be made in a controlled setting, such as a laboratory, or made on more or less inaccessible or unmanipulatable objects such as stars or human populations. The measurements often require specialized scientific instruments such as thermometers, spectroscopes, or voltmeters, and the progress of a scientific field is usually intimately tied to their invention and development.

Uncertainty

Measurements in scientific work are also usually accompanied by estimates of their uncertainty. The uncertainty is often estimated by making repeated measurements of the desired quantity. Uncertainties may also be calculated by consideration of the uncertainties of the individual underlying quantities that are used. Counts of things, such as the number of people in a nation at a particular time, may also have an uncertainty due to limitations of the method used. Counts may only represent a sample of desired quantities, with an uncertainty that depends upon the sampling method used and the number of samples taken.

Definition

Measurements demand the use of operational definitions of relevant quantities. That is, a scientific quantity is described or defined by how it is measured, as opposed to some more vague, inexact or "idealized" definition. For example, electrical current, measured in amperes, may be operationally defined in terms of the mass of silver deposited in a certain time on an electrode in an electrochemical device that is described in some detail. The operational definition of a thing often relies on comparisons with standards: the operational definition of "mass" ultimately relies on the use of an artifact, such as a certain kilogram of platinum-iridium kept in a laboratory in France.

The scientific definition of a term sometimes differs substantially from its natural language usage. For example, mass and weight overlap in meaning in common discourse, but have distinct meanings in mechanics. Scientific quantities are often characterized by their units of measure which can later be described in terms of conventional physical units when communicating the work.

New theories sometimes arise upon realizing that certain terms had not previously been sufficiently clearly defined. For example, Albert Einstein's first paper on relativity begins by defining simultaneity and the means for determining length. These ideas were skipped over by Isaac Newton with, "I do not define time, space, place and motion, as being well known to all." Einstein's paper then demonstrates that they (viz., absolute time and length independent of motion) were approximations. Francis Crick cautions us that when characterizing a subject, however, it can be premature to define something when it remains ill-understood.^[37] In Crick's study of consciousness, he actually found it easier to study awareness in the visual system, rather than to study free will, for example. His cautionary example was the gene; the gene was much more poorly understood before Watson and Crick's pioneering discovery of the structure of DNA; it would have been counterproductive to spend much time on the definition of the gene, before them.

Example of characterizations

DNA-characterizations

The history of the discovery of the structure of DNA is a classic example of the elements of scientific method: in 1950 it was known that genetic inheritance had a mathematical description, starting with the studies of Gregor Mendel. But the mechanism of the gene was unclear. Researchers in Bragg's laboratory at Cambridge University made X-ray diffraction pictures of various molecules, starting with crystals of salt, and proceeding to more complicated substances. Using clues which were painstakingly assembled over the course of decades, beginning with its chemical composition, it was determined that it should be possible to characterize the physical structure of DNA, and the X-ray images would be the vehicle. ..2. DNA-hypotheses

Precession of Mercury

Precession of the perihelion (exaggerated)

The characterization element can require extended and extensive study, even centuries. It took thousands of years of measurements, from the Chaldean, Indian, Persian, Greek, Arabic and European astronomers, to record the motion of planet Earth. Newton was able to condense these measurements into consequences of his laws of motion. But the perihelion of the planet Mercury's orbit exhibits a precession that is not fully explained by Newton's laws of motion. The observed difference for Mercury's precession between Newtonian theory and relativistic theory (approximately 43 arc-seconds per century), was one of the things that occurred to Einstein as a possible early test of his theory of General Relativity.

Hypothesis development

A hypothesis is a suggested explanation of a phenomenon, or alternately a reasoned proposal suggesting a possible correlation between or among a set of phenomena.

Normally hypotheses have the form of a mathematical model. Sometimes, but not always, they can also be formulated as existential statements, stating that some particular instance of the phenomenon being studied has some characteristic and causal explanations, which have the general form of universal statements, stating that every instance of the phenomenon has a particular characteristic.

Scientists are free to use whatever resources they have — their own creativity, ideas from other fields, induction, Bayesian inference, and so on — to imagine possible explanations for a phenomenon under study. Charles Sanders Peirce, borrowing a page from Aristotle (Prior Analytics, 2.25) described the incipient stages of inquiry, instigated by the "irritation of doubt" to venture a plausible guess, as abductive reasoning. The history of science is filled with stories of scientists claiming a "flash of inspiration", or a hunch, which then motivated them to look for evidence to support or refute their idea. Michael Polanyi made such creativity the centerpiece of his discussion of methodology.

William Glen observes that

the success of a hypothesis, or its service to science, lies not simply in its perceived "truth", or power to displace, subsume or reduce a predecessor idea, but perhaps more in its ability to stimulate the research that will illuminate … bald suppositions and areas of vagueness.^[38]

In general scientists tend to look for theories that are "elegant" or "beautiful". In contrast to the usual English use of these terms, they here refer to a theory in accordance with the known facts, which is nevertheless relatively simple and easy to handle. Occam's Razor serves as a rule of thumb for making these determinations.

DNA-hypotheses

Linus Pauling proposed that DNA might be a triple helix.^[39] This hypothesis was also considered by Francis Crick and James Watson but discarded. When Watson and Crick learned of Pauling's hypothesis, they understood from existing data that Pauling was wrong^[40] and that Pauling would soon admit his difficulties with that structure. So, the race was on to figure out the correct structure (except that Pauling did not realize at the time that he was in a race—see section on "DNA-predictions" below)

Predictions from the hypothesis

Any useful hypothesis will enable predictions, by reasoning including deductive reasoning. It might predict the outcome of an experiment in a laboratory setting or the observation of a phenomenon in nature. The prediction can also be statistical and only talk about probabilities.

It is essential that the outcome be currently unknown. Only in this case does the eventuation increase the probability that the hypothesis be true. If the outcome is already known, it's called a consequence and should have already been considered while formulating the hypothesis.

If the predictions are not accessible by observation or experience, the hypothesis is not yet useful for the method, and must wait for others who might come afterward, and perhaps rekindle its line of reasoning. For example, a new technology or theory might make the necessary experiments feasible.

DNA-predictions

James Watson, Francis Crick, and others hypothesized that DNA had a helical structure. This implied that DNA's X-ray diffraction pattern would be 'x shaped'.^[41][42] This prediction followed from the work of Cochran, Crick and Vand^[14] (and independently by Stokes). The Cochran-Crick-Vand-Stokes theorem provided a mathematical explanation for the empirical observation that diffraction from helical structures produces x shaped patterns.

Also in their first paper, Watson and Crick predicted that the double helix structure provided a simple mechanism for DNA replication, writing "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material". ..4. DNA-experiments

General relativity

Einstein's prediction (1907): Light bends in a gravitational field

Einstein's theory of General Relativity makes several specific predictions about the observable structure of space-time, such as a prediction that light bends in a gravitational field and that the amount of bending depends in a precise way on the strength of that gravitational field. Arthur Eddington's observations made during a 1919 solar eclipse supported General Relativity rather than Newtonian gravitation.

Experiments

Once predictions are made, they can be tested by experiments. If test results contradict predictions, then the hypotheses are called into question and explanations may be sought. Sometimes experiments are conducted incorrectly and are at fault. If the results confirm the predictions, then the hypotheses are considered likely to be correct but might still be wrong and are subject to further testing. The experimental control is a technique for dealing with observational error. This technique uses the contrast between multiple samples (or observations) under differing conditions, to see what varies or what remains the same. We vary the conditions for each measurement, to help isolate what has changed. Mill's canons can then help us figure out what the important factor is. Factor analysis is one technique for discovering the important factor in an effect.

Depending on the predictions, the experiments can have different shapes. It could be a classical experiment in a laboratory setting, a double-blind study or an archaeological excavation. Even taking a plane from New York to Paris is an experiment which tests the aerodynamical hypotheses used for constructing the plane.

Scientists assume an attitude of openness and accountability on the part of those conducting an experiment. Detailed record keeping is essential, to aid in recording and reporting on the experimental results, and providing evidence of the effectiveness and integrity of the procedure. They will also assist in reproducing the experimental results. Traces of this tradition can be seen in the work of Hipparchus (190-120 BCE), when determining a value for the precession of the Earth, while controlled experiments can be seen in the works of Muslim scientists such as Geber (721-815 CE), al-Battani (853–929) and Alhacen (965-1039).

DNA-experiments

Watson and Crick showed an initial (and incorrect) proposal for the structure of DNA to a team from Kings College - Rosalind Franklin, Maurice Wilkins, and Raymond Gosling. Franklin immediately spotted the flaws which concerned the water content. Later Watson saw Franklin's detailed X-ray diffraction images which showed an X-shape and confirmed that the structure was helical.^[15][43] This rekindled Watson and Crick's model building and led to the correct structure. ..1. DNA-characterizations

Evaluation and improvement

The scientific process is iterative. At any stage it is possible that some consideration will lead the scientist to repeat an earlier part of the process. Failure to develop an interesting hypothesis may lead a scientist to re-define the subject they are considering. Failure of a hypothesis to produce interesting and testable predictions may lead to reconsideration of the hypothesis or of the definition of the subject. Failure of the experiment to produce interesting results may lead the scientist to reconsidering the experimental method, the hypothesis or the definition of the subject.

Other scientists may start their own research and enter the process at any stage. They might adopt the characterization and formulate their own hypothesis, or they might adopt the hypothesis and deduce their own predictions. Often the experiment is not done by the person who made the prediction and the characterization is based on experiments done by someone else. Published results of experiments can also serve as a hypothesis predicting their own reproducibility.

DNA-iterations

After considerable fruitless experimentation, being discouraged by their superior from continuing, and numerous false starts, Watson and Crick were able to infer the essential structure of DNA by concrete modeling of the physical shapes of the nucleotides which comprise it.^[16][44] They were guided by the bond lengths which had been deduced by Linus Pauling and by Rosalind Franklin's X-ray diffraction images. ..DNA Example

Confirmation

Science is a social enterprise, and scientific work tends to be accepted by the community when it has been confirmed. Crucially, experimental and theoretical results must be reproduced by others within the science community. Researchers have given their lives for this vision; Georg Wilhelm Richmann was killed by ball lightning (1753) when attempting to replicate the 1752 kite-flying experiment of Benjamin Franklin.^[45]

To protect against bad science and fraudulent data, government research granting agencies like NSF and science journals like Nature and Science have a policy that researchers must archive their data and methods so other researchers can access it, test the data and methods and build on the research that has gone before. Scientific data archiving can be done at a number of national archives in the U.S. or in the World Data Center.

Models of scientific inquiry

Classical model

The classical model of scientific inquiry derives from Aristotle^[46], who distinguished the forms of approximate and exact reasoning, set out the threefold scheme of abductive, deductive, and inductive inference, and also treated the compound forms such as reasoning by analogy.

Pragmatic model

Charles Sanders Peirce (1839-1914) considered scientific inquiry to be a species of the genus inquiry, which he defined as any means of fixing belief, that is, any means of arriving at a settled opinion on a matter in serious question. He observed that inquiry in general begins with a state of uncertainty and struggles toward a state of certainty sufficient at least to terminate the inquiry for the time being. In 1877^[47], he outlined four methods for the settlement of doubt, graded by their success in achieving a sound fixation of belief:

1. The method of tenacity (persistence in that which one is inclined to think) — which leads to irreconcilable disagreements.
2. The method of authority — which overcomes disagreements but sometimes brutally.
3. The method of congruity or the a priori or the dilettante or "what is agreeable to reason" — which promotes conformity less brutally but leads to sterile argumentation and, like the others, gets finally nowhere.
4. The scientific method — the method wherein inquiry regards itself as fallible and actually tests itself and criticizes, corrects, and improves itself.

Peirce held that slow and stumbling ratiocination can be dangerously inferior to instinct, sentiment, and tradition in practical matters, and that the scientific method is best suited to theoretical research,^[48] which in turn should not be trammeled by the other methods and practical ends; reason's "first rule" is that, in order to learn, one must desire to learn and, as a corollary, must not block the way of inquiry.^[49] What recommends the scientific method of inquiry above all others is that it is deliberately designed to arrive, eventually, at the most secure beliefs, upon which the most successful actions can eventually be based.^[50]

In Peirce's view, the conception of inquiry depends on, but also informs, the conceptions of truth and the real; to reason is to presuppose (and at least to hope), as a principle of the reasoner's self-regulation, that the truth is discoverable and independent of our vagaries of opinion. He defined truth as the correspondence of a sign (in particular, a proposition) to its object and, pragmatically, not as any actual consensus of any finite community (i.e., such that to inquire would be to poll the experts), but instead as that ideal final opinion which all reasonable scientific intelligences would reach sooner or later but still inevitably if they were to push investigation far enough^[51]. In tandem he defined the real as a true sign's object (be that object a possibility or quality, or an actuality or brute fact, or a necessity or norm or law), which is what it is independently of any finite community's opinion and, pragmatically, has dependence only on the ideal final opinion. That is an opinion as far or near as the truth itself to you or me or any finite community of minds. Thus his theory of inquiry boils down to "do the science." At the same time those conceptions of truth and the real involve the idea of a community, both without definite limits and capable of definite increase of knowledge.^[52] As inference, "logic is rooted in the social principle".^[53]

Paying special attention to the generation of explanations, Peirce outlined scientific method as a collaboration of kinds of inference in a purposeful cycle aimed at settling doubts, as follows^[54]:

1. Abduction (or retroduction). Guessing, inference to the best explanation, generation of explanatory hypothesis. From abduction, Peirce distinguishes induction as inferring, on the basis of tests, the proportion of truth in the hypothesis. Every inquiry, whether into ideas, brute facts, or norms and laws, arises as a result of surprising observations in the given realm or realms (for example at any stage of an inquiry already underway) and the pondering of the phenomenon in all its aspects in the attempt to resolve the wonder. All explanatory content of theories is reached by way of abduction, the most insecure among modes of inference. One can hope to discover only that which time would reveal sooner or later anyway, so the point is to expedite it, for which the economics of research demands and even governs the inferential "leap" of abduction^[55], whose modicum of success depends on one's being somehow attuned to nature by instincts developed and likely inborn. Abduction has general justification inductively in that it works often enough and that nothing else works^[56], at least not quickly enough when science is already properly rather slow, the work of indefinitely many generations. Peirce calls his pragmatism "the logic of abduction"^[57]. His Pragmatic Maxim is: "Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object"^[51]. His pragmatism is a method of sorting out conceptual confusions by equating the meaning of any concept with the conceivable practical consequences of whatever it is which the concept portrays. It is a method of experimentational mental reflection arriving at conceptions in terms of conceivable confirmatory and disconfirmatory circumstances — a method hospitable to the generation of explanatory hypotheses, and conducive to the employment and improvement of verification to test the truth of putative knowledge. Given abduction's dependence on instinctive attunement to nature and its aim to economize inquiry, its explanatory hypotheses should have a simplicity optimal in terms of the "facile and natural" (for which Peirce cites Galileo and which Peirce distinguishes from "logical simplicity"). Given abduction's insecurity, it should imply consequences with conceivable practical bearing leading at least to mental tests, and, in science, lending themselves to scientific testing.

2. Deduction. Analysis of hypothesis and deduction of its consequences in order to test the hypothesis. Two stages:

i. Explication. Logical analysis of the hypothesis in order to render it as distinct as possible.

ii. Demonstration (or deductive argumentation). Deduction of hypothesis's consequence. Corollarial or, if needed, Theorematic.

3. Induction. The long-run validity of the rule of induction is deducible from the principle (presuppositional to reasoning in general^[51]) that the real is only the object of the final opinion to which adequate investigation would lead^[58] In other words, if there were something to which an inductive process involving ongoing tests or observations would never lead, then that thing would not be real. Three stages:

i. Classification. Classing objects of experience under general ideas.

ii. Probation (or direct Inductive Argumentation): Crude (the enumeration of instances) or Gradual (new estimate of proportion of truth in the hypothesis after each test). Gradual Induction is Qualitative or Quantitative; if Quantitative, then dependent on measurements, or on statistics, or on countings.

iii. Sentential Induction. "...which, by Inductive reasonings, appraises the different Probations singly, then their combinations, then makes self-appraisal of these very appraisals themselves, and passes final judgment on the whole result"^[54].

Computational approaches

Many subspecialties of applied logic and computer science, such as artificial intelligence, machine learning, computational learning theory, inferential statistics, and knowledge representation, are concerned with setting out computational, logical, and statistical frameworks for the various types of inference involved in scientific inquiry. In particular, they contribute hypothesis formation, logical deduction, and empirical testing. Some of these applications draw on measures of complexity from algorithmic information theory to guide the making of predictions from prior distributions of experience, for example, see the complexity measure called the speed prior from which a computable strategy for optimal inductive reasoning can be derived.

Communication, community, culture

Frequently a scientific method is employed not only by a single person, but also by several people cooperating directly or indirectly. Such cooperation can be regarded as one of the defining elements of a scientific community. Various techniques have been developed to ensure the integrity of that scientific method within such an environment.

Peer review evaluation

Scientific journals use a process of peer review, in which scientists' manuscripts are submitted by editors of scientific journals to (usually one to three) fellow (usually anonymous) scientists familiar with the field for evaluation. The referees may or may not recommend publication, publication with suggested modifications, or, sometimes, publication in another journal. This serves to keep the scientific literature free of unscientific or crackpot work, helps to cut down on obvious errors, and generally otherwise improve the quality of the scientific literature.

Documentation and replication

Sometimes experimenters may make systematic errors during their experiments, unconsciously veer from a scientific method (Pathological science) for various reasons, or, in rare cases, deliberately falsify their results. Consequently, it is a common practice for other scientists to attempt to repeat the experiments in order to duplicate the results, thus further validating the hypothesis.

Archiving

As a result, researchers are expected to practice scientific data archiving in compliance with the policies of government funding agencies and scientific journals. Detailed records of their experimental procedures, raw data, statistical analyses and source code are preserved in order to provide evidence of the effectiveness and integrity of the procedure and assist in reproduction. These procedural records may also assist in the conception of new experiments to test the hypothesis, and may prove useful to engineers who might examine the potential practical applications of a discovery.

Data sharing

When additional information is needed before a study can be reproduced, the author of the study is expected to provide it promptly - although a small charge may apply. If the author refuses to share data, appeals can be made to the journal editors who published the study or to the institution which funded the research.

Limitations

Note that it is not possible for a scientist to record everything that took place in an experiment. He must select the facts he believes to be relevant to the experiment and report them. This may lead, unavoidably, to problems later if some supposedly irrelevant feature is questioned. For example, Heinrich Hertz did not report the size of the room used to test Maxwell's equations, which later turned out to account for a small deviation in the results. The problem is that parts of the theory itself need to be assumed in order to select and report the experimental conditions. The observations are hence sometimes described as being 'theory-laden'.

Dimensions of practice

The primary constraints on contemporary western science are:

• Publication, i.e. Peer review
• Resources (mostly funding)

It has not always been like this: in the old days of the "gentleman scientist" funding (and to a lesser extent publication) were far weaker constraints.

Both of these constraints indirectly bring in a scientific method — work that too obviously violates the constraints will be difficult to publish and difficult to get funded. Journals do not require submitted papers to conform to anything more specific than "good scientific practice" and this is mostly enforced by peer review. Originality, importance and interest are more important - see for example the author guidelines for Nature.

Criticisms (see Critical theory) of these restraints are that they are so nebulous in definition (e.g. "good scientific practice") and open to ideological, or even political, manipulation apart from a rigorous practice of a scientific method, that they often serve to censor rather than promote scientific discovery.^{[citation needed]} Apparent censorship through refusal to publish ideas unpopular with mainstream scientists (unpopular because of ideological reasons and/or because they seem to contradict long held scientific theories) has soured the popular perception of scientists as being neutral or seekers of truth and often denigrated popular perception of science as a whole.

Philosophy and sociology of science

Philosophy of science looks at the underpinning logic of the scientific method, at what separates science from non-science, and the ethic that is implicit in science. There are basic assumptions derived from philosophy that form the base of the scientific method - namely, that reality is objective and consistent, that humans have the capacity to perceive reality accurately, and that rational explanations exist for elements of the real world. These assumptions from methodological naturalism form the basis on which science is grounded. Logical Positivist, empiricist, falsificationist, and other theories have claimed to give a definitive account of the logic of science, but each has in turn been criticized.

Thomas Samuel Kuhn examined the history of science in his The Structure of Scientific Revolutions, and found that the actual method used by scientists differed dramatically from the then-espoused method. His observations of science practice are essentially sociological and do not speak to how science is or can be practiced in other times and other cultures.

Imre Lakatos and Thomas Kuhn have done extensive work on the "theory laden" character of observation. Kuhn (1961) said the scientist generally has a theory in mind before designing and undertaking experiments so as to make empirical observations, and that the "route from theory to measurement can almost never be traveled backward". This implies that the way in which theory is tested is dictated by the nature of the theory itself, which led Kuhn (1961, p. 166) to argue that "once it has been adopted by a profession ... no theory is recognized to be testable by any quantitative tests that it has not already passed".

Paul Feyerabend similarly examined the history of science, and was led to deny that science is genuinely a methodological process. In his book Against Method he argues that scientific progress is not the result of applying any particular method. In essence, he says that "anything goes", by which he meant that for any specific methodology or norm of science, successful science has been done in violation of it. Criticisms such as his led to the strong programme, a radical approach to the sociology of science.

In his 1958 book, Personal Knowledge, chemist and philosopher Michael Polanyi (1891-1976) criticized the common view that the scientific method is purely objective and generates objective knowledge. Polanyi cast this view as a misunderstanding of the scientific method and of the nature of scientific inquiry, generally. He argued that scientists do and must follow personal passions in appraising facts and in determining which scientific questions to investigate. He concluded that a structure of liberty is essential for the advancement of science - that the freedom to pursue science for its own sake is a prerequisite for the production of knowledge through peer review and the scientific method.

The postmodernist critiques of science have themselves been the subject of intense controversy. This ongoing debate, known as the science wars, is the result of conflicting values and assumptions between the postmodernist and realist camps. Whereas postmodernists assert that scientific knowledge is simply another discourse (note that this term has special meaning in this context) and not representative of any form of fundamental truth, realists in the scientific community maintain that scientific knowledge does reveal real and fundamental truths about reality. Many books have been written by scientists which take on this problem and challenge the assertions of the postmodernists while defending science as a legitimate method of deriving truth.^[59]

History

The development of the scientific method is inseparable from the history of science itself. Ancient Egyptian documents describe empirical methods in astronomy,^[60] mathematics,^[61] and medicine.^[62] The Greeks observed and then described the method of empiricism used by the Egyptians thousands of years before them.^[63][64] The first experimental scientific method was developed by Muslim scientists, who introduced the use of experimentation and quantification to distinguish between competing scientific theories set within a generally empirical orientation, which emerged with Alhazen's optical experiments in his Book of Optics (1021).^[65][66] The modern scientific method crystallized no later than in the 17th and 18th centuries. In his work Novum Organum (1620) — a reference to Aristotle's Organon — Francis Bacon outlined a new system of logic to improve upon the old philosophical process of syllogism. Then, in 1637, René Descartes established the framework for a scientific method's guiding principles in his treatise, Discourse on Method. The writings of Alhazen, Bacon and Descartes are considered critical in the historical development of the modern scientific method, as are those of John Stuart Mill.^[67]

In the late 19th century, Charles Sanders Peirce proposed a schema that would turn out to have considerable influence in the development of current scientific method generally. Peirce 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 complementary rather than competitive context (the latter of which had been the primary trend at least since David Hume, who wrote in the mid-to-late 18th century). Secondly, and of more direct importance to modern 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, as discussed above in this article, play a role in 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.

Karl Popper denied the existence of evidence^[68] and of scientific method.^[69] Popper holds that there is only one universal method, the negative method of trial and error. It covers not only all products of the human mind, including science, mathematics, philosophy, art and so on, but also the evolution of life. Beginning in the 1930s and with increased vigor after World War II, he argued that a hypothesis must be falsifiable and, following Peirce and others, that science would best progress using deductive reasoning as its primary emphasis, known as critical rationalism. ^[70] His formulations of logical procedure helped to rein in excessive use of inductive speculation upon inductive speculation, and also strengthened the conceptual foundation for today's peer review procedures.

Relationship with mathematics

Science is the process of gathering, comparing, and evaluating proposed models against observables. A model can be a simulation, mathematical or chemical formula, or set of proposed steps. Science is like mathematics in that researchers in both disciplines can clearly distinguish what is known from what is unknown at each stage of discovery. Models, in both science and mathematics, need to be internally consistent and also ought to be falsifiable (capable of disproof). In mathematics, a statement need not yet be proven; at such a stage, that statement would be called a conjecture. But when a statement has attained mathematical proof, that statement gains a kind of immortality which is highly prized by mathematicians, and for which some mathematicians devote their lives^[71].

Mathematical work and scientific work can inspire each other^[72]. For example, the technical concept of time arose in science, and timelessness was a hallmark of a mathematical topic. But today, the Poincaré conjecture has been proven using time as a mathematical concept in which objects can flow (see Ricci flow).

Nevertheless, the connection between mathematics and reality (and so science to the extent it describes reality) remains obscure. Eugene Wigner's paper, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, is a very well-known account of the issue from a Nobel Prize physicist. In fact, some observers (including some well known mathematicians such as Gregory Chaitin, and others such as Lakoff and Nunez) have suggested that mathematics is the result of practitioner bias and human limitation (including cultural ones), somewhat like the post-modernist view of science.

George Pólya's work on problem solving^[73], the construction of mathematical proofs, and heuristic^[74][75] show that mathematical method and scientific method differ in detail, while nevertheless resembling each other in using iterative or recursive steps.

In Pólya's view, understanding involves restating unfamiliar definitions in your own words, resorting to geometrical figures, and questioning what we know and do not know already; analysis, which Pólya takes from Pappus^[76], involves free and heuristic construction of plausible arguments, working backward from the goal, and devising a plan for constructing the proof; synthesis is the strict Euclidean exposition of step-by-step details^[77] of the proof; review involves reconsidering and re-examining the result and the path taken to it.

Gauss, when asked how he came about his theorems, once replied

• durch planmässiges Tattonieren (through systematic palpable experimentation). —Carl Friedrich Gauss^[78]

See also

Problems and issues

History, philosophy, sociology

Notes and references

Further reading

External links

Wikibooks has a book on the topic of The Scientific Method

• An Introduction to Science: Scientific Thinking and a scientific method by Steven D. Schafersman.
• Introduction to a scientific method
• Theory-ladenness by Paul Newall at The Galilean Library
• Lecture on Scientific Method by Greg Anderson
• Using the scientific method for designing science fair projects
• SCIENTIFIC METHODS an online book by Richard D. Jarrard