Scientific method

## Contents

* 1 Overview
* 2 Introduction to scientific method
* 3 Truth and belief
* 4 Elements of scientific method
* 4.1 DNA example
* 4.2 Characterizations
* 4.2.1 Uncertainty
* 4.2.2 Definition
* 4.2.3 DNA-characterizations
* 4.2.4 Precession of Mercury
* 4.3 Hypothesis development
* 4.3.1 DNA-hypotheses
* 4.4 Predictions from the hypothesis
* 4.4.1 DNA-predictions
* 4.4.2 General relativity
* 4.5 Experiments
* 4.5.1 DNA-experiments
* 5 Evaluation and iteration
* 5.1 Testing and improvement
* 5.1.1 DNA-iterations
* 5.2 Confirmation
* 6 Models of scientific inquiry
* 6.1 Classical model
* 6.2 Pragmatic model
* 6.3 Computational approaches
* 7 Philosophy and sociology of science
* 8 Communication, community, culture
* 8.1 Peer review evaluation
* 8.2 Documentation and replication
* 8.2.1 Archiving
* 8.2.2 Dearchiving
* 8.2.3 Limitations
* 8.3 Dimensions of practice
* 9 History
* 10 Relationship with mathematics
* 11 Notes and references
* 12 Further reading
* 13 See also
* 13.1 Synopsis of related topics
* 13.2 Logic, mathematics, methodology
* 13.3 Problems and issues
* 13.4 History, philosophy, sociology
* 14 External links

## Overview

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Scientific method refers to the body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. It is 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 predict dependably any future results. Theories that encompass wider domains of inquiry may bind many hypotheses together in a coherent 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 must be objective to reduce a biased interpretation of the results. Another basic expectation is to document, archive and share all data and methodology so it is 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

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Ibn al-Haytham, 965–1039, Basra

From Ibn al-Haytham (Alhacen, 965–1039, a pioneer of scientific method) to the present day, 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]

Alhacen (1000): light travels in straight lines

The conjecture that "Light travels through transparent bodies in straight lines only", was corroborated by Alhacen 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 do
2. Conjecture an explanation \- when nothing else is yet known, try to state your explanation, to someone else, or to your notebook.
3. Deduce a prediction from that explanation\- if 2 were true, then state a consequence of that explanation.
4. Test  \- look for the opposite of that 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.

This model underlies the scientific revolution. One thousand years ago, Alhacen 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 2 can never be shown to be absolutely true by scientific method[7]; only that 2 can be shown to be absolutely false by scientific method. (This is what Einstein meant when he said "No amount of experimentation can ever prove me right; a single experiment can prove me wrong.")

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. These considerations are discussed below.

## Truth and belief

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Truth Belief can alter observations; those with a particular belief will often see things as reinforcing their belief, even if they do not.[8] Needham's Science and Civilization in China uses the 'flying horse' image as an example of observation: in it, a horse's legs are depicted as splayed, when the stop-action picture 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. Earlier paintings depict the incorrect flying horse observation. 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 the scientific method is to test a hypothesis, a belief about how things are, via repeatable experimental observations which can contradict the hypothesis so as to fight this observer bias.

## Elements of scientific method

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There are many ways of outlining the basic method shared by all fields of scientific inquiry. The following examples are typical classifications of the most important components of the method on which there is wide agreement in the scientific community and among philosophers of science. There are, however, disagreements about some aspects.

The following set of methodological elements and organization of procedures tends to be more characteristic of natural sciences than social sciences. In the social sciences mathematical and statistical methods of verification and hypotheses testing may be less stringent. Nonetheless the cycle of hypothesis, verification and formulation of new hypotheses will resemble the cycle described below.

The essential elements[9][10][11] of a scientific method[12] are iterations,[13] recursions,[14] interleavings, and orderings of the following:

* Characterizations (observations,[15] definitions, and measurements of the subject of inquiry)

* Hypotheses[16][17] (theoretical, hypothetical explanations of observations and measurements of the subject)[18]

* Predictions (reasoning including logical deduction[19] from the hypothesis or theory)

* Experiments[20] (tests of all of the above)

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.[21]

Scientific method is not a recipe: it requires intelligence, imagination, and creativity.[22] 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 observations that increase our confidence in them also increase our confidence in Newton's approximations to them.

A linearized, pragmatic scheme of the four points above is sometimes offered as a guideline for proceeding:[23]

1. Define the question
2. Gather information and resources (observe)
3. Form hypothesis
4. Perform experiment and collect data
5. Analyze data
6. Interpret data and draw conclusions that serve as a starting point for new hypothesis
7. Publish results
8. Retest (frequently done by other scientists)

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,[24] 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" model combines the concepts of factory-style processing, operational definition, and utility:

The essential elements of a scientific method are operations, observations, models, and a utility function for evaluating models.

* Operation \- Some action done to the system being investigated

* Observation \- What happens when the operation is done to the system

* Model \- A fact, hypothesis, theory, or the phenomenon itself at a certain moment

* Utility Function \- A measure of the usefulness of the model to explain, predict, and control, and of the cost of use of it. One of the elements of any scientific utility function is the refutability of the model. Another is its simplicity, on the Principle of Parsimony also known as Occam's Razor.

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?.

### DNA example

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Each element of scientific method is illustrated below by an 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.
* DNA-predictions: from earlier work on tobacco mosaic virus, Watson was aware of the significance of Crick's formulation of the transform of a helix.[25] Thus he was primed for the significance of the X-shape in photo 51.
* DNA-experiments: Watson sees photo 51.

The examples are continued in "Evaluations and iterations" with DNA-iterations.

### Characterizations

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Scientific method depends upon increasingly more sophisticated characterizations of subjects of the 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.

* "I am not accustomed to saying anything with certainty after only one or two observations."[26] \--Andreas Vesalius (1546)

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

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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

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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.[27] 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.

#### DNA-characterizations

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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

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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 which 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

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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.[28]

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

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Linus Pauling proposed that DNA was a triple helix. Francis Crick and James Watson learned of Pauling's hypothesis, understood from existing data that Pauling was wrong and realized that Pauling would soon realize his mistake. 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!  ..3. DNA-predictions

### Predictions from the hypothesis

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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

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When Watson and Crick hypothesized that DNA was a double helix, Francis Crick predicted that an X-ray diffraction image of DNA would show an X-shape. Also in their first paper they predicted that the double helix structure that they discovered would prove important in biology, 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

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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

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Template:Mainarticle

The control is very important. 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.

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

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Before proposing their model Watson and Crick had previously seen x-ray diffraction images by Rosalind Franklin, Maurice Wilkins, and Raymond Gosling. However, they later reported that Franklin initially rebuffed their suggestion that DNA might be a double helix. Franklin had immediately spotted flaws in the initial hypotheses about the structure of DNA by Watson and Crick. The X-shape in X-ray images helped confirm the helical structure of DNA[29].  ..1. DNA-characterizations

## Evaluation and iteration

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### Testing and improvement

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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

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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. 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

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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 lightning (1753) when attempting to replicate the 1752 kite-flying experiment of Benjamin Franklin.[30]

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

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Main article: Models of scientific inquiry

### Classical model

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The classical model of scientific inquiry derives from Aristotle[31], 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

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Main article: Pragmatic theory of truth

Charles 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 question. He observed that inquiry in general begins with a state of uncertainty and moves toward a state of certainty, sufficient at least to terminate the inquiry for the time being.

Peirce held that, in practical matters, slow and stumbling ratiocination is not generally to be automatically preferred over instinct and tradition, and held that scientific method is best suited to theoretical inquiry. What recommends the specifically scientific method of inquiry above all others is the fact that it is deliberately designed to arrive, eventually, at the ultimately most secure beliefs, upon which the most successful actions can eventually be based.[32] In 1877[33], he outlined four methods for the fixation of belief, the settlement of doubt, graded by their success in achieving a sound settlement of belief.
1\. The method of tenacity -- persisting in that which one is inclined to think.
2\. The method of authority -- conformity to a source of ready-made beliefs.
3\. The method of congruity or the a priori or the dilettante or "what is agreeable to reason" -- leading to argumentation that gets finally nowhere.
4\. The scientific method.

Peirce characterized scientific method in terms of the uses of inference, and paid special attention to the generation of explanations. As a question of presuppositions of reasoning, 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 go ask the experts for the answers), but instead as that ideal final opinion which all reasonable scientific intelligences would reach, sooner or later but still inevitably, if they pushed investigation far enough[34].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." He characterized the scientific method as follows[35]:

1\. Abduction (or retroduction). 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, 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. Induction as a process is far too slow for that job, so economy of research demands abduction, whose modicum of success depends on one's being somehow attuned to nature, by dispositions learned and, some of them, likely inborn. Abduction has general justification inductively in that it works often enough and that nothing else works, 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"[36]. 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"[34]. 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 mental processes not necessarily conscious and deliberate but, in any case, attuned to nature, and given abduction's being driven by the need to economize the inquiry process, its explanatory hypotheses should be optimally simple in the sense of "natural" (for which Peirce cites Galileo and which Peirce distinguishes from "logically simple"). Given abduction's insecurity, it should have 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[34]) that the real is only the object of the final opinion to which adequate investigation would lead[37] 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"[35].

### Computational approaches

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Many subspecialties of applied logic and computer science, to name a few, 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, 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.

## Philosophy and sociology of science

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Main article: Philosophy of science

Further information: Sociology of science

While the philosophy of science has limited direct impact on day-to-day scientific practice, it plays a vital role in justifying and defending the scientific approach. 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.

We find ourselves in a world that is not directly understandable. We find that we sometimes disagree with others as to the facts of the things we see in the world around us, and we find that there are things in the world that are at odds with our present understanding. The scientific method attempts to provide a way in which we can reach agreement and understanding. A "perfect" scientific method might work in such a way that rational application of the method would always result in agreement and understanding; a perfect method would arguably be algorithmic, and so not leave any room for rational agents to disagree. As with all philosophical topics, the search has been neither straightforward nor simple. 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.

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 and heated dialogue. This ongoing debate, known as the science wars, is the result of the conflicting values and assumptions held by the postmodernist and realist camps. Whereas postmodernists assert that scientific knowledge is simply another discourse 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.[38][39][40][41][42]

## Communication, community, culture

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Frequently the scientific method is not employed by a single person, but 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 the scientific method within such an environment.

### Peer review evaluation

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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. Work announced in the popular press before going through this process is generally frowned upon. Sometimes peer review inhibits the circulation of unorthodox work, especially if it undermines the establishment in the particular field, and at other times may be too permissive. Other drawbacks includes cronyism and favoritism. The peer review process is not always successful, but has been very widely adopted by the scientific community.

### Documentation and replication

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Sometimes experimenters may make systematic errors during their experiments, unconsciously veer from the 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

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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.

#### Dearchiving

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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 who funded the research.

#### Limitations

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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

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Further information: Rhetoric of science

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. 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.

## History

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Main article: History of scientific method

See also: Timeline of the history of scientific method

The development of the scientific method is inseparable from the history of science itself. Ancient Egyptian documents, such as early papyri, describe methods of medical diagnosis. In ancient Greek culture, the method of empiricism was described. 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 Alhacen's optical experiments in his Book of Optics (1021).[43][44] 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 Alhacen, Bacon and Descartes are considered critical in the historical development of the modern scientific method.

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) [3], 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[45] and of scientific method.[46] 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.[47]

## Relationship with mathematics

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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[48].

Mathematical work and scientific work can inspire each other[49]. For example, the concept of time arose in science, and timelessness was a hallmark of a mathematical topic. But today, the Poincaré conjecture is in the process of being proven, using time as a mathematical concept, in which objects can flow (see Ricci flow).

George Pólya's work on problem solving[50], the construction of mathematical proofs, and heuristic[51][52] show that mathematical method and scientific method differ in detail, while resembling each other in the use of iterative or recursive steps.

| Mathematical method | Scientific method

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1 | Understanding | Characterization from experience and observation
2 | Analysis | Hypothesis: a proposed explanation
3 | Synthesis | Deduction: prediction from the hypothesis
4 | Review/Extend | Test and experiment

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[53], 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[54] of the proof; review involves reconsidering and re-examining the result and the path taken to it.

## Notes and references

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1. ↑ Isaac Newton (1687, 1713, 1726). "[4] Rules for the study of natural philosophy", Philosophiae Naturalis Principia Mathematica, Third edition. The General Scholium containing the 4 rules follows Book 3, The System of the World. Reprinted on pages 794-796 of I. Bernard Cohen and Anne Whitman's 1999 translation, University of California Press ISBN 0-520-08817-4, 974 pages.
2. ↑ scientific method, Merriam-Webster Dictionary.
3. ↑ Alhazen (Ibn Al-Haytham) Critique of Ptolemy, translated by S. Pines, Actes X Congrès internationale d'histoire des sciences, Vol I Ithaca 1962, as referenced on p. 139 of Shmuel Sambursky (ed. 1974) Physical Thought from the Presocratics to the Quantum Physicists ISBN 0-87663-712-8
4. ↑ Alhazen, translated into English from German by M. Schwarz, from "Abhandlung über das Licht", J. Baarmann (ed. 1882) Zeitschrift der Deutschen Morgenländischen Gesellschaft Vol 36 as referenced on p.1 36 by Shmuel Sambursky (1974) Physical thought from the Presocratics to the Quantum Physicists ISBN 0-87663-712-8
5. ↑ p. 136, as quoted by Shmuel Sambursky (1974) Physical thought from the Presocratics to the Quantum Physicists ISBN 0-87663-712-8
6. ↑ "... the statement of a law - A depends on B - always transcends experience." p. 6 —Max Born (1949), Natural Philosophy of Cause and Chance
7. ↑ "I believe that we do not know anything for certain, but everything probably." —Christiaan Huygens, Letter to Pierre Perrault, 'Sur la préface de M. Perrault de son traité del'Origine des fontaines' [1763], Oeuvres Complétes de Christiaan Huygens (1897), Vol. 7, 298. Quoted in Jacques Roger, The Life Sciences in Eighteenth-Century French Thought, ed. Keith R. Benson and trans. Robert Ellrich (1997), 163. Quotation selected by W.F. Bynum and Roy Porter (eds., 2005), Oxford Dictionary of Scientific Quotations ISBN 0-19-858409-1 p. 317 quotation 4.
8. ↑ "Observation and experiment are subject to a very popular myth. ... The knower is seen as a ... Julius Caesar winning his battles according to ... formula. Even research workers will 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 have produced a readiness for stylized (that is directed and restricted) perception and action; until an answer becomes largely pre-formed in the question, and a decision confined merely to 'yes' or 'no' or perhaps to a numerical determination; until methods and apparatus automatically carry out the greatest part of the mental work for us." Fleck labels this thought style (Denkstil). Ludwik Fleck, p.84 of Genesis and Development of a Scientific Fact (written in German, 1935, Entstehung und Entwickelung einer wissenschaftlichen Tatsache: Einführung in die Lehre vom Denkstil und Denkkollectiv) ISBN 0-226-25325-2
9. ↑ See the hypothethico-deductive method, for example: p.236 —Peter Godfrey-Smith (2003), Theory and Reality: An introduction to the philosophy of science ISBN 0-226-30063-3
10. ↑ pp.265-6 (in the Dover edition) —William Stanley Jevons (1873), The principles of science: a treatise on logic and scientific method. ISBN 1430487755
11. ↑ pp.65,73,92,398 —Andrew J. Galambos, Sic Itur ad Astra ISBN 0-88078-004-5(AJG learned scientific method from Felix Ehrenhaft)
12. ↑ Galileo Galilei Linceo (1638), Discorsi e Dimonstrazioni Matematiche, intorno a due nuoue scienze. In Leida, Apresso gli Elsevirri M.D.C.XXXVIII. Two New Sciences was selected from the collection of the Library of Congress by Leonard C. Bruno (1988), The Landmarks of Science ISBN 0-8160-2137-6
13. ↑ Iteration example: Chaldean astronomers such as Kidinnu compiled astronomical data. Hipparchus was to use this data to calculate the precession of the Earth's axis. Fifteen hundred years after Kiddinu, Al-Batani, born in what is now Turkey, would use the collected data and improve Hipparchus' value for the precession of the Earth's axis. Al-Batani's value, 54.5 arc-seconds per year, compares well to the current value of 49.8 arc-seconds per year (26,000 years for Earth's axis to round the circle of nutation).
14. ↑ Recursion example: the Earth is itself a magnet, with its own North and South Poles William Gilbert (in Latin 1600) De Magnete, or On Magnetism and Magnetic Bodies. Translated from Latin to English, selection by Forest Ray Moulton and Justus J. Schifferes (eds., Second Edition 1960) The Autobiography of Science pp.113-117
15. ↑ "The foundation of general physics ... is experience. These ... everyday experiences we do not discover without deliberately directing our attention to them. Collecting information about these is observation." —Hans Christian Ørsted("First Introduction to General Physics" ¶13, part of a series of public lectures at the University of Copenhagen. Copenhagen 1811, in Danish, printed by Johan Frederik Schulz. In Kirstine Meyer's 1920 edition of Ørsted's works, vol.III pp. 151-190. ) "First Introduction to Physics: the Spirit, Meaning, and Goal of Natural Science". Reprinted in German in 1822, Schweigger's Journal für Chemie und Physik 36, pp.458-488. Translated to English by Karen Jelved, Andrew D. Jackson, and Ole Knudsen, (translators 1997) Selected Scientific Works of Hans Christian Ørsted, ISBN 0-691-04334-5 p. 292
16. ↑ "When it is not clear under which law of nature an effect or class of effect belongs, we try to fill this gap by means of a guess. Such guesses have been given the name conjectures or hypotheses." —Hans Christian Ørsted(1811) "First Introduction to General Physics" ¶18. Selected Scientific Works of Hans Christian Ørsted, ISBN 0-691-04334-5 p.297
17. ↑ "In general we look for a new law by the following process. First we guess it. ...", p. 156 —Richard Feynman (1965), The Character of Physical Law ISBN 0-262-56003-8
18. ↑ "... the statement of a law - A depends on B - always transcends experience." p.6 —Max Born (1949), Natural Philosophy of Cause and Chance
19. ↑ "The student of nature ... regards as his property the experiences which the mathematican can only borrow. This is why he deduces theorems directly from the nature of an effect while the mathematician only arrives at them circuitously." —Hans Christian Ørsted(1811) "First Introduction to General Physics" ¶17. Selected Scientific Works of Hans Christian Ørsted, ISBN 0-691-04334-5 p.297
20. ↑ Salviati speaks: "I greatly doubt that Aristotle ever tested by experiment whether it be true that two stones, one weighing ten times as much as the other, if allowed to fall, at the same instant, from a height of, say, 100 cubits, would so differ in speed that when the heavier had reached the ground, the other would not have fallen more than 10 cubits." p.61[1] —Galileo (1638), Two New Sciences as translated from Italian to English by Henry Crew and Alfonso di Salvio (1914). A more extended quotation is referenced on pp.80-81 by Forest Ray Moulton and Justus J. Schifferes (eds., Second Edition 1960) The Autobiography of Science
21. ↑ In the inquiry-based education paradigm, the stage of "characterization, observation, definition, …" is more briefly summed up under the rubric of a Question.
22. ↑ "To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science." p.92, Albert Einstein and Leopold Infeld (1938), The Evolution of Physics: from early concepts to relativity and quanta ISBN 0-671-20156-5
23. ↑ Crawford S, Stucki L (1990), "Peer review and the changing research record", "J Am Soc Info Science", vol. 41, pp 223-228
24. ↑ See, e.g., Gauch, Hugh G., Jr., Scientific Method in Practice (2003), esp. chapters 5-8
25. ↑ Cochran W, Crick FHC and Vand V. (1952) "The Structure of Synthetic Polypeptides. I. The Transform of Atoms on a Helix", Acta Cryst., 5, 581-586.
26. ↑ Andreas Vesalius, Epistola, Rationem, Modumque Propinandi Radicis Chynae Decocti (1546), 141. Quoted and translated in C.D. O'Malley, Andreas Vesalius of Brussels, (1964), 116. As quoted by W.F. Bynum & Roy Porter (2005), Oxford Dictionary of Scientific Quotations Andreas Vesalius, 597:1 ISBN 0-19-858409-1
27. ↑ Crick, Francis (1994), The Astonishing Hypothesis ISBN 0-684-19431-7 p.20
28. ↑ Glen,William (ed.), The Mass-Extinction Debates: How Science Works in a Crisis, Stanford University Press, Stanford, CA, 1994. ISBN 0-8047-2285-4. pp. 37-38.
29. ↑ "The instant I saw the picture my mouth fell open and my pulse began to race." -- James D. Watson (1968), The Double Helix, page 167. New York: Atheneum, Library of Congress card number 68-16217. Page 168 shows the X-shaped pattern of the B-form of DNA, clearly indicating crucial details of its helical structure to Watson and Crick.
30. ↑ See, e.g., Physics Today, Vol. 59, #1, p42. [2]
31. ↑ Aristotle, "Prior Analytics", Hugh Tredennick (trans.), pp. 181-531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
32. ↑ Peirce, C.S., "Lectures on Pragmatism", Cambridge, MA, March 26 – May 17, 1903. Reprinted in part, Collected Papers, CP 5.14–212, Eprint. Reprinted with Introduction and Commentary, Patricia Ann Turisi (ed.), Pragmatism as a Principle and a Method of Right Thinking: The 1903 Harvard "Lectures on Pragmatism", State University of New York Press, Albany, NY, 1997. Reprinted, pp. 133–241, Peirce Edition Project (eds.), The Essential Peirce, Selected Philosophical Writings, Volume 2 (1893–1913), Indiana University Press, Bloomington, IN, 1998.
33. ↑ Peirce, C.S. (1877), "The Fixation of Belief", Popular Science Monthly, vol. 12, pp. 1–15. Reprinted (Chance, Love, and Logic, pp. 7-31), (Collected Papers vol. 5, paras. 358–387), (Philosophical Writings of Peirce, pp. 5-22), (Selected Writings, pp. 91-112), (Writings of Charles S. Peirce: The Chronological Edition, vol. 3, pp. 242–257), (The Essential Peirce: Volume 1, pp. 109–123), (Peirce on Signs, pp. 144-159). Eprint. Internet Archive Popular Science Monthly 12.
34. ↑ 34.0 34.1 34.2 Peirce, C.S. (1877), "How to Make Our Ideas Clear", Popular Science Monthly, vol. 12, pp. 286–302. Reprinted (Chance, Love, and Logic, pp. 32-60), (Collected Papers, vol. 5, pp. 388–410), (Philosophical Writings of Peirce, pp. 23-41), (Selected Writings, pp. 113-136), (Writings of Charles S. Peirce: The Chronological Edition, vol. 3, pp. 257–276), (The Essential Peirce: Volume 1, pp. 124–141), (Peirce on Signs, pp. 160-179). Eprint. Arisbe Eprint. Internet Archive Popular Science Monthly 12.
35. ↑ 35.0 35.1 Peirce, C.S. (1908), "A Neglected Argument for the Reality of God", Hibbert Journal vol. 7, pp. 90-112. Reprinted (Collected Papers, vol. 6, paras. 452-485), (Selected Writings, pp. 358-379), (The Essential Peirce: Volume 2, 434-450), (Peirce on Signs, pp. 260-278). Internet Archive Hibbert Journal 7.
36. ↑ See "Pragmatism -- The Logic of Abduction", Collected Papers, vol. 5, paras. 195-205, especially para. 196. Eprint.
37. ↑ Peirce, C.S., (1878) "The Probability of Induction", Popular Science Monthly, vol. 12, pp. 705-718. Reprinted (Chance, Love, and Logic, pp. 82-105), (Collected Papers vol. 2, paras. 669-693), (Philosophical Writings of Peirce, pp. 174-189), (Writings of Charles S. Peirce: The Chronological Edition, vol. 3, pp. 290-305), (The Essential Peirce: Volume 1, pp. 155-169). Popular Science Monthly 12 Eprint at Internet Archive.
38. ↑ Higher Superstition: The Academic Left and Its Quarrels with Science, The Johns Hopkins University Press, 1997
39. ↑ Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science, Picador; 1st Picador USA Pbk. Ed edition, 1999
40. ↑ The Sokal Hoax: The Sham That Shook the Academy, University of Nebraska Press, 2000 ISBN 0803279957
41. ↑ A House Built on Sand: Exposing Postmodernist Myths About Science, Oxford University Press, 2000
42. ↑ Intellectual Impostures, Economist Books, 2003
43. ↑ Rosanna Gorini (2003), "Al-Haytham the Man of Experience, First Steps in the Science of Vision", International Society for the History of Islamic Medicine, Institute of Neurosciences, Laboratory of Psychobiology and Psychopharmacology, Rome, Italy:

> "According to the majority of the historians al-Haytham was the pioneer of the modern scientific method. With his book he changed the meaning of the term optics and established experiments as the norm of proof in the field. His investigations are based not on abstract theories, but on experimental evidences and his experiments were systematic and repeatable."

44. ↑ David Agar (2001). Arabic Studies in Physics and Astronomy During 800 - 1400 AD. University of Jyväskylä.
45. ↑ Logik der Forschung, new appendix *XIX (not yet available in the English edition Logic of scientific discovery)
46. ↑ Karl Popper: On the non-existence of scientific method. Realism and the Aim of Science (1983)
47. ↑ Karl Popper: Objective Knowledge (1972)
48. ↑ "When we are working intensively, we feel keenly the progress of our work; we are elated when our progress is rapid, we are depressed when it is slow." page 131, in the section on 'Modern heuristic'-- the mathematician George Pólya (1957), How to solve it, Second edition.
49. ↑ "Philosophy [i.e., physics] is written in this grand book--I mean the universe--which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth." —Galileo Galilei, Il Saggiatore (The Assayer, 1623) as referenced by G. Toraldo di Francia (1981), The Investigation of the Physical World ISBN 0-521-29925-X
50. ↑ George Pólya, How to Solve It
51. ↑ George Pólya, Mathematics and Plausible Reasoning Volume I: Induction and Analogy in Mathematics,
52. ↑ George Pólya, Mathematics and Plausible Reasoning Volume II: Patterns of Plausible Reasoning.
53. ↑ George Pólya (1957), How to Solve It Second edition p.142
54. ↑ George Pólya (1957), How to Solve It Second edition p.144

## Further reading

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* Bacon, Francis Novum Organum (The New Organon), 1620. Bacon's work described many of the accepted principles, underscoring the importance of theory, empirical results, data gathering, experiment, and independent corroboration.

* Bauer, Henry H., Scientific Literacy and the Myth of the Scientific Method, University of Illinois Press, Champaign, IL, 1992

* Beveridge, William I. B., The Art of Scientific Investigation, Vintage/Alfred A. Knopf, 1957.

* Bernstein, Richard J., Beyond Objectivism and Relativism: Science, Hermeneutics, and Praxis, University of Pennsylvania Press, Philadelphia, PA, 1983.

* Bozinovski, Stevo, Consequence Driven Systems: Teaching, Learning, and Self-Learning Agents, GOCMAR Publishers, Bitola, Macedonia, 1991.

* Brody, Baruch A., and Grandy, Richard E., Readings in the Philosophy of Science, 2nd edition, Prentice Hall, Englewood Cliffs, NJ, 1989.

* Burks, Arthur W., Chance, Cause, Reason — An Inquiry into the Nature of Scientific Evidence, University of Chicago Press, Chicago, IL, 1977.

* Chomsky, Noam, Reflections on Language, Pantheon Books, New York, NY, 1975.

* Dewey, John, How We Think, D.C. Heath, Lexington, MA, 1910. Reprinted, Prometheus Books, Buffalo, NY, 1991.

* Earman, John (ed.), Inference, Explanation, and Other Frustrations: Essays in the Philosophy of Science, University of California Press, Berkeley & Los Angeles, CA, 1992.

* Fraassen, Bas C. van, The Scientific Image, Oxford University Press, Oxford, UK, 1980.

* Feyerabend, Paul K., Against Method, Outline of an Anarchistic Theory of Knowledge, 1st published, 1975. Reprinted, Verso, London, UK, 1978.

* Gadamer, Hans-Georg, Reason in the Age of Science, Frederick G. Lawrence (trans.), MIT Press, Cambridge, MA, 1981.

* Giere, Ronald N. (ed.), Cognitive Models of Science, vol. 15 in 'Minnesota Studies in the Philosophy of Science', University of Minnesota Press, Minneapolis, MN, 1992.

* Hacking, Ian, Representing and Intervening, Introductory Topics in the Philosophy of Natural Science, Cambridge University Press, Cambridge, UK, 1983.

* Heisenberg, Werner, Physics and Beyond, Encounters and Conversations, A.J. Pomerans (trans.), Harper and Row, New York, NY 1971, pp. 63–64.

* Holton, Gerald, Thematic Origins of Scientific Thought, Kepler to Einstein, 1st edition 1973, revised edition, Harvard University Press, Cambridge, MA, 1988.

* Jevons, William Stanley, The Principles of Science: A Treatise on Logic and Scientific Method, 1874, 1877, 1879. Reprinted with a foreword by Ernst Nagel, Dover Publications, New York, NY, 1958.

* Kuhn, Thomas S., "The Function of Measurement in Modern Physical Science", ISIS 52(2), 161–193, 1961.

* Kuhn, Thomas S., The Structure of Scientific Revolutions, University of Chicago Press, Chicago, IL, 1962. 2nd edition 1970. 3rd edition 1996.

* Kuhn, Thomas S., The Essential Tension, Selected Studies in Scientific Tradition and Change, University of Chicago Press, Chicago, IL, 1977.

* Latour, Bruno, Science in Action, How to Follow Scientists and Engineers through Society, Harvard University Press, Cambridge, MA, 1987.

* Losee, John, A Historical Introduction to the Philosophy of Science, Oxford University Press, Oxford, UK, 1972. 2nd edition, 1980.

* Maxwell, Nicholas, The Comprehensibility of the Universe: A New Conception of Science, Oxford University Press, Oxford, 1998. Paperback 2003.

* McComas, William F., ed. Template:PDFlink, from The Nature of Science in Science Education, pp53-70, Kluwer Academic Publishers, Netherlands 1998.

* Misak, Cheryl J., Truth and the End of Inquiry, A Peircean Account of Truth, Oxford University Press, Oxford, UK, 1991.

* Newell, Allen, Unified Theories of Cognition, Harvard University Press, Cambridge, MA, 1990.

* Peirce, C.S., Essays in the Philosophy of Science, Vincent Tomas (ed.), Bobbs–Merrill, New York, NY, 1957.

* Peirce, C.S., "Lectures on Pragmatism", Cambridge, MA, March 26 – May 17, 1903. Reprinted in part, Collected Papers, CP 5.14–212. Reprinted with Introduction and Commentary, Patricia Ann Turisi (ed.), Pragmatism as a Principle and a Method of Right Thinking: The 1903 Harvard "Lectures on Pragmatism", State University of New York Press, Albany, NY, 1997. Reprinted, pp. 133–241, Peirce Edition Project (eds.), The Essential Peirce, Selected Philosophical Writings, Volume 2 (1893–1913), Indiana University Press, Bloomington, IN, 1998.

* Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1-6, Charles Hartshorne and Paul Weiss (eds.), vols. 7-8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931-1935, 1958. Cited as CP vol.para.

* Piattelli-Palmarini, Massimo (ed.), Language and Learning, The Debate between Jean Piaget and Noam Chomsky, Harvard University Press, Cambridge, MA, 1980.

* Poincaré, Henri, Science and Hypothesis, 1905, Eprint

* Popper, Karl R., The Logic of Scientific Discovery, 1934, 1959.[4]

* Popper, Karl R., Unended Quest, An Intellectual Autobiography, Open Court, La Salle, IL, 1982.

* Putnam, Hilary, Renewing Philosophy, Harvard University Press, Cambridge, MA, 1992.

* Rorty, Richard, Philosophy and the Mirror of Nature, Princeton University Press, Princeton, NJ, 1979.

* Salmon, Wesley C., Four Decades of Scientific Explanation, University of Minnesota Press, Minneapolis, MN, 1990.

* Shimony, Abner, Search for a Naturalistic World View: Vol. 1, Scientific Method and Epistemology, Vol. 2, Natural Science and Metaphysics, Cambridge University Press, Cambridge, UK, 1993.

* Thagard, Paul, Conceptual Revolutions, Princeton University Press, Princeton, NJ, 1992.

* Ziman, John (2000). Real Science: what it is, and what it means. Cambridge, Uk: Cambridge University Press.

## See also

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* Baconian method
* Empirical method

* Historical method
* Philosophical method

* Quantitative research
* Scholarly method

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### Synopsis of related topics

[edit | edit source]

* Confirmability
* Contingency
* Falsifiability
* Hypothesis
* Hypothesis testing

* Inquiry
* Reproducibility
* Research
* Statistics
* Strong inference

* Tautology
* Testability
* Theory
* Verification and Validation

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### Logic, mathematics, methodology

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* Inference
* Abductive reasoning
* Deductive reasoning
* Inductive reasoning

* Information theory
* Logic
* Mathematics
* Methodology

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### Problems and issues

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* Ockham's razor
* Poverty of the stimulus
* Reference class problem

* Underdetermination
* Holistic science
* Pseudoscience

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### History, philosophy, sociology

[edit | edit source]

* Cudos
* Epistemology
* Epistemic truth
* History of science

* History of scientific method
* Philosophy of science
* Science studies

* Social research
* Sociology of scientific knowledge
* Timeline of scientific method

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## External links

[edit | edit source]

* 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

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