The scientific method is an empirical method for acquiring knowledge through careful observation, rigorous skepticism, hypothesis testing, and experimental validation. Developed from ancient and medieval practices, it acknowledges that cognitive assumptions can distort the interpretation of the observation. The scientific method has characterized science since at least the 17th century. Scientific inquiry includes creating a testable hypothesis through inductive reasoning, testing it through experiments and statistical analysis, and adjusting or discarding the hypothesis based on the results. Although procedures vary across fields, the underlying process is often similar. In more detail: the scientific method involves making conjectures (hypothetical explanations), predicting the logical consequences of hypothesis, then carrying out experiments or empirical observations based on those predictions. A hypothesis is a conjecture based on knowledge obtained while seeking answers to the question. Hypotheses can be very specific or broad but must be falsifiable, implying that it is possible to identify a possible outcome of an experiment or observation that conflicts with predictions deduced from the hypothesis; otherwise, the hypothesis cannot be meaningfully tested. While the scientific method is often presented as a fixed sequence of steps, it actually represents a set of general principles. Not all steps take place in every scientific inquiry (nor to the same degree), and they are not always in the same order. Numerous discoveries have not followed the textbook model of the scientific method, and, in some cases, chance has played a role.
History
The history of the scientific method is different from the history of science itself. The development of rules for scientific reasoning has not been straightforward; the scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the primacy of various approaches to establishing scientific knowledge. Different early expressions of empiricism and the scientific method can be found throughout history, for instance with the ancient Stoics, Aristotle, Epicurus, Alhazen, Avicenna, Al-Biruni, Roger Bacon, and William of Ockham. In the Scientific Revolution of the 16th and 17th centuries, some of the most important developments were the furthering of empiricism by Francis Bacon and Robert Hooke, the rationalist approach described by René Descartes, and inductivism, which was further brought to particular prominence by scientists such as Isaac Newton and those who followed him. Newton postulated four principles which form the basis of modern science, and refined the scientific method. Experiments were advocated by Francis Bacon and performed by Giambattista della Porta, Johannes Kepler, and Galileo Galilei. There was particular development aided by theoretical works by the skeptic Francisco Sanches, by idealists as well as empiricists John Locke, George Berkeley, and David Hume. C. S. Peirce formulated the hypothetico-deductive model in the 20th century, and the model has undergone significant revision since. The term scientific method emerged in the 19th century, as a result of significant institutional development of science, and terminologies establishing clear boundaries between science and non-science, such as scientist and pseudoscience. Throughout the 1830s and 1850s, when Baconianism was popular, naturalists like William Whewell, John Herschel, and John Stuart Mill engaged in debates over "induction" and "facts," and were focused on how to generate knowledge. In the late 19th and early 20th centuries, a debate over realism vs. antirealism was conducted as powerful scientific theories extended beyond the realm of the observable.
Modern use and critical thought The term scientific method came into popular use in the twentieth century; Dewey's 1910 book, How We Think, inspired popular guidelines. It appeared in dictionaries and science textbooks, although there was little consensus on its meaning. Although there was growth through the middle of the twentieth century, by the 1960s and 1970s numerous influential philosophers of science such as Thomas Kuhn and Paul Feyerabend had questioned the universality of the "scientific method", and largely replaced the notion of science as a homogeneous and universal method with that of it being a heterogeneous and local practice. In particular, Paul Feyerabend, in the 1975 first edition of his book Against Method, argued against there being any universal rules of science; Karl Popper, and Gauch 2003, disagreed with Feyerabend's claim. Later stances include physicist Lee Smolin's 2013 essay "There Is No Scientific Method", in which he espouses two ethical principles, and historian of science Daniel Thurs' chapter in the 2015 book Newton's Apple and Other Myths about Science, which concluded that the scientific method is a myth or, at best, an idealization. As myths are beliefs, they are subject to the narrative fallacy, as pointed out by Taleb. Philosophers Robert Nola and Howard Sankey, in their 2007 book Theories of Scientific Method, said that debates over the scientific method continue, and argued that Feyerabend, despite the title of Against Method, accepted certain rules of method and attempted to justify those rules with a meta methodology. Staddon (2017) argues it is a mistake to try following rules in the absence of an algorithmic scientific method; in that case, "science is best understood through examples". But algorithmic methods, such as disproof of existing theory by experiment have been used since Alhacen (1027) and his Book of Optics, and Galileo (1638) and his Two New Sciences, and The Assayer, which still stand as scientific method.
Elements of inquiry
Overview
The scientific method is the process by which science is carried out. As in other areas of inquiry, science (through the scientific method) can build on previous knowledge, and unify understanding of its studied topics over time. Historically, the development of the scientific method was critical to the Scientific Revolution. The overall process involves making conjectures (hypotheses), predicting their logical consequences, then carrying out experiments based on those predictions to determine whether the original conjecture was correct. However, there are difficulties in a formulaic statement of method. The scientific method represents general principles rather than a fixed sequence, not all steps occur in every inquiry, nor always in the same order. It requires intelligence, imagination, and creativity rather than rigid adherence to procedure.
Factors of scientific inquiry 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 experimental 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.The scientific method is an iterative, cyclical process through which information is continually revised. It is generally recognized to develop advances in knowledge through the following elements, in varying combinations or contributions:
Characterizations (observations, definitions, and measurements of the subject of inquiry) Hypotheses (theoretical, hypothetical explanations of observations and measurements of the subject) Predictions (inductive and deductive reasoning from the hypothesis or theory) Experiments (tests of all of the above) Each element of the scientific method is subject to peer review for possible mistakes. These activities do not describe all that scientists do but apply mostly to experimental sciences (e.g., physics, chemistry, biology, and psychology). The elements above are often taught in the educational system as "the scientific method". The scientific method is not a single recipe: it requires intelligence, imagination, and creativity. In this sense, it is not a mindless set of standards and procedures to follow but is rather 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 massive, the feather-light, and the extremely fast are removed from Einstein's theories – all phenomena Newton could not have observed – Newton's equations are what remain. Einstein's theories are expansions and refinements of Newton's theories and, thus, increase confidence in Newton's work. An iterative, pragmatic scheme of the four points above is sometimes offered as a guideline for proceeding:
Define a question Gather information and resources (observe) Form an explanatory hypothesis Test the hypothesis by performing an experiment and collecting data in a reproducible manner Analyze the data Interpret the data and draw conclusions that serve as a starting point for a new hypothesis Publish results Retest (frequently done by other scientists) The iterative cycle inherent in this step-by-step method goes from point 3 to 6 and back to 3 again. While this schema outlines a typical hypothesis/testing method, many philosophers, historians, and sociologists of science, including Paul Feyerabend, claim that such descriptions of scientific method have little relation to the ways that science is actually practiced.
Characterizations The basic elements of the scientific method are illustrated by the following example (which occurred from 1944 to 1953) from the discovery of the structure of DNA (marked with and indented).
In 1950, it was known that genetic inheritance had a mathematical description, starting with the studies of Gregor Mendel, and that DNA contained genetic information (Oswald Avery's transforming principle). But the mechanism of storing genetic information (i.e., genes) in DNA 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 painstakingly assembled over 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. The scientific method depends upon increasingly sophisticated characterizations of the subjects of investigation. (The subjects can also be called unsolved problems or the unknowns.) For example, Benjamin Franklin conjectured, correctly, that St. Elmo's fire was electrical in nature, but it has taken a long series of experiments and theoretical changes to establish this. While seeking the pertinent properties of the subjects, careful thought may also entail some definitions and observations; these observations often demand careful measurements and/or counting that can take the form of expansive empirical research. A scientific question can refer to the explanation of a specific observation, as in "Why is the sky blue?" but can also be open-ended, as in "How can I design a drug to cure this particular disease?" This stage frequently involves finding and evaluating evidence from previous experiments, personal scientific observations or assertions, as well as the work of other scientists. If the answer is already known, a different question that builds on the evidence can be posed. When applying the scientific method to research, determining a good question can be very difficult and it will affect the outcome of the investigation. The systematic, careful collection of measurements or counts of relevant quantities is often the critical difference between pseudo-sciences, such as alchemy, and science, such as chemistry or biology. Scientific measurements 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, particle accelerators, or voltmeters, and the progress of a scientific field is usually intimately tied to their invention and improvement.
I am not accustomed to saying anything with certainty after only one or two observations.
Definition 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 are sometimes developed after realizing certain terms have 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. 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.
Hypothesis development
Linus Pauling proposed that DNA might be a triple helix. This hypothesis was also considered by Francis Crick and James D. Watson but discarded. When Watson and Crick learned of Pauling's hypothesis, they understood from existing data that Pauling was wrong. and that Pauling would soon admit his difficulties with that structure. 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, inductive reasoning, Bayesian inference, and so on – to imagine possible explanations for a phenomenon under study. Albert Einstein once observed that "there is no logical bridge between phenomena and their theoretical principles." 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. In general, scientists tend to look for theories that are "elegant" or "beautiful". Scientists often use these terms to refer to a theory that is following the known facts but is nevertheless relatively simple and easy to handle. Occam's Razor serves as a rule of thumb for choosing the most desirable amongst a group of equally explanatory hypotheses. To minimize the confirmation bias that results from entertaining a single hypothesis, strong inference emphasizes the need for entertaining multiple alternative hypotheses, and avoiding artifacts.
Predictions from the hypothesis James D. 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'. This prediction followed from the work of Cochran, Crick and Vand (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. In their first paper, Watson and Crick also noted that the double helix structure they proposed 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".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 deal only with probabilities. It is essential that the outcome of testing such a prediction be currently unknown. Only in this case does a successful outcome increase the probability that the hypothesis is true. If the outcome is already known, it is 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 testable and so will remain to that extent unscientific in a strict sense. A new technology or theory might make the necessary experiments feasible. For example, while a hypothesis on the existence of other intelligent species may be convincing with scientifically based speculation, no known experiment can test this hypothesis. Therefore, science itself can have little to say about the possibility. In the future, a new technique may allow for an experimental test and the speculation would then become part of accepted science. For example, Einstein's theory of general relativity makes several specific predictions about the observable structure of spacetime, such as 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
Watson and Crick showed an initial (and incorrect) proposal for the structure of DNA to a team from King's College London – Rosalind Franklin, Maurice Wilkins, and Raymond Gosling. Franklin immediately spotted the flaws which concerned the water content. Later Watson saw Franklin's photo 51, a detailed X-ray diffraction image, which showed an X-shape and was able to confirm the structure was helical. Once predictions are made, they can be sought by experiments. If the test results contradict the predictions, the hypotheses which entailed them are called into question and become less tenable. Sometimes the experiments are conducted incorrectly or are not very well designed when compared to a crucial experiment. If the experimental results confirm the predictions, then the hypotheses are considered more likely to be correct, but might still be wrong and continue to be 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, or populations, under differing conditions, to see what varies or what remains the same. We vary the conditions for the acts of 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 that tests the aerodynamical hypotheses used for constructing the plane. These institutions thereby reduce the research function to a cost/benefit, which is expressed as money, and the time and attention of the researchers to be expended, in exchange for a report to their constituents. Current large instruments, such as CERN's Large Hadron Collider (LHC), or LIGO, or the National Ignition Facility (NIF), or the International Space Station (ISS), or the James Webb Space Telescope (JWST), entail expected costs of billions of dollars, and timeframes extending over decades. These kinds of institutions affect public policy, on a national or even international basis, and the researchers would require shared access to such machines and their adjunct infrastructure. Scientists assume an attitude of openness and accountability on the part of those experimenting. Detailed record-keeping is essential, to aid in recording and reporting on the experimental results, and supports the effectiveness and integrity of the procedure. They will also assist in reproducing the experimental results, likely by others. Traces of this approach 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 al-Battani (853–929 CE) and Alhazen (965–1039 CE).
Communication and iteration
Watson and Crick then produced their model, using this information along with the previously known information about DNA's composition, especially Chargaff's rules of base pairing. 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.
The scientific method is iterative. At any stage, it is possible to refine its accuracy and precision, so 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 under consideration. 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 an experiment to produce interesting results may lead a scientist to reconsider the experimental method, the hypothesis, or the definition of the subject. This manner of iteration can span decades and sometimes centuries. Published papers can be built upon. For example: By 1027, Alhazen, based on his measurements of the refraction of light, was able to deduce that outer space was less dense than air, that is: "the body of the heavens is rarer than the body of air". In 1079 Ibn Mu'adh's Treatise On Twilight was able to infer that Earth's atmosphere was 50 miles thick, based on atmospheric refraction of the sun's rays. This is why the scientific method is often represented as circular – new information leads to new characterisations, and the cycle of science continues. Measurements collected can be archived, passed onwards and used by others. 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.
Confirmation
Science is a social enterprise, and scientific work tends to be accepted by the scientific community when it has been confirmed. Crucially, experimental and theoretical results must be reproduced by others within the scientific 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. If an experiment cannot be repeated to produce the same results, this implies that the original results might have been in error. As a result, it is common for a single experiment to be performed multiple times, especially when there are uncontrolled variables or other indications of experimental error. For significant or surprising results, other scientists may also attempt to replicate the results for themselves, especially if those results would be important to their own work. Replication has become a contentious issue in social and biomedical science where treatments are administered to groups of individuals. Typically an experimental group gets the treatment, such as a drug, and the control group gets a placebo. John Ioannidis in 2005 pointed out that the method being used has led to many findings that cannot be replicated. Peer review—anonymous expert evaluation of research—assesses experimental soundness rather than certifying correctness. Some journals request that the experimenter provide lists of possible peer reviewers, especially if the field is highly specialized. Specialists review methodology and design; if approved (sometimes requiring additional experiments), the prestige of the journal where the work is published indicates perceived quality. Scientists typically are careful in recording their data, a requirement promoted by Ludwik Fleck (1896–1961) and others. Though not typically required, they might be requested to supply this data to other scientists who wish to replicate their original results (or parts of their original results), extending to the sharing of any experimental samples that may be difficult to obtain. To protect against bad science and fraudulent data, government research-granting agencies such as the National Science Foundation, and science journals, including Nature and Science, have a policy that researchers must archive their data and methods so that other researchers can test the data and methods and build on the research that has gone before. Scientific data archiving can be done at several national archives in the U.S. or the World Data Center.
Foundational principles
Honesty, openness, and falsifiability
The unfettered principles of science are to strive for accuracy and the creed of honesty; openness already being a matter of degrees. Openness is restricted by the general rigour of scepticism. And of course the matter of non-science. Smolin, in 2013, espoused ethical principles rather than giving any potentially limited definition of the rules of inquiry. His ideas stand in the context of the scale of data–driven and big science, which has seen increased importance of honesty and consequently reproducibility. His thought is that science is a community effort by those who have accreditation and are working within the community. He also warns against overzealous parsimony. Popper previously took ethical principles even further, going as far as to ascribe value to theories only if they were falsifiable. Popper used the falsifiability criterion to demarcate a scientific theory from a theory like astrology: both "explain" observations, but the scientific theory takes the risk of making predictions that decide whether it is right or wrong:
"Those among us who are unwilling to expose their ideas to the hazard of refutation do not take part in the game of science."
Theory's interactions with observation Science has limits. Those limits are usually deemed to be answers to questions that aren't in science's domain, such as faith. Science has other limits as well, as it seeks to make true statements about reality. The nature of truth and the discussion on how scientific statements relate to reality is best left to the article on the philosophy of science here. More immediately topical limitations show themselves in the observation of reality.
It is the natural limitations of scientific inquiry that there is no pure observation as theory is required to interpret empirical data, and observation is therefore influenced by the observer's conceptual framework. As science is an unfinished project, this does lead to difficulties. Namely, that false conclusions are drawn, because of limited information. An example here are the experiments of Kepler and Brahe, used by Hanson to illustrate the concept. Despite observing the same sunrise the two scientists came to different conclusions—their intersubjectivity leading to differing conclusions. Johannes Kepler used Tycho Brahe's method of observation, which was to project the image of the Sun on a piece of paper through a pinhole aperture, instead of looking directly at the Sun. He disagreed with Brahe's conclusion that total eclipses of the Sun were impossible because, contrary to Brahe, he knew that there were historical accounts of total eclipses. Instead, he deduced that the images taken would become more accurate, the larger the aperture—this fact is now fundamental for optical system design. Another historic example here is the discovery of Neptune, credited as being found via mathematics because previous observers didn't know what they were looking at.
Empiricism, rationalism, and more pragmatic views Scientific endeavour can be characterised as the pursuit of truths about the natural world or as the elimination of doubt about the same. The former is the direct construction of explanations from empirical data and logic, the latter the reduction of potential explanations. It was established above how the interpretation of empirical data is theory-laden, so neither approach is trivial. The ubiquitous element in the scientific method is empiricism, which holds that knowledge is created by a process involving observation; scientific theories generalize observations. This is in opposition to stringent forms of rationalism, which holds that knowledge is created by the human intellect; later clarified by Popper to be built on prior theory. The scientific method embodies the position that reason alone cannot solve a particular scientific problem; it unequivocally refutes claims that revelation, political or religious dogma, appeals to tradition, commonly held beliefs, common sense, or currently held theories pose the only possible means of demonstrating truth. In 1877, C. S. Peirce characterized inquiry in general not as the pursuit of truth per se but as the struggle to move from irritating, inhibitory doubts born of surprises, disagreements, and the like, and to reach a secure belief, the belief being that on which one is prepared to act. His pragmatic views framed scientific inquiry as part of a broader spectrum and as spurred, like inquiry generally, by actual doubt, not mere verbal or "hyperbolic doubt", which he held to be fruitless. This "hyperbolic doubt" Peirce argues against here is of course just another name for Cartesian doubt associated with René Descartes. It is a methodological route to certain knowledge by identifying what can't be doubted. A strong formulation of the scientific method is not always aligned with a form of empiricism in which the empirical data is put forward in the form of experience or other abstracted forms of knowledge as in current scientific practice the use of scientific modelling and reliance on abstract typologies and theories is normally accepted. In 2010, Hawking suggested that physics' models of reality should simply be accepted where they prove to make useful predictions. He calls the concept model-dependent realism.
Rationality The following section will first explore beliefs and biases, and then get to the rational reasoning most associated with the sciences.
Beliefs and biases
Scientific methodology often directs that hypotheses be tested in controlled conditions wherever possible. This is frequently possible in certain areas, such as in the biological sciences, and more difficult in other areas, such as in astronomy. The practice of experimental control and reproducibility can have the effect of diminishing the potentially harmful effects of circumstance, and to a degree, personal bias. For example, pre-existing beliefs can alter the interpretation of results, as in confirmation bias; this is a heuristic that leads a person with a particular belief to see things as reinforcing their belief, even if another observer might disagree (in other words, people tend to observe what they expect to observe).
[T]he action of thought is excited by the irritation of doubt, and ceases when belief is attained. A historical example is the belief that the legs of a galloping horse are splayed at the point when none of the horse's legs touch the ground, to the point of this image being included in paintings by its supporters. However, the first stop-action pictures of a horse's gallop by Eadweard Muybridge showed this to be false, and that the legs are instead gathered together. Another important human bias that plays a role is a preference for new, surprising statements (see Appeal to novelty), which can result in a search for evidence that the new is true. Poorly attested beliefs can be believed and acted upon via a less rigorous heuristic. Goldhaber and Nieto published in 2010 the observation that if theoretical structures with "many closely neighboring subjects are described by connecting theoretical concepts, then the theoretical structure acquires a robustness which makes it increasingly hard – though certainly never impossible – to overturn". When a narrative is constructed its elements become easier to believe. Fleck (1979), p. 27 notes "Words and ideas are originally phonetic and mental equivalences of the experiences coinciding with them. ... Such proto-ideas are at first always too broad and insufficiently specialized. ... Once a structurally complete and closed system of opinions consisting of many details and relations has been formed, it offers enduring resistance to anything that contradicts it". Sometimes, these relations have their elements assumed a priori, or contain some other logical or methodological flaw in the process that ultimately produced them. Donald M. MacKay has analyzed these elements in terms of limits to the accuracy of measurement and has related them to instrumental elements in a category of measurement.
Deductive and inductive reasoning
The idea of there being two opposed justifications for truth has shown up throughout the history of scientific method as analysis versus synthesis, non-ampliative/ampliative, or even confirmation and verification. (And there are other kinds of reasoning.) One to use what is observed to build towards fundamental truths – and the other to derive from those fundamental truths more specific principles. Deductive reasoning derives specific conclusions from established general principles—if the premises are true, the conclusion must be true. Inductive reasoning builds general principles from observations—conclusions are probable but not guaranteed. Scientific inquiry employs both: induction generates hypotheses from observations; deduction predicts testable consequences. This process requires stringent scepticism regarding observed phenomena, because cognitive assumptions can distort the interpretation of initial perceptions.
An example for how inductive and deductive reasoning works can be found in the history of gravitational theory. It took thousands of years of measurements, from the Chaldean, Indian, Persian, Greek, Arabic, and European astronomers, to fully record the motion of planet Earth. Kepler(and others) were then able to build their early theories by generalizing the collected data inductively, and Newton was able to unify prior theory and measurements into the consequences of his laws of motion in 1727. Another common example of inductive reasoning is the observation of a counterexample to current theory inducing the need for new ideas. Le Verrier in 1859 pointed out problems with the perihelion of Mercury that showed Newton's theory to be at least incomplete. The observed difference of Mercury's precession between Newtonian theory and observation was one of the things that occurred to Einstein as a possible early test of his theory of relativity. His relativistic calculations matched observation much more closely than Newtonian theory did. Though, today's Standard Model of physics suggests that we still do not know at least some of the concepts surrounding Einstein's theory, it holds to this day and is being built on deductively. A theory being assumed as true and subsequently built on is a common example of deductive reasoning. Theory building on Einstein's achievement can simply state that 'we have shown that this case fulfils the conditions under which general/special relativity applies, therefore its conclusions apply also'. If it was properly shown that 'this case' fulfils the conditions, the conclusion follows. An extension of this is the assumption of a solution to an open problem. This weaker kind of deductive reasoning will get used in current research, when multiple scientists or even teams of researchers are all gradually solving specific cases in working towards proving a larger theory. This often sees hypotheses being revised again and again as new proof emerges. This way of presenting inductive and deductive reasoning shows part of why science is often presented as being a cycle of iteration. It is important to keep in mind that that cycle's foundations lie in reasoning, and not wholly in the following of procedure.
Certainty, probabilities, and statistical inference Claims of scientific truth can be opposed in three ways: by falsifying them, by questioning their certainty, or by asserting the claim itself to be incoherent. Incoherence, here, means internal errors in logic, like stating opposites to be true; falsification is what Popper would have called the honest work of conjecture and refutation — certainty, perhaps, is where difficulties in telling truths from non-truths arise most easily. Scientific measurements include uncertainty estimates, calculated through repeated measurements, error propagation from underlying quantities, or sampling limitations. uncertainty. Counts of things may represent a sample of desired quantities, with an uncertainty that depends upon the sampling method used and the number of samples taken. In the case of measurement imprecision, there will simply be a 'probable deviation' expressing itself in a study's conclusions. Statistics are different. Inductive statistical generalisation will take sample data and extrapolate more general conclusions, which has to be justified — and scrutinised. It can even be said that statistical models are only ever useful, but never a complete representation of circumstances. In statistical analysis, expected and unexpected bias is a large factor. Research questions, the collection of data, or the interpretation of re