Scientific method

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

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^[68][69] and was able to confirm the structure was helical.^[70][71][h]

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

These institutions thereby reduce the research function to a cost/benefit,[76] which is expressed as money, and the time and attention of the researchers to be expended,^[76] in exchange for a report to their constituents.^[77] Current large instruments, such as CERN's Large Hadron Collider (LHC),^[78] or LIGO,^[79] or the National Ignition Facility (NIF),^[80] or the International Space Station (ISS),^[81] or the James Webb Space Telescope (JWST),^[82][83] 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.^[θ][84]

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

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.

modeling of the physical shapes of the nucleotides which comprise it.^[74][91][92] 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.

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.

Elements of integrity

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.^[ε] 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 ascrible 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:^[94][95]

"Those among us who are unwilling to expose their ideas to the hazard of refutation do not take part in the game of science."

— Karl Popper, The Logic of Scientific Discovery (2002 [1935])

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).^[33]

[T]he action of thought is excited by the irritation of doubt, and ceases when belief is attained.

— 

C.S. Peirce, How to Make Our Ideas Clear (1877)^[59]

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.^[97] Poorly attested beliefs can be believed and acted upon via a less rigorous heuristic.^[98]

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".^[99] When a narrative is constructed its elements become easier to believe.^[100][34]

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.^[101]

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.^[102] 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.^[103]

The process of peer review involves the evaluation of the experiment by experts, who typically give their opinions anonymously. Some journals request that the experimenter provide lists of possible peer reviewers, especially if the field is highly specialized. Peer review does not certify the correctness of the results, only that, in the opinion of the reviewer, the experiments themselves were sound (based on the description supplied by the experimenter). If the work passes peer review, which occasionally may require new experiments requested by the reviewers, it will be published in a peer-reviewed scientific journal. The specific journal that publishes the results indicates the perceived quality of the work.^[κ]

Scientists typically are careful in recording their data, a requirement promoted by

The idea of there being two opposed justifications for truth has shown up through-out 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.^[106]

Deductive reasoning is the building of knowledge based on what has been shown to be true before. It requires the assumption of fact established prior, and, given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion. Inductive reasoning builds knowledge not from established truth, but from a body of observations. It 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.^[k] 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.^[l] 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.^[m]

Another common example of inductive reasoning is the observation of a

Deductive reasoning based on the assumption of the theory as true leading to further observations is then attributed as a prediction or test and validates the theory. Scientists, assuming the theory of relativity to be true, deductively reasoned tests of general relativity. A historic comparison here is the discovery of Neptune credited as being found via mathematics, because previous observers didn't know what they were looking at.

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.

Confirmation theory

During the course of history, one theory has succeeded another, and some have suggested further work while others have seemed content just to explain the phenomena. The reasons why one theory has replaced another are not always obvious or simple. The philosophy of science includes the question: What criteria are satisfied by a 'good' theory. This question has a long history, and many scientists, as well as philosophers, have considered it. The objective is to be able to choose one theory as preferable to another without introducing cognitive bias.^[111] Though different thinkers emphasize different aspects,^[μ] a good theory:

• is accurate (the trivial element);
• is consistent, both internally and with other relevant currently accepted theories;
• has explanatory power, meaning its consequences extend beyond the data it is required to explain;
• has unificatory power; as in it's organizing otherwise confused and isolated phenomena
• and is fruitful for further research.

In trying to look for such theories, scientists will, given a lack a guidance by empirical evidence, try to adhere to:

• parsimony in causal explanations
• and look for invariant observations.
• Scientists will sometimes also list the very subjective criteria of "formal elegance" which can indicate multiple different things.

The goal here is to make the choice between theories less arbitrary. Nonetheless, these criteria contain subjective elements, and should be considered

It also is debatable whether existing scientific theories satisfy all these criteria, which may represent goals not yet achieved. For example, explanatory power over all existing observations is satisfied by no one theory at the moment.[119]^[120]

Parsimony, elegance, and invariance

The desiderata of a "good" theory have been debated for centuries, going back perhaps even earlier than Occam's razor,^[121] which is often taken as an attribute of a good theory.

Science tries to be simple. When gathered data supports multiple explanations, the most simple explanation for phenomena or the most simple formation of a theory is recommended by the principle of parsimony.^[122] Scientists go as far as to call simple proofs of complex statements beautiful.

We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

— Isaac Newton, Philosophiæ Naturalis Principia Mathematica (1723 [3rd ed.])^[1]

Where Newton espoused parsimony in causal explanations, expressed before him in Occam's razor, others after him have expanded on science's general need to be economical.^[D] This expanded idea of not just concise theory but the way work is done stands in context with what C. S. Pierce called Musement; inquiry's phase of free-ranging thought.^[ν] As he put it: "if we truly desire the goal of the inquiry we are not to waste our resources."^[73][4]

Occam's razor might fall under the heading of "simple elegance", but it is arguable that parsimony and elegance pull in different directions. Introducing additional elements could simplify theory formulation, whereas simplifying a theory's ontology might lead to increased syntactical complexity.^[123]

Sometimes ad-hoc modifications of a failing idea may also be dismissed as lacking "formal elegance". This appeal to what may be called "aesthetic" is hard to characterise, but essentially about a sort of familiarity. Though, argument based on "elegance" is contentious and over-reliance on familiarity will breed stagnation.^[113]

The idea of good ideas being those hard-to-vary has been a theme in scientific writing since at least the early 1900s.^[λ] As David Deutsch put it in 2009: "the search for hard-to-vary explanations is the origin of all progress".^[115]

Einstein's famous thought experiment of a lab suspended in empty space is an example of a useful invariant observation. He imagined the absence of gravity and an experimenter free floating in the lab. — If now an entity pulls the lab upwards, accelerating uniformly, the experimenter would perceive the resulting force as gravity. The entity however would feel the work needed to accelerate the lab continuously. Through this experiment Einstein was able to equate gravitational and inertial mass; something unexplained by Newton's laws of motion, and an early foundation for his theory of relativity.^[o]

The feature, which suggests reality, is always some kind of invariance of a structure independent of the aspect, the projection.

— M. Born, ‘Physical Reality’ (1953), 149 — as quoted by Weinert (2004)^[114]

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.^[p] 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.

Measurements in scientific work are also usually accompanied by estimates of their

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.

In statistical analysis, expected and unexpected bias is a large factor.^[125] Research questions, the collection of data, or the interpretation of results, all are subject to larger amounts of scrutiny than in comfortably logical environments. One could even say that awareness of potential biases is more important than the hard logic; errors in logic are easier to find in peer review, after all.^[q] More general, claims to rational knowledge, and especially statistics, have to be put into their appropriate context.^[127] Simple statements such as '9 out of 10 doctors recommend' are therefore of unknown quality because they do not justify their methodology.

Lack of familiarity with statistical methodologies can result in erroneous conclusions. Foregoing the easy example,^[r] multiple probabilities interacting is where, for example medical professionals,^[128] have shown a lack of proper understanding. Bayes' theorem is the mathematical principle lining out how standing probabilities are adjusted given new information. The boy or girl paradox is a common example. In knowledge representation, Bayesian estimation of mutual information between random variables is a way to measure dependence, independence, or interdependence of the information under scrutiny.^[129]

Beyond commonly associated

Most experimental results do not produce large changes in human understanding; improvements in theoretical scientific understanding typically result from a gradual process of development over time, sometimes across different domains of science.[131] Scientific models vary in the extent to which they have been experimentally tested and for how long, and in their acceptance in the scientific community. In general, explanations become accepted over time as evidence accumulates on a given topic, and the explanation in question proves more powerful than its alternatives at explaining the evidence. Often subsequent researchers re-formulate the explanations over time, or combined explanations to produce new explanations.

The ubiquitous element in the scientific method is empiricism. This is in opposition to stringent forms of rationalism: the scientific method embodies the position that reason alone cannot solve a particular scientific problem. 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; in current scientific practice, however, the use of scientific modelling and reliance on abstract typologies and theories is normally accepted. The scientific method counters 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.^[13][73]

Properties of scientific inquiry

Scientific knowledge is closely tied to empirical findings and can remain subject to falsification if new experimental observations are incompatible with what is found. That is, no theory can ever be considered final since new problematic evidence might be discovered. If such evidence is found, a new theory may be proposed, or (more commonly) it is found that modifications to the previous theory are sufficient to explain the new evidence. The strength of a theory relates to how long it has persisted without major alteration to its core principles.

Theories can also become subsumed by other theories. For example, Newton's laws explained thousands of years of scientific observations of the planets almost perfectly. However, these laws were then determined to be special cases of a more general theory (relativity), which explained both the (previously unexplained) exceptions to Newton's laws and predicted and explained other observations such as the deflection of light by gravity. Thus, in certain cases independent, unconnected, scientific observations can be connected, unified by principles of increasing explanatory power.^[132][99]

Since new theories might be more comprehensive than what preceded them, and thus be able to explain more than previous ones, successor theories might be able to meet a higher standard by explaining a larger body of observations than their predecessors.^[132] For example, the theory of evolution explains the diversity of life on Earth, how species adapt to their environments, and many other patterns observed in the natural world;^[133][134] its most recent major modification was unification with genetics to form the modern evolutionary synthesis. In subsequent modifications, it has also subsumed aspects of many other fields such as biochemistry and molecular biology.

Models of scientific inquiry

The classical model of scientific inquiry derives from Aristotle,^[135] 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.

The hypothetico-deductive model or method is a proposed description of the scientific method. Here, predictions from the hypothesis are central: if one assumes the hypothesis to be true, what consequences follow? If a subsequent empirical investigation does not demonstrate that these consequences or predictions correspond to the observable world, the hypothesis can be concluded to be false.

In 1877,

Philosophy of science looks at the underpinning logic of the scientific method, at what separates science from non-science, and the ethic that is implicit in science. There are basic assumptions, derived from philosophy by at least one prominent scientist,^[E][138] that form the base of the scientific method – namely, that reality is objective and consistent, that humans have the capacity to perceive reality accurately, and that rational explanations exist for elements of the real world.^[138] These assumptions from methodological naturalism form a basis on which science may be grounded. Logical positivist, empiricist, falsificationist, and other theories have criticized these assumptions and given alternative accounts of the logic of science, but each has also itself been criticized.

There are several kinds of modern philosophical conceptualizations and attempts at definitions of the method of science.^[ξ] The one attempted by the unificationists, who argue for the existence of a unified definition that is useful (or at least 'works' in every context of science). The pluralists, arguing degrees of science being too fractured for a universal definition of its method to by useful. And those, who argue that the very attempt at definition is already detrimental to the free flow of ideas.

Additionally, there have been views on the social framework in which science is done, and the impact of the sciences social envrionment on research. Also, there is 'scientific method' as popularised by Dewey in How We Think (1910) and Karl Pearson in Grammar of Science (1892), as used in fairly uncritical manner in education.

Pluralism

Scientific pluralism is a position within the

Unificationism

Unificationism, in science, was a central tenet of logical positivism.^[140][141] Different logical positivists construed this doctrine in several different ways, e.g. as a reductionist thesis, that the objects investigated by the special sciences reduce to the objects of a common, putatively more basic domain of science, usually thought to be physics; as the thesis that all theories and results of the various sciences can or ought to be expressed in a common language or "universal slang"; or as the thesis that all the special sciences share a common scientific method.

Development of the idea has been troubled by accelerated advancement in technology that has opened up many new ways to look at the world.

The fact that the standards of scientific success shift with time does not only make the philosophy of science difficult; it also raises problems for the public understanding of science. We do not have a fixed scientific method to rally around and defend.

— Steven Weinberg, 1995^[139]

Anti-formalism

Paul Feyerabend examined the history of science, and was led to deny that science is genuinely a methodological process. In his book Against Method he argued that no description of scientific method could possibly be broad enough to include all the approaches and methods used by scientists, and that there are no useful and exception-free methodological rules governing the progress of science. In essence, he said that for any specific method or norm of science, one can find a historic episode where violating it has contributed to the progress of science. He jokingly suggested that, if believers in the scientific method wish to express a single universally valid rule, it should be 'anything goes'.^[142] As has been argued before him however, this is uneconomic; problem solvers, and researchers are to be prudent with their resources during their inquiry.^[D]

A more general inference against formalised method has been found through research involving interviews with scientists regarding their conception of method. This research indicated that scientists frequently encounter difficulty in determining whether the available evidence supports their hypotheses. This reveals that there are no straightforward mappings between overarching methodological concepts and precise strategies to direct the conduct of research.^[144]

Myth, education, and scientific literacy

In education, the idea of a general and universal scientific method has been notably influential, and numerous studies (in the US) have shown that this framing of method often forms part of both students’ and teachers’ conception of science.^[145][146] This convention of traditional education has been argued against by scientists, as there is a consensus that educations' sequential elements and unified view of scientific method do not reflect how scientists actually work.^{[147][148][149]}

Historian of science Daniel Thurs' chapter in the 2015 book Newton's Apple and Other Myths about Science, concluded that the scientific method is a myth or, at best, an idealization.^[150]

Educations approach to scientific method was inspired by Karl Pearson’s Grammar of Science (1892),^[151] and Dewey's 1910 book, How We Think.^[29][e] Van der Ploeg (2016) indicated that Dewey's views^[t] on education had long been used to further an idea of citizen education removed from "sound education", claiming that references to Dewey in such arguments were undue interpretations (of Dewey).^[152]

Sociology of knowledge

The sociology of knowledge is a concept in the discussion around scientific method, claiming the underlying method of science to be sociological. King explains that sociology distinguishes here between the system of ideas that govern the sciences through an inner logic, and the social system in which those ideas arise.^[ο]

Thought collectives

A perhaps accessible lead into what is claimed is Fleck's thought, echoed in Kuhn's concept of normal science. According to Fleck, scientists' work is based on a thought-style, that cannot be rationally reconstructed. It gets instilled through the experience of learning, and science is then advanced based on a tradition of shared assumptions held by what he called thought collectives. Fleck also claims this phenomenon to be largely invisible to members of the group.^[155]: 177

Comparably, following the field research in an academic scientific laboratory by Latour and Woolgar, Karin Knorr Cetina has conducted a comparative study of two scientific fields (namely high energy physics and molecular biology) to conclude that the epistemic practices and reasonings within both scientific communities are different enough to introduce the concept of "epistemic cultures", in contradiction with the idea that a so-called "scientific method" is unique and a unifying concept.^[156][u]

Situated cognition and relativism

On the idea of Fleck's thought collectives sociologists built the concept of "situated cognition": that the perspective of the researcher fundamentally affects their work; and, too, more radical views.

The postmodernist critiques of science, especially in its extreme variants of "social constructivism" and "solipsism", have themselves been the subject of intense controversy. This ongoing debate, known as the science wars, is the result of conflicting values and assumptions between the postmodernist and realist camps. Whereas postmodernists assert that scientific knowledge is simply another discourse (this term has special meaning in this context) and not representative of any form of fundamental truth, realists in the scientific community maintain that scientific knowledge does reveal real and fundamental truths about reality. Many books have been written by scientists which take on this problem and challenge the assertions of the postmodernists while defending science as a legitimate method of deriving truth.^[163]

Limits of method

Role of chance in discovery

Somewhere between 33% and 50% of all

Psychologist Kevin Dunbar says the process of discovery often starts with researchers finding bugs in their experiments. These unexpected results lead researchers to try to fix what they think is an error in their method. Eventually, the researcher decides the error is too persistent and systematic to be a coincidence. The highly controlled, cautious, and curious aspects of the scientific method are thus what make it well suited for identifying such persistent systematic errors. At this point, the researcher will begin to think of theoretical explanations for the error, often seeking the help of colleagues across different domains of expertise.[164]^[165]

Relationship with statistics

When the scientific method employs statistics as a key part of its arsenal, there are mathematical and practical issues that can have a deleterious effect on the reliability of the output of scientific methods. This is described in a popular 2005 scientific paper "Why Most Published Research Findings Are False" by John Ioannidis, which is considered foundational to the field of metascience.^[126] Much research in metascience seeks to identify poor use of statistics and improve its use, an example being the misuse of p-values.^[167]

The particular points raised are statistical ("The smaller the studies conducted in a scientific field, the less likely the research findings are to be true" and "The greater the flexibility in designs, definitions, outcomes, and analytical modes in a scientific field, the less likely the research findings are to be true.") and economical ("The greater the financial and other interests and prejudices in a scientific field, the less likely the research findings are to be true" and "The hotter a scientific field (with more scientific teams involved), the less likely the research findings are to be true.") Hence: "Most research findings are false for most research designs and for most fields" and "As shown, the majority of modern biomedical research is operating in areas with very low pre- and poststudy probability for true findings." However: "Nevertheless, most new discoveries will continue to stem from hypothesis-generating research with low or very low pre-study odds," which means that *new* discoveries will come from research that, when that research started, had low or very low odds (a low or very low chance) of succeeding. Hence, if the scientific method is used to expand the frontiers of knowledge, research into areas that are outside the mainstream will yield the newest discoveries.^{[needs copy edit]}

Science of complex systems

Science applied to complex systems can involve elements such as transdisciplinarity, systems theory, control theory, and scientific modelling.

In general, the scientific method may be difficult to apply stringently to diverse, interconnected systems and large data sets. In particular, practices used within Big data, such as predictive analytics, may be considered to be at odds with the scientific method,^[168] as some of the data may have been stripped of the parameters which might be material in alternative hypotheses for an explanation; thus the stripped data would only serve to support the null hypothesis in the predictive analytics application. Fleck (1979), pp. 38–50 notes "a scientific discovery remains incomplete without considerations of the social practices that condition it".^[169]

Relationship with mathematics

Science is the process of gathering, comparing, and evaluating proposed models against

Mathematical work and scientific work can inspire each other.[38] For example, the technical concept of time arose in science, and timelessness was a hallmark of a mathematical topic. But today, the Poincaré conjecture has been proved using time as a mathematical concept in which objects can flow (see Ricci flow).^[171]

Nevertheless, the connection between mathematics and reality (and so science to the extent it describes reality) remains obscure. Eugene Wigner's paper, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", is a very well-known account of the issue from a Nobel Prize-winning physicist. In fact, some observers (including some well-known mathematicians such as Gregory Chaitin, and others such as Lakoff and Núñez) have suggested that mathematics is the result of practitioner bias and human limitation (including cultural ones), somewhat like the post-modernist view of science.^[172]

George Pólya's work on problem solving,^[173] the construction of mathematical proofs, and heuristic^[174][175] show that the mathematical method and the scientific method differ in detail, while nevertheless resembling each other in using iterative or recursive steps.

In Pólya's view, understanding involves restating unfamiliar definitions in your own words, resorting to geometrical figures, and questioning what we know and do not know already; analysis, which Pólya takes from

Lakatos proposed an account of mathematical knowledge based on Polya's idea of heuristics. In Proofs and Refutations, Lakatos gave several basic rules for finding proofs and counterexamples to conjectures. He thought that mathematical 'thought experiments' are a valid way to discover mathematical conjectures and proofs.^[183]

• Empirical limits in science
   – Idea that knowledge comes only/mainly from sensory experiencePages displaying short descriptions of redirect targets
• Evidence-based practices
   – Pragmatic methodologyPages displaying short descriptions of redirect targets
• Methodology – Study of research methods
• Metascience – Scientific study of science
• Quantitative research – All procedures for the numerical representation of empirical facts
• Research transparency
• Scientific law – Statement based on repeated empirical observations that describes some natural phenomenon
• Testability – Extent to which truthness or falseness of a hypothesis/declaration can be tested
• Timeline of the history of scientific method

Notes

Notes: Problem-solving via scientific method

If there is no algorithmic scientific method, then science is best understood through examples.

— 

John Staddon^[185]

Notes: Philosophical expressions of method

1. ^ His assertions in the Opus Majus that "theories supplied by reason should be verified by sensory data, aided by instruments, and corroborated by trustworthy witnesses"^[16] were (and still are) considered "one of the first important formulations of the scientific method on record".^[17]
2. ^ ...an experimental approach was advocated by Galileo in 1638 with the publication of Two New Sciences.^[22]
3. ^ Sanches and Locke were both physicians. By his training in Rome and France, Sanches sought a method of science beyond that of the Scholastic Aristotelian school. Botanical gardens were added to the universities in Sanches' time to aid medical training before the 1600s. See Locke (1689) An Essay Concerning Human Understanding Berkeley served as foil to the materialist System of the World of Newton; Berkeley emphasizes that scientist should seek 'reduction to regularity'.^[24] Atherton (ed.) 1999 selects Locke, Berkeley, and Hume as part of the empiricist school.^[25]
4. ^ Popper, in his 1963 publication of Conjectures and Refutations argued that merely Trial and Error can stand to be called a 'universal method'.^[30]
5. ^ ^{a b} Lee Smolin, in his 2013 essay "There Is No Scientific Method",^[31] espouses two ethical principles. Firstly: "we agree to tell the truth and we agree to be governed by rational argument from public evidence". And secondly, that ..."when the evidence is not sufficient to decide from rational argument, whether one point of view is right or another point of view is right, we agree to encourage competition and diversification". Thus echoing Popper (1963), p. viii
6. ^ The topics of study, as expressed in the vocabulary of its scientists, are approached by a "single unified method".^{[29]: pp.8, 13, 33–35, 60} A topic is unified by its predicates, which describe a system of mathematical expressions.^{[39]: 93–94, 113–117} The values which a predicate might take, then serve as witness to the validity of a predicated expression (that is, true or false; 'predicted but not yet observed'; 'corroborates', etc.).
7. ^ From the hypothesis, deduce valid forms using modus ponens, or using modus tollens. Avoid invalid forms such as affirming the consequent.
8. C.S. Peirce^[59]
9. ^ The scientific method requires testing and validation a posteriori before ideas are accepted.^[76]
10. ^ In Two New Sciences, there are three 'reviewers': Simplicio, Sagredo, and Salviati, who serve as foil, antagonist, and protagonist. Galileo speaks for himself only briefly. But Einstein's 1905 papers were not peer-reviewed before their publication.
11. ^ ^{a b} Friedel Weinert in The Scientist as Philosopher (2004) noted the theme of invariance as a fundamental aspect of a scientific account of reality in many writings from around 1900 onward, such as works by Henri Poincaré (1902), Ernst Cassirer (1920), Max Born (1949 and 1953), Paul Dirac (1958), Olivier Costa de Beauregard (1966), Eugene Wigner (1967), Lawrence Sklar (1974), Michael Friedman (1983), John D. Norton (1992), Nicholas Maxwell (1993), Alan Cook (1994), Alistair Cameron Crombie (1994), Margaret Morrison (1995), Richard Feynman (1997), Robert Nozick (2001), and Tim Maudlin (2002).^[114] — Deutsch in a 2009 TED talk proclaimed that "the search for hard-to-vary explanations is the origin of all progress".^[115]
12. ^ Differing accounts of which elements constitute a good theory:
    • Kuhn (1977) identified: accuracy; consistency (both internal and with other relevant currently accepted theories); scope (its consequences should extend beyond the data it is required to explain); simplicity (organizing otherwise confused and isolated phenomena); fruitfulness (for further research);^[112]
    • Colyvan (2001) listed simplicity/parsimony, unificatory/explanatory power, boldness/fruitfulness, and elegance;^[113]
    • Weinert (2004) noted the recurring theme of invariance;^[λ]
    • Hawking (2010): simplicity/parsimony, unificatory/explanatory power, and elegance, but did not mention fruitfulness.^[116]
13. ^ C. S. Pierce called inquiry's phase of free-ranging thought Musement. It carried attendant feelings of doubt, belief, perplexity etc. According to him, this phase of inquiry with no attempt at discovery of an order stands in order prior to retrodiction (the evaluation of what is known) and abduction.^[4]
14. ^ There is no universally agreed upon definition of the method of science. This was expressed with Neurath's boat already in 1913. There is however a consensus that stating this somewhat nihilistic assertion without introduction and in too unexpected a fashion is counterproductive, confusing, and can even be damaging. There may never be one, too. As Weinberg described it in 1995:^[139]

    The fact that the standards of scientific success shift with time does not only make the philosophy of science difficult; it also raises problems for the public understanding of science. We do not have a fixed scientific method to rally around and defend.

15. ^

    The sociology of knowledge is concerned with "the relationship between human thought and the social context in which it arises."^[153] So, on this reading, the sociology of science may be taken to be considered with the analysis of the social context of scientific thought. But scientific thought, most sociologists concede, is distinguished from other modes of thought precisely by virtue of its immunity from social determination — insofar as it is governed by reason rather than by tradition, and insofar as it is rational it escapes determination by "non-logical" social forces.

    — M. D. King leading into his article on Reason, tradition, and the progressiveness of science (1971)^[154]

16. ^ ^{a b} Stillwell's review (p. 381) of Poincaré's efforts on the Euler characteristic notes that it took five iterations for Poincaré to arrive at the Poincaré homology sphere.^[182]

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35. OCLC 144602109. There is a large core of people who think there is such a thing as a scientific method that can be justified, although not all agree as to what this might be. But there are also a growing number of people who think that there is no method to be justified. For some, the whole idea is yesteryear's debate, the continuation of which can be summed up as yet more of the proverbial 'flogging a dead horse'. We beg to differ. ... We shall claim that Feyerabend did endorse various scientific values, did accept rules of method (on a certain understanding of what these are), and did attempt to justify them using a meta methodology somewhat akin to the principle of reflective equilibrium
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54. ^ Judson (1979), p. 157. "'The structure that we propose is a three-chain structure, each chain being a helix' – Linus Pauling"
55. ^ McElheny (2004), pp. 49–50: January 28, 1953 — Watson read Pauling's pre-print, and realized that in Pauling's model, DNA's phosphate groups had to be un-ionized. But DNA is an acid, which contradicts Pauling's model.
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64. ^ McElheny (2004), p. 43: June 1952 — Watson had succeeded in getting X-ray pictures of TMV showing a diffraction pattern consistent with the transform of a helix.
65. ^ Cochran W, Crick FHC and Vand V. (1952) "The Structure of Synthetic Polypeptides. I. The Transform of Atoms on a Helix", Acta Crystallogr., 5, 581–586.
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71. ^ Watson (1968), p. 167: "The instant I saw the picture my mouth fell open and my pulse began to race." 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.
72. ^ ^{a b c} Peirce, Charles S. (1902), Carnegie application, see MS L75.329330, from Draft D Archived 2011-05-24 at the Wayback Machine of Memoir 27: "Consequently, to discover is simply to expedite an event that would occur sooner or later, if we had not troubled ourselves to make the discovery. Consequently, the art of discovery is purely a question of economics. The economics of research is, so far as logic is concerned, the leading doctrine concerning the art of discovery. Consequently, the conduct of abduction, which is chiefly a question of heuretic and is the first question of heuretic, is to be governed by economical considerations."
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88. ^ McElheny (2004), p. 53: The weekend (January 31 – February 1) — After seeing photo 51, Watson informed Bragg of the X-ray diffraction image of DNA in B form. Bragg permitted them to restart their research on DNA (that is, model building).
89. ^ McElheny (2004), p. 54: Sunday, February 8, 1953 — Maurice Wilkes gave Watson and Crick permission to work on models, as Wilkes would not be building models until Franklin left DNA research.
90. ^ McElheny (2004), p. 56: Jerry Donohue, on sabbatical from Pauling's lab and visiting Cambridge, advises Watson that the textbook form of the base pairs was incorrect for DNA base pairs; rather, the keto form of the base pairs should be used instead. This form allowed the bases' hydrogen bonds to pair 'unlike' with 'unlike', rather than to pair 'like' with 'like', as Watson was inclined to model, based on the textbook statements. On February 27, 1953, Watson was convinced enough to make cardboard models of the nucleotides in their keto form.
91. ^ Watson (1968), pp. 194–197: "Suddenly I became aware that an adenine-thymine pair held together by two hydrogen bonds was identical in shape to a guanine-cytosine pair held together by at least two hydrogen bonds. ..."
92. ^
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96. ^ Needham & Wang (1954), p. 166 shows how the 'flying gallop' image propagated from China to the West.
97. ^ Goldhaber & Nieto (2010), p. 940.
98. ^ Ronald R. Sims (2003). Ethics and corporate social responsibility: Why giants fall. p. 21: "'A myth is a belief given uncritical acceptance by members of a group ...' – Weiss, Business Ethics p. 15."
99. ^ ^{a b} Goldhaber & Nieto (2010), p. 942.
100. ^ Lakatos (1976), pp. 1–19.
101. S2CID 110623159
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116. ^ Stephen Hawking; Leonard Mlodinow (2010). "What is reality?". The Grand Design. Random House Digital, Inc. p. 51.
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117. ^ For example, Hawking/Mlodinow say, "The above criteria are obviously subjective. Elegance, for example, is not something easily measured, but it is highly prized among scientists." The idea of 'too baroque' is connected to 'simplicity': "a theory jammed with fudge factors is not very elegant. To paraphrase Einstein, a theory should be as simple as possible, but not simpler". Hawking, S.; Mlodinow, L. (2010). The Grand Design. Random House Publishing Group. p. 52.
     ISBN 978-0-553-90707-0. Retrieved 2024-04-21. — See also: Simon Fitzpatrick (5 April 2013). "Simplicity in the Philosophy of Science". Internet Encyclopedia of Philosophy. and Baker, Alan (25 February 2010). "Simplicity"
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118. ^ Bird, Alexander (11 August 2011). "§4.1 Methodological Incommensurability". In Edward N. Zalta (ed.). The Stanford Encyclopedia of Philosophy (Spring 2013 Edition).
119. ^ See Stephen Hawking; Leonard Mlodinow (2010). The Grand Design. Random House Digital, Inc. p. 8.
     ISBN 978-0553907070
     . It is a whole family of different theories, each of which is a good description of observations only in some range of physical situations...But just as there is no map that is a good representation of the earth's entire surface, there is no single theory that is a good representation of observations in all situations.
120. ^ E Brian Davies (2006). "Epistemological pluralism". PhilSci Archive. p. 4. Whatever might be the ultimate goals of some scientists, science, as it is currently practised, depends on multiple overlapping descriptions of the world, each of which has a domain of applicability. In some cases this domain is very large, but in others quite small.
121. ^ Occam's razor, sometimes referred to as "ontological parsimony", is roughly stated as: Given a choice between two theories, the simplest is the best. This suggestion commonly is attributed to William of Ockham in the 14th-century, although it probably predates him. See Baker, Alan (25 February 2010). "Simplicity; §2: Ontological parsimony". The Stanford Encyclopedia of Philosophy (Summer 2011 Edition). Retrieved 2011-11-14.
122. ^ Gauch (2003), p. 269.
123. ^ Baker, Alan (25 February 2010). "Simplicity". In Edward N. Zalta (ed.). The Stanford Encyclopedia of Philosophy (Summer 2011 Edition).
124. ISBN 978-0-521-81689-2
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125. ISSN 0032-5473
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126. ^
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127. ISBN 978-0-521-81689-2
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128. gynaecologists got an example question on Bayes' theorem right. Book, including the assertion, introduced in Kremer, William (6 July 2014). "Do doctors understand test results?"
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129. ^ Christopher M. Bishop (2006) Pattern Recognition and Machine Learning pp. 21, 30, 55, 152, 161, 277, 360, 448, 580
130. ^ ^{a b} Peirce, Charles S., Carnegie application (L75, 1902), New Elements of Mathematics v. 4, pp. 37–38: "For it is not sufficient that a hypothesis should be a justifiable one. Any hypothesis that explains the facts is justified critically. But among justifiable hypotheses we have to select that one which is suitable for being tested by experiment."
131. ^ Stanovich, Keith E. (2007). How to Think Straight About Psychology. Boston: Pearson Education. p. 123
132. ^ ^{a b} Brody (1993), pp. 44–45.
133. ISBN 978-0-7637-0066-9
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134. ISBN 978-0-19-517234-8. Archived
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135. ^ Aristotle (1938). "Prior Analytics". Aristotle, Volume 1. Loeb Classical Library. Translated by Hugh Tredennick. London: William Heinemann. pp. 181–531.
136. ^ Ketner, Kenneth Laine (2009). "Charles Sanders Peirce: Interdisciplinary Scientist". The Logic of Interdisciplinarity. By Peirce, Charles S. Bisanz, Elize (ed.). Berlin: Akademie Verlag.
137. ^ Peirce, Charles S. (October 1905). "Issues of Pragmaticism". The Monist. Vol. XV, no. 4. pp. 481–499, see p. 484, and p. 491. Reprinted in Collected Papers v. 5, paragraphs 438–463, see 443 and 451.
138. ^ ^{a b} Einstein, Albert (1936, 1956) One may say "the eternal mystery of the world is its comprehensibility." From the article "Physics and Reality" (1936), reprinted in Out of My Later Years (1956). 'It is one of the great realizations of Immanuel Kant that the setting up of a real external world would be senseless without this comprehensibility.'
139. ^ ^{a b} Weinberg, (1995) “The Methods of Science … And Those By Which We Live”, page: 8
140. ISBN 978-94-007-0142-7
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141. JSTOR 40399117
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142. ^ Feyerabend, Paul K., Against Method, Outline of an Anarchistic Theory of Knowledge, 1st published, 1975. Reprinted, Verso, London, 1978.
143. ^ Tao, Terence (13 February 2007). "What is good mathematics?". arXiv.org. Retrieved 2024-04-11.
144. ISSN 1879-4912
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145. ISSN 0036-8326
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146. ISSN 0950-0693
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147. ISBN 978-0-252-06436-4
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148. ISSN 0036-6803
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149. ISSN 0002-7685
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150. ISBN 978-0-674-91547-3, archived
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151. ^ Hepburn, Brian; Andersen, Hanne (1 June 2021) [13 November 2015]. Zalta, Edward N. (ed.). "Scientific Method". Stanford Encyclopedia of Philosophy (Summer 2021 Edition). Retrieved 2024-03-12. The [philosophical] study of scientific method is the attempt to discern the activities by which [the success of science] is achieved. Among the activities often identified as characteristic of science are systematic observation and experimentation, inductive and deductive reasoning, and the formation and testing of hypotheses and theories.
152. ISSN 1746-1979
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153. ^ Here, King quotes Peter L. Berger and Thomas Luckman, The Social Construction of Reality (London, 1967), 16.
154. JSTOR 2504396
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155. JSTOR 285293
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156. OCLC 39539508
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157. ^ As cited in Fleck (1979), p. 27, Fleck (1979), pp. 38–50
158. ^ Fleck (1979), p. xxviii
159. ^ Fleck (1979), p. 27
160. ISBN 978-0-521-05197-2
161. ISBN 978-1-4432-5544-8
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162. ^ Feyerabend, Paul K (1960) "Patterns of Discovery" The Philosophical Review (1960) vol. 69 (2) pp. 247–252
163. ^ For example:
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     • A House Built on Sand: Exposing Postmodernist Myths About Science, Oxford University Press, 2000
     • Intellectual Impostures, Economist Books, 2003
164. ^ ^{a b c} Dunbar, K., & Fugelsang, J. (2005). Causal thinking in science: How scientists and students interpret the unexpected. In M.E. Gorman, R.D. Tweney, D. Gooding & A. Kincannon (Eds.), Scientific and Technical Thinking (pp. 57–79). Mahwah, NJ: Lawrence Erlbaum Associates.
165. ^
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166. ^ Taleb, Nassim N. "Antifragility — or— The Property Of Disorder-Loving Systems". Archived from the original on 2013-05-07.
167. PMID 6711862. Archived
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168. ^ Anderson, Chris (2008) The End of Theory: The Data Deluge Makes the Scientific Method Obsolete Archived 2021-05-02 at the Wayback Machine. Wired Magazine 16.07
169. ^ Ludwik Fleck (1979) Genesis and Development of a Scientific Fact Archived 2021-08-26 at the Wayback Machine
170. ^ Pólya (1957), p. 131 in the section on 'Modern heuristic': "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."
171. ^ Huai-Dong Cao and Xi-Ping Zhu (3 Dec 2006) Hamilton-Perelman’s Proof of the Poincaré Conjecture and the Geometrization Conjecture
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172. ^ George Lakoff and Rafael E. Núñez (2000) Where Mathematics Comes From
173. ^ "If you can't solve a problem, then there is an easier problem you can solve: find it." —Pólya (1957), p. 114
174. ^ George Pólya (1954), Mathematics and Plausible Reasoning Volume I: Induction and Analogy in Mathematics.
175. ^ George Pólya (1954), Mathematics and Plausible Reasoning Volume II: Patterns of Plausible Reasoning.
176. ^ Pólya (1957), p. 142.
177. ^ Pólya (1957), p. 144.
178. Euler's formula for polyhedra
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179. ISBN 9780486614809
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180. ^ "Charles A. Weibel (ca. 1995) History of Homological Algebra" (PDF). Archived (PDF) from the original on 2021-09-06. Retrieved 2021-08-28.
181. ^ Henri Poincaré, Sur l’analysis situs, Comptes rendusde l’Academie des Sciences 115 (1892), 633–636. as cited by Lakatos (1976), p. 162
182. ^ John Stillwell, reviewer (Apr 2014). Notices of the AMS. 61 (4), pp. 378–383, on Jeremy Gray's (2013) Henri Poincaré: A Scientific Biography (PDF Archived 2021-07-04 at the Wayback Machine).
183. ^ Lakatos (1976), p. 55.
184. ^ Mackay (1991), p. 100.
185. ^ Staddon, John Eric Rayner (October 2020). Whatever happened to history of science? How scholarship became politicized story-telling. CHOPE working paper. Durham, NC: Duke University, Center for the History of Political Economy. Retrieved 2024-04-06. Full quote: "I tend to agree with Paul Feyerabend’s Against Method to the extent that if there is no algorithmic scientific method, then science is best understood through examples[.]"

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Further reading

• Bauer, Henry H., Scientific Literacy and the Myth of the Scientific Method, University of Illinois Press, Champaign, IL, 1992
• Heinemann
  , Melbourne, Australia, 1950.
• Bernstein, Richard J., Beyond Objectivism and Relativism: Science, Hermeneutics, and Praxis, University of Pennsylvania Press, Philadelphia, PA, 1983.
• Brody, Baruch A. and Capaldi, Nicholas, Science: Men, Methods, Goals: A Reader: Methods of Physical Science Archived 2023-04-13 at the Wayback Machine
  , W.A. Benjamin, 1968
• 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.
• Chalmers, Alan, What Is This Thing Called Science?. Queensland University Press and Open University Press, 1976.
• ISBN 978-0-465-09137-9
  .
• Crombie, A.C. (1953), Robert Grosseteste and the Origins of Experimental Science 1100–1700, Oxford: Clarendon
• 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, 1980.
• ISBN 978-1-59403-207-3
  .
• 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, 1983.
• Heisenberg, Werner, Physics and Beyond, Encounters and Conversations, A.J. Pomerans (trans.), Harper and Row, New York, 1971, pp. 63–64.
• Thematic Origins of Scientific Thought: Kepler to Einstein
  , 1st edition 1973, revised edition, Harvard University Press, Cambridge, MA, 1988.
• ISBN 978-0-674-25894-5
  .
• 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, 1972. 2nd edition, 1980.
• Maxwell, Nicholas, The Comprehensibility of the Universe: A New Conception of Science, Oxford University Press, Oxford, 1998. Paperback 2003.
• Maxwell, Nicholas, Understanding Scientific Progress Archived 2018-02-20 at the Wayback Machine, Paragon House, St. Paul, Minnesota, 2017.
• McComas, William F., ed. (1998). "The Principal Elements of the Nature of Science: Dispelling the Myths" (PDF). The Nature of Science in Science Education. Netherlands: Kluwer Academic Publishers. pp. 53–70. Archived from the original (PDF) on 2014-07-01.
• Misak, Cheryl J., Truth and the End of Inquiry, A Peircean Account of Truth, Oxford University Press, Oxford, 1991.
• Oreskes, Naomi, "Masked Confusion: A trusted source of health information misleads the public by prioritizing rigor over reality", Scientific American, vol. 329, no. 4 (November 2023), pp. 90–91.
• Piattelli-Palmarini, Massimo (ed.), Language and Learning, The Debate between Jean Piaget and Noam Chomsky, Harvard University Press, Cambridge, MA, 1980.
• 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, 1993.
• Thagard, Paul, Conceptual Revolutions, Princeton University Press, Princeton, NJ, 1992.
• Ziman, John (2000). Real Science: what it is, and what it means. Cambridge: Cambridge University Press.

External links

Wikimedia Commons has media related to Scientific method.

Wikibooks has a book on the topic of: The Scientific Method

Wikiversity has learning resources about Thinking Scientifically

Library resources about
Scientific method

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• Resources in your library

• Andersen, Hanne; Hepburn, Brian. "Scientific Method". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
• "Confirmation and Induction". Internet Encyclopedia of Philosophy.
• Scientific method at PhilPapers
• Scientific method at the
  Indiana Philosophy Ontology Project
• An Introduction to Science: Scientific Thinking and a scientific method Archived 2018-01-01 at the Wayback Machine by Steven D. Schafersman.
• Introduction to the scientific method at the University of Rochester
• The scientific method from a philosophical perspective
• Theory-ladenness by Paul Newall at The Galilean Library
• Lecture on Scientific Method by Greg Anderson (archived 28 April 2006)
• Using the scientific method for designing science fair projects
• Scientific Methods an online book by Richard D. Jarrard
• Richard Feynman on the Key to Science (one minute, three seconds), from the Cornell Lectures.
• Lectures on the Scientific Method by Nick Josh Karean, Kevin Padian, Michael Shermer and Richard Dawkins (archived 21 January 2013).
• "How Do We Know What Is True?" (animated video; 2:52)