A hypothesis in the empirical disciplines (e.g. physics, chemistry, and biology) is a proposition proposed to predict or explain a reoccurring phenomenon, and in the a priori disciplines (e.g. mathematics, statistics, and logic) it is a proposition proposed as the basis of an argument. The term derives from the ancient Greek, hypotithenai meaning "to put under" or "to suppose." The nature of the hypothesis is a topic of study primarily reserved for philosophy of science.
In early usage, scholars often referred to a clever idea or to a convenient mathematical approach that simplified cumbersome calculations as a hypothesis. St. Robert Bellarmine (1542-1621) gave a famous example of the older sense of the word in the warning issued to Galileo in the early seventeenth century: that he must not treat the motion of the Earth as a reality, but merely as a hypothesis.
During the eighteenth century, physicists (or “natural philosophers” as they were called) began to use the term ‘hypothesis’ in a pejorative sense, suggesting that hypothetico-deduction (explained later) was an inferior form of scientific reasoning. For example, Isaac Newton (1643-1727) made a famous phrase about the use of hypotheses in science in the General Scholium of his classic 1726 text The Mathematical Principles of Natural Philosophy:
I have not as yet been able to deduce from phenomena the reason for these properties of gravity, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy (Newton  1999, 943).
In common usage in the twent-first century, a hypothesis refers to an educated guess about why some phenomenon or phenomenological regularity occurs. Hypotheses, in common usage, are provisional and not accepted as true until they are tested. Thus hypotheses are always testable claims. Actually, the requirement that hypotheses are testable is a tenet among philosophers of science as well, especially Karl Popper (1902-1994) and Carl Gustav Hempel (1905-1997).
For example, suppose that Tamara is in her home and she hears her car alarm sound. She immediately formulates two hypotheses. First, someone is stealing her car. Second, someone accidentally initiated the alarm (e.g. by standing too close to the car). Tamara favors the second hypothesis because she lives in a safe neighborhood. A test of Tamara’s hypothesis would be simple. All she would need to do is walk over to the window and look to see what happened. If she sees a bunch of teenagers near her car she can rest assured that her hypothesis was true. However, if instead she sees that her car is missing, then her first guess was probably right.
Hypotheses in empirical disciplines (e.g. physics) are propositions proposed to predict or explain regular phenomena. Using hypotheses to predict or explain regular phenomena is often called “the hypothetico-deductive method” in science.
An example of a famous hypothetico-deduction is Joseph John Thomson’s (1856-1940) hypothesis that cathode rays are streams of subatomic negatively-charged particles that we now call electrons. Cathode rays are emanations from electrodes in vacuum tubes that travel the length of the tube to hit a phosphorous-coated screen and produce a luminous spot. Cathode ray tubes are used in most ordinary televisions. At any rate, several physicists in the late 1800s thought that cathode rays were uncharged streams of electromagnetic waves. In fact, in 1883 Heinrich Hertz (1857-1894) showed that cathode rays were not deflected by electrically charged metal plates, and in 1892 Hertz showed that cathode rays could penetrate thin metal foils, unlike any known particles.
However, J.J. Thomson (1897) disagreed with Hertz and posited electrons as the true components of cathode rays. In 1895 Jean Perrin (1870-1942) showed that electrically charged metal plates could deflect cathode rays, and Thomson confirmed Perrin’s result in 1897 by reproducing the experiment and measuring the magnitude of the miniscule deflection. Nevertheless, the controversial part of Thomson’s hypothesis was that cathode rays were composed of particles instead of waves.
However, assuming that cathode rays were composed of particles, Thomson was able to predict and explain several strange but regular phenomena about cathode rays. For example, with the electron Thomson was able to explain how it is possible to measure a stable mass to electric charge ratio of cathode ray particles when passing it through a uniform magnetic field and why the mass-to-charge ratio was smaller than any known mass-to-charge ratio for atomic compounds.
In 1906, J.J. Thomson was awarded the Nobel Prize in Physics for discovering the electron and introducing the field of subatomic physics. Ironically, Thomson’s son George Paget Thomson was awarded a Nobel Prize in 1937 for showing that the electron is a wave. Nonetheless, this historical example shows how hypotheses in the empirical disciplines function to predict or explain regular phenomena.
Hypotheses in a priori disciplines (e.g. mathematics) have a different role. These sorts of hypotheses function as a conjectural basis of an argument. Hypotheses in this sense are usually claims that are temporarily assumed to be true for the sake of a proof because they are needed in the proof and the claim seems plausible. However, as soon as a contradiction or other absurdity is derived from the hypothesis, the hypothesis is rejected.
For example, statisticians devise hypothesis tests regularly to test null hypotheses about statistical data. A null hypothesis is usually a hypothesis positing no difference in a certain parameter (e.g. statistical mean) of two or more populations of data. During statistical hypotheses tests, a null hypothesis is chosen and then a probabilistic calculation is made from the data about how likely it is that the null hypothesis is true (usually called a “P-value”). Given an antecedent cut-off point for unlikeliness (usually called the “significance level”), a statistician will reject the null hypothesis if the P-value falls below the significance level, but accept it otherwise.
Philosophers tend to use both empirical and a priori hypotheses. For example, some metaphysicans (known as “metaphysical realists”) accept the hypothesis that properties and relations (sometimes jointly referred to as “universals”) exist because the hypothesis provides the simplest explanation for the phenomena of why humans experience similarities and why almost all human languages use type predicates (e.g. nouns).
However, other metaphysicians (known as “nominalists”) reject the existence of universals because adopting the hypothesis leads to one or more absurdities. For instance, some nominalists think that the relationship between a particular thing and the property it instantiates (e.g. an orange and the color orange), sometimes called “exemplification,” is itself a relation and thus cannot be explained with metaphysical realism without circular reasoning.
Yet another distinction in hypotheses—or at least empirical hypotheses—is between causal and merely correlational claims made in hypotheses. Namely, some hypotheses are meant to provide causal explanations of some particular phenomenological regularity, whereas other hypotheses are just meant to provide a means for predicting phenomenological regularities.
For example, suppose that John’s knees hurt each time he jogs on the sidewalk. That is a regular phenomenon that deserves some sort of explanation. John’s hypothesis is that his shoes are worn. So he buys new shoes and sure enough his knees no longer hurt when he jogs.
Now what John has done is coincidentally found a solution that correlates with the cause of his pain even though he has not identified the cause of his pain. As a physiologist might point out, the cause of John’s pain is probably poor shock absorption in his patello-femoral joint and subsequent excitation of nerve fibers. Thus John has stumbled upon a hypothesis that predicts the phenomenological regularity (worn shoes) although he has not discovered the hypothesis that accounts for the cause of the phenomenological regularity (worn knee joints and associated nerve firing).
Evaluating (empirical) hypotheses according to the hypothetico-deductive approach requires the use of a few methodological virtues. Philosophers of science have debated these virtues for many years, but they are still worth mentioning:
Testability is the feature of hypotheses that makes them susceptible to rejection. Karl Popper (1959) claims that what makes a hypothesis scientific is its ability to be observationally tested, or as he puts it, falsified. Thus a hypothesis must be testable in order to entertain it as a possible explanation of scientific phenomena.
In science and other empirical disciplines, the hypothesis test is usually—but not always—empirical. In mathematics and other a priori disciplines, the test is conceptual (e.g. Does the hypothesis not imply an absurdity?). But some test is needed to identify a hypothesis. Otherwise, there would be no difference between a hypothesis and a mere belief.
Empirical adequacy is one of the oldest and most uncontroversial virtues used to evaluate hypotheses. A hypothesis is empirically adequate when it predicts or explains the phenomenological regularity that it was proposed to predict or explain. This means that an empirically adequate hypothesis is one that—together with certain auxiliary assumptions—deductively imply the phenomenological regularity as an observation.
However, some notions of empirical adequacy extend far beyond the original regular phenomenon to all relevant and observable phenomena. Thus, for example, Thomson’s hypothesis about the existence of electrons should not only predict the behavior of cathode rays, but also other physical phenomena involving electric currents. The exact meaning of ‘empirical adequacy’ has been debated among philosophers of science for years, leading some philosophers such as Thomas Kuhn (1922-1996), to claim that no physical theory has ever been empirically adequate.
Simplicity has been a desired feature of hypotheses ever since William of Ockham (c. 1295–1349) introduced the value of simplicity in his often-cited principle known as Ockham’s Razor, which roughly states that hypotheses should be as ontologically parsimonious as possible. Dozens of important scientists throughout history have endorsed the use of simplicity in hypothesis construction. For example, Isaac Newton’s first rule for the study of natural philosophy (or physics) is the following:
“No more causes of natural things should be admitted than are both true and sufficient to explain their phenomena” (Newton  1999, 794).
Nevertheless, the ontological defense of simplicity became an unpopular position in the twentieth-century, largely because of how obviously complex nature has turned out to be. Instead, twentieth-century philosophers of science explored epistemological defenses of simplicity as a virtue of hypotheses. For example, Karl Popper (1959) argued that simpler hypotheses are more easily testable and thus have more empirical content and scientific value. In Popper’s words:
“Simple statements, if knowledge is our object, are to be prized more highly than less simple ones because they tell us more; because their empirical content is greater; and because they are better testable” (Popper 1959, 142).
Similarly, George Smith (2002) has argued that simplicity can be valuable in a scientific method known as successive approximation through idealization—a method first introduced by Isaac Newton ( 1999).
Despite these defenses, feminist philosophers of science have attacked traditionalists for being too vague about what counts as a “simpler” hypothesis and also the general worth of simpler hypotheses in all domains of science. One feminist philosopher, Helen Longino (1990) has argued that ontological heterogeneity is sometimes more valuable to the biological sciences than ontological simplicity. For example, in reproductive biology, a diverse array of reproductive mechanisms should be entertained in biological hypotheses to fully account for reproductive phenomena across living systems.
Scope is the feature of hypotheses that measures the number or diversity of phenomena a hypothesis predicts or explains. So to say that a hypothesis has wide scope is to say that it predicts (or explains) a lot of phenomena in one scientific field or it predicts (or explains) phenomena in different scientific fields. For example, Thomson’s hypothesis about the existence of electrons has wide scope because it explains the behavior of cathode rays in physics, oxidation-reduction (or “redox”) reactions in chemistry, and even photosynthesis in biology. Sometimes scope is included in empirical adequacy.
Fruitfulness is the extent to which the acceptance of a hypothesis can positively impact scientific practice (Kuhn 1977). For instance, Thomson’s hypothesis about the existence of the electron was very fruitful and Thomson knew it would be when he proposed it. The acceptance of electrons, among other benefits, started the discipline of subatomic physics. This benefit alone was enough for Thomson’s contemporaries to seriously consider the hypothesis of the electron.
The internal consistency of a hypothesis and the external consistency of a hypothesis with already accepted hypotheses (often called “theories” or “laws”) is usually given as a desirable feature of hypotheses. For one, if a hypothesis is not internally consistent (e.g. if it contains a logical or analytic contradiction), then any observational consequence follows from the hypothesis as a matter of logic. This means that no observational test can confirm or conflict with the hypothesis.
However, external consistency is usually seen as more controversial than internal consistency since the use of the virtue supposes that accepted hypotheses should have been accepted. But then if these hypotheses were accepted in part from external consistency, then external consistency as a virtue is circular and unhelpful in evaluating hypotheses. It is no surprise that feminist philosophers of science have questioned this virtue as well (Longino 1990).
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