2.3: The Modern Scientific Method

The modern scientific method is an iterative process that depends on putting forth hypotheses, predicting outcomes based on these hypotheses, and observing whether the predictions hold through experimentation. The term scientific method dates from the nineteenth century when terminologies establishing clear boundaries between science and non-science were being developed (Harrison et al. 2011). The fundamental feature of science, and an inherent part of the scientific method, is that a scientific theory is one that can make definite predictions that can be tested against experience (Popper 1989). If experience does not match the predictions, then the corresponding theory is false.

Karl Popper used this argument to separate scientific theories such as Einstein's Theory of General Relativity, which was first empirically verified in 1919 when an expedition led by Eddington confirmed general relativity's prediction for the deflection of starlight by the sun during the total solar eclipse of 1919, from what they considered non-scientific theories such as Freud's psychoanalytic theory, which could not be reconciled with empirical findings. In practice, it should be noted that this viewpoint may be overly simplistic in practice.

Hence, scientific inquiry and the scientific method are an iterative process where theory and observation complement one another. For example, Newton's gravitational theory made specific predictions about the how the planets should behave as they orbit the sun. These predictions could be empirically verified except for the planet Uranus, because observations of Uranus varied from the theory in a consistent way. Two scientists, John Couch Adams working in England and Urbain Le Verrier working in France, independently suggested in 1846 that there was a yet undiscovered planet whose gravitational pull was responsible for the observed behavior of Uranus. That same year the planet Neptune was observed for the first time.

The key idea here is that Newton’s entire theory was not abandoned based on these observations, particularly because the theory apparently correctly predicted the behavior of the other known planets. Instead, the hypothesized theory and observation led to a new prediction that would explain why the empirical observations for Uranus did not match what the theory predicted. The new viewpoint was that there was another planet that was affecting the system in a way that is consistent with the hypothesized theory. Of course, the modified view was verified in short order in this case. If no such planet had been observed, then the theory would have been modified in a different way and tested again.

Another key element of the scientific method is the concept of induction. Earlier we stated that deduction is making a conclusion that logically follows from another. The argument in our example used the deduction to conclude that if all rocks sink in water, and we find a rock, then it will also sink in water. An inductive argument is one that moves from conclusions about cases we know about to a case we do not know about. In the example of the rocks, we might observe that six rocks have been observed to sink in water. An inductive argument, or inductive inference, would be used to conclude that a seventh rock will sink when placed in water. Hence, we take the knowledge about objects we have observed and apply it to try to make a conclusion about another object for which we have no observations.

Definition: Induction

A conclusion is based on induction if it is generalized from a set of observations.

Of course, inductive inference can be more dangerous than deductive inference. If the assumed premise is true, then a deductive conclusion always holds, whereas an inductive conclusion may not. In the example of the rocks the inductive inference obviously does not hold because what we observed in the six rocks is not true for all rocks.

The modern scientific method is heavily dependent on inductive inference. For example, the scientific method takes the notion that if we observe that the set of known planets all follow elliptical orbits around the sun, then we would conclude that if a new planet were observed, it too would follow this pattern. As an example from everyday life, the conclusion that a medical treatment is safe depends on what has been observed up to that point but may not always hold for someone who has not been observed to have the treatment. As we shall see, modern statistical theory attempts to mitigate this problem by assessing the risk of something that has not been observed will follow an established pattern from what has been observed. In fact, inductive reasoning is used any time one looks at data and draws general conclusions from it. In practice this is often referred to as empirical proof or experimental proof, but it is not proof in the sense of using a deductive argument.

While admitting that we use inductive inference almost constantly in our lives, David Hume insisted that inductive inference cannot be rationally justified, and that we are unconsciously assuming what he called the uniformity of nature (Okasha 2002). For example, if the first three eggs in a carton are good, then concluding that the rest in the carton will also be good makes an inherent assumption about the nature of the uniformity of egg goodness. Whenever an airplane takes off, we implicitly assume that the laws of gravity will continue to hold, and in fact will hold for that airplane on that flight; otherwise, we would probably not board the plane. While there is no logical reason for the universe to continue to work exactly as it has been, we implicitly believe this to be true. Because of these assumptions inductive inference apparently cannot be justified logically. This is known as Hume's Problem of Induction, a problem with which scientific philosophers struggle to this day.

Another type of reasoning used in science is in some ways closely related to inductive inference. This type of reasoning is known as inference to the best explanation. When using inference to the best explanation, a scientist considers all the information and produces the best plausible explanation for the observations. Suppose that you leave for class in the morning, and you leave a box of tasty donuts on the table in the kitchen. Your roommate is still sleeping as they have a later class, and they were out late the night before. You arrive home after your class and the box of donuts is empty. You conclude that your roommate ate the donuts in your absence. You do not know this for a fact, but you look at the information you have. The only other person who lives with you is your roommate, no one else usually visits on class days, and you were not gone that long. This conclusion is not a logical deduction from the information that is given, as there is a myriad of other possible explanations. Perhaps you accidentally left the door ajar, someone saw the donuts, came in and ate them, and left while your roommate slept. Perhaps a mouse got in and ate all the donuts. The conclusion that your roommate ate the donuts seems to be the most plausible, or best, explanation.

This type of reasoning may not seem to be inductive reasoning because the conclusion that your roommate ate your donuts does not generalize previous donut eating behavior. You did not observe your roommate eating the first few donuts and then conclude that they ate the rest of the donuts based on those observations. Some would argue, though, that your conclusion may be based on previous experience. You know by experience that it is not likely someone came into your apartment and just ate the donuts and left. You know by experience that your roommate is perfectly capable of eating your donuts in your absence. From this perspective some may then argue that this is a type of inductive reasoning. There is no correct answer to using this terminology, and it really does not matter if we are consistent. In our context we will use the term inductive inference for reasoning about the same situation. Donuts to doughnuts, so to speak.

In application, inference to the best explanation is one of the most used methods for scientific inquiry, but it can also be the most haphazard. The main problem stems from the fact that it can be very difficult to settle on which of a competing series of hypotheses about a question presents the most plausible explanation. The development of the Darwinian theory of evolution is based on observations of similarities between species and the conclusion that these species share a common ancestor as the most plausible explanation. This reasoning certainly did not prove that evolution was the mechanism of the natural development of species, and even in the face of modern advances in genetic theory, the theory is still debated today (Thagard and Findlay 2010; Hildering et al. 2013; Diogo 2020; Cavallo and McCall 2008; Crivellaro and Sperduti 2014; Cobern 1994; Gilson 2009).

Another example of this type of development occurred with the study of Brownian motion. In 1827 the botanist Robert Brown noted that when he observed pollen suspended in water through a microscope, the grains of pollen moved in an irregular fashion. Over the next roughly 80 years, several explanations for the phenomenon were proposed, including theories based on the electrical attraction between particles and convection currents in the water. The actual reason for the movement is because of the bombardment of the water molecules against the pollen grains, a theory proposed in the late 19th century. However, a theoretical mathematical treatment of the theory was elusive, and hence it was not accepted until the work of Albert Einstein in 1905. What is interesting about the theory is that it postulated the existence of molecules and atoms, and in a symbiotic logical relationship bolstered scientific belief in this theory as well (Okasha 2002; Haw 2002; Maiocchi 1990; Marchesoni and Hänggi 2005; Bigg 2008).

One of the key elements in accepting a theory as being plausible is based on the idea of parsimony or simplicity. It is usually much easier to believe that a simple explanation is the cause of a phenomenon rather than a complicated one. But this theory provokes a deep question about whether this is the preferred structure of the universe (Okasha 2002). Is the universe necessarily based on the simplest explanation? This concept is still widely debated (Huemer 2009; Stewart 1993; Friday 1982; Aarts 2007; Kluge 2001; Simon 2002; Schlesinger 1975).

So where does this leave us with the modern scientific method? Essentially the modern view of the scientific method is of an iterative process that relies on a cycle of hypothesis and testing, usually represented with a framework as shown in Figure \(\PageIndex{4}\). There are many other representations with varying degrees of complexity, but the basic process is essentially the same. The scientific method begins with observation. Some type of behavior is observed in the universe, and we would like to use the scientific method to explain why it has occurred. The second step is then to form a hypothesis about why the behavior might occur. In the best cases this hypothesis is something that can be tested through experimentation;, otherwise the hypothesis is just a theory that has not been verified. The next step involves testing the hypothesis through experimentation. Generally, what happens is that the hypothesis is used to make predictions about what should occur under conditions that are controlled or observed by the researcher. The experiment is performed, and data is collected, and this brings us to the next step, which is to analyze the data to see if the data support or are contradictory to what was predicted by the hypothesis. At this point a formal conclusion is made. If the data are contradictory to what was predicted by the hypothesis, then we have observed something new, and a new hypothesis is needed. Then the process starts again. If the data support the predictions of the hypothesis, then in some sense we have confirmed our theory, though this is usually not the end.

Figure \(\PageIndex{4}\): A conceptual flowchart of the modern scientific method visualized as a cycle of observation, hypothesis, testing, and analysis (Created by the authors).

Richard Feynman summarized this situation in the following way:

“The exception tests the rule.” Or, put another way,
“The exception proves that the rule is wrong.”
That is the principle of science.
If there is an exception to any rule, and if it can be proved by observation, that rule is wrong.

The problem is that theories are never fully confirmed by the scientific method. What happens in the cyclical process is that evidence in support of a hypothesis is slowly built until there is a consensus in the scientific community that the hypothesis is accepted. However, we can never be certain that a hypothesis is correct.

An interesting example to consider is the development of the theory of the simple dynamics of physical bodies. Isaac Newton introduced three laws of motion in his book Mathematical Principles of Natural Philosophy published in 1687 (see Figure \(\PageIndex{5}\)). It is thought that Newton derived these laws based on empirical observation and mathematical logic. Similarly, Galileo considered empirical data on the motion of objects in his book The Discourses and Mathematical Demonstrations Relating to Two New Sciences published in 1638. In fact, it has been proven that the laws of motion could have been solely derived from this data (Katsikadelis 2015).

Figure \(\PageIndex{5}\): The title page of Newton’s Mathematical Principles of Natural Philosophy (public domain image).

These laws were accepted as fact up until the twentieth century, based partly on the supporting mathematics and partly on the ability of the laws to make accurate predictions of the everyday behavior of objects. However, the scientific theory of gravitational laws changed when Albert Einstein published his theory of general relativity in 1915. This theory shows that there are corrections due to the size of the gravitational effect and the velocity of the object that are not accounted for in Newton's laws. Indeed, there has been no possible way to even observe these effects until recently, and in practice the Newtonian theory of gravity is a good approximation when gravitational effects are weak, and objects are moving slowly compared to the speed of light (Goldstein et al. 2002).

All of this does not mean that the scientific method is not useful, or that we cannot gain practical knowledge using the scientific method. What it means is that we must be diligent in applying the scientific method, and that we should consider the accumulated knowledge that scientific experimentation affords us. Scientific progress has cured many diseases, prevented many others, and has generally improved the quality of life for those in modern society. The development of the polio vaccine is an excellent example of the application of the scientific method in practice that has had a fundamental effect on our lives.

In the early part of the twentieth century the United States was suffering from a major polio epidemic that lasted forty years, claiming hundreds of thousands of victims, many of whom were children. Polio was a disease that tended to affect affluent communities, and this observation provided the basis for the hypothesis that a vaccine could be developed to prevent the disease. It was thought that children who lived in less affluent areas were exposed to mild cases of the disease at a very early age while they were still protected by antibodies from their mother. After becoming infected, these children would develop their own antibodies that would protect them from a more severe infection later. Hence, the hypothesis was that a vaccine could be used to train the immune systems of children to fight the disease. This led to the development of a vaccine that was used in test trials in the mid-1950s. By the end of the twentieth century polio was essentially eliminated in the United States due to the development of this vaccine.