The Logic of Scientific Discovery

“Accordingly I shall distinguish between the process of conceiving a new idea, and the methods and results of examining it logically.”

Popper’s philosophical inquiry differs strongly from his contemporaries and from the canon of epistemology. While philosophers like John Locke, Plato, David Hume, and Immanuel Kant concerned themselves with the origins of ideas, Popper argued that understanding from where or how an idea is created has no bearing on the logic of scientific discovery. It does not matter how an idea forms when one is applying deductive reasoning to it.

“The game of science is, in principle, without end. He who decides one day that scientific statements do not call for any further test, and that they can be regarded as finally verified, retires from the game.”

Popper compares the methodology of scientific experimentation to the logic of chess. In many ways, the scientific method functions like the logic of gameplay. However, this game has no end. It is predicated upon the idea that any theory or universal statement can be falsified at any time. This idea connects to the theme The Aim of Falsifiability. Popper argues that any scientist who believes in the verifiability of a scientific theory relinquishes the role of scientist and, instead, enters the realm of pseudoscience.

“Once a hypothesis has been proposed and tested, and has proved its mettle, it may not be allowed to drop out without ‘good reason.’”

This second rule of scientific methodology is Popper’s further attempt to draw a distinction between science and non-science, contributing to the theme Demarcation of Science and Non-Science. In this rule, Popper proposes that a scientific statement cannot be abandoned if it has held up under testing. It can only be replaced by a better theory or dropped if it has been determined false. In this way, scientific theories build upon one another and get closer to truth—although they will never fully reach a definitive truth.

“Theories are nets cast to catch what we call ‘the world’: to rationalize, to explain, and to master it. We endeavor to make the mesh even finer and finer.”

Throughout the work, Popper asserts that there can never be a pure scientific truth. He rejects any field that presents itself as science but asserts that ideas can be proven with empirical science. Instead, Popper proposes empirical science as a singular The Aim of Falsifiability. Adhering to a concept of universal truth is The Problem with Inductive Logic. Instead of seeking out universal truths, Popper argues that deductive logic and falsifiability bring the world closer to truth; the scientific method refines ideas to get them as close to truth as possible. However, to suggest any theory is proven as universally true is to deny the heart of deductive logic.

“In this formulation we see that natural laws might be compared to ‘proscriptions’ or ‘prohibitions.’ They do not assert that something exists or is the case: they deny it. They insist on the non-existence of certain things or states of affairs, proscribing or prohibiting, as it were, these things or states of affairs: they rule them out.”

For Popper, strictly universal statements embrace falsifiability. They do not attempt to enforce a set of laws upon the world with total authority; to do so represents the Demarcation of Science and Non-Science. Popper’s assertion in this passage may seem contradictory. He proposes that universal laws are inherently vulnerable to deniability. A surface understanding of something described as “universal” or as a “law” is that it is unequivocally true, that it has been proven. Popper proposes that any universal statement projected as true reveals its charade; nothing can ever be categorized as empirically true and to do so indicates its deception. Empirical science is defined by its deniability.

“Whenever the ‘classical’ system of the day is threatened by the results of new experiments which might be interpreted as falsifications according to my point of view, the system will appear unshaken to the conventionalist. He will explain away the inconsistencies which may have arisen.”

This quotation marks the distinction that Popper marks between science and non-science. For the philosopher, empirical evidence serves to falsify, not to verify. Those who practice pseudoscience find confirmation in every experience. A person who is thinking about switching jobs may hear a voice in a radio advertisement ask, “Have you ever thought about changing jobs?” Popper would argue that this represents a form of inductive logic. The person listening to the radio manipulates the data to affirm a desired outcome. This corresponds with the theme The Problem with Inductive Logic. Popper asserts that inductive logic is non-scientific because it seeks to affirm rather than verify ideas.

“If the degree of falsifiability is increased, then introducing the hypothesis has actually strengthened the theory: the system now rules out more than it did previously: it prohibits more.”

As Popper outlines the requirements for a robust scientific method, he suggests that theories, or basic statements, should be selected for their ability to be falsified. The more testable a theory is, the more sound it is scientifically. This stands in opposition to inductive reasoning, outlined in the theme The Problem with Inductive Logic. Rather than selecting a theory based on the perception of its truth, a scientist should select it based upon its falsifiability.

“This requirement of consistency plays a special role among the various requirements which a theoretical system, or an axiomatic system, must satisfy. It can be regarded as the first of the requirements to be satisfied by every theoretical system.”

One of Popper’s main goals in The Logic of Scientific Discovery is to outline a clear methodology for a scientific method that emphasizes deductive rather than inductive reasoning. Consistency marks a need for a control in scientific experimentation; it also emphasizes the importance of maintaining a strict adherence to a methodology in each test to determine corroboration or falsifiability.

“Science is merely an attempt to classify and describe this perceptual knowledge, these immediate experiences whose truth we cannot doubt; it is the systematic presentation of our immediate convictions.”

At first glance, Popper’s statement appears to diverge from his philosophy that scientific statements can never be verified. However, his argument in this quotation is not an assertion that science can be proven; rather, it represents an understanding of what the focus of science should be. Popper argues that scientific inquiry should seek to refine human understanding by questioning and testing accepted knowledge.

“There is only one way to make sure of the validity of a chain of logical reasoning. This is to put it in the form in which it is most easily testable: we break it up into many small steps, each easy to check by anybody who has learnt the mathematical or logical technique of transforming sentences.”

Infinite regress refers to the logical chain that is referenced in this passage. Popper argues that it is not enough to make logical assumptions based on previously accepted statements. Instead, those assumptions should be divided and tested for falsifiability, connecting to the theme The Aim of Falsifiability.

“The event must be an ‘observable’ event; that is to say, basic statements must be testable, inter-subjectively, by ‘observation.’”

One of Popper’s criticisms of psychologism is its use of unobservable data. He argues that a proper scientific methodology requires observation and tangible examples of corroboration or falsifiability. The use of observation further defines The Demarcation of Science and Non-Science. If theories cannot be perceived, then inductive logic could easily be utilized.

“Thus it can be said that the amount of empirical information conveyed by a theory, or its empirical content, increases with its degree of falsifiability.”

Popper has already established that observation is an important component of distinguishing between science and non-science. In this quotation, he asserts that raising the level of observable content leads to a greater openness to falsifiability. As Popper outlines various methods for determining statements, the degree of empirical content weighs heavily on the decision.

“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 argues that simplicity is an important consideration for and characteristic of scientific hypotheses. As simple statements move to universal statements, they become simpler and, therefore, preferable. Popper suggests that simple statements have a greater degree of falsifiability and improbability. They can be tested more easily because they seek to falsify rather than verify. Although Popper does not clearly define simplicity, he provides examples of what he believes simplicity is not. His theories on simplicity have been largely criticized for their opaqueness.

“From my point of view, a system must be described as complex in the highest degree if, in accordance with conventionalist practice, one holds fast to it as a system established forever which one is determined to rescue, whenever it is in danger, by the introduction of auxiliary hypotheses. For the degree of falsifiability of a system thus protected is equal to zero.”

This quotation speaks to the heart of why Popper emphasizes The Aim of Falsifiability. Whenever a scientist adheres to the concept of accepted truth or unspoken rules, that scientist denies the opportunity for experimentation and testing that may falsify the claim. Any contradictory evidence can be swept away under the name of conventionalism. Popper calculates that any conventionalist theories will always have a zero degree of falsifiability because there is no way to falsify a claim that is rooted in unjustified belief.

“We have, as it were, the feeling that not a scientist but only a prophet could predict them. And yet, it is just this incalculability that makes us conclude that the calculus of probability can be applied to these events.”

Popper connects the concept of probability to his ideas about conventionalism. For the philosopher, probability is the wrong focus for scientific inquiry. He correlates the prediction of generating conditions to the inductive practice of establishing natural law. Instead, he argues that scientists should seek improbability, or falsifiability.

“Thinkers with inductivist leanings mostly regard it as a fundamental law of nature, not reducible to any simpler statement; as a peculiarity of our world which has simply to be accepted.”

This quotation illustrates the theme The Problem with Inductive Logic. Popper’s ideas are closely connected to logical fallacies. Popper dismisses inductive logic as rooted in belief and conventionalist practices. Inductive statements do not leave room for falsifiability because they assume verification. Popper argues that inductive logic limits human understanding of the world and prevents scientific progress and the refinement of ideas.

“The laws we find are always hypotheses; which means that they may always be superseded, and that they may possibly be deduced from probability estimates.”

For Popper, nothing is set in stone. Scientific hypotheses are not etched into a tablet to be taught and accepted for centuries. Instead, they are fluid and open to the possibility of being tossed in the trash bin. To deny this fundamental principle is to embrace pseudoscience. In The Logic of Scientific Discovery, Popper advocates for a distinct boundary line, a Demarcation of Science and Non-Science. The eradication of ideas like “belief” and “truth” from scientific methodology emboldens that line.

“The lesson of all this is that we should try to find strict laws—prohibitions—that can founder upon experience. Yet we should abstain from issuing prohibitions that draw limits to the possibilities of research.”

Popper shows the two sides of his theories about limitations. Popper argues that testing should introduce limitations, or prohibitions, that will increase the simplicity and, as a byproduct, the falsifiability of the experiment. However, he also suggests that science itself should never be limited or prohibited. Popper views inductive reasoning as a limitation of science; by accepting some ideas as truth, science is restricted in its exploration of those ideas.

“Consistently with my attitude towards other metaphysical questions, I abstain from arguing for or against faith in the existence of regularities in our world. But I shall try to show that the non-verifiability of theories is methodologically important.”

Popper does not directly address systems of belief or the validity of belief. He merely argues that it has no place in scientific methodology. This statement corresponds to The Aim of Falsifiability. Rather than speaking about faith in general, Popper explores how faith limits scientific inquiry.

“The symmetry between verifiability and falsifiability accepted by classical inductivist logic suggests the belief that it must be possible to correlate with these ‘undecidable’ probability statements some scale of degrees of validity.”

Popper rejects a principle of quantum theory that suggests some aspects can never be precisely measured. He correlates the idea of probability with the conventionalist and positivist practices of inductive reasoning. The symmetry he references in this quotation refers to the idea that verifiability and falsifiability are of equal weight and importance. Popper, instead, argues that the two are not equal. Falsifiability has more scientific validity.

“Corroboration is therefore not a ‘truth value’; that is, it cannot be placed on par with the concepts ‘true’ and ‘false’ (which are free from temporal subscripts).”

Popper closes by clarifying the meaning of corroboration. When a hypothesis is corroborated, it is not determined as true or set as a law. Instead, it means the outcome of testing is the same as previous testing outcomes. Corroboration is important because it helps to refine theories, but it is not as important as falsifiability, which Popper argues provides more information about the world.

“Science is not a system of certain, or well-established, statements nor is it a system which steadily advances towards a state of finality. Our science is not knowledge (epistēmē): it can never claim to have attained truth, or even a substitute for it, such as probability.”

Popper’s work falls into a specific niche of philosophical work. Popper is not interested in exploring or understanding the epistemology of where knowledge or ideas originate, nor is he interested in establishing truth or beliefs. Instead, his work sits squarely in the middle. He is interested in the process by which ideas become refined through testing. This process is never finished; the end goal of truth is never achieved. However, Popper argues that this does not mean that the work of scientific discovery is unimportant. It is a continuous journey that brings humans ever closer to an understanding of the world.

“The wrong view of science betrays itself in the craving to be right; for it is not his possession of knowledge, or irrefutable truth, that makes the man of science, but his persistent and recklessly critical quest for truth.”

If all science has The Aim of Falsifiability, then the purpose of falsifiability is to engage in a continual search for truth. Popper’s philosophy on the function and goal of science has interesting implications in contemporary discussion. For example, the prevalence of conclusive ideologies that deny concepts like climate change are in direct contrast to Popper’s theories on falsifiability, testability, and methodology.