Conjectures and Refutations

Popper recounts how he first began to question what differentiates science from pseudo-science. As a student at the University of Vienna in 1919, he became interested in various branches of science and philosophy, such as Einstein’s theory of gravitation, Marxism, and Freudian and Adlerian theories. However, the more he studied, the more he became disillusioned with the scientific nature of the latter three theories.

Popper realized that disciples of Marx, Freud, and Adler saw confirmation of their theories in daily life. Every scenario, no matter how irrelevant in Popper’s eyes, could be explained in Marxist, Freudian, or Adlerian terms by their defenders. By contrast, students who studied Einstein’s theory were much more concerned with testing both its validity and its limitations.

Popper realized that theories based solely on instances of verification could not be scientific, since they can explain everything and they only encourage the search for more instances of confirmation up to the point where they become irrefutable. He observes that this closely resembles astrology, where any prediction horoscopes make can be confirmed if they are vague enough.

Popper proposes instead that confirmations only hold weight if they result from risky predictions. Sound scientific theory should be prohibitive rather than all-encompassing, and genuine tests of theories are attempts to refute them. These are the foundational principles of Popper’s theory of falsifiability.

Scientific theories often originate from myth. For example, the theory of evolution was, at the very start, closer to conjecture than conclusion. Only with additional testing could scientists confirm certain aspects of it and reject others. As a result, Popper warns that falsifiability has nothing to do with a theory’s meaningfulness or acceptability, but with demarcation: Its purpose is to differentiate, as clearly as possible, science from pseudo-science.

After critiquing these other disciplines, Popper points out that even empirical evidence and a priori reasoning—which form the basis of scientific reasoning—are inherently biased processes. In both cases, human interpretations are necessarily added to these experimental observations. For example, a professor cannot simply ask their students to “observe!” without confusing them about what they should focus on. The very act of guiding students to observe a specific aspect of an experiment is a result of human intent.

Even more broadly, the very act of induction—of associating two things, or of finding regularities in events or ideas—is a biased process. These logical connections are founded on past experience or human instinct, but even though both can lead to an observable truth, neither are guaranteed to be correct. In other words, the universe does not necessarily function according to how humans instinctively or logically think it might function. Despite the human propensity to look for regularities in the world, it is not guaranteed that these regularities exist objectively.

Popper concludes that people whose reasoning relies solely on finding similarities and regularities are dogmatic, whereas people who are ready to amend or give up their beliefs when presented with contrary evidence are critical. Dogmatic thinking is characteristic of pseudo-science, whereas critical thinking is closer to Popper’s ideal of the true scientific attitude. Of course, this does not mean suppositions and hypotheses cannot be made—after all, without raw materials, there is nothing to critique or attempt to falsify. Popper’s theory argues that the fundamental difference between pseudo-science and science is a matter of attitude: Logical argumentation, reasoning, and observation are all important to build theories with a high degree of corroboration, but a true scientific attitude welcomes any attempts at falsifying or criticizing these theories to avoid falling into the trap of presupposing our inductions to be true.

Popper explains why philosophizing—the act of using logical reasoning to arrive at theories—is important, despite there being some truth in philosopher Ludwig Wittgenstein’s thesis that philosophy is no more meaningful in generating knowledge than stringing random words together. According to Wittgenstein, genuine problems are all scientific in nature, whereas philosophy only answers pseudo-problems through pseudo-theories and pseudo-propositions, which are irrelevant to the search for true knowledge.

Popper begins by explaining Wittgenstein’s theory, then criticizes it. He first points out that Wittgenstein categorizes philosophy as a distinct field in the same way that physics or mathematics or history are all categorized according to their subject matter. Popper argues that this is a residue of an outdated practice: It is done for administrative convenience and to organize teaching. Subject matter do not objectively have categorizations; they were assigned categories by people. Popper emphasizes that scholars should be students of problems, which may cut across these traditional disciplinary borders. Thus, as long as philosophy is capable of inducing meaningful questions, it remains as worthwhile as any other science.

Popper addresses whether philosophy is capable of inducing meaningful questions. According to Wittgenstein, this is impossible, because he classifies all worthless questions as philosophical ones, and all worthwhile ones as scientific. He reprises a system established by mathematician and philosopher Bertrand Russell, which categorizes expressions of a language into true statements, false statements, and meaningless expressions (i.e., pseudo-statements). False statements are meaningful because their negation must be true. For example, “3 times 4 equals 173” is a false statement, but its negation, “3 times 4 does not equal 173” is true, and thereby imparts a certain degree of meaning. By contrast, a meaningless statement, such as “3 times 4 are cows,” is completely worthless because its negation, “3 times 4 are not cows,” gives equally unsatisfactory information. Since philosophy is centered upon reasoning about ideas and can produce contradictions that cannot be resolved, Wittgenstein claims its statements are as meaningless as a groan or sigh.

Wittgenstein then proceeds to classify all statements into four categories: Purely logical or mathematical statements; factual statements that can be proven by empirical science; statements that are a combination of the first two; and meaningless pseudo-problems, such as “Do all cats equal 173?” He concludes that philosophy is nothing but attempts to solve linguistic puzzles that have little factual weight.

Popper concedes that philosophy, like every other discipline, can devolve in a way until it no longer tackles genuine problems. This is especially true if philosophy is taught in a prima facie way, whereby students are asked to read the works of great philosophers and think only on an abstract level. This leads to students thinking more and more in abstractions, often losing track of what problem they were trying to solve in the first place. However, this loss of meaning can be prevented if philosophers continue to try to solve concrete and urgent problems outside of abstraction. For example, if a question arose regarding atomic theory, but was closely connected with the theories discussed by philosophers, then there should be no reason to think this problem is unrelated to philosophy.

Similarly, spectral terms, which are a phenomenon in physics, can be best explained by purely mathematical calculations, but there is no reason to conclude that this is a problem confined to the realm of mathematics. Since solutions to problems may transcend traditional disciplinary boundaries, philosophy—and by extension, pure reasoning—can very well be useful.

Throughout the rest of Chapter 2, Popper uses the development of Greek atomic theory to argue that philosophical problems have roots in science. For example, both Pythagoras and Democritus believed all things in the natural world could be explained using arithmetic (counting) on its smallest particle (atom), and this could explain even the existence of abstract concepts, such as balance and harmony. This theory was defeated with the discovery of irrational numbers (such as the square root of 2), and subsequent philosophers such as Euclid, Archimedes, and Copernicus have turned to geometry to measure tangible things in nature.

Popper asserts that both of these theories should be seen as attempts to explain the visible world using instruments of theoretical science, such as mathematics and physics. He adds that visible matter can be explained by hypotheses about invisible structures too small to be seen. In other words, physics and mathematics are called to answer questions about cosmology, and some of these efforts have led to great scientific discoveries, such as the Copernican, Newtonian, and Einstein revolutions. Should these questions belong purely to mathematics and physics, when the starting incentive was to answer questions about the universe? Popper’s answer is a resounding “no.”

From these historical instances, philosopher Immanuel Kant concludes that knowledge is acquired not because humans are passively receiving and sensing information sent to it by nature, but because they possess intellect and a desire to understand. It is not that the laws of nature are “discovered,” but rather that people impose their interpretation of observable phenomena on nature. Popper partly agrees with this theory, as he also believes in intellectual curiosity as an important spur to scientific progress. However, he thinks it too convenient that people merely impose their will on nature, because this would lead to the absurd conclusion that anyone could have the authority to understand deep cosmological problems, yet only a few people actually make great discoveries.

Popper instead proposes that laws of nature are not simply human impositions; they may actually objectively exist, but this truth is hard to come by. It requires risky predictions, deep attempts at falsification, and trial and error.

This chapter provides an overview of the Galilean tradition and how this evolved into the instrumentalist view of knowledge (i.e., knowledge as nothing but a tool to help humans achieve arbitrary goals). This view is now the most accepted approach to the philosophy of science. Popper then critiques instrumentalism and proposes to view knowledge acquisition not only as a tool, but as a legitimate attempt at finding the truth. To prove his point, Popper traces the history of physics from Galileo’s time to the more recent discovery of quantum mechanics.

The issue at stake with instrumentalism is that it is at risk of losing the “rationalist tradition” which has been passed down from the ancient Greeks and which, according to Popper, is the essence of western civilization and the power behind science as a liberalizing force. Dogmatism discourages critical thought and the adoption of new beliefs, which can supersede old prejudices and myths. Thus, there is a risk of falling into the trap of thinking all knowledge cannot ultimately reveal the truth about the universe, bringing into question human freedom and threatening the validity of science.

Galilean philosophy of science includes three fundamental doctrines:

1. The aim of the scientist is to find a true theory that describes the world and that can explain observable facts.

2. It is possible for scientists to establish these theories as true beyond reasonable doubt.

3. Theories that have reached this point are ultimate explanations; they describe the very essence of things and reveal their real nature.

Instrumentalists oppose this tradition because they reject the idea that science can help people uncover real truths. They do not believe in the third doctrine about essences: Some reject the very existence of “essences” of things, while others believe that the “essence” is a manifestation of God, whose existence is fundamentally unknowable by humans through research. They all conclude that humans do not have the ability to describe any real truth, and their method is therefore just an instrument for the sake of growing theoretical knowledge.

Popper disagrees with the instrumentalist approach because, if it is true that “essences” do not exist or can never be understood by humans barring divine revelation, then it follows that no real truths can ever be known about the physical world. Thus, instrumentalists must conclude that science has never proven anything of consequence about the functioning of the world and the second Galilean doctrine must be mistaken. All scientific theories are only useful as far as they help develop mathematical predictions within defined boundaries, but none truly reflect the true “essence” of the universe.

This is why instrumentalism also tends towards relativist reasoning. For example, it can argue that stating that the earth rotates is meaningless, because Einstein’s general principle has disproven the concept of absolute motion: Any matter, including Earth, can be seen as inert depending on the observer’s chosen point of reference. Thus, no scientific statement matters outside of its limits, and it is only useful within the confines of its uses. In other words, all theories (including those that have been subsequently disproven) are always true, within the confines of their delineated limits—which is the very pitfall of a circular argument.

This conclusion is unbelievable to Popper because, for the purpose of delineating between science and myth, it would mean rejecting every groundbreaking scientific discovery, from the rotation of the earth to quantum physics, as nothing more than pseudo-knowledge. It would mean concluding that science cannot glimpse at the essence of things because essences either do not exist or are impossible to be understood by humans, and is only useful insofar as it demonstrates a law that must be true within the limits that humans set for the purpose of forcing it to be true.

Instrumentalism neglects falsification and thus obfuscates research. Popper finds the same fault in the Galilean philosophy of science. Though he may not disagree that “essences” of things could exist, he finds they are irrelevant to the purpose of research and are, like instrumentalism, liable to create obstacles to new discoveries.

For example, Newton’s theory of gravity dictates that every particle has the power to attract other particles (gravity) and the ability to resist change in its state of motion (inertia). Since every particle inherently possesses both gravity and inertia, they must be proportional to that particle’s mass. Newton’s law is therefore a mathematical description of the state of motion of a particle due to its inherent properties. In essentialist terms, it describes the “essential nature of matter” (104) and the mathematical equations that ensue explain the behavior of that matter.

Some scientists believed at the time that Newton’s theory was complete and no further explanation was necessary to prove its truth, the only exception being the addendum that God created matter to act this way. However, we know now that Newton’s theories are not without fault, and questions such as what causes gravity are essential to ameliorating this theory. Thus, the Galilean reflex of accepting scientific discoveries as having provided ultimate explanations that do not need any further examination can harm research and prevent further questions from being raised.

Popper agrees with the first Galilean doctrine, and sides with the second Galilean doctrine rather than the Instrumentalists, but firmly rejects the last doctrine, as he does not believe it is possible for any scientific theory to become all-encompassing. No matter how well-established these theories are, they must remain malleable and falsifiable to ensure their growth and their ability to be refined by later generations. For theories to be true beyond reasonable doubt, humans must have an exhaustive list of tests they can perform to prove this, which is an impossible task.

Finally, Popper proposes a third view to the philosophy of science: He asserts that science is capable of real discoveries but that the “truths” they glimpse are genuine conjectures that describe aspects of the real world. Rather than separate between the observable world of humans and the “real” (or “essential”) world of ultimate reality, Popper proposes that people view science as descriptive of the various layers of the real world.

For example, a piano need not be divided between its physical, observable state and its unobservable, logically-constructed atoms. Neither should its appearance be viewed as an illusion in comparison to its atomic makeup (which is “real” because it follows verified quantum principles). Both versions of the piano are reflections of reality, and all genuine conjectures in relation to their existence and behavior are equally capable of describing their real state.

States of affairs are real if the statements that describe them are true, and truths can exist insofar as theories can be falsified. This is because disproving a rule guarantees that certain events cannot happen, which then “asserts something about reality” (117). In other words, theories that clash against reality prove its existence: It guarantees that something is capable of pushing back against human ideas.

In Chapter 4, Popper discusses how science is a tradition in the same way that celebrations are traditions, but the fundamental difference between the two is that science encourages criticism and change. Popper identifies as a rationalist, but he does not agree with the standard rationalist critique of tradition, which stipulates that all myths and traditions are inferior to science because they are not based on observed phenomena.

Popper underlines that science is not different from any other myth because human observation is necessarily biased. Scientific discoveries are all based on previously accumulated human knowledge—they are different only because they refine and challenge these preexisting ideas. Science, just like myths, is founded upon previous attempts at explaining the world. It is different from religious myths only in that it invites critique and encourages change, which allowed for the development of systematic observation—the act of applying a theory to test its validity.

The chapter first traces how myths are created. Popper begins by observing how the scientific tradition came about. The ancient Greeks achieved something when they began discussing observable phenomena, and it is this act of negotiating and contesting existing beliefs that allowed them to establish a new tradition of valuing critical attitudes towards old myths. Of course, the conclusion of their discussion could have been to create another myth to replace the old one, but the very act of critiquing is groundbreaking for new discoveries. Scientific discoveries might originate from myth, but they are different from religious myths because they invite criticism and refining.

The function of tradition in social life is very similar to that of science. There is a need for traditions in social life because they help guide people’s actions by bringing a certain order of predictability. Without a basic order of things, people would be anxious and disoriented. Similarly, science can bring order into the chaos of the world by trying to make it rationally predictable.

People cling to myths because they bring a certain uniformity and predictability to the world, even if they are untrue. They are generally afraid of change and irregularity; by searching for means to validate myths, they help convince others of their rationality and predictability.

According to philosopher Karl Bühler, language has three functions:

1. An expressive function, to communicate the emotions and thoughts of the speaker

2. A signaling or stimulative function, to stimulate a reaction in the listener

3. A descriptive function, to illustrate the state of affairs of a phenomenon or object

Popper adds a fourth function for the purpose of his own theory:

4. An argumentative or explanatory function, to present and compare ideas in connection with problems or questions

Popper argues that without this final function, language can be used to spread falsehood. Descriptions by themselves can discuss something true, or they may be used to spread propaganda and pseudo-arguments. Thus, the argumentative and explanatory function of language can help refine people’s understanding of the world and critically assess information relayed to them.

Popper wishes to return to the rationalism of the Pre-Socratics because they tackled cosmological questions and questions related to the theory of knowledge. Here, cosmology is defined as a field whose purpose is to glimpse at the truths of the world. Popper’s interest in science and philosophy lies in their respective attempts at understanding the universe—they lose their attraction if they are taken as nothing but instruments for research.

The Pre-Socratics attempted to answer bold questions about the proper functioning of the universe. Thales, the founder of the Ionian School, stipulated that the earth was suspended in water and shook during earthquakes the same way boats tilt when hit by strong waves. His and the Pre-Socratics’ questions were admirable because they did not purely stem from observation, since there was no way to observe the entirety of the earth at the time. Their hypotheses were accepted or rejected based on tests they could perform and on reasoning. Thus, the foundation of their rationality lies not in their ability to observe the natural world, but in their critical assessment and testing of their hypothesis.

Anaximander, the student of Thales, proposed that the earth is suspended in space and not supported by anything else. It can remain suspended because it is at an equal distance from all other things in space and thus maintains its equilibrium. This rudimentary theory is not based on any observable fact, but it is revolutionary in its resemblance to Newton’s idea of gravitational forces. Popper stipulates that Anaximander formed this theory to critique his teacher from a logical reasoning standpoint. It could be reasoned that, if the earth were stabilized by an ocean, then that ocean must be supported by something else—a situation of infinite regression. Anaximander’s theory removes this problem by proposing a theory based on the internal symmetry of the universe, which is relative and does not require an ultimate source of support.

Since Anaximander’s theory cannot be empirical, as he did not have the instruments to observe the earth and space, many would relegate his reasoning to within the realm of philosophy. Popper, however, disagrees with this impulse: If scientific thought is defined by its origin in observations, then very few scientific theories would fit this mold, since there are countless phenomena impossible to see with the human eye. Popper instead proposes that scientific theories should be measured for their explanatory power and their ability to stand up to criticisms and tests.

The rest of the chapter discusses the general problem of change and the general theory of change. Greek philosopher Heraclitus believed that everything was in flux, and nothing remained static. For example, though the timber of a house might look unchanging, it is every second going through the process of decay; though rocks are viewed as solid, they are going through the very slow process of withering. Viewed this way, everything in the world is in motion and nothing is a solid, unchanging body.

However, this creates the problem of change. In order for something to change, it must first have something fundamentally unique to it, and that something must not be lost in the process of changing. For example, a leaf changes when it turns from green to brown, but a green leaf does not “change” if we substitute it for a brown leaf, because we consider those two leaves to be separate entities. Therefore, the green leaf that turned brown must undergo a metamorphosis, yet still retain its identity so that it is still recognizable.

This logical paradox led many philosophers to believe that our world is made of appearances whereas the “true” world of the gods is unfathomable. To the human experience, things can shift between defined states, such as going from good to bad or asleep to awake, but these are all illusions, and to God, these states are one and the same. Parmenides concluded that change and motion are therefore born of human senses, and to God, all things are the same and there is no change. From this logic, the theory of change concludes that all qualitative changes that humans perceive are in fact movement of unchanging bits of matter (atoms) across the void.

Popper admires the quantity and originality of the new philosophies and cosmologies that emerged in ancient Greece. Later generations would revise and test their mentors’ works, an act only possible because there existed a tradition of critical discussion. Every culture has its own version of cosmological and religious teaching, but not all welcome critical discussion. Often, new ideas are considered heretical, and students are expelled if they deviate from the school’s doctrine. This encourages an atmosphere where every attempt at engaging with the doctrine is a re-statement of earlier sayings.

Popper believes it was Thales who founded this new tradition of critical discussion between master and pupil. Anaximander, his pupil, was allowed to criticize his master’s work, despite Thales being the founder of the Ionian school and one of the Seven Sages. Anaximander would probably only have felt comfortable doing so if his master not only tolerated students pushing back, but actively encouraged it. The Ionian school is thus historically recognized as producing students who each attempted to improve upon the works of their masters. The same school could thus produce work in a plurality of fields and encourage intellectual growth. This tradition was lost with the rise of the Aristotelian school, briefly found again during the Renaissance by Galileo Galilei, and lost again today.

It is this rationalist tradition that Popper wishes to revitalize. He believes the only way to expand human knowledge is through critical discussion, as neither observation nor logic are, in themselves, scientific. Thus, every attempt at understanding the world is only guesswork; but through a dialogue of producing conjectures and refutations, ideas are rationally tested for their validity. Rationality is the search for knowledge and truth through critical discussion.