The Logic of Scientific Discovery

In the fields of logic and mathematics, an axiomatized, or axiomatic, system is a set of statements that can be taken as true and work together to form a complete system. Popper suggests that this system of statements must exclude any superfluous assumptions and that the axioms should only be selected based on their relation to the subject.

When Popper refers to the methodology of the scientific process, he refers to the rules of this process as “conventions.” Popper outlines two conventions he feels should be an inherent part of the scientific process: (1) science should be unending and never reach a conclusion, and (2) new ideas should be based on established ones that have proven their worth through extreme testing.

In contrast to the definition of “conventions” is the concept of “conventionalism.” This refers to the philosophical idea that universal principles may be created based on societal agreements. Popper refers to conventionalism as a form of belief used by those who sought to excuse certain concepts from rationalistic scrutiny.

Deductive logic, or deductive reasoning, is a scientific approach that emphasizes deductive inferences. For Popper, this meant that scientific experimentation should seek to falsify a claim rather than verify it.

Demarcation refers to creating a separation or boundary of lines. In science, demarcation refers to the problem of separating science from non-science. Popper’s rejection of inductive logic is an attempt to clarify the line of distinction. He suggests that epistemology and psychologism fall within the realms of philosophy but not science.

This term refers to the establishment of a set of principles as inherently true. Popper argues that scientists must reject dogmatism and regard it as dangerous.

Empiricism is a philosophical theory that states that all knowledge is born out of sense-experience. Eighteenth century philosophers like David Hume and John Locke established an empiricist approach to science that emphasized seeking proof through experience. Popper translated these ideas to mean that empirical science required robust testing in as many ways as possible.

Epistemology refers to the theory and study of knowledge, including its origin and development. Throughout history, many philosophers have sought to understand how knowledge works. Popper proposes a scientific approach to epistemology. Rather than concerning himself with the origin of an idea, Popper focuses on the rigorous testing of an idea with the purpose of falsification.

Falsification refers to the aim of determining a theory or an idea to be false. Popper believed that falsification should be the sole aim of scientists. His work with falsification stood in direct contrast to the positivistic approaches of his fellow philosophers. Popper proposed that all theories had the potential to be falsified; therefore, the only logical scientific approach would be to seek this falsification.

Frequency theory was developed by Karl Popper as an answer to the problems he saw with probability. Frequency theory is illustrated when a scientist performs the same or similar experiments repeatedly over time. The same outcome each time, or generating condition, represents the propensity Popper categorizes as “frequency.”

Fries’s Trilemma, also called the Münchhausen trilemma, is a thought experiment that illustrates the impossibility of affirming a truth. The trilemma seeks to show how neither dogmatism, infinite regress, nor psychologism determines truth. Popper argues that the trilemma becomes obsolete when one recognizes that elements of all three are necessary in scientific experimentation.

Popper applies his theories of falsifiability and simplicity to the work of Werner Heisenberg in the field of quantum mechanics. Heisenberg developed the uncertainty principle, which states that the velocity of an object can never be measured with preciseness. Popper challenges this idea and argues that quantum mechanics can, and should, be measured precisely by emphasizing falsifiability over verification.

Inductive logic, or inductive reasoning, is a scientific approach of drawing conclusions from evidence. Popper calls inductive logic the “positivistic dogma” (40). He suggests that inductive reasoning requires the declaration of statements of truth based on limited information. Popper argues that humans can never be fully assured of any idea because any theory can be falsified.

Infinite regress represents a series of statements believed to be true or justified because they build off other statements. A way to explain this is as follows: because x is true, y must be true, and because y must be true, z must be true also. The series has an infinite continuation.

In philosophy, objectivity refers to truth that is based on ideas independent of personal bias and experiences. Popper argues that the scientific method requires objectivity, but he argues that science can never achieve universal statements of truth.

In the scientific realm, probability represents the chance or likelihood of particular generating conditions. Popper argues that seeking probability is less important than seeking improbability.

Psychologism is a term used by philosophers to distinguish between psychological principles and the scientific world. Popper’s use of the word marks his perception that psychology does not adhere to the necessary requirements of the scientific method, including falsification. Popper provides his own definition of the term on page 94, where he suggests that psychologism represents the justification of theories through experience.

The Western philosophical position of rationalism argues that humans acquire knowledge through their inherent ability to reason. Rationalists believe existence contains a series of universal truths that humans understand through logic. Some rationalists believe humans are born with an understanding of some truths.