Conjectures and Refutations

Isaac Newton (1643-1727) was an English astronomer and mathematician best known for having theorized about the three laws of motion, which remain to this day the foundational principles of modern physics. His work improves upon the scientific discoveries of Galileo Galilei, Johannes Kepler, and Nicolaus Copernicus by proving the solar system’s heliocentricity and by providing a means to calculate the laws of planetary motion.

Newton’s work characterized the start of the Enlightenment period and heavily influenced the field of philosophy by altering people’s understanding of the universe. In Popper’s writing, Newton’s scientific discoveries are examples of highly risky predictions that have withstood, for a long time, vigorous testing. Although they have since been partly replaced by Albert Einstein’s even more precise calculations, they remain a perfect example of how high-content, risky predictions supplant low-content and safe predictions as the greatest kind of scientific discovery.

Nicolaus Copernicus (1473-1543) was a Prussian mathematician and astronomer best known for his publication, On the Revolutions of the Celestial Spheres (De revolutionibus orbium coelestium), which, for the first time, placed the sun rather than the earth at the center of the solar system. Copernicus’s work revolutionized contemporary mathematicians’ understanding of the model of the universe and propelled the Scientific Revolution, which would later produce other great scientists such as Galileo Galilei, Johannes Kepler, and Isaac Newton.

Copernicus figures in Conjectures and Refutations primarily as an example of someone whose thought defied dogmatic empiricism. Copernicus could not have empirically observed heliocentricity, as he hardly had the tools to travel to space; thus, it is clear that part of his conjectures must have been based on logical deductions. His theory was also risky for going against the commonly-accepted Ptolemaic model of the heavens, which placed the earth at the center of the universe. Despite being based on a hypothetical conjecture rather than empirical evidence, Copernicus’s theory withstood vigorous testing and the basics of the model remain true to this day. This proves Popper’s idea that ad hoc hypotheses need not be the basis of all great scientific discoveries, and that imagination can play a big role in the process of acquiring knowledge.

Albert Einstein (1879-1955) was a German-American theoretical physicist best known for developing the theory of relativity and furthering research on quantum mechanics. His work provided a structure for the evolution of the universe and earned him the 1921 Nobel Prize in Physics. His work heavily influenced other mathematicians, logicians, physicists, and philosophers, including Rudolf Carnap and Karl Popper.

In Conjectures and Refutations, Einstein’s discoveries are cited as having refuted some of Newton’s theories by virtue of being even more high-risk and having withstood even more rigorous testing. This shows that knowledge acquisition is a process characterized by greater theories partly or wholly supplanting older ones.

Rudolf Carnap (1891-1970) was a German philosopher known for having founded the field of the philosophy of science and for having defended the principle of logical positivism. Central to his school of thought was the belief in refining semantics to yield empirical and inductive logic of greater accuracy. Carnap made several attempts at refining scientific language to remove from its syntax what he deemed useless phrases. His work was heavily influenced by Immanuel Kant, Ludwig Wittgenstein, and Albert Einstein.

Although logical positivism has become less favored since the 1950s, Carnap remains a central figure in the history of modern European philosophy. His work on semantics figures as the focal point of Popper’s critiques in Chapter 11, where Popper argues that it is a futile endeavor to make a perfect axiomatic scientific language: Any self-contained and complete system cannot be proven true using its own rules, and language, as a tool for communication, need not be perfect to achieve its intended purpose.

Ludwig Wittgenstein (1889-1951) was an Austrian philosopher of logic, language, and mathematics. He is best known for his thesis, Tractatus Logico-Philosophicus, which attempted to define the limits of science and the use of philosophy by reviewing the relationship between language and reality. He is posthumously known for the publication Philosophical Investigations, which criticized traditional philosophy for being too dogmatic in its approach to solving problems.

Wittgenstein’s work heavily influenced Popper and features prominently in Chapter 2 of Conjectures and Refutations. Despite Popper’s respect for him, Wittgenstein’s theory on the futility of philosophy is heavily criticized for being too dogmatic, especially when some of the greatest scientific discoveries, such as the Copernicus Revolution, were sparked by philosophical inspirations rather than empirical evidence.