The Bayesian approach to the philosophy of science was developed in the first half of the twentieth century. Karl Popper and Thomas Kuhn are twentieth-century philosophers of science who later proposed alternative approaches.
It will be convenient to start with the Bayesian approach since we already talked about probability and Thomas Bayes in this post. The Bayesian approach (mainly associated with Ramsey and Savage) can be regarded as a verification-based philosophy of science; it is based on different scientists gradually updating, according to new empirical evidence, their (different) prior (subjective) probabilities of scientific explanations and theories, until the cumulative evidence is strong enough to reach a common conclusion.
One difficulty with the Bayesian approach is that in cases of disagreement, there are also disagreements on the interpretation of the evidence.
Bayesian view does not give a way to test a scientific theory but rather to update our beliefs in the theory given new evidence. In practice, scientific theories primarily explain existing observations. For example, the main motivation of Newtonian mechanics and the main support for its validity was the explanation of Kepler’s laws. Kepler’s laws concerning the elliptic orbits of planets around the sun were discovered seventy years before they were explained by Newtonian mechanics.
Karl Popper Thomas Kuhn
Popper is famous for basing philosophy of science on the notion of falsification. According to Popper, the mark of a theory as scientific is falsifiability: the possibility to empirically refute the theory – in principle. This is in contrast with other approaches that can be viewed as basing philosophy of science on confirmation or verification. Famously, two principal examples of non-scientific theories according to Popper are the Marxist theory of capital and Freudian psychoanalysis.
If the Bayesian approach, like approaches based on verification, suggests that the optimal way for a scientific theory to proceed is by making safe conjectures which may lead to small incremental progress, Popper’s approach suggests making bold and risky conjectures. One concern about practical implication of the Popperian approach is the fact that bold conjectures and theories that pass the falsifiability test are of little value if they are absurd or simply false to begin with.
Critics assert that neither Popper’s theory nor earlier approaches based on verification give a proper description of how science is practiced. Also, they have limited normative value regarding how science ought to be practiced. It is especially difficult to use the insights from philosophy of science for scientific theories under development.
Thomas Kuhn is famous for his notions of paradigm shifts and scientific revolutions. According to Kuhn, science is normally carried out inside a certain paradigm that is shared by a community of scientists, and it is furthermore characterized by “paradigm shifts,” which occur when the current paradigm is no longer capable of explaining the new evidence. Kuhn referred to the process of switching from the common paradigm to a new one as a “scientific revolution.” An important example of a scientific revolution analyzed by Kuhn is the shift from Newtonian mechanics to Einstein’s theory of relativity.
It may be useful to put things described here in a larger context and give a few more details.
Verification approaches towards philosophy of science: Verification- (or confirmation-) based approaches to scientific theories were developed in the first half of the twentieth century and became quite dominant in the philosophy of science until today. An important role in their development was played by the Vienna circle, a group of philosophers, who shared common basic attitudes towards philosophy, and who gathered in Vienna mainly between the two world wars. According to most of these verification-based approaches, scientific theories are gradually examined and updated in view of new empirical evidence.
Philosophy and logic: The Vienna circle approach towards philosophy of science is part of their larger approach to philosophy centered on the rejection of metaphysics (and religion, in particular). This approach, called “logical positivism,” is related to a greater move associated with Bertrand Russell and others to base mathematics, science and philosophy on logic. Logical positivism has led not only to distinctions of “what is scientific” and “what is unscientific”, but also to an attempted classification of “what is meaningful” and “what is meaningless”. As a result, for many decades the central interest in philosophy moved away from traditional issues like “justice,” “ethics”, and “beauty” which were labeled as unscientific and even meaningless. (At a later time, attempts to distinguish “meaningless” from “unscientific” were made, and eventually the main interest in philosophy moved back to where it was before “logical positivism”.)
Critiques of early versions of confirmation approaches in the philosophy of science were made, at the beginning of the 20th century, by French philosopher Pierre Duhem and by Henri Poincaré. Duhem’s approach asserts that the main test of a scientific theory is its internal coherence and consistency. Both Duhem and Poincaré gave much weight to “intuition” and “insights.” This dispute is related to a famous debate between Poincare and Russell on the role of logic in mathematics.
Probability: Probability plays an important role in some of the verification-based approaches to the philosophy of science. Often they rely on a logical (objective) notion of probability rather than “subjective probability” which is central to the Bayesian approach. Foundational questions regarding probability theory again come into play. Logical probability (also referred to as “partial deduction”) is based on the idea that probability can describe a logical relation between two statements. This idea goes back to Wittgenstein, Caynes, and perhaps even to Leibniz. Rudolf Carnap, a central member of the Vienna circle, had a programme which he believed could lead to a whole logical calculus of probability starting with answer to the question: “What is the probability of a statement A given the validity of statement B?” and ending with an answer to “What is the probability that a theory X is correct?”.
Popper deliberately diminished the role of probability in his approach to philosophy of science. A (parhaps familiar) critique of Popper was expressed by Oded Schramm who wrote (after reading an earlier version of this post): “I remember when I read Popper, I was very disappointed with his treatment of probability. It was totally unsatisfactory. (This was much before I became seriously interested in probability.) Probability statements are never falsifiable.”