Philosophy of Science - Part III

Thomas Kuhn

Thomas Kuhn is probably best understood as a historian of science rather than a philosopher of science. His book, The Structure of Scientific Revolutions, however, is a significant text for an understanding of the philosophy of science. Prof. Kasser described a pattern Kuhn discovered in the history of science—“normal science punctuated by periods of revolution.” Kuhn, according to the lecturer, dealt logical positivism its most severe blow.

Popper and the positivists focused heavily on the scientific method and the rationale by which science increases understanding about the world. However, for Kuhn, the underlying method and logic was not nearly as important as understanding how scientific views are adopted and modified. Kuhn believed that the way to study science itself is to evaluate the activities that scientists spend most of their time doing. Science generally had been taught in terms of its success only. Kuhn described this history being taught to future scientists as similar to brainwashing. Thus, science textbooks are filled with heroes, hyperbole, and drama about experiments. Kuhn argued that science is governed by a paradigm:

1. A paradigm is, first and foremost, an object of consensus. 2. Exemplary illustrations of how scientific work is done are particularly important components of a paradigm. Scientific education is governed more by examples than by rules or methods.

Paradigms create consensus concerning the way in which work should be done in a particular field and this is unique to science. Puzzle-solving is the work of normal science. This paradigm “identifies puzzles, governs expectations, assures scientists that each puzzle has a solution, and provides standards for evaluating solutions. It is generally assumed to be correct and doing science involves fitting into the categories of this paradigm, observations about the behavior of nature.

Thus, the paradigm is a test for the scientist in that failing to solve a puzzle reflects poorly upon the scientist rather than on the paradigm itself. Sometimes, a crisis occurs in a particular scientific community when its members lose their “faith” in the paradigm. According to Kuhn, these crises often occur as a result of anomalies and puzzles that scientists have repeatedly failed to answer. Thus, this is a kind of crisis of confidence. Kuhn argued that Popper’s view was that this was the normal state of science. Not so, according to Kuhn, if this were true science would fail to accomplish anything. Sometimes, paradigms may be abandoned in favor of new ones. Kuhn argued that this is a good thing for understanding and for science as long as it occurs rather rarely.

A lot of Kuhn’s assertions can be boiled down to “his insistence that rival paradigms cannot be judged on a common scale. They are incommensurable. This means they cannot be compared via a neutral or objectively correct measure.” Therefore, changing paradigms resembles something of a “conversion experience.” Since individual psychology has a lot to do with how individuals “convert” to a new paradigm, Hungarian philosopher Imre Lakatos referred to Kuhn’s model of science as “one of mob psychology.”

Imre Lakatos was the first to try to reconcile the rationalism of the “received view” and Kuhn’s “historicism.” His methodology concerning scientific research attempts to incorporate both Popper’s openness to criticism and Kuhn’s attachment to theories. Methodological rules retroactively judge science research as either progressive or degenerative. Paul Feyerabend, another significant philosopher of science, views Kuhn’s model as dull, mindless scientific activity. “In arguments alternately sober and outlandish, Feyerabend defends scientific creativity and epistemological anarchism.”

Sociology and postmodernism have also provided some insight into science. One researcher believed that science was often reduced to semantic absurdities. He entered a bogus scientific “white paper” as a presentation to a scientific symposium. These are supposed to be reviewed for originality and quality. His phony, meaningless presentation was accepted and he went through with the ruse undetected, only to reveal the deception later in an attempt to bee constructive.

All right, at this point, I’m ready to wrap things up. However, there is still an immense amount of material covered in the lecture series that I haven’t even mentioned. There are arguments about how values and objectivity influence science. Most importantly there is a lot of discussion about language and how language influences our construction and understanding of reality. This has been a major movement within philosophy. Consider now that the Massachusetts Institute of Technology houses their philosophy and linguistics programs in the same department. Unfortunately, the limitations of my meager skills to reduce this material to something worthy of being called a summary prevent me from condensing this material.

While these subjects and others are vitally important to a full understanding of the philosophy of science, I choose instead to devote the remainder of my final installment to subjects with which I am more familiar due to my own academic background: probability and Bayesian Theory.

The history of probability is quite interesting: its basic mathematical theory came about only around the year 1660. This might have been because people did not consider probability something that could be theorized about effectively. It also might have been the result of the Christian notion that everything is determined by God’s will. However, it was the great Blaise Pascal who really got probability theory going when someone asked him to solve some problems concerning dividing up gambling stakes fairly. It quickly spread through the fields of business and law.

Probability is critical to the conception of evidence in the modern sense. Probability was first associated with testimony: Opinions were considered probable if they were “grounded in reputable authorities.” Probability gradually changed enough to come to bear on the “causes” of natural sciences like physics and astronomy and was further utilized in “low sciences” like medicine. Such sciences relied on testimony until the Renaissance when diagnosis was established to differentiate from authority and testimony on one side and dissections and deduction used as proof on the other.

The 19^th century saw the rise of probability and statistics thinking which undermined deterministic trends. Governments kept better records of births, deaths, crimes and began to see patterns that were predictive. Statistics moved from disciplines like sociology into the hard sciences like physics. This then gave rise to quantum mechanics which held that the universe is governed by statistical laws.

The mathematics that underlies probability theory is relatively straightforward. All probabilities are given as a value between 0 and 1. A necessary truth is assigned the probability of 1. If we say that event A and B are mutually exclusive, the probability that one or the other will occur is the sum of their singular probabilities. Thus, if there is a 30% chance that you will eat pizza for dinner and a 40% chance that you will eat spaghetti for dinner, there is a 70% chance that you will have either. It is more complicated when events are not mutually exclusive. So the chance that you will have pizza or spaghetti (when you might also eat both) is the chance of pizza plus the chance of spaghetti minus the chance of both.

As probability theory continues to build in complexity there are three ways to interpret the mathematics. Frequency theories put probability in real world context and this is the most common use of probability within a statistical context. “Probabilities could be construed as actual relative frequencies.” This, however, creates a problem that the probabilistic account is “too empiricist” in that it connects scientific research too closely to actual experience:

A coin that has been tossed an odd number of times cannot, on this view, have a probability of .5 of coming up heads. In addition, a coin that has been tossed once and landed on heads has, on this view, a probability of 1 of landing on heads. Such single-case probabilities are a real problem for many conceptions of probability. One might go with hypothetical limit frequencies: The probability of rolling a seven using two standard dice is the relative frequency that would be found if the dice were rolled forever. We saw an idea like this in the pragmatic vindication of induction. This version might not be empiricist enough. The empiricist will want to know how our experience in the actual world tells us about worlds in which, for example, dice are rolled forever without wearing out.

Logical theories use probabilities as statements about relationships for evidence of phenomena. Probability, thus, gives “partial” or “incomplete” evidence similar to the way deduction provides conclusive evidence. Just like with deduction, probabilistic evidence must be consistent. If we have assigned a probability of 0.8 to p then we must make a 0.2 to ‘not p.’ “Having coherent beliefs is not sufficient for getting the world right, but having incoherent beliefs is sufficient for having gotten part of it wrong. Probabilistic coherence is a matter of how well an agent’s partial beliefs hang together.” On the other hand, if the evidence does not present a reason to prefer one outcome to another they should be regarded as equally probable. “The mathematics of probability does not require this principle, and it turns out to be very troublesome. There are many possible ways of distributing indifference, and it’s hard to see that rationality requires favoring one of these ways.”

Bayesian conceptions of probabilistic reasoning combine a subjectivist interpretation of probability statements with the demand that rational agents revise their degrees of belief in accordance with Bayes’s Theorem. Bayesianism attempts to combine the positivists’ demand for rules governing rational choice with a Kuhnian interpretation of values and subjectivity. In the process, Bayesianism has revitalized philosophy of science with respect to confirmation and evidence.

Bayes’s theorem begins with a subjective interpretation of probability statements. These statements are of conditional probability, meaning that they characterize degrees of belief of the person. Partly it resembles gambling behavior: “the more unlikely you think a statement is, the higher the payoff you would insist on for a bet on the truth of the statement. Your degrees of belief need not align with any particular relative frequencies, and they need not obey any principle of indifference.” The main importance is coherence in probabilistic coherence.

The Dutch book argument is designed to show the importance of probabilistic coherence. To say that a Dutch book can be made against you is to say that, if you put your degrees of belief into practice, you could be turned into a money pump. If I assign a .6 probability to the proposition that it will rain today and a .6 probability to the proposition that it will not rain today, I do not straightforwardly contradict myself.  The problem emerges when I realize that I should be willing to pay $6 for a bet that pays $10 if it rains, and I should be willing to pay $6 for a bet that pays $10 if it does not rain. At the end of the day, whether it rains or not, I will have spent $12 and gotten back only $10. It seems like a failing of rationality if acting on my beliefs would cause me to lose money no matter how the world goes. It can be shown that if your degrees of belief obey the probability calculus, no Dutch book can be made against you.

However, some rather ridiculous beliefs can maintain probabilistic coherence. Bayesianism uses a theory of how evidence should be handled which helps it become a serious scientific theory of rationality. The first element of this theory is the idea that confirmation raises the probability of a hypothesis. “E confirms H just in case E raises the prior probability of H. This means that the probability of H given E is higher than the probability of H had been: P(H/E) > P(H). E disconfirms H if P(H/E) < P(H).” This is done in a subjective interpretation of probability.

The second element critical to Bayesianism is that beliefs should be updated in accordance with Bayes’s Theorem. Non- Bayesians acknowledge the truth of Bayes’s theorem but don’t find it as useful as Bayesians.

The classic statement of the theorem is:

P(E/H)×P(H)

P(H/E)=

P(E)

.

The more unexpected a given bit of evidence is against a given hypothesis and the more expected it is according to the hypothesis, the more confirmatory the evidence of the hypothesis.

The course began by asking what it is that makes science special from a philosophical perspective. It is unclear how much we would like to separate scientific theorizing from everyday theorizing. Unlike those who would dismiss philosophy, it is hopefully apparent that philosophical inquiry exists on a continuum with scientific inquiry. One is helpful in understanding, clarifying, challenging, and enlarging the other. It is quite obvious that controversy will continue to exist about this matter.

Course notes for the lecture conclude, quite eloquently:

Philosophy, especially philosophy of science, is hard. It compensates us only with clarity, with the ability to see that the really deep problems resist solutions. But clarity is not such cold comfort after all. As Bertrand Russell argued, it can be freeing. When things go well, philosophy can help us to see things and to say things that we wouldn’t have been able to see or to say otherwise. 

I know that this has been quite a saga, quite an undertaking for this insignificant little blog. However, I hope, at the very least that it would plant the seed in someone’s mind that science is a useful tool but not the end-all be-all of understanding. It rests on certain axioms about the material world which should never be ignored. Keep thinking. And, as always, happy learning!

I am so glad this one is over.