Tok Essay - Question 5 2010

Karl Popper, one of the greatest philosophers of science of the 20th century, first proposed the concept of falsification and Popperian scepticism in the natural sciences as an alternative to relativism or subjectivism. Popper held that no scientific theory is ever proven, and that verification is therefore impossible. By the same token, the only way proposed by Popper to attach any epistemic value to a scientific theory was through attempts at falsification. Popper seems to think that good scientists can and should be willing to hold to their hypotheses very tentatively, and they should be willing to give them up quickly and easily.

Popperian falsificationism maintains that all scientific conclusions are almost entirely provisional. Popper denies the existence of any form of ultimate verification in science, ensuring that a conclusion is always to be held provisionally. Shermer’s absolute claim that science holds a “belief in the provisional nature of all conclusions” runs parallel to Popper’s claim, refuting verification of any kind of scientific conclusion.

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III.        The Natural Sciences in Practice

Unfortunately for Shermer and advocates of Popper, the sociological reality of the natural science community is very different from his ideal vision. In The Structure of Scientific Revolutions, Kuhn proposed that the natural sciences go through cycles, periods of normal science and incremental progress followed by periods of revolutionary science and extraordinary progress. The reasons for this, suggests Kuhn, is that science practitioners are able to establish periods of broad consensus in which clusters of theories and laws are more or less accepted as “given” by most scientists. Such consensually accepted theories form what Kuhn calls a “paradigm”, and during a period when a paradigm is accepted and stable, “normal science” occurs. “Normal science”, as defined by Kuhn, consists of experiments that test subsidiary hypotheses and that seem to be natural extensions of the dominant paradigm.  

Scientists are liable to ignore, suppress and discredit experimental results that disprove or throw into doubt a key theory of that paradigm. Exhibiting something similar to “confirmation bias”, a scientist who was trained under a certain scientific paradigm is highly unlikely to abandon that paradigm even when presented with anomalous data. The perihelion of Mercury, the time at which Mercury is closest to the sun during its orbit, was inconsistent with Newtonian mechanics for many years. Despite several ad-hoc solutions that were consistent with Newtonian mechanics (e.g. a hypothesized unseen planet called “Vulcan”), it became clear that science did not truly have an answer for this discrepancy. Einstein’s general theory of relativity proposed instead that the bending of light around the sun was responsible for this anomaly.

Does this indicate that the natural sciences are in fact not provisional? Einstein appears to have “proven” Newton wrong, yet Newtonian mechanics still plays an important role in physics today. The reason Newtonian mechanics is still used is because Newton was not wrong. Newton’s equations simply did not hold true for situations that he had not even considered, such as objects approaching the speed of light, and objects with a very large mass, such as planets, stars or black holes. When calculating the trajectory of, for example, a bullet, Newtonian mechanics remains useful, because the difference caused by relativity will be so small as to be immeasurable.

A more humble, every day example of the continued relevance of an outdated paradigm regards the shape of the Earth. For many hundreds of years, humans believed the Earth was flat, until the first circumnavigation of the globe. Now, as a navigator prepares to direct a transatlantic flight, he must take the curvature of the earth into account. However road maps, the distances between cities, and the length of an Olympic track are all calculated as if the Earth was flat.  

The practice of both the social and natural sciences requires an extensive network of collaboration, communication and trust between different academic institutions. Conferences on topics as diverse as cold fusion and industrial psychology are held every year, and nearly every scientific theory produced in modern times relied on previous theories and hypotheses dreamed up by scientists of a bygone age, who worked with relatively imprecise instruments and faulty methods, yet are still proved valid year after year. Shermer’s statement fails to take into account the extensive trust that is placed in older scientists by modern scientists and exaggerates the tendency for scientists to hold their views provisionally.  

IV.        The value of provisional conclusions in mathematics

Shermer’s claim implies more than he perhaps intended. Shermer makes an implicit value judgement that “provisional conclusions” are in fact a positive contribution to science, and what separates it and makes it “superior” to other areas of knowledge. Shermer’s definition of science, however, is not clear, and there is a possibility that he also includes mathematics under this definition.

 The debate about whether or not mathematics is an area of science has raged since Popper first defined science as experimentally falsifiable. Initially, philosophers argued that, as mathematics is completely logical and does not relate to the physical world in any precise terms, it cannot be qualified as science. However, advances in the field of mathematical logic later showed that mathematics cannot be reduced to pure logic. This would indicate that mathematical conjectures are hypothetical and deductive, similar to hypotheses in scientific disciplines such as chemistry and physics. Charles Peirce, a leading light in the philosophy of science at the time, summarised this connection between mathematics and the sciences by stating that any science "must, if it is to be properly grounded, be made to depend upon the Conditional or Hypothetical Science of Pure Mathematics, whose only aim is to discover not how things actually are, but how they might be supposed to be, if not in our universe, then in some other". 

Assuming that mathematics is a hypothetical, falsifiable area of knowledge, provisional mathematical conclusions are liable to be falsified extremely quickly, as most mathematics is easily tested by conceptual experimentation and manipulation, a feat not possible in the physical sciences that deal with the finite universe. For this reason, certainty is a critical element of any mathematical proof, and mathematical conjectures that have not been proven are rarely taken seriously by mathematicians. As younger students of mathematics know well, assuming that integers exist conceptually is much easier than proving their existence before learning addition.

V.        Conclusion

At face value, Shermer’s claim would seem implausible. His statement that the “provisional nature of all conclusions in science” differentiates it from “all other human activity” is an absolute statement that is hard to take seriously, as it is almost certain that other human activities do hold at least some knowledge provisionally, reducing the effectiveness of the logical-positivist statement that Shermer is trying to make.

Shermer’s claim also fails to recognize the extensive communication and cooperation network that has characterized scientific endeavour since it has been recorded. A modern scientist depends on his forbears for the principles from which he creates a hypothesis, and if these principles of science were constantly questioned as provisional conclusions, scientific discoveries would grind to a halt in a storm of attempted falsification.

Furthermore Shermer’s claim contains an implicit value judgement, one open to challenge. “Provisionality” is not necessarily always a value in all areas of knowledge. “Certainty” would seem to be a more important value, at least in Mathematics. Other disciplines may or may not be more or less provisional in character. But if Mathematics is any guide, just because other disciplines hold their conclusions non-provisionally should not alone incline us to think they are incapable of producing knowledge worthy of the name.

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Bibliography

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Bird, Alexander. Thomas Kuhn. Stanford Encyclopaedia of Philosophy. August 13, 2004. <http://plato.stanford.edu/entries/thomas-kuhn/>

Brinton, Crane. The Anatomy of a Revolution. Rev. Ed. London, UK: Vintage Books, 1965. Print.

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Kuhn, Thomas. The Structure of Scientific Revolutions. 2nd ed. Chicago, USA: UCP, 1970. Print

Peirce, C.S. Lectures on Pragmatism. Cambridge, MA. March 26 – May 17, 1903.

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Thornton, Stephen. Karl Popper. Stanford Encyclopaedia of Philosophy. November 13, 1997. <http://plato.stanford.edu/entries/popper/>

Weisstein, Eric. Kelvin, Lord William Thompson. 2007<http://wolfram.com/biography/Kelvin.html>  

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