3. The Black Swan
Scientific laws have a limited range of verified applicability, and those limits define the conditions in which they are sure to work.
This is the fourth post in this series. If you haven’t read the Introduction titled The Myth of Scientific Uncertainty, and posts 1 and 2, you may want to do those first. See them at
We now address the second pillar of science uncertainty, i.e., consistency is not certainty. The black swan is the iconic example of the argument that no matter how consistent a set of observations, the possibility of an exception cannot be ruled out. Since only white swans were known in Europe, one could confidently say, “all swans are white.” This uniformity was upset in 1836, when a Dutch sailor sighted black swans in the waters of Western Australia. Rephrasing the lesson this anomaly teaches, James Thurber quipped, “There is no exception to the rule that every rule has an exception.”
Philosophers from David Hume on have repeated the assertion ‘there is no guarantee against a contrary observation’ to a scientific law. Karl Popper emphasized this point suggesting that scientists should look for conditions in which accepted laws might fail. Popper referred to such conditions as ‘falsifications’ with the implication that such exceptions weaken or invalidate a law.
But do they? If they did, most of our widely used laws would be weak and undependable. Take a few examples: light travels in a straight line unless passing a mass that distorts space, water freezes at 0 ºC if it is free of dissolved substances, the gas law is only accurate for ideal gases, and so on. In fact, most of the scientific laws we apply routinely have conditions that are exceptions to their applicability[1]. But scientists take those conditions into account, treating them as limits or boundaries on a law’s applicability. These limits prevent laws from being universally true.
But the essential point is, we can trust verified laws to continue to work within their tested limits. It has been said that Einstein’s relativity has proven Newton’s laws to be wrong[2]. If so, why do we still teach and use them? It’s because what Einstein found was not a revocation of Newton’s laws, but a limit or boundary on their accurate application[3]. He found a condition in which they don’t apply. Except for objects with relativistic velocities, our applications of Newton’s laws have not changed. So conditions which are exceptions do not discredit a law, they just define a limit on its accurate application.
The discovery of a new limit to a law arises from an observation of its failure under previously untested conditions. The addition of a new boundary does not affect the reliability of a law within its previously known limits. Instead, it adds to our knowledge of the phenomenon. A new limit might reveal an unexpected phenomenon to study[4] or drive a field in a new direction.
I would rephrase David Hume’s point that we cannot assume that any uniformity will apply over all time and space to “the conditions under which a law has been tested, which are necessarily limited, define the range of the law’s assured applicability.” Since testing under all conditions is impossible, no law can confidently be assumed to be a universality[5],[6].
Many have recognized that laws are dependable within the range of tested conditions. Mariano Artigas, a Spanish physicist and philosopher, using the word ‘stipulation’ rather than ‘limit’ said[7], “It is possible to achieve inter-subjective formulations and demonstrations based on… stipulations that restrict the domain of consideration.” In other words, the acknowledgement of limits and the empirical affirmation of reality within those limits resolves the no-miracles quandary and supplies the assurance we have been looking for. Unfortunately, he did not develop this insight further. Others have, but with highly restrictive caveats.
For example, Erica Thompson[8] says that some models “can do extremely well” where “the observations do not stray much outside the data used to generate the models.” While acknowledging the usefulness of some laws (which here she is calling models), her implication is that such instances of reliability are ‘special.’ I disagree.
Most of the laws we use have a range of tested conditions that is broad enough to make them useful. If that were not so, our technological devices would require controlled environments in which to work. There would be no TVs, airplanes, or cellphones.
In the next post, we’ll look more deeply into the nature of explanations and their essential contribution to scientific knowledge. We will see why the white swan regularity, because it lacked an explanation, was not scientific.
[1] A. Potochnik, Idealization and the Aims of Science, (The University of Chicago Press, Chicago and London, 2017) p.19.
[2] M. Strevens, The Knowledge Machine, How Irrationality Created Modern Science (Liverright Publishing, New York, London, 2020) p. 111.
[3] T. Kuhn, The Structure of Scientific Revolutions, 3rd ed, (University of Chicago Press, Chicago, London, 1962) p.99
[4] F. Wilczek, A Beautiful Question, Finding Nature’s Deep Design (Penguin Books, New York, 2015) p. 203.
[5] A. Potochnik, Idealization and the Aims of Science, (The University of Chicago Press, Chicago and London, 2017) P. 25.
[6] N. Cartwright, The Dappled World, A Study of the Boundaries of Science (Cambridge University Press, 1999) p.4.
[7] A. Mariano, Knowing Things for Sure, Science and Truth (University Press of America, Lanham, Oxford, 2006), p. 202.
[8] Erica Thompson, Escape from Model Land, (Basic Books, New York 2022) p. 26.
This statement of yours is golden: "These limits prevent laws from being universally true. But the essential point is, we can trust verified laws to continue to work within their tested limits."