6. Exceptions to laws within known limits?
Short of cataclysm, explanations rule them out.
This is the seventh post in this series. If you haven’t read the Introduction titled The Myth of Scientific Uncertainty, and posts numbered 1-5, you may want to do those first.
Here we address the final aspect of the second pillar of scientific uncertainty: ‘Consistency is no proof of certainty.’ An exception to any regularity or uniformity could be found at any time.’
We have seen how it is common for laws to apply inaccurately or not at all under certain conditions. We called these conditions limits on a law’s applicability. But are we sure there is no combination of factors within those limits, that could also be exceptions? For most expressions, it would be impossible to test every infinitesimal value of every factor. Even the simple equation for velocity, distance, and time (velocity equals distance divided by time) has not been tested at every combination of velocity, time, and distance and with every object everywhere on earth. Lacking such verification, how can we be sure there isn’t some specific combination of those factors for which the equation does not work?
Here is where explanations play another essential role. There is no valid rebuttal to the consistency argument if we consider only the empirical data upon which the proposed regularity relies, i.e., when we don’t consider our reason for the phenomenon following that expression. An explanation for the behavior expressed by the law often provides the means to assess whether a peculiar circumstance within the tested range is a rational possibility.
Here is an example. If you hold a book out and let it go, it will surely fall. We’re certain this will happen every time. “Unsupported books will fall toward the earth” is an expression of this relationship between its losing support and its downward motion. As expected, there are limits. The book must not be moving with respect to the earth when it is released, and the book must be denser than the surrounding medium (for instance, air).
But within known limits, do we need to test this expression with every book in every location on the planet to be sure of it? No. And that is because of our explanation for the interaction between the book and the earth. We understand that the book and the earth have mass and that masses attract each other. So we can reliably predict that, known limits aside, all unsupported books will fall toward earth.
If a circumstance were discovered where this gravitational attraction was absent, we could conclude that a condition exists in that situation that interferes with or counteracts gravity. In other words, we would have discovered a new limit. We would then have new information on the nature of gravity and a torrent of gravity-defying inventions would ensue.
Another useful example is the Gas Law (for a given amount of gas, the pressure times the volume is proportional to the temperature). The kinetic theory of gases imagines gas molecules as hard spheres moving through space with a velocity that increases with their temperature. The collisions of these molecules with the walls of their container create pressure on the walls.
This picture or model provides a way to make sense of Boyle’s Law. It also tells us that an exception (within the gas law’s known limits) could only happen if the gas molecules ceased to have velocities, or no longer collided with the walls of their container. On this basis, the need to confirm the Gas Law for every combination of parameters and every kind of gas is precluded.
Karl Popper, for whom the concept of exceptions was a key part of his work, commented on what could happen that would cause currently accepted laws to fail. His answer is:[1]
It is perfectly possible that the world as we know it, with all its pragmatically relevant regularities, may completely disintegrate in the next second.
This example supports the idea that a verified law will only fail under a new condition. It also suggests that some laws would not fail unless the change was drastic. I agree. I can't think of a condition in which electrons lose their charge, masses do not attract, or CO2 gas no longer absorbs infrared radiation—which is not also cataclysmic. So, applied within their tested conditions, our laws will work as long as we’re around to care about it.
The framework of the thesis advanced here about what science we know for sure is necessarily empirical, but not wholly so because of the critical role of a credible rationale for the empirical evidence. To have knowledge, we need the data from which the relationship was formed and the reason for it. To be scientific, the observations must be real, and the explanation must be at least theoretically testable.
It may seem like circular reasoning to use the explanation, which we have already said may be subject to revision, as the means to exclude exceptions within tested limits. But even a disproved explanation will be replaced by another consistent behavior model that will serve equally well. As we go on, we will see that individual expression/explanation combinations are not isolated entities but parts of an interlocking and mutually supporting network of knowledge that makes each of its components more robust.
Next time, we will address the problem of whether we can trust what we use instruments to observe.
[1] K. Popper, in D. Miller, Popper Selections (Princeton U. Press, Princeton, 1985) p. 115.