circular arguments in 19th and 20th century science

Physicists in the late 19th and early 20th centuries made the following assumptions about electrically charged particles which were thought to make up all physical objects: The particles would oscillate in simple harmonic motion when e-m radiation was absorbed. The particles would emit e-m radiation while oscillating.

At the time, it was impossible to provide evidence for the existence of these charged oscillators, but we now know that these oscillators exist in the form of electrons which oscillate around an atom’s nucleus in quantized energy levels. However, earlier physicists made these assumptions regardless and justified their use of the assumptions through various means, including the following two arguments. The first argument is the following: Maxwell’s laws, which can explain all electric and magnetic phenomena, entail that the only cause of e-m waves is accelerated charges. It has been shown that the electric and magnetic fields radiated from furnace walls were changing at regular frequencies, and thus would only be produced by electrical charges that were oscillating at the frequencies of the waves they produced. The second argument, now, goes as follows: Planck used the assumption that the walls of the furnace are made up of electrically charged oscillators to predict a distribution of frequencies. This calculated distribution was consistent with the true distribution of frequencies emitted from the walls, and thus the assumption is confirmed by its accurate prediction. I argue that the second justification is stronger than the first, due to the first’s circular nature, and further, I note that the two arguments can be combined in order to produce an argument stronger than both of them individually.

In order to show that the first argument is circular, let us break the argument up into its premises and conclusions:

P1: Maxwell’s laws suggest that the only cause of electromagnetic waves is accelerated changes in electric and magnetic fields.

P2: The electromagnetic radiation emitted from the walls of furnaces exhibits characteristics consistent with electromagnetic waves. C: Therefore, the walls of the furnaces are composed of electrically charged oscillators because these oscillators would be a natural source of the regularly changing electric and magnetic fields required to produce such radiation. The implicit connection between premise 1 and the conclusion is where the circularity becomes apparent: the conclusion attempts to prove that furnace walls must be made of electrically charged oscillators because changes in electric and magnetic fields are required to produce electromagnetic waves – the latter half of the previous statement is an exact copy of premise 1. In other words, the conclusion essentially restates the assumption from premise 1, rather than providing independent justification for the idea that electrically charged oscillators must be a natural source of these fields. The second argument is essentially the hypothetico-deductive method: Planck assumed the hypothesis of the existence of electrically charged oscillators in order to make his predictions about frequencies emitted by the wall, and deduced that his prediction aligned with the true results of these frequencies when measured. This argument has the usual pitfalls of using the hypothetico-deductive method in this way: it is limited by the amount of predictions and confirmations made, and that there may have been various other assumptions that Planck could have made that provided coherent deductions (perhaps similar to the assumptions made in our current understanding of quantum mechanics). However, because of the inherent circularity in the first argument, it is more compelling. However, we can use the previous two arguments to create a third, stronger argument that aligns more with the scientific method. I hold that scientific arguments which appeal to the scientific method as I define it are stronger than the simple predictive argument that the hypothetico-deductive argument makes. By most definitions, the scientific method requires the following three steps: abduction (the process by which scientists create a hypothesis that is the best explanation of phenomena), deduction (inferring what should be the case if the hypotheses are the case), and induction (testing the hypothesis). We can use the first argument I detailed above during the abductive process — we can conclude that a reasonable hypothesis (rather than a conclusive scientific statement) would be that “the walls of the furnaces are composed of electrically charged oscillators” because “these oscillators would be a natural source of the regularly changing electric and magnetic fields required to produce such radiation.” Then, we can use the predictions made by Planck in the second argument to deduce the measurements that would need to be true in order for the hypothesis to be the case. Finally, we can test the hypothesis during the inductive process, and thus we have scientific grounds to make the assumptions about these oscillating particles. A counter argument would be that the first argument is actually stronger on the grounds that a more charitable reading would include the following implied premise: P3: Electrically charged oscillators are the only possible source of regularly changing electric and magnetic fields. While this does seem to eliminate some circularity, there is still no justification or basis for P3, and the conclusion also seems to restate P3 almost directly.