# Explanatory Power The Explanatory Power of a theory is based on two main components: 1. It's Empirical [Content](Content.md) and Predictive Power 2. It's Description of the Underlying Structure (the *how* and *why*) A theory's explanatory power, for Popper, comes from both its success in empirically accounting for phenomena (rooted in high empirical content and leading to good predictions) and its ability to provide a descriptive account of the underlying structure of the world that makes these phenomena and predictions understandable in terms of cause and effect or governing laws. ## Empirical Content This refers to what a theory states can happen; what it *constrains*. A theory says something of the form "$x$ will happen". And then we have the ability to falsify it if $x$ does not happen. A theory explains phenomena by successfully accounting for them, which often means making predictions that are confirmed by observation. The more specific and risky the predictions a theory makes (and are successfully corroborated—survive attempted falsification), the higher it's empirical content and, consequently, it's potential to explain the phenomena it predicts. Popper writes: > "The maximum degree of the explanatory power of a theory... depends upon the (informative or empirical) content of the theory" High empirical content, measured by the class of potential falsifiers, is the basis for making specific predictions that can explain phenomena. ## Describing Certain Structural Properties This refers to proposing a model or description of the underlying reality or structural properties of the world that *cause* the observed phenomena and allows for the deduction of the predictions. This is the *how* and the *why* portion of explanatory power. Popper writes: > "Explanatory theories describe certain structural properties of the world, and which permit us to deduce, with the help of initial conditions, the effects to be explained (i.e. the empirical content)". Thus we see that explanation involves describing structure to logically derive the phenomena. He also writes: > "The theorist's interest in explanation is irreducible to the practical technological interest in the deduction of predictions" In other words, without an interest in explanation, we won't be able to arrive at theories with empirical content. A way to identify if a theory is describing the structure of a situation (the how and how) is to ask the following: if we varied the theory, would it still have the same logical consequences? If it would, then it likely isn't ## The Copenhagen Interpretation of Quantum Theory CI retains the empirical content of quantum theory—it's predictions. Thus, it still retains quite high explanatory power. It still allows us to describe an incredibly broad set of phenomena (particle dynamics nearly anywhere in the universe) according to very hard to vary mathematical laws (e.g. it very accurately describes *how* probabilities will distribute in an experiment). It is bold and risky and exposes itself to an incredible degree of criticism. However, CI effectively states that once we have reached this level, we are not allowed to seek any deeper explanation. We can ask no more "how" or "why" questions. We can't try and come up with a deeper understanding of how these particles interact or why they follow these laws. We can't try and come up with a deeper, underlying regularity that exists. Thus, the Copenhagen interpretation, while retaining the first aspect (empirical success/prediction), is seen by Popper as discarding the second (describing underlying reality). ###### The Inconsistency of CI Notice that explanatory theories aim to "describe certain structural properties of the world" which permit the deduction of effects to be explained. In order to come up with the mathematics describing CIQT, theorists needed to try and describe certain structural properties of the world! Namely, how did particles move through slits. They described this via mathematical equations. But, most importantly, they attempted to explain structural properties of the world. And then they said "but the buck stops here. We can describe and explain no deeper". This is inconsistent. They were happy to seek explanations when it suited them, and then they arbitrarily said it was no longer allowed. ###### A Bit of Nuance If (2) is required to generate (1), then how do we ever end up with (1) in the CIQT? The answer is that the CI still solves problems and describes certain structural components of reality. We had the problem of understanding the results of certain experiments (say the double slit). A mathematical theory was conjectured that described how these particles would behave—according to very specific mathematical laws. These laws had empirical content, constraining what could and could not happen, and this could be tested against. The issue is just that the CI decided to stop there. It said "we can't ask any more questions about how or why this occurs". Put another way, CI did manage to answer part of a "how" question. It answered "how" do particles move through the double slit by proposing a mathematical formula. This is explanatory and has great content. It just decided that at that point we could ask no more questions, and seek no more deeper explanations Thus, the Copenhagen interpretation keeps the empirical content and predictive power because the theory's mathematical framework provides a precise description of how phenomena behave according to specific mathematical rules, allowing for successful deduction of observable results. This constitutes a significant form of explanatory power related to empirical success. However, the CI deliberately severs off the component of explanation that seeks to understand the underlying physical reality, the physical mechanism, or the structural properties of the world that cause or govern why these mathematical rules are followed. It focuses on the recipe for prediction and successful application, rather than the physical story of what is happening behind the scenes. If we followed this methodological rule, and chopped off portions of our explanation that lead to new problems, we would never have arrived at the mathematical formalism of CI in the first place! The philosophy espoused by CI seems to contradict the very dynamic process of problem-solving and reality-seeking that allowed science to reach the quantum realm in the first place. ## Explanatory Content While Popper never explicitly refers to "explanatory content", I would say it is synonymous with with explanatory power. --- Date: 20250520 Links to: [Content](Content.md) [Logical Content](Logical%20Content.md) Tags: References: * []()