The regularity assumption is a concept that comes from this author (Max Sklar) which says that patterns exist in the universe. Or alternatively, reality contains patterns.
This is the weakest possible assumption upon which we can philosophically justify science, belief, probabilities, or data analysis. In fact, it is the assumption upon which the argument by analogy relies. It is much simpler than most discussions on the philosophy of science, but also much easier to justify.
Meaning of the Regularity Assumption
Rather than assuming that everything in the universe is governed by natural laws or has a specific cause, the regularity assumption says that patterns exists. It does not say that every physical law is ironclad (though it does not preclude the possibility) - merely that some laws, or more accurately rules of thumb - will work more than statistically expected.
To see why this assumption is true, it is helpful to imagine a world without the regularity assumption.
For one, if there are no patterns, there could be no language. A word that conveys similar meaning every time it is uttered or written down would constitute a pattern. In fact, planets and solar systems would also be impossible because those are physical patterns of matter organizing itself on a large scale. Finally, even the rules that govern particles would have to be completely dismantled. While the laws of quantum physics are non-deterministic, they still constitute patterns and rules that one expects the universe to obey more often than not.
In short - without the regularity assumption nothing could exist!
Thought Experiment of the Image
Suppose that we have a digital image. What does the regularity assumption say about the image? The patterns that exist in this image could be quite complex and contain many layers of abstraction above the grid of pixels. For example, it might contain people, animals, or landscapes - which are 2D representations of complex patterns created by our universe and planet.
These images also have simpler patterns and regularities. For example, pixels that are close to each other tend to have similar color more often than pixels that are far away. In cases where this doesn’t happen, we see an edge or boundary.
If there was no correlation between the pixels, then the image would be essentially blank, or static. Every pixel would be drawn from the same probability distribution of colors, and the only thing one could learn by examining the image would be to get a better estimate on that single distribution.
In short, an image that violates the regularity assumption (as much as possible) is a boring image that cannot be analyzed beyond a single property.
Relationship to Argument by Analogy
If the regularity assumption holds, then it must be the case that arguments by analogy sometimes work (at least more than expected at random). This opens up the discussion of which analogies are true and which analogies are false. The wisdom and common sense of a person relies on good judgement of that question. However, to deny analogical arguments altogether is a denial of reality.
For more information, listen to Episode 57 of The Local Maximum on Data Science Analogies, and Nearest Neighbors.