Toward Formalizing Non-Monotonic Reasoning in Physics: the Use of Kolmogorov Complexity to Formalize the Notions “Typically” and “Normally”

When a physicist writes down equations, or formulates a theory in any other terms, he or she usually means not only that these equations are true for the real world, but also that the model corresponding to the real world is “typical” among all the solutions of these equations. This type of argument is used when physicists conclude that some property is true by showing that it is true for “almost all” cases. There are formalisms that partially capture this type of reasoning, e.g., techniques based on the Kolmogorov-Martin-Löf definition of a random sequence. The existing formalisms, however, have difficulty formalizing, e.g., the standard physicists’ argument that a kettle on a cold stove cannot start boiling by itself, because the probability of this event is too small. We present a new formalism that can formalize this type of reasoning. This formalism also explains “physical induction”(if some property is true in sufficiently many cases, then it is always true), and many other types of physical reasoning.