under construction...
(for a very long time)
date: 2025.04.19
One of the fundamental mechanisms underlying human cognition is the interplay between inductive reasoning, which derives the general from the particular, and deductive reasoning, which derives the particular from the general. In fact, induction and deduction are intricately intertwined. In order to engage in deduction, one must begin with a general premise a priori, and to justify this premise, induction becomes necessary. (However, the question of which comes first is itself a complex philosophical issue.) The fatal flaw of induction lies in its circularity: it lacks logical necessity and relies instead on repeated observation.
Philosopher J.S.Mill proposed the principle of the uniformity of nature, which asserts that the future will resemble the past. This principle underlies all natural science, particularly physics, because the fundamental assumption of physics is that there exist invariant and objective physical quantities that can be measured and quantified by humans. Thus, to even begin doing physics, one must accept the existence of fixed objective truths, the existence of spacetime, and the preservation of causality in the physical world. Without these assumptions, science would be impossible from the outset.
But how can we know that this principle is actually true? The fact that laws have held until today does not guarantee they will continue to hold tomorrow. The only thing we truly know is that natural laws have never once been violated, so far. In order to claim that natural laws are true, we must resolve the circularity of inductive reasoning, but this is, in principle, impossible. As a result, natural laws cannot be said to hold the status of absolute truth.
This problem has a long history. Even during the age of Newtonian mechanics (then considered a form of natural philosophy) such views were already being challenged. Newton (as a theologian) justified his mechanics by appealing to the will of God. However, appeals to divinity are no longer satisfying for modern scholars. Today, there are broadly two recognized strategies used to justify the logical inconsistencies inherent in natural science.
(Pragmatic) Axiomatization
Despite the fact that natural science relies on induction, it possesses remarkable predictive power and cannot, by its very nature, escape from empirical validation. Since human inquiry into the workings of the external world must be grounded in that world itself, science is deemed epistemologically rational—even if not logically flawless.
Reductio ad absurdum (Null Hypothesis Approach)
If we reject the principle of uniformity, then we are left with a stance in which human beings can say absolutely nothing about the world. Such a position renders not only natural science but also human civilization—including economics and social structures—completely meaningless. Moreover, although there is a non-zero probability that the uniformity of nature could fail, this probability is so vanishingly small that it is irrational to deny the principle solely based on such a possibility. Hence, we are compelled to assume it. (This reasoning also appears in the interpretation debates of statistical mechanics and quantum mechanics, often dividing Bayesian and frequentist schools of thought. Statistics, as a field, emerged in part to address this kind of reasoning mathematically.)
Ultimately, scientific discovery and belief in natural laws are not upheld on the basis of strict logical validity, but rather on the strength of how persuasive and rational they are. To put it more intuitively, the methodology and reasoning forms of natural science serve as rules of inference, while natural laws can be seen as theorems derived from these rules, assuming the laws themselves are treated axiomatically. Unfortunately, no logical resolution to the flaws of inductive reasoning has yet been found.