Logical Consistency

As Neil deGrasse Tyson aptly stated, "the universe is under no obligation to make sense to [us]." This highlights the notion that while we may harbor preconceived notions about how reality operates, we must adhere to the findings of science over our assumptions. Nonetheless, there exists a fundamental expectation within the scientific community that the universe should exhibit a form of consistency. This expectation rests at the core of scientific inquiry. When scientists develop a theory that contradicts another, they typically conclude that only one of these theories can be correct.

This belief aligns with our intuitive understanding; it seems illogical for two opposing theories to coexist. Thus, when faced with a robustly supported theory that dismisses a lesser-known one, we often feel justified in rejecting the latter, at least for the time being. Regardless of whether we align with the Baconian or Popperian perspectives, the principle of logical consistency remains paramount. Science fundamentally relies on this consistency.

The Dilemma

What occurs when two theories both appear valid? This is the conundrum presented by general relativity and quantum mechanics. Both frameworks have proven invaluable and have withstood rigorous testing. However, a complication arises: both theories make predictions in certain contexts, particularly in extreme environments.

General relativity primarily deals with large-scale phenomena, such as celestial bodies traversing the cosmos. It superseded Newtonian physics, treating the universe as a smooth space-time structure influenced by mass and energy. On the other hand, quantum mechanics focuses on the subatomic level, presenting the universe as somewhat coarse rather than smooth. Typically, quantum mechanics does not intersect with the types of phenomena addressed by general relativity, averting conflicts.

However, in peculiar situations, like near black holes, general relativity and quantum mechanics clash, each making predictions that cannot be reconciled with the other. Consequently, scientists recognize the necessity for a new theoretical framework that can seamlessly integrate both realms—a "grand unification."

Several theories, including string theory and superstring theory, have been proposed to extend quantum mechanics into the realm of large-scale predictions. Yet, these theories currently lack testable predictions, rendering them non-scientific in nature. They remain mathematical extensions of quantum mechanics, leaving us in a state of uncertainty. Nevertheless, scientists remain optimistic about future advancements.

But What If...

Perhaps the issue lies not with general relativity or quantum mechanics, but with our foundational understanding of reality. It’s conceivable that both theories are correct. As emphasized earlier, a key assumption in science is that reality is consistent; a proposition cannot be simultaneously true and false. However, a domain of mathematics exists that explores logical frameworks allowing for such contradictions.

This area is known as paraconsistent mathematics. Contrary to common belief, it does not imply that anything is permissible. In most instances, paraconsistent logic operates similarly to traditional mathematics, albeit with a more flexible approach. It permits contradictions under certain conditions, avoiding the "explosion" phenomenon where asserting both truth and falsehood leads to the conclusion that anything can be true.

My interest in paraconsistent logic stems from its potential to address another significant issue: the fragility of Bayesian inference. Resolving this vulnerability could transform science into a system that enhances our confidence—albeit provisionally—in the veracity of a reality model. Presently, science is confined to falsification, revealing only when we might be incorrect. There’s no basis for declaring a theory true or even likely true simply because it has withstood scrutiny. This dilemma is known as "the problem of induction."

However, if my investigations into paraconsistent logic yield promising outcomes, we might reformulate our theories within this framework, potentially resolving the problem of induction. This would enable us to regard science not merely as a means of identifying errors but as a pathway to assert that our well-tested theories are indeed true. The implications of this shift are significant, though they could lead to scenarios where two contradictory theories might both hold validity, a notion that challenges our understanding of reality. At present, the conflict between general relativity and quantum mechanics stands as a primary reason to consider that reality may not conform to a consistent framework.

Summary

The problem of induction has perplexed philosophers of science for centuries. Popper circumvented this dilemma by framing science as a system of falsification, which, while useful, does not provide insight into the likelihood of a theory being true. Reconsidering certain assumptions about reality might lead to a solution for the problem of induction, thereby explaining the efficacy of scientific inquiry. However, incorporating paraconsistent mathematics introduces profound complexities that could fundamentally alter our grasp of reality.

Further Reading

Master Index | Cultural Politics

Science currently hinges on the law of non-contradiction as it stands, but what underpins this reliance? Additionally, what truly constitutes science?