The Weird In-Between State and How Quantum Logic Addresses That
According to Aristotle (Plato's most well-known pupil and the father of Western thought, on the philosophical level), a statement can either be true or false, valid or invalid. Logicians (yes, there is such a thing, and I've had intriguing discourses with one, back in the day) adhere to this premise. This is very much like any Geometry professional would adhere to the axioms of the Geometry he/she practices, be it Euclidean or Riemannian. What about all these logical paradoxes, though? That's something that has intrigued many puzzle aficionados over the years, including some content creators like Kevin from Vsauce2. Not all paradoxes are logic-related, but some of them are so important that have incited serious debate and the development of an alternative logic framework, parallel to the Boolean Logic one that dominates the realm of Mathematics.
When I was a Master's student, I looked into one such Logic framework, namely Trinary/Ternary Logic (TL), and examined how it could be applied to the problem of Map Overlays, a standard application in the Geographical Information Systems (GIS), which were quite a popular field of IT at the time. Although many people are aware of this framework, few people have studied it enough since it's not tied to a particular field of science (even if applicable in some niche ways). Naturally, since there is no upper bound on how many states a Logic framework can have, there are people who have explored higher-order such frameworks (e.g., Quaternary Logic). Yet, none of them gained enough traction, even if they have a place in academic research. Nevertheless, there is an alternative Logic framework that seems to transcend all of these, namely Quantum Logic (QL), which aims to describe and facilitate the complex operations taking place in the Quantum world. The latter is the cornerstone of Quantum Physics and the Engineering framework that stems from it, namely, Quantum Mechanics. All of that has brought about the latest computing advent, namely Quantum Computing (QC), which has a significant role to play in the years to come. QL also has philosophical ties, as explained in this article from the Internet Encyclopedia of Philosophy.
What we have failed to grasp ever since we've started exploring Logic was a subtle but key element: the in-between state of True and False and its relationship to the other states. By coding it as -1 or 2 (in TL), we miss the whole point that it's not yet another state but rather a state beyond the other states. It's akin to the state of a quantum particle until it's observed/measured. That state, which is referred to as superposition is a state of being both and neither at the same time. Until someone looks at the damn thing, the superposition state will hold, confusing everyone around it, used to the binary view of things. However, once someone looks at that quantum particle, the superposition collapses and therefore the particle is either in state A or state B.
Going back to the real world, we don't have to worry about superposition that much since things are more clear-cut. If we look at a product, it's either on sale, or it isn't. A person is either dead or alive (except perhaps in some Hollywood movies!). So, where does the superposition come into play? (hint: it does involve us all, even if we aren’t aware of it). This discussion is a long one and probably better suited for a different article. Meanwhile, I'd love to hear your thoughts on the topic. Cheers!