This discussion makes me wonder how boolean logic fits in with classical logic. My extensive Google search found the definition of classical logic to be true to most people’s description: black or white, true or false. Classical logic is bivariant. Boolean logic is a stricter version of classical logic: it’s still bivariant, but only deals with true (assigned the value 1) and false (assigned the value 0). This bivariant system is highly useful for deductive reasoning and deductive inferences, statements of the type “if P, then Q” and so on. This is probably why it shows up so much in the sciences: classical logic fits very nicely with our current step-by-step definition of the scientific method. But it also lends itself to paradoxes, and this is where quantum logic comes in.
The whole concept of “embrace the grey” is exciting and intuitively pleasing: of course we need to diversify our logic toolbox when we find out just classical logic fails us! Bring on the quantum logic! Quantum logic is highly useful and necessary to understand some physical phenomena, however, it is not the cure-all for our scientific and paradoxical ills. We already incorporate these shades of truth; Science and the rest of the STEM fields are not as strictly binary as most people have made them out to be.
Think of the decisions that go into measuring something, for example. If I am studying operations research and I want to know what university is a good partner university for my business, I must first make decisions about what to measure. What makes a “good” partner? The number of faculty in my area of expertise? The freshman retention rate? The cleanliness of the dorms? There is no single set of metrics that I know to be true and absolutely correct. Even though I use statistics to analyze my metrics, there’s a significant amount of fuzziness in the process. And this non-binary decision making is present across all the sciences. If I am deciding how to design a pharmaceutical study, I make decisions about my sample set that are not necessarily true or false: should I test my drug on older women, or younger men, or both? If I am trying to decide how to code a piece of software, I know there is not one right way to write my code: I base that design on how easy it is for my fellow software engineers to follow. Even scientific conclusions shy away from absolute truth or absolute falseness: true to scientific form we can only say we are fairly confident we have achieved a result. Gravity is only a well-supported theory. The point to all of this is that although STEM uses classical and binary logic, I do not think it is characterized by it.
I think this is a question of efficiency of representation. Since any number can be represented in binary, insofar as science deals with quantitative questions binary is sufficient. However, to represent paradox (aka superposition) and interconnectedness (aka entanglement), binary or classical logic is highly inefficient, e.g. for 150 qubits we need more classical bits than atoms contained in the earth.
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