The Quantum Nightmare

Perhaps the best illustration of this dilemma is quantum mechanics. Quantum mechanics has been riddled with controversy which opened the way to incredibly toxic abuse from pseudoscience. I attribute this almost entirely to the fact that physicists, who were baffled by the success of a theory they couldn't interpret intuitively, introduced ideas and terminologies that could only be described as the perfect breeding ground for pseudoscience, mysticism, and metaphysics more generally. Most of these frankly horrendous mistakes arise from two main sources: the so-called measurement problem, and quantum entanglement. The first, in particular, had been tied to consciousness, despite the relation being entirely absurd (see Wigner and his friend). This notion alone spawned spiritual and mystical interpretations that hinder popular understanding of science today. However, there are other notions, which, though potentially useful in some ways, are very much misled away from scientific values. For instance, the solution via the many-worlds interpretation, where the measurement of a quantum system causes the world to split into many according to the possible outcomes, is incredibly useful in modeling the (at least apparent) non-deterministic aspect of quantum measurement; however, it is also unfalsifiable and has spurred metaphysical interpretations that further inject dangerous ideologies into society. As for quantum entanglement, people have linked it to some magical abilities of communication in practice and have used it to justify anything from astrology, to scam medical practices and support for monadic spiritual beliefs, which, themselves, form the basis of authoritarianism and totalitarianism.

This, of course, for a well-meaning scientist and logician, is unacceptable, and it should be unacceptable to any well-meaning citizen, anyway. The reason behind all of this is clear: physicists are uncomfortable in having found theories that work well but that do not answer their metaphysical questions about the substance of Nature. After too long, they have finally realised that quantum science must refrain from such questions and decided to "just shut up and calculate". But how often are we repeating this mistake right now, and when, if ever, will we stop this massacre?

The Good Pain

Still in the theme of physics, here's a question I would like you to ask yourself. Pause any of your more advanced physics knowledge, and consider this innocent question: if nothing ever leaves a black hole and we can never have access to its insides, does it even make sense to discuss of whether its guts are shaped like a point, a ball, or a shawarma wrap? Alice, a scientist abiding by a notion of intensionality, would have to say yes, it does make sense. The inners of a black hole must have some shape, and we strive to know it. Alice refuses to give up and spends her academic career trying to find hints about the contents of a black hole. On the other hand, Bob, our pragmatic extensionalist, who, so far, we've portrayed as just "correct", would say that this question is irrelevant and that the inners of a black hole belong to metaphysics; a black hole is precisely that, a hole with nothing interesting inside, it just sucks, and that's it.

Of course, in hindsight, we know that Alice was right. Black holes are not inert. To begin with, they communicate gravitationally with the rest of the universe. They also produce Hawking radiation, which might also leak information that the black hole ate up in the past. The inner shape of a black hole must also not be a point because black holes inherit angular momentum from their parent star. In short, the shape of a black hole does have observable impacts, and Bob must not have abandoned his attempts so early on.

What this tells us is that while the process of science is, and must be, extensional, the motivation for science being intensional has desirable consequences. The pain of being unable to resolve the contents of a black hole had its opium in extensionally: it doesn't matter anyway. However, that that opium hid a deeper, healthier solution: it does matter, and we can know things about it.

The End of Plato's Grip on Nature

So far in the natural sciences, it seems that an intensional motivation has never failed us… yet. A drive to search for the absolute did fail us in the formal science however. No matter how hard David Hilbert, one of the most enlightened mathematicians in history, dreamt about discovering all truths mechanistically, Gödel's incompleteness theorems meant, for any reasonably expressive logic, and any reasonable process of deducing truths from any reasonable accepted set of axioms, and assuming there is a Platonic universe where things are always either true or false, there are sentences which we will never be able to ascertain or disprove. Formal sciences, which, at the time of Hilbert, followed the track of a theory of everything, are quickly pulling back to synthetic, contextual theories with great success. This is notably reflected in the huge wave of constructivist and synthetic approaches in computer science a naturally more pragmatic science with, e.g., formal verification through types and the Curry-Howard/BHK correspondence, as well as the plethora of purpose-built logics. This is a movement that has also also transferred to the more traditional analytic mathematics via homotopy type theory, synthetic topology, and others.

The question to reflect upon now is: will natural science suffer the same end? Will we reach a point where we admit that it is pointless to look for a singular exhaustive description of Nature? Hints are indeed appearing from quantum gravity where some doubt is appearing on the existence of a meaningful, falsifiable, unifying theory. Will Plato's grip on Nature ever be released, and if so, how?