Scientism is a Real Problem

Mathematical models can give you rigorous empirical predictions, but you cannot arrive at ontological statements about the nature of reality from mathematical postulates alone.

It is similar to an is/ought dilemma: an argument's conclusions cannot be stronger than its premises. Purely mathematical postulates will only get you to further mathematical conclusions. To say something about the nature of reality, you need an ontological postulate.

An ontological postulate is an assumption about the nature of reality and about how that reality relates to the mathematics. It goes beyond simply stating what the mathematical structure is or what predictions follow from it.

It is sort of like this: if you gave me a body of mathematics, I used it to make empirical predictions, and those predictions turned out to be correct, I would probably turn to you, astonished, and ask: Why are they correct? What does this mathematics mean? What does it represent?

Of course, you can be a pure pragmatist and not care about the answers to those questions at all. But almost no one is. Most people do care about ontological questions, such as "What is real?"

The important point, however, is that ontological postulates are not part of the mathematical framework itself. They are therefore not empirical in the same sense as the predictions generated by the mathematical model, and they cannot necessarily be experimentally proved or falsified.

That does not mean they are arbitrary. They still have to be consistent with the mathematics of the theory, and they still have to be coherent. Even if they cannot be empirically demonstrated, they must still be justified by some other means.

When I talk about "scientism," I am talking specifically about people who conflate ontological postulates with mathematical postulates, treating them as though they were one and the same and as though the former necessarily followed from the latter.

These people then provide no philosophical justification for their ontological postulates because they insist that those postulates have already been proved beyond any reasonable doubt by the mathematics and empirical evidence alone. In fact, if you ask them to justify their ontological assumptions, they will accuse you of being a science denier, a crackpot, or a crank simply for questioning the "scientific community."

Let me give you a simple example: fields.

Mathematically, a field is, roughly speaking, a quantity assigned to every point in some domain, such as 3D physical space. People often assume that these mathematical fields correspond to an ontological field: an invisible substance that permeates space and acts on particles, causing them to behave in particular ways. They therefore speak of fields as entities that exist in the world and have causal effects on particles.

However, it does not automatically follow from the empirical success of the mathematics of fields that we should interpret that mathematics as representing an ontological field, meaning an all-pervading invisible substance.

Suppose you turn on an electromagnet and observe iron filings arranging themselves along the familiar field lines. One interpretation is that the magnetic field acts on the iron filings and causes them to move into that configuration. But another interpretation is that the behavior of the iron filings follows from their own nature. The particles have certain dispositions to behave in certain ways under certain conditions, and the mathematics of fields describes those dispositions.

This is sometimes called a "dispositional" approach in the literature. The "nature" of an object is often described as its "disposition." To talk about the dispositional nature of particles is simply to talk about what those particles do given certain conditions, as a consequence of the laws governing their behavior, without proposing an additional invisible entity "from the outside" that acts upon them and causes them to move.

Notice what I have done here. I have questioned the ontological postulate that the mathematical field corresponds to an ontological field. But I have not questioned the mathematical field itself.

In other words, I am not questioning the efficacy of the mathematical model or its ability to predict what we observe. If I held this view, I would not be denying any empirical predictions made by the model, nor would I be denying any of the scientific evidence supporting those predictions. I would only be questioning what the mathematical model represents about reality.

This is just one example, and a relatively simple one at that. There are much more complicated examples when it comes to the ontological assumptions underlying theories of relativity or quantum mechanics.

Yet questioning an ontological postulate like this will quite often get you flamed, harassed, or attacked by large numbers of people because they equate ontological postulates with mathematical postulates. They then paint you as a "science denier," a "crank," a "flat-earther," or a "crackpot." They may accuse you of being "arrogant" or a "know-it-all" for "daring to question the scientific consensus." A newer insult I've encountered is the claim, made without evidence, that such ideas are the product of "AI psychosis."

If you point out that these personal attacks are unfair and that you'd like a real rebuttal to your argument, they then accuse you of "being upset that we did not automatically believe you without question and actually pushed back," even though their pushback never actually addresses the substance. This is because the person practicing scientism cannot address the substance because they don't know themselves why they believe those ontological postulates. They just take them as a given, without question, so they have no idea how to defend them other than to shut the skeptic down with personal attacks and appeals to popularity without ever actually addressing their argument.

For a real-life example of what I would consider scientism, consider Chad Orzel's TED-Ed talk on Schrödinger's cat. Schrödinger did not believe that the mathematical representation of a quantum superposition of states literally, ontologically, represents a system in multiple states at the same time. Orzel then presents Schrödinger's position as though rejecting this ontological interpretation of quantum superposition amounts to rejecting the science itself.

But Schrödinger obviously was not denying the empirical evidence or the mathematics. He was one of the people who developed the mathematics underlying quantum mechanics. His objection was to the interpretation of what that mathematics says about physical reality.

It is therefore disingenuous to frame disagreement over the ontology of quantum superposition as a rejection of science. Believing that a cat can literally be dead and alive at the same time in ontological reality is not a necessary condition for applying the mathematics of quantum mechanics or for building technologies based upon it.

When I refer to "scientism," then, I am referring to the failure to recognize that the mathematical postulates of scientific models are not, by themselves, sufficient to draw conclusions about the ontology of the world, the "truth" of the world.

To make ontological claims, you also need to put forward and defend ontological postulates. Those postulates are not themselves empirical observations, and they do not automatically follow from the mathematics.

The belief that ontological conclusions flow directly and necessarily from the mathematics is what causes people to become so dogmatic about them. A successful physical theory can effectively be elevated into a kind of religious faith: everyone repeats the associated ontological claims, those who question them are ostracized, and alternative possibilities are dismissed.

Yet when you ask for a philosophical defense of those ontological claims, there may be very little offered because the claims are simply assumed to have been empirically proven, despite the fact that the claims are non-empirical and cannot ever be empirically proven.

The irony is that none of this requires rejecting the science. You can accept the mathematics, accept the empirical evidence, accept the predictive success of the theory, and still ask a fundamentally different question: What, exactly, does this mathematical structure tell us about what reality is?