Although science informs us about reality, it does not have as much to do with reality as we would like to think. Science has restricted itself to the small local reality it can empirically observe, while largely neglecting the vast external reality we rationally infer. It suffers from an excess of empiricism and a deficit of rationalism.
The Small Reality We Empirically Observe
Most scientists are realists, meaning that they believe that external reality exists, independent of our observation of it. They also believe that the purpose of science, beyond its practical benefits for medicine and engineering, is to understand reality. However, science has not generally dealt with the challenge this creates.
The Inadequacy of Observation
The problem is that we, including all our observations (data), are only a small part of the universe. I will call this the “internal” portion of the universe, since all of our observations are internal to our brains and other measuring devices. These devices were designed for the sole purpose of observation, and we know exactly what we observe (our data).
But observation is never an end in itself. The question of interest always concerns external and future reality, and these are never directly observable (by definition). The only reason we have a brain, and make observations, is to understand external reality and predict the future. An observation is internal evidence about an external and future reality that we can never directly observe or know with certainty. We can only infer and predict given the limited evidence we have.
The Model Selection Problem
Our evidence favors some models over others, but it is impossible to identify the correct model (the one that actually matches external and future reality). This is known in statistics as “the model selection problem.”
The problem is much worse than our inability to know which model is correct. Given any set of observations, there will always be an infinite number of models of external and future reality that are not only plausibly correct, but predict our observations with equal accuracy (see example below). Additional observations (more empirical evidence) may rule some out in the future, and favor some models over others. But we are always left with an infinite number that are plausibly correct, and a smaller but still infinite number that are equally supported by our observations.
A famous example concerns models of planetary motion. Ptolemy developed a geocentric model of an orbit with about 50 epicycles. Kepler much later introduced a heliocentric model with 1 ellipse. Both models predict the observed motion of the planets equally well. Therefore the empirical support for each is equal. Although we prefer the simplicity of Kepler’s model, nature need not be simple. Perhaps a real orbital features 21,834 epicycles. That seems ridiculous, but the empirical support for such a model is just as strong as for Kepler’s model. If a curve can be fit by two parameters, it can also be fit by any number greater than two.
The Small Science of the Observable
Because of this type of problem, some scientists have argued that the purpose of science should only be accurate prediction of our observations, and that external reality should be left to philosophers. Indeed, the dominant philosophy among scientists is a form of empiricism that says science should be only about that which we can observe.
Cats Are Not Observable
It is commonly said that to be scientific, a hypothesis must be falsifiable. If “falsifiable” is taken literally, no hypothesis of interest is truly falsifiable. Our interest is always that which is external or past or future, and since these are not observable, hypotheses about them are not falsifiable.
I may see a cat, but that observation is in my head, and real cats can only exist in the external world. Real cats are not observable.
Before anyone overreacts to this claim, I should confess that I am twisting our common language. I only mean that real cats are not observable in the literal sense. The cats we see and imagine are both observable and observed, and our observations are certainly real. Even the Jellicle Cats in our dreams are real. They just aren’t real cats.
Science is simply incapable of proving or disproving any hypothesis about real cats, or any other aspect of external reality. All we can do is to collect internal evidence for and against hypotheses about external and future reality.
Predictive Models versus Ontological Models
Of course our evidence for existence of real cats in the external world is overwhelming, so it is not of much importance to measure it. But there are many competing models in science for which the evidence appears comparable and should be measured.
For example, scientists have proposed a variety of distinct models of the reality that lies behind quantum mechanics. One of these, known as “the many worlds interpretation,” proposes that every time an observation is made, a new universe is created. The problem is that many of these models make exactly the same predictions about what we will observe, so there is no way to provide experimental evidence for one over the other. The empirical support for each model is equivalent, and it always will be, just as in the case of Ptolemy’s epicycles versus Kepler’s ellipse.
These models are equally successful as what I call predictive models (or algorithmic models), as measured by the accuracy of their predictions. However, we prefer Kepler’s model as an ontological model, meaning a model of reality, because it is a simpler. Everyone prefers simplicity, and most scientists accept it as a valid criterion. However, preference for simplicity is not justified empirically, and not everyone accepts it as scientific. Furthermore, scientists are nowhere close to agreeing on precisely what ‘simplicity’ means, let alone how to measure it.
Among scientists who are fully aware of the severity of this problem, the nearly universal response has been to argue that science should not concern itself with external reality. They say that science should be concerned only with predictive models, not models of reality. They say that to be objective and scientific, science must be small, concerning itself with only the tiny portion of the universe that we actually observe. Unfortunately that portion is so small that it does not include actual cats.
The Observed Universe is Smaller than the Brain
It is commonly said that the observed universe is extremely large compared to a person, spanning many galaxies. But in fact our observations are never anything more than what fits inside our brains and other measuring devices. Galaxies have never been observed, only inferred from evidence that fits in our heads (a very small portion of our heads; well over 99.9% of neurons know nothing about galaxies).
The internal reality of our observations is an exceedingly small portion of the reality we believe to exist.
The Vast Reality We Rationally Infer
Fortunately science need not be as small as our observations. We feel like we are dealing with external reality because we are, albeit indirectly. An organism cannot survive by merely turning inwards and being satisfied with its internal reality, since that reality can only be maintained through a sufficient understanding of external reality. As a practical matter we deal with external reality in a remarkably successful manner because we have a lot of evidence about it, even if we cannot adequately express that evidence in language or mathematics. It should also be obvious that we are capable of mathematically measuring evidence. The problem is that science has not had the formal and explicit philosophy and mathematics that is necessary to properly deal with external reality.
Reason Connects Internal Observation to External Reality
To have a science of reality, rather than merely a science of observations and algorithms, requires that we abandon the sort of radical empiricism that has long dominated science, and recognize that not all evidence comes from observation. We can prove that some of our evidence is from reason alone simply by noting that the evidence that any two or more propositions are all true must be less than or equal to the evidence that any one of them is true. Empirical evidence cannot be properly measured until we have measured this more primitive non-empirical evidence. This non-empirical evidence has generally been ignored or at least neglected in the formal practice of science. The excessive empiricism of science needs a dose of rationalism.
My unpublished calculations indicate that if Ptolemy’s model of an orbital has 50 parameters, and Kepler’s 2 parameters (which are necessary to specify one ellipse), and they both predict our observations equally well, the empirical and non-empirical evidence together (observation and reason) favor Kepler’s model by a factor of 221. This is an example of how probability theory can allow science to identify the best model of reality, rather than merely predicting observations. I do not explain this calculation here, but I provide some background to it in The Measure of Evidence.
Science and the Brain Serve the Same Function
The purpose of the brain is fundamentally the same as the purpose of science, and the same principles of evidence and observation apply to both. Although science is typically conceived to be more macroscopic than the brain, being spatially and temporally extended across many brains and other measuring devices, it is nonetheless small and local in space and time relative to our planet, let alone the universe. Like the brain, science can only infer/predict unobserved external and future reality given the evidence in its present and internal observed reality.
Probability theory does not distinguish the evidence of science from the evidence of any other local observer. However, when we deal with evidence in science (or society), we are not concerned about its physical manifestation. The challenge addressed by Rational Observer Theory is to specify both physical reality and its relation to evidence.