A concept which will in no way ever make a difference, is meaningless.
I would argue that occams razor is unfalsifiable but is still a great principle.
Occam's razor is provable, in the sense it's a heuristic based on probability. Out of the two alternative hypotheses explaining the same observations to the same degree, the simpler one is more likely to be true.
In the domains where simplicity prevails Occam's razor is more probable.
In domains where complexity prevails Hickam's dictum is more probable.
I see how it makes sense, given it comes from medicine - the very field dedicated to literally the single most complex system we know of: the human body. But I don't see it as an opposite to Occam's razor - rather, a missing lower bound. That is, I see Hickam's dictum as a reminder that some hypotheses may be too simple.
My guess at how one would formalize this is, when you're comparing hypotheses explaining something in a given domain (such as "behavior of things being thrown", or "health of a human body"), there is a level of complexity inherent to the domain. A hypothesis that's so simple as to fall below that level is too simple - it doesn't have enough bits to express what's happening within the domain. The further below the complexity threshold it is, the more likely it is to be falsified by new evidence. In contrast, hypotheses above the domain complexity level are all capable of explaining the domain fully; however, the more complex a hypothesis, the more likely it is to be at least partially wrong.
This gives us the following takes:
- Occam's razor: for hypotheses above the domain complexity threshold, the least complex one is most likely to be true.
- Hickam's dictum: your hypothesis is way below the domain complexity threshold - which you didn't notice, because you don't appreciate how complex the domain is in the first place.
Reconciliation:
- The closer a hypothesis is to the domain complexity level, the more likely it is to correctly explain new evidence. The best hypothesis matches the complexity of the domain. Above it, hypotheses gain superfluous parts, which are either redundant (unlikely), or wrong (very likely). Below it, hypotheses are always wrong - they're too simple to account for all possible predictions, so new evidence will eventually falsify them. The tricky part is - even though we both postulate hypotheses and define their domain, we tend to hand-wave the latter a lot, so in some cases (like medicine) we may not realize that our hypotheses are too simple.
Assume complexity then move towards simplicity.
Assume simplicity then move towards complexity.
One of them will succeed sooner than the other. Dialectic...
Which is where it becomes probabilistic. The answer to what it means for one model to be "simpler" than another is part of information theory, and that is essentially the flip side of probability theory. Information is (unsurprisingly) counted in bits, and one way of defining "a bit" is as amount of information that cuts your uncertainty by half.
> If the models make the same predictions, neither can be said to be more true than the other. But if there is a difference in falsifiable predictions, this can be used to determine which model is best - but then occams razor does not apply. The most correct model wins, whether or not it is the simplest.
The point of applying the razor is that, if there's no evidence to support one model over other, your best bet is to chose the simpler one now, because when new evidence comes to light that will favor one over other, it's more likely to favor the simpler one.
I highly doubt that. The history of science has plenty of examples where more complex hypotheses turn out to be more correct. E.g Einsteins relativity is more complex than Newtonian mechanics, but nevertheless better matches observations. The current model of the universe is far more complex than the Ptolmaic model, the periodic system is more conplex than the four elements etc.
Occams razor applies if two models make the same predictions and therefore neither can be more correct than the other.
Yes, but that's after people made observations that couldn't be explained by Newtonian mechanics. If you were living at the time the latter were formulated, and someone came to you with relativistic equations, showing that their result all line up perfectly with Newtonian ones, but otherwise offering no example of divergence, nor any explanation why the person chose these particular equations - you'd be right to call them a kook and ignore them. After all, there would be no way to distinguish between Newtonian formulation, Einstein's formulation, and an infinite amount of other formulations that also give the exact same results.
Ockham's razor makes sense only if some two models in question, which today make the same predictions, can also make divergent predictions that you expect to be testable in the future. The Razor tells you to stick with the simpler one, because it's most likely to remain the best model. The more complex model has more moving parts, requiring more bits of information to identify among many possible variations of same or greater complexity - bits you don't have, because if you had them, you could use them to disprove the simpler model.
In other words: the Razor worked for Newtonian mechanics despite Einstein, because a Newton's contemporary couldn't just randomly come up with the exact formulation of relativity we use today, given evidence available then. So whatever theory they would propose, it would overwhelmingly likely be wrong - as in, made bad predictions where Newtonian mechanics still made good ones.
> Occams razor applies if two models make the same predictions and therefore neither can be more correct than the other.
So to reiterate: Ockham's razor is future-facing; it applies to theories that can generate divergent predictions, but which you can't test just yet. If you expect the two models to always give the same predictions, now and in the future, then... they're literally the same thing, just expressed in different ways. There is no meaningful difference there, and you may just pick whichever one you like more, or whichever is easier to work with.
Occams Razor litterally just says that you should eliminate unnecessary entities from an explanation. It is a philosophical principle and not a statment about the natural world.
But the statments “the simplest of two theories is most likelily to be true” on the other hand is itself a hypothesis about the world which can be examined empirically. But I very much doubt this have been proven true for real world scientific theories. Perhaps for randomly generated theories it would be true, but theories are not typically generated at random. To follow the theme of the article - how would you falsify this hypothesis?
"Eliminate unnecessary entities" is a nice way of saying "minimize information-theoretic complexity" without having the formal framework to express it in. The intuition behind "counting entities" points in the right direction.
As for the philosophical part - once you take a piece of philosophy seriously and try to refine it into purity, it tends to turn into either mathematical theorem or a natural science hypothesis.
> But the statments “the simplest of two theories is most likelily to be true” on the other hand is itself a hypothesis about the world which can be examined empirically. But I very much doubt this have been proven true for real world scientific theories. Perhaps for randomly generated theories it would be true, but theories are not typically generated at random. To follow the theme of the article - how would you falsify this hypothesis?
This is exactly what information theory and probability theory deal with, among other things. They give a formal framework to define a measure of simplicity for a hypothesis, and to study its relation with probability of a hypothesis being correct. That framework can deal with correlated hypotheses just fine. So to answer your final question: when you strip away the vagueness, Occam's razor becomes a mathematical theorem, which you can prove or falsify using the tools of mathematics.
As for whether there is any reason for mathematics to apply to the real world, this ultimately follows from the basic axiom that the universe around us follows rules that we can infer from observations. If you accept it, you can use the tools of mathematics - including Ockham's razor - to understand the world. If you don't - well, if that axiom is wrong, then reality becomes completely arbitrary - nothing makes any sense whatsoever, nor it can ever make any sense, and we're better off giving up on the whole "thinking" thing, moving back into caves, and spending our days hunting and gathering and finger-painting stick figures on cave walls.
So information theory might give you a measure of the complexity of a theory, but can’t (on its own) say anyting about whether it is true or not.
But hypothetically there could (as you suggest) be a correlation between the complexity of competing scientific theories and which theory turns out to best match evidence. But is there any empirical evidence for this to be the case? Just because it would be nice does not make it true, and it is not something you can prove mathematically.
Is is true? What makes it true?
>A concept which will in no way ever make a difference, is meaningless.
So what would falsify this statement? How would you convince yourself that you are wrong?