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> 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 n

> 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.

TeMPOraL 3y ago
> 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. 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.
- QuantumGood 3y ago
  Thank you both for a great thread.
- deleted 3y ago
  [deleted]
- bazoom42 3y ago
  Maybe you are thinking of a different principle? What you are saying sounds reasonable, but it is just not Occams Razor. 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?
  - TeMPOraL 3y ago
    > 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. "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.

TeMPOraL 3y ago

> 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. 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.

QuantumGood 3y ago
Thank you both for a great thread.
deleted 3y ago
[deleted]
bazoom42 3y ago
Maybe you are thinking of a different principle? What you are saying sounds reasonable, but it is just not Occams Razor. 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?
- TeMPOraL 3y ago
  > 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. "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.