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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

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.
- bazoom42 3y ago
  It is important to understand the limitations of logic and maths. They are fundamentally tautological systems - they can’t give you genuinely new knowledge about the world. Logic can’t tell you if purple swans exist or whether planetary orbits are circular or elliptical. You need empirical evidence for that. 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.

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.

bazoom42 3y ago
It is important to understand the limitations of logic and maths. They are fundamentally tautological systems - they can’t give you genuinely new knowledge about the world. Logic can’t tell you if purple swans exist or whether planetary orbits are circular or elliptical. You need empirical evidence for that. 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.