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I have a related question to this topic. Is probability axiomatic to reality? Does it exist on the same level as logic where logic is axiomatic to reality and j

I have a related question to this topic. Is probability axiomatic to reality? Does it exist on the same level as logic where logic is axiomatic to reality and just assumed to be true? Or is it simply a phenomenon arising from logic? It seems like probability just happens to work without explanation? Intuitively this seems a bit strange since it feels as though probability should be derived from something else. Not sure if I'm correct here. What confuses me even more is that I do know logic can be defined in terms of probability. Causal connections can be probabilistic. If A then 25% chance of B and so on.

BOOSTERHIDROGEN 4y ago
Also in relation to reductionism.
quickthrower2 4y ago
A lot of what probability is, is the extent of lack of information. The Monty Hall Problem is a great example of this. So I would say the more fundamental thing might be information theory. This my layman view. Not an expert.
- lupire 4y ago
  Probability is weight/count of cases of interest divided by weight/count of all possible cases.
  - quickthrower2 4y ago
    I just rolled a 6 sided die here and looked at the outcome. For you the probability it is a 6 is 1/6. For me is isn’t 1/6. Same object!
    - deltasevennine 4y ago
      For you it isn't 1/6 but for him it is. From your perspective can you derive from the knowledge you have why that for him the probability is 1/6? And I mean derive as in derive the mathematical probability from all your knowledge about physics and the dice to explain why the lack of knowledge appears to him as a probability. This is the essence of my question. We assume it. Probability is taken to be true for no reason, similar to how we just assume logic to be true.
      - quickthrower2 4y ago
        Probability is an abstract concept so if he has a really good model of the universe there is no reason he couldn’t have better information. We don’t really know if “god plays dice” so to speak. We probably will never fully understand the underlying fabric of the universe even with lots of theories and experiments. It is like we get to run valgrind on the program but never see the source code.
        deltasevennine 4y ago
        > Probability is an abstract concept so if he has a really good model of the universe there is no reason he couldn’t have better information. It's not about reasoning. Sure he could have better information but this isn't the point. It's all about WHY probability works. Why are these laws suddenly obeyed when there's a lack of information? Do we assume it's fundamental? Or can the laws of probability be derived from deeper axioms, like logic.
  - mturmon 4y ago
    Perhaps you're just kidding around, but of course that's not good enough for a definition. It doesn't handle continuous random quantities. It doesn't even handle situations with a discrete outcome but where counting the possible cases isn't well-defined (Buffon's needle being one, but an even better one being the chance of a tossed thumbtack landing point-up). It also doesn't handle cases where symmetry or physics can give the answer, but you can't count cases because they aren't finite or aren't necessarily a-priori equiprobable.
kqr 4y ago
There are two things we mean by "probability". The first is propensity, and this has clear links to information theory, as another person commented about already. It's important to emphasise that in terms of propensity, it doesn't matter whether or not the event has occurred, what matters is your knowledge about it. A flipped fair coin has a definite side up (as can be verified by a silent third observer) but for you, who has not yet observed which side it is, your best guess is still either side with 50 % probability. Similarly, if you only know there's a soccer game going on, you might guess that the stronger team will win with 60 % probability (based on historic frequencies of exchangeable situations), but someone who has seen the score and knows the weaker team has a lead and knows there's only a few minutes left of the game will judge there to be a 2 % probability the stronger team wins. Same situation, different information, different judgements. That's the first meaning of "probability". What we also mean with that word is "the rules of probabilistic calculation". These are based on mathematical ideas like coherency (if one of two things can happen, their probabilities should add up to 100 %) and can definitely be taken as axiomatic. All of this is not an answer to your question, but it might make the discussion richer.
- kgwgk 4y ago
  There are multiple interpretations (corresponding to your first part). One of them is indeed about “propensities” but the most common ones are about “frequencies” and about “uncertainty”.
ThomPete 4y ago
Probability does not exist in reality as it's open ended. It does however exist in ex a deck of cards and a game that's defined. Probability is often being misused to say things about reality though. You see that especially in computer simulation whether used in economics, weather etc. Different initial conditions are put into the models and simulated. And the probability is calculated based on what the majority of those models say. But those initial conditions are guesses not actual objective explanations. If they were you only needed to run one simulation rather than a range. A lot of statistics is pure placebo. Purely retrospective. In reality it either is or it isn't. If you have good explanations like we do in physics you don't need probability. David Deutsch IMO has the most sane rebuttal of the probability. http://www.daviddeutsch.org.uk/2014/08/simple-refutation-of-the-bayesian-philosophy-of-science/ http://www.daviddeutsch.org.uk/2014/08/simple-refutation-of-...
- fjkdlsjflkds 4y ago
  > In reality it either is or it isn't. If you have good explanations like we do *in physics you don't need probability*. So... are you saying Statistical Mechanics (to give an example) is not part of Physics? In real life, the amount of information you have (and can have) about a physical process is limited. You can either throw your hands up and say "we can't know for sure", or you can use probabilities to try to get somewhere. How do you define the position of an electron without using probabilities?
  - ThomPete 4y ago
    Just because it's limited doesn't mean I can assign probability to it. As I said. The difference is closed and open systems. No problem with probability of getting a given card based on what have already been dealt in ex a game. The problem arises when it's applied to predicting reality in open ended systems as I said weather, economics, climate etc. and where history is being used as some sort of benchmark of the future. There is no probability whether an astroid is on the path towards earth. It either is or it isn't. In other words. We can either explain or not.
    - 4y ago
nyc111 4y ago
Probability, seems to me, cannot be fundamental, because, a machine built to flip a coin with always the same pressure, can be adjusted to always give heads, or tails. In such a setup there won't be probability. From George Boole's The Laws of Thought, p.244: "Probability is expectation founded upon partial knowledge. A perfect acquaintance with _all_ the circumstances affecting the occurence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities." Can we deduce from this that nature is not probabilistic?
- likeabbas 4y ago
  What if the machine was built with 99% precision?
- notafraudster 4y ago
  It is true that (at least above the level of quantum physics) we tend to believe that reality is deterministic. When the meteorologist gives a chance of rain, in truth if they had perfect forward information on all of the clouds and pressure systems, they would simply declare whether or not there was future rain. In cases like physical phenomenon, you can think of observed uncertainty or chance as being a product of the exact settings of the unmodeled but deterministic factors underlying a particular outcome, or else errors in the functional form of the model with respect to the measure. We tend to assume that unmodeled factors are as-if orthogonal to the causes we are interested in modelling, and thus zero-centered, and our models minimize error predicated on this assumption. In your proposed flipping model, there are likely to be very small physical imprecisions (vibrations in the flipper, say, drifting tension of some kind of spring or actuator, or small amounts of circulating air, or perhaps tiny imprecisions in the way the coin is loaded into a slot). The machine might always flip heads, but it's still possible to say that whatever arbitrary degree of certainty you need to model the coin's behaviour in the air to achieve 100% accuracy, there could still be arbitrarily smaller error below that threshold, and we'd view this as "randomness" even if it isn't by the laws of physics.
- empyrrhicist 4y ago
  Not a physicist, but your argument is pretty unconvincing in that it relies entirely on intuition about classical physics, ignoring quantum phenomena entirely. If one were to argue that probability were fundamental, they'd very likely start by describing wave functions, which are probabilistic and seem pretty close to fundamental to observable reality.
panda-giddiness 4y ago
Probability theory can be interpreted as an extension to logic where variables can take fractional values (rather than just be 0/false or 1/true). E.g., ((A or B) and C) = (A and C) or (B and C) => P[(A or B) and C] = P[(A and C) or (B and C)] = P[(A and C)] + P[(B and C)] - P[(A and B) and (A and C)] = P[(A and C)] + P[(B and C)] - P[A and B and C] = P[A|C] P[C] + P[B|C] P[C] - P[A and B and C] Notice the last couple lines -- this is the way in which probability extends logic. In you take the limit where P[A], P[B], P[C] = 0, 1, then the probability statement reduces to the logic statement at the top.
- deltasevennine 4y ago
  I already mentioned that logic can be defined in terms of probability above. Here's the strange part. Let's say we make those probabilities to be 100% thus we have ordinary logic without probability. Then let's create a physical closed Newtonian system: The interior of a cube with no gravity and a bunch of identical bouncing balls which obey Newtonian physics and therefore logic. Let's say those balls all have a random initial velocity at a random direction but all those balls are initially positioned near one corner in the cube. Thus the balls from a position stand point start with low entropy. I use the term random, but it's not really random as you have perfect knowledge of these numbers, you know what they all are. As time increases, entropy increases. The balls as a system begin to increase in entropy. Entropy continues to rise towards an equilibrium. That is the question. Entropy is a probabilistic phenomenon. It occurs because ball configurations that are spread out have higher probabilities of occurring then balls that are concentrated in a corner. Thus given enough time the balls occupy the higher entropy state. My question is, WHY does this occur. Probability (aka Entropy) is ARISING out of a perfect Newtonian system following perfect logic without any probabilistic extensions. Can entropy be derived from Newtonian physics? The better question is, can probability be derived from Newtonian physics because entropy is in actuality a phenomenon of probability? Any system that uses pure logic (and completely avoids probability in any part of its definition) exhibits this sort of rule as long as you introduce a sort of randomness into initial parameters above. Probability permeates everything.
  - kgwgk 4y ago

BOOSTERHIDROGEN 4y ago

Also in relation to reductionism.

quickthrower2 4y ago

A lot of what probability is, is the extent of lack of information. The Monty Hall Problem is a great example of this. So I would say the more fundamental thing might be information theory. This my layman view. Not an expert.

lupire 4y ago
Probability is weight/count of cases of interest divided by weight/count of all possible cases.
- quickthrower2 4y ago
  I just rolled a 6 sided die here and looked at the outcome. For you the probability it is a 6 is 1/6. For me is isn’t 1/6. Same object!
  - deltasevennine 4y ago
    For you it isn't 1/6 but for him it is. From your perspective can you derive from the knowledge you have why that for him the probability is 1/6? And I mean derive as in derive the mathematical probability from all your knowledge about physics and the dice to explain why the lack of knowledge appears to him as a probability. This is the essence of my question. We assume it. Probability is taken to be true for no reason, similar to how we just assume logic to be true.
    - quickthrower2 4y ago
      Probability is an abstract concept so if he has a really good model of the universe there is no reason he couldn’t have better information. We don’t really know if “god plays dice” so to speak. We probably will never fully understand the underlying fabric of the universe even with lots of theories and experiments. It is like we get to run valgrind on the program but never see the source code.
      - deltasevennine 4y ago
        > Probability is an abstract concept so if he has a really good model of the universe there is no reason he couldn’t have better information. It's not about reasoning. Sure he could have better information but this isn't the point. It's all about WHY probability works. Why are these laws suddenly obeyed when there's a lack of information? Do we assume it's fundamental? Or can the laws of probability be derived from deeper axioms, like logic.
- mturmon 4y ago
  Perhaps you're just kidding around, but of course that's not good enough for a definition. It doesn't handle continuous random quantities. It doesn't even handle situations with a discrete outcome but where counting the possible cases isn't well-defined (Buffon's needle being one, but an even better one being the chance of a tossed thumbtack landing point-up). It also doesn't handle cases where symmetry or physics can give the answer, but you can't count cases because they aren't finite or aren't necessarily a-priori equiprobable.

kqr 4y ago

There are two things we mean by "probability". The first is propensity, and this has clear links to information theory, as another person commented about already. It's important to emphasise that in terms of propensity, it doesn't matter whether or not the event has occurred, what matters is your knowledge about it. A flipped fair coin has a definite side up (as can be verified by a silent third observer) but for you, who has not yet observed which side it is, your best guess is still either side with 50 % probability. Similarly, if you only know there's a soccer game going on, you might guess that the stronger team will win with 60 % probability (based on historic frequencies of exchangeable situations), but someone who has seen the score and knows the weaker team has a lead and knows there's only a few minutes left of the game will judge there to be a 2 % probability the stronger team wins. Same situation, different information, different judgements. That's the first meaning of "probability". What we also mean with that word is "the rules of probabilistic calculation". These are based on mathematical ideas like coherency (if one of two things can happen, their probabilities should add up to 100 %) and can definitely be taken as axiomatic. All of this is not an answer to your question, but it might make the discussion richer.

kgwgk 4y ago
There are multiple interpretations (corresponding to your first part). One of them is indeed about “propensities” but the most common ones are about “frequencies” and about “uncertainty”.

ThomPete 4y ago

Probability does not exist in reality as it's open ended. It does however exist in ex a deck of cards and a game that's defined. Probability is often being misused to say things about reality though. You see that especially in computer simulation whether used in economics, weather etc. Different initial conditions are put into the models and simulated. And the probability is calculated based on what the majority of those models say. But those initial conditions are guesses not actual objective explanations. If they were you only needed to run one simulation rather than a range. A lot of statistics is pure placebo. Purely retrospective. In reality it either is or it isn't. If you have good explanations like we do in physics you don't need probability. David Deutsch IMO has the most sane rebuttal of the probability. http://www.daviddeutsch.org.uk/2014/08/simple-refutation-of-the-bayesian-philosophy-of-science/ http://www.daviddeutsch.org.uk/2014/08/simple-refutation-of-...

fjkdlsjflkds 4y ago
> In reality it either is or it isn't. If you have good explanations like we do *in physics you don't need probability*. So... are you saying Statistical Mechanics (to give an example) is not part of Physics? In real life, the amount of information you have (and can have) about a physical process is limited. You can either throw your hands up and say "we can't know for sure", or you can use probabilities to try to get somewhere. How do you define the position of an electron without using probabilities?
- ThomPete 4y ago
  Just because it's limited doesn't mean I can assign probability to it. As I said. The difference is closed and open systems. No problem with probability of getting a given card based on what have already been dealt in ex a game. The problem arises when it's applied to predicting reality in open ended systems as I said weather, economics, climate etc. and where history is being used as some sort of benchmark of the future. There is no probability whether an astroid is on the path towards earth. It either is or it isn't. In other words. We can either explain or not.
  - 4y ago

nyc111 4y ago

Probability, seems to me, cannot be fundamental, because, a machine built to flip a coin with always the same pressure, can be adjusted to always give heads, or tails. In such a setup there won't be probability. From George Boole's The Laws of Thought, p.244: "Probability is expectation founded upon partial knowledge. A perfect acquaintance with _all_ the circumstances affecting the occurence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities." Can we deduce from this that nature is not probabilistic?

likeabbas 4y ago
What if the machine was built with 99% precision?
notafraudster 4y ago
It is true that (at least above the level of quantum physics) we tend to believe that reality is deterministic. When the meteorologist gives a chance of rain, in truth if they had perfect forward information on all of the clouds and pressure systems, they would simply declare whether or not there was future rain. In cases like physical phenomenon, you can think of observed uncertainty or chance as being a product of the exact settings of the unmodeled but deterministic factors underlying a particular outcome, or else errors in the functional form of the model with respect to the measure. We tend to assume that unmodeled factors are as-if orthogonal to the causes we are interested in modelling, and thus zero-centered, and our models minimize error predicated on this assumption. In your proposed flipping model, there are likely to be very small physical imprecisions (vibrations in the flipper, say, drifting tension of some kind of spring or actuator, or small amounts of circulating air, or perhaps tiny imprecisions in the way the coin is loaded into a slot). The machine might always flip heads, but it's still possible to say that whatever arbitrary degree of certainty you need to model the coin's behaviour in the air to achieve 100% accuracy, there could still be arbitrarily smaller error below that threshold, and we'd view this as "randomness" even if it isn't by the laws of physics.
empyrrhicist 4y ago
Not a physicist, but your argument is pretty unconvincing in that it relies entirely on intuition about classical physics, ignoring quantum phenomena entirely. If one were to argue that probability were fundamental, they'd very likely start by describing wave functions, which are probabilistic and seem pretty close to fundamental to observable reality.

panda-giddiness 4y ago

Probability theory can be interpreted as an extension to logic where variables can take fractional values (rather than just be 0/false or 1/true). E.g., ((A or B) and C) = (A and C) or (B and C) => P[(A or B) and C] = P[(A and C) or (B and C)] = P[(A and C)] + P[(B and C)] - P[(A and B) and (A and C)] = P[(A and C)] + P[(B and C)] - P[A and B and C] = P[A|C] P[C] + P[B|C] P[C] - P[A and B and C] Notice the last couple lines -- this is the way in which probability extends logic. In you take the limit where P[A], P[B], P[C] = 0, 1, then the probability statement reduces to the logic statement at the top.

deltasevennine 4y ago
I already mentioned that logic can be defined in terms of probability above. Here's the strange part. Let's say we make those probabilities to be 100% thus we have ordinary logic without probability. Then let's create a physical closed Newtonian system: The interior of a cube with no gravity and a bunch of identical bouncing balls which obey Newtonian physics and therefore logic. Let's say those balls all have a random initial velocity at a random direction but all those balls are initially positioned near one corner in the cube. Thus the balls from a position stand point start with low entropy. I use the term random, but it's not really random as you have perfect knowledge of these numbers, you know what they all are. As time increases, entropy increases. The balls as a system begin to increase in entropy. Entropy continues to rise towards an equilibrium. That is the question. Entropy is a probabilistic phenomenon. It occurs because ball configurations that are spread out have higher probabilities of occurring then balls that are concentrated in a corner. Thus given enough time the balls occupy the higher entropy state. My question is, WHY does this occur. Probability (aka Entropy) is ARISING out of a perfect Newtonian system following perfect logic without any probabilistic extensions. Can entropy be derived from Newtonian physics? The better question is, can probability be derived from Newtonian physics because entropy is in actuality a phenomenon of probability? Any system that uses pure logic (and completely avoids probability in any part of its definition) exhibits this sort of rule as long as you introduce a sort of randomness into initial parameters above. Probability permeates everything.
- kgwgk 4y ago