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OK, but this "inference" is not a valid substitute for a logical inference because it produces a different type of result - probabilistic, not certain. The cr

by lngnmn 9y ago

OK, but this "inference" is not a valid substitute for a logical inference because it produces a different type of result - probabilistic, not certain. The crucial difference is that statistical inference does not consider any causation, its domain is observations only, and observations only cannot establish a causation in principle. Correlation is not a causation. Substituting a Bayesian inference for a logical inference should result in a Type Error (where are all these static typing zealots when we need them?). This is, by the way, one of the most important principles - universe exist, probabilities and numbers does not. Every causation in the universe is due to its laws and related structures and processes. Causation has nothing to do with numbers or observations. This is why most of modern "science" are non-reproducible piles of crap. Any observer is a product of the universe. The Bayesian sect is trying to make it the other way around. Mathematical Tantras of the digital age.

marmaduke 9y ago
Bayesian inference is just an extension of logical inference to probability distributions. The "correlation is not causation" reaction is off base here.
- lngnmn 9y ago
  No, it is not. Logic of any kind is a step-by-step process of induction, based on a valid premises in each step (just one false premise is enough to refute the whole thing, and it must always be verified) while all the premises must be traced (validated) back to one of the fundamental laws of the universe, to what is. Otherwise it is just a form of bullshit. Socrates is mortal not because he is a man, but because biology is bound by physics of this universe (in which compound structures are impermanent and what we call energy is eternal, being transformed from one form into another) and because a man is a biological process, he is impermanent or mortal. (Ancient Buddhists got it right, by the way). Logic is possible because the given Universe has a certain stable (eternal) properties, so processes and structures are possible. Abstract logic is a bullshit (hello, Hegelians!). Mathematical logic works because each one inductive step rests on the valid premises due to the fact that numbers as an abstraction capture a valid aspect of reality revealed to an observer. But it cannot be applied to anything but numbers. Different types of premises and inductions are required for different domains (while the process is fundamentally the same). The sun will rise in the sky tomorrow not because of some probabilistic inference but because such a physical process cannot be quickly changed. Causes are always real (physical), not imaginary (mathematical).
Houshalter 9y ago
Logical inference is just a special case of more general bayesian inference. Anything you can do with logical inference you can do with bayesian inference. Just imagine the probabilities are 0 and 1. Here's an entire book on the subject: http://bayes.wustl.edu/etj/prob/book.pdf http://bayes.wustl.edu/etj/prob/book.pdf But true logical inference doesn't exist in the real world. Because you can never be 100% sure of anything, not even mathematical facts. It's just an approximation of superior bayesian inference: http://lesswrong.com/lw/mp/0_and_1_are_not_probabilities/ http://lesswrong.com/lw/mp/0_and_1_are_not_probabilities/ You can even deduce causation from purely observational data. And here's how: http://lesswrong.com/lw/ev3/causal_diagrams_and_causal_models/ http://lesswrong.com/lw/ev3/causal_diagrams_and_causal_model...
- lngnmn 9y ago
  > Logical inference is just a special case of more general bayesian inference NO. This is a fucking sectarian crap. Logic of any kind is possible only because the Universe has its laws and structure. It always comes first. Logic is a uninterrupted chain of steps of induction which must be validated by tracing back the whole chain to some validated, fundamental principle. It is a universal process. Inductive steps and premises are domain-specific. Logic could be applied to abstractions like numbers as an exception, because numbers represents valid aspects or properties of reality, not the other way around. Numbers are imaginary. Universe is real. It makes an observer possible, but does not require one, which means that an observer and all his inferences could be excluded completely from the "mechanics" of what is. Time, for example. And numbers, of course.
  - Houshalter 9y ago
    You are speaking a bunch of incoherent nonsense. Logical inference is just a simplification of proper Bayesian inference. There are no problems you can model with logic that can't be modeled by Bayesian logic. You just take a set of logical premises and set their probabilities to be 0 or 1. But this is only an approximation, and is fundamentally wrong in principle for any real world problem. You can never be 100% certain of anything, even mathematical proofs. After all, errors are found in published mathematical proofs all the time. And people regularly make mistakes doing even simple arithmetic. That's the thing, we live in an uncertain world and can never have true certainty about anything. Especially in most real world problems that we care about. All forms or reasoning and inference are part of the mind, not reality. Reality doesn't have to respect your axioms or logical inferences. At any time reality can bite back and say your logic was wrong. And you must change your map, not argue that the territory is incorrect. Bayesian inference is the process of drawing maps of a territory. And realizing that they are just maps. That we can make more and more accurate maps, but we can never have maps that are 100% perfect and certain. Reality doesn't grant us certainty, and that's ok.

by lngnmn 9y ago

marmaduke 9y ago

Bayesian inference is just an extension of logical inference to probability distributions. The "correlation is not causation" reaction is off base here.

lngnmn 9y ago
No, it is not. Logic of any kind is a step-by-step process of induction, based on a valid premises in each step (just one false premise is enough to refute the whole thing, and it must always be verified) while all the premises must be traced (validated) back to one of the fundamental laws of the universe, to what is. Otherwise it is just a form of bullshit. Socrates is mortal not because he is a man, but because biology is bound by physics of this universe (in which compound structures are impermanent and what we call energy is eternal, being transformed from one form into another) and because a man is a biological process, he is impermanent or mortal. (Ancient Buddhists got it right, by the way). Logic is possible because the given Universe has a certain stable (eternal) properties, so processes and structures are possible. Abstract logic is a bullshit (hello, Hegelians!). Mathematical logic works because each one inductive step rests on the valid premises due to the fact that numbers as an abstraction capture a valid aspect of reality revealed to an observer. But it cannot be applied to anything but numbers. Different types of premises and inductions are required for different domains (while the process is fundamentally the same). The sun will rise in the sky tomorrow not because of some probabilistic inference but because such a physical process cannot be quickly changed. Causes are always real (physical), not imaginary (mathematical).

Houshalter 9y ago

Logical inference is just a special case of more general bayesian inference. Anything you can do with logical inference you can do with bayesian inference. Just imagine the probabilities are 0 and 1. Here's an entire book on the subject: http://bayes.wustl.edu/etj/prob/book.pdf http://bayes.wustl.edu/etj/prob/book.pdf But true logical inference doesn't exist in the real world. Because you can never be 100% sure of anything, not even mathematical facts. It's just an approximation of superior bayesian inference: http://lesswrong.com/lw/mp/0_and_1_are_not_probabilities/ http://lesswrong.com/lw/mp/0_and_1_are_not_probabilities/ You can even deduce causation from purely observational data. And here's how: http://lesswrong.com/lw/ev3/causal_diagrams_and_causal_models/ http://lesswrong.com/lw/ev3/causal_diagrams_and_causal_model...

lngnmn 9y ago
> Logical inference is just a special case of more general bayesian inference NO. This is a fucking sectarian crap. Logic of any kind is possible only because the Universe has its laws and structure. It always comes first. Logic is a uninterrupted chain of steps of induction which must be validated by tracing back the whole chain to some validated, fundamental principle. It is a universal process. Inductive steps and premises are domain-specific. Logic could be applied to abstractions like numbers as an exception, because numbers represents valid aspects or properties of reality, not the other way around. Numbers are imaginary. Universe is real. It makes an observer possible, but does not require one, which means that an observer and all his inferences could be excluded completely from the "mechanics" of what is. Time, for example. And numbers, of course.
- Houshalter 9y ago
  You are speaking a bunch of incoherent nonsense. Logical inference is just a simplification of proper Bayesian inference. There are no problems you can model with logic that can't be modeled by Bayesian logic. You just take a set of logical premises and set their probabilities to be 0 or 1. But this is only an approximation, and is fundamentally wrong in principle for any real world problem. You can never be 100% certain of anything, even mathematical proofs. After all, errors are found in published mathematical proofs all the time. And people regularly make mistakes doing even simple arithmetic. That's the thing, we live in an uncertain world and can never have true certainty about anything. Especially in most real world problems that we care about. All forms or reasoning and inference are part of the mind, not reality. Reality doesn't have to respect your axioms or logical inferences. At any time reality can bite back and say your logic was wrong. And you must change your map, not argue that the territory is incorrect. Bayesian inference is the process of drawing maps of a territory. And realizing that they are just maps. That we can make more and more accurate maps, but we can never have maps that are 100% perfect and certain. Reality doesn't grant us certainty, and that's ok.