3 ms·

I think, what I said is the same as what you said, just with some more maths. > you can't conclude A causes B right, this is what I referred to as "=>" > plu

I think, what I said is the same as what you said, just with some more maths. > you can't conclude A causes B right, this is what I referred to as "=>" > plus an explanatory theory of the causation, plus evidence yes, this all works together to build up the "how much smaller". An explanatory theory basically allows you to make predictions and run tests to collect more data to pump into the application of Bayes' theorem as used by that proof, improving your confidence of the difference between P(a|c) and P(a).

jsprogrammer 10y ago
Belief in "correlation implies causation" admits the Law of Excluded Middle fallacy. Just because you make an observation consistent with your beliefs, does not mean that you can claim all other explanations (complement of your beliefs) are invalid (primarily because you do not know what they are or could be).
JadeNB 10y ago
> > you can't conclude A causes B > right, this is what I referred to as "=>" Except that it isn't quite, since you were careful to clarify that your \implies (i.e., '=>' or '⇒') was the \implies of propositional logic, which explicitly disclaims any causal relationship. \implies in that context says precisely and only that the antecedent is false, or the consequent is true. In this sense, 2 + 2 = 4 \implies Barack Obama is currently the president of the US, and 2 + 2 = 5 \implies George Bush is currently the president of the US, even though there is no causal relationship in either case.
- infinity0 10y ago
  "is" in language can often mean "is a subset of", I was using the term that way. Whilst you are right that "=>" disclaims any philosophical relationship, the proof covers all definitions of "cause" that one might reasonably come up with. So "you can't conclude A => B" implies (with probability 1) that "you can't conclude A causes B": The proof only defines "causation" as some event "a" for which "P(c|a) = 1". This is the same property that "=>" has in propositional logic, and there is no implication of philosophical causation here either. But the proof still works, as a consequence of its definitions. So in other words, the proof says: if causation causes correlation then P(a|c) > P(a) (i.e. correlation is evidence of causation) but we can't say causation is definitely true (P(a) = 1), however you want to define "causes" as long as it has the property that P(c|a) = 1.
  - dragonwriter 10y ago
    That's not entirely true, at least, using the normal definition of "causes" that is of interest in correlation vs. causation discussions, which certainly includes "causes" which are contributors to the occurrence of an effect but do not alone guarantee it (e.g., smoking causes cancer, but it is not true that smoking implies cancer in the propositional logic sense.)

jsprogrammer 10y ago

Belief in "correlation implies causation" admits the Law of Excluded Middle fallacy. Just because you make an observation consistent with your beliefs, does not mean that you can claim all other explanations (complement of your beliefs) are invalid (primarily because you do not know what they are or could be).

JadeNB 10y ago

> > you can't conclude A causes B > right, this is what I referred to as "=>" Except that it isn't quite, since you were careful to clarify that your \implies (i.e., '=>' or '⇒') was the \implies of propositional logic, which explicitly disclaims any causal relationship. \implies in that context says precisely and only that the antecedent is false, or the consequent is true. In this sense, 2 + 2 = 4 \implies Barack Obama is currently the president of the US, and 2 + 2 = 5 \implies George Bush is currently the president of the US, even though there is no causal relationship in either case.

infinity0 10y ago
"is" in language can often mean "is a subset of", I was using the term that way. Whilst you are right that "=>" disclaims any philosophical relationship, the proof covers all definitions of "cause" that one might reasonably come up with. So "you can't conclude A => B" implies (with probability 1) that "you can't conclude A causes B": The proof only defines "causation" as some event "a" for which "P(c|a) = 1". This is the same property that "=>" has in propositional logic, and there is no implication of philosophical causation here either. But the proof still works, as a consequence of its definitions. So in other words, the proof says: if causation causes correlation then P(a|c) > P(a) (i.e. correlation is evidence of causation) but we can't say causation is definitely true (P(a) = 1), however you want to define "causes" as long as it has the property that P(c|a) = 1.
- dragonwriter 10y ago
  That's not entirely true, at least, using the normal definition of "causes" that is of interest in correlation vs. causation discussions, which certainly includes "causes" which are contributors to the occurrence of an effect but do not alone guarantee it (e.g., smoking causes cancer, but it is not true that smoking implies cancer in the propositional logic sense.)