The Armchairians would have noted this recurring cycle of events and our apparent inability to learn from history. ]]>

Pearl certainly was an engineer who studied decision theory, so he was even more contaminated by causal thinking than most humans. I probably should not have said Pearl claimed to *be* an armchairian, just that he claimed to have at some point disbelieved in causality and derived a belief in causality from non-causality (a claim that I misunderstood, see end). If he developed bayes nets without seeking causality, it is easy to imagine armchairians doing the same thing.

In the 1982 paper about tree bayes nets, Pearl does not mention causality. In 1984 or 1985, he says “This paper takes the position that human obsession with causation is computationally motivated. Causal models are only attractive because they provide effective data-structures for representing empirical knowledge…” which seems to be the assertion that armchairians would introduce such models. I don’t put much stake in an argument from authority: what does he know of armchairians? If he developed the 1982 paper with no thought of causality, I think that is strong evidence. But the lack of mention of causality in the paper is only weak evidence of his thoughts.

In the 1985 paper of full-fledged DAG bayes nets, he is more enthusiastic about causality, but is still nervous about its reality.

Actually, I misremembered the passage that lead me to describe past-Pearl as an armchairian. He does not claim to have ever disbelieved in causality or avoided talking about it (though he does seem to avoid it in the 1982 paper). From the preface of Causality, the passage is: “Ten years ago [in 1988] I was working in the empiricist position…[I held] that] causality simply provides useful ways of abbreviating and organizing intricate patterns of probabilistic relationships…I now take causal relationships to be the fundamental building blocks…” He is talking about a later transition. If he could make that transition, maybe armchairians could, but it is pretty weak evidence. But I don’t think the armchairians need to make that transition to count for Scott’s purposes.

]]>P(A OR NOT B) ? Also not quite good. Any other asymmetrical measures? ]]>

Moreover, the only effect can be derived, for which external world performs experiment for you, and performs it frequently enough to compute statistics. So, it is very hard to imagine what would lead to the prediction of computer design with its operations (given that core of it is from quantum mechanics – band structure of solid state bodies ). It took many controlled experiments based on the results of previous experiments in refining, and cleaning conditions, that it has very small probability of being performed by the nature in natural conditions.

]]>Check it out.

]]>‘It depends entirely on what we mean by “developing the notion of cause and effect”‘

One simple way of mathematizing “cause and effect” is to factor a joint distribution in terms of conditional probabilities.

There are some apparently natural mathematical definitions which can allow one to derive unique factorizations of a joint distribution into tables of conditional probabilities.

One example (of many):

http://en.wikipedia.org/wiki/Bayesian_information_criterion

Thus if the Armchairians can do something like the mathematical reasoning we are familiar with, they could reasonably be expected to have the capability of reasoning about something formal that equates pretty well with our notion of cause and effect. This is no different from our ability to reason about a mathematical model of the universe which lacks cause and effect (presumably mostly not very interesting models to us, but we can nonetheless reason about them).

On the other hand, would an Armcharian venture to make an absolute statement about cause and effect? In fact, should even those of us capable of interventionist experiments make such a statement? I would argue no. It is always possible (although vanishingly improbable), that in a finite numbers of samples of an experiment we have seen a series of outcomes that would lead us to an incorrect conclusion (unless you are assuming a deterministic universe and a sufficiently rich experimental model to capture this determinism).

The reason interventionist experiments seem the natural gold standard for causation is that they exactly sample from the distribution of interest. Mathematically: P(outcome | intervention leading to an event A) rather than P(outcome | A). The former is the distribution of interest precisely because we have the *option* of sampling from it in the future, and depending on the nature of the intervention there can be subtle differences between the two (we rarely have an intervention that we can be confident will produce exactly and only A). To Armchairians this would likely be of much more theoretical interest, since they do not have a natural reason to care about potential distinctions between A and some intervention leading to A.

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