The concern of the philosophers is the idea of ‘true causation’ as independent from merely apparent causation. In particular, they have in mind the idea that even if the laws of the universe were deterministic there would be a sense in which certain events could be said to be causes of others even though mathematically, the configuration of the universe at any time completely entails it at all others. Frankly, this question arises out of half-baked arguments about whether events cause latter events or if god has predetermined and causes all events individually and I don’t take it seriously.
My take is that there is no such thing as causation. Correlation is all there is and the fact that many correlations are usefully and compactlly described by Bayesian causal models is actually support for the idea that the ascription of causation reflects nothing more than how the arrows happen to point in those causal models we find most compelling. In other words I don’t think it makes sense to look under your model to ask about what is truly causation but we should be clear that is what the philosophers mean.
Despite my great respect for Bayesian causal models it doesn’t let us deduce causality from correlation and I can prove it.
Given results about k events (assume for simplicity they are binary True/False events) E_1...E_k (so E_1 might be burglary, E_2 earthquake, E_3 recession and a trial is each year) and any ordering < on 1..k there is a causal model such that E_i is a causal antecedant of E_j iff i < j that perfectly agrees with the given probabilities. In other words at the expense of potentially having every E_i with i <* j affect the probability of E_i I can have any causal order I want on the events and get the same results.
To see this is true start with whatever event we want to occur first, say E_{i1}. Now we compute the probabilities that the next event E{i2} occurs conditional on E{i1} and it’s negation. For E{i3} we compute the probabilities that this event occurs conditional on all 4 outcomes for the pair E{i1}, E{i_2} and so on. This gives the correct probability to each set of outcomes and thus matches all observations. Alternatively, we can always make the E_i all dependent on some invisible common causes that match the appropriate priors.
True, these diagrams might be less simple in some sense than other diagrams we might draw but that doesn’t mean they are false. Indeed, we might have very good general reasons for preferring some more complicated theory, e.g., even if a simpler causal model could explain the data but requires causal dependence on effects later in time reject it in favor of some more complicated model. This is a useful generalization we have about the world and following it helps us reach better predictions when we have limited data. Thus the mere number of arrows can’t simply be minimized.
In other words all you’ve got is the same old crap about preferring the simpler theory where that has no principled mathematical definition and more or less means ‘prefer whatever your priors say the causal model really looks like.’ In other words we haven’t gotten any closer to infering causation.
Just the opposite. The use of Bayesian causal models explains extremely well why, even if events are truly all effects caused by the choices of some unseen mover the notion of causation would be likely to evolve.
In other words at the expense of potentially having every Ei with i <* j affect the probability of E_i I can have any causal
order I want on the events and get the same results.
Causal models have to do with interventions not with node orders in a Bayesian network. A causal model is not the same thing as a Bayesian network (which Eliezer got wrong in his post, and has yet to fix, by the way). Causal models are not about making better predictions, they are about cause effect relationships (causal effects, mediation analysis, confounders, things like that). I think reading standard stuff on interventionist causality might be a good idea: Pearl’s Causality book or the CMU book (Causation, Prediction and Search).
. In particular, they have in mind the idea that even if the laws of the universe were deterministic there would be a sense in which certain events could be said to be causes of others even though mathematically, the configuration of the universe at any time completely entails it at all others.
What;s the problem with that? If the universe is causally deterministic, it is causal. True,it is necesary to distinguish
causal deterninism form acausal determinism (eg fatalism) and philosophy can do that. Or is your concern with
future events entailing past ones? Then adopt two-way causality.
Correlation is all there is and the fact that many correlations are usefully and compactlly described by Bayesian causal models is actually support for the idea that the ascription of causation reflects nothing more than how the arrows happen to point in those causal models we find most compelling
I don’t follow that. The existence of a map doesn’t usually prove the non-existence of a territory.
In other words all you’ve got is the same old crap about preferring the simpler theory where that has no principled mathematical definition
The consequencesof abandoning the razor are much worse than those of having a subjective razor.
I’m afraid I haven’t followed the maths at all, but when you say that there is no causation, only corration, do you mean that you cannot prove causation, or that it actually never exists? Because that last option surely isn’t true? Back in ‘The Useful Idea of Truth’ we discussed how photons from shoelaces cause you to become entangled with their untangeledness. If there is no causation, you couldn’t observe or know anything.
If you mean you just can’t prove causation, could you please say it more simply (for me please)?
The concern of the philosophers is the idea of ‘true causation’ as independent from merely apparent causation. In particular, they have in mind the idea that even if the laws of the universe were deterministic there would be a sense in which certain events could be said to be causes of others even though mathematically, the configuration of the universe at any time completely entails it at all others. Frankly, this question arises out of half-baked arguments about whether events cause latter events or if god has predetermined and causes all events individually and I don’t take it seriously.
My take is that there is no such thing as causation. Correlation is all there is and the fact that many correlations are usefully and compactlly described by Bayesian causal models is actually support for the idea that the ascription of causation reflects nothing more than how the arrows happen to point in those causal models we find most compelling. In other words I don’t think it makes sense to look under your model to ask about what is truly causation but we should be clear that is what the philosophers mean.
Despite my great respect for Bayesian causal models it doesn’t let us deduce causality from correlation and I can prove it.
Given results about k events (assume for simplicity they are binary True/False events) E_1...E_k (so E_1 might be burglary, E_2 earthquake, E_3 recession and a trial is each year) and any ordering < on 1..k there is a causal model such that E_i is a causal antecedant of E_j iff i < j that perfectly agrees with the given probabilities. In other words at the expense of potentially having every E_i with i <* j affect the probability of E_i I can have any causal order I want on the events and get the same results.
To see this is true start with whatever event we want to occur first, say E_{i1}. Now we compute the probabilities that the next event E{i2} occurs conditional on E{i1} and it’s negation. For E{i3} we compute the probabilities that this event occurs conditional on all 4 outcomes for the pair E{i1}, E{i_2} and so on. This gives the correct probability to each set of outcomes and thus matches all observations. Alternatively, we can always make the E_i all dependent on some invisible common causes that match the appropriate priors.
True, these diagrams might be less simple in some sense than other diagrams we might draw but that doesn’t mean they are false. Indeed, we might have very good general reasons for preferring some more complicated theory, e.g., even if a simpler causal model could explain the data but requires causal dependence on effects later in time reject it in favor of some more complicated model. This is a useful generalization we have about the world and following it helps us reach better predictions when we have limited data. Thus the mere number of arrows can’t simply be minimized.
In other words all you’ve got is the same old crap about preferring the simpler theory where that has no principled mathematical definition and more or less means ‘prefer whatever your priors say the causal model really looks like.’ In other words we haven’t gotten any closer to infering causation.
Just the opposite. The use of Bayesian causal models explains extremely well why, even if events are truly all effects caused by the choices of some unseen mover the notion of causation would be likely to evolve.
I keep having to link this:
http://www.smbc-comics.com/index.php?db=comics&id=1994
Causal models have to do with interventions not with node orders in a Bayesian network. A causal model is not the same thing as a Bayesian network (which Eliezer got wrong in his post, and has yet to fix, by the way). Causal models are not about making better predictions, they are about cause effect relationships (causal effects, mediation analysis, confounders, things like that). I think reading standard stuff on interventionist causality might be a good idea: Pearl’s Causality book or the CMU book (Causation, Prediction and Search).
What;s the problem with that? If the universe is causally deterministic, it is causal. True,it is necesary to distinguish causal deterninism form acausal determinism (eg fatalism) and philosophy can do that. Or is your concern with future events entailing past ones? Then adopt two-way causality.
I don’t follow that. The existence of a map doesn’t usually prove the non-existence of a territory.
The consequencesof abandoning the razor are much worse than those of having a subjective razor.
I’m afraid I haven’t followed the maths at all, but when you say that there is no causation, only corration, do you mean that you cannot prove causation, or that it actually never exists? Because that last option surely isn’t true? Back in ‘The Useful Idea of Truth’ we discussed how photons from shoelaces cause you to become entangled with their untangeledness. If there is no causation, you couldn’t observe or know anything. If you mean you just can’t prove causation, could you please say it more simply (for me please)?