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entropy1
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If we observe that: IF A happens THEN B happens, we speak of correlation and not of causation, right?
So when do we speak of causation?
So when do we speak of causation?
Generally language like "If A then B" implies causation, not just correlation.entropy1 said:If we observe that: IF A happens THEN B happens, we speak of correlation and not of causation, right?
If events A and B are spacelike separated, yes.entropy1 said:depending of the way the inertial frame of the observer moves with respect to the frame of A and the frame of B, either A can be observed to happen before B, or B before A, right?
That is the general assumption for spacelike separated events in relativity, yes.entropy1 said:But then it seems to me there can be no causal mechanism between A and B, right?
So just to get this clear, is that a prerequisite for :PeterDonis said:If events A and B are spacelike separated, yes.
entropy1 said:either A can be observed to happen before B, or B before A
That was not my approach; I aimed at A and B satisfying the truth table of IF A THEN B. This is statistics, right?PeterDonis said:Generally language like "If A then B" implies causation, not just correlation.
Yes.entropy1 said:So just to get this clear, is that a prerequisite for
Well, that truth table is satisfied if A is false, with B being either true or false; in other words, the only way "if A then B" is false is if A is true and B is false. Is that really what you intended?entropy1 said:I aimed at A and B satisfying the truth table of IF A THEN B.
If you're doing statistics, truth tables are irrelevant. You should be looking at correlation coefficients. We say A and B are correlated if the correlation coefficient between them is positive (and the more positive, i.e., the closer to 1, the better).entropy1 said:I aimed at A and B satisfying the truth table of IF A THEN B. This is statistics, right?
Is there a problem if I did?PeterDonis said:Is that really what you intended?
Ok, that is useful to me. Otherwise I might have had to conclude that a causal mechanism can be seen as retrocausal.PeterDonis said:Yes.
Aside from the issue about statistics that I raised, yes: if A is false it makes no sense to say that A caused B, or that A is correlated with B, even if B is true. So saying you are using the truth table for "if A then B" includes cases where it makes no sense to talk about the things you say you want to talk about.entropy1 said:Is there a problem if I did?
I can't follow you so I can't answer that one.PeterDonis said:Aside from the issue about statistics that I raised, yes: if A is false it makes no sense to say that A caused B, or that A is correlated with B, even if B is true. So saying you are using the truth table for "if A then B" includes cases where it makes no sense to talk about the things you say you want to talk about.
This just goes to show that we have to be careful with natural language: context is everything, and there are nearly always additional unstated assumptions implied by that context. Without context, the statement "If A then B" could mean any of several different things:entropy1 said:That was not my approach; I aimed at A and B satisfying the truth table of IF A THEN B. This is statistics, right?
See the last sentence of my post #4.entropy1 said:if A and B are spacelike separated, can there be a causal mechanism between them?
If I take the equivalent version of IF NOT(B) THEN NOT(A), can I accommodate the objection?PeterDonis said:Aside from the issue about statistics that I raised, yes: if A is false it makes no sense to say that A caused B, or that A is correlated with B, even if B is true. So saying you are using the truth table for "if A then B" includes cases where it makes no sense to talk about the things you say you want to talk about.
It "generally" can. It says that "A cannot be true when B is false" or equally that "B cannot be false when A is true". So the causation can go in either direction.PeterDonis said:Generally language like "If A then B" implies causation, not just correlation.
No, it can't, since B can still be true when A is false, so "if B then A" might not be true..Scott said:the causation can go in either direction.
No.entropy1 said:if I take the equivalent version of IF NOT(B) THEN NOT(A), can I then accommodate your objection?
You could, but that still wouldn't be the same as the correlation coefficient.entropy1 said:You can correlate how often the truth table is satisfied statistically, right?
But to measure how often A and B satisfy the truth table is a different correlation, right?PeterDonis said:You could, but that still wouldn't be the same as the correlation coefficient.
It's not a correlation at all. The correlation coefficient tells how often A and B are the same (both true or both false, assuming you are dealing with binary measurements--with measurements that can have more than two results or where the results can be continuously distributed, it's more complicated). Measuring how often A and B satisfy the truth table tells you nothing useful about their relationship, since, as I've already noted, they will satisfy the truth table if A is false regardless of whether B is true or false.entropy1 said:to measure how often A and B satisfy the truth table is a different correlation, right?
Go back and read post #2.entropy1 said:if you can predictically manipulate the correlation between A an B, that counts as causation?
Yes, measurement error can cause a particular run of an experiment to not detect A causing B even if it actually does. However, note that in post #2, @.Scott described manipulating A in an experiment and then seeing what happens to B. That means varying A and seeing if there is a corresponding variation in B. So you're not just looking at one run; you're looking at a lot of runs over which A varies, and seeing if B varies in a corresponding way. The only way measurement error will cause you to fail to detect that is if your measurements are so poor that you can't measure variation in A or B at all. In which case you wouldn't even be doing the experiment in the first place because you would know it couldn't tell you anything useful.entropy1 said:I can image that in a physics experiment, if A would cause B, there still would be trials where measurment is not agreeing with this due to minimal margins of error.
It would depend on the context; @Nugatory in post #13 gave examples where it would and examples where it wouldn't. I agree that my original statement in post #4 that it generally does imply causality was too strong.stevendaryl said:I am not in agreement that “if A then B” says anything about causality.
If the roads are dry, then it is rain-free.PeterDonis said:No, it can't, since B can still be true when A is false, so "if B then A" might not be true.
The logical connective that expresses "the causation can go in either direction" is equivalence--the truth values of A and B must be the same--which is not the same as "if A then B".
Rain | Rain-free | |
Dry Roads | No | Possible |
Wet Roads | Possible | Possible |
Correlation is something that we measure. Causation is a theoretical concept that we use to explain the causation. If we don't want to explain the correlation, then we can talk about correlation without talking about causation.entropy1 said:If we observe that: IF A happens THEN B happens, we speak of correlation and not of causation, right?
So when do we speak of causation?
I wrote a paper once (unpublished; it was a paper for a college class) suggesting this notion of causality. The moon causes the tides because, in the thought experiment in which we take the moon far from the Earth, there would be no tides. It's a little more difficult to use this to argue that the phases of the moon do not cause the tides, because you can't easily manipulate the phases of the moon without also changing all sorts of other things (particularly, the position of the moon relative to the Earth and Sun).atyy said:However, there is a different (?) agent-based conception. A causes or contributes to causing B if manipulating A affects B.
If C is the common cause of X and Y, and there is no causal link between X and Y, then manipulating X will not affect Y, and manipulating Y will not affect X, even though X and Y are correlated. One has to manipulate C to affect X and Y.
Correlation refers to a relationship between two variables, where a change in one variable can be associated with a change in the other variable. Causation, on the other hand, is a relationship where one variable directly causes a change in the other variable.
To determine causation, we need to conduct a controlled experiment where one variable is manipulated while keeping all other variables constant. If the manipulated variable causes a change in the other variable, then we can establish a causal relationship.
No, correlation does not imply causation. Just because two variables are correlated does not mean that one causes the other. There could be other factors at play that are causing the observed relationship.
It is important to understand the difference between correlation and causation because mistaking correlation for causation can lead to incorrect conclusions and decisions. It is crucial to establish causation in order to make accurate predictions and inform effective interventions.
To avoid mistaking correlation for causation, it is important to consider other factors and conduct controlled experiments to establish causation. Additionally, it is important to critically analyze data and not make assumptions based on correlation alone.