[cornelis]

Again, thanks for joining and raising the bar. I'm reading your replies with interest.

The challenge though is for all of the correspondents to choose one for our debate It's impossible to work in and through an infinity, so its good to set them out in order a basic order. Some of the discussion hinges on difference of perspective, as you describe. Concerning correlation, for example, if speaking with curiosity he says "I don't know about causality, but there is only one kind of correlation, and I defined it above." Of course, this is one of the drawbacks of an open forum, where the good and bad is in the mix.

[curiosity]

I just realized I made a mistake. There are a few different types of correlation in probability theory. I gave you the definition of Pearson correlation. There are slighly different measures for the extent to which random variabels are related. For instance, there is Spearman correlation, which measures the extent to which the ranking of observations of two random variable are related.

Nevertheless, my basic point stands: correlation, no matter how you measure it, is a property of random variables. Anything non-random by definition is not correlated with anything.

[Alamo-Girl]

Thank you so much for your reply and your encouragements, dear cornelis!

curiosity is correct in that a “correlation coefficient” in statistics and probability theory is a numerical measure of the strength of a relationship between two random variables.

That is one meaning. However, in the context I was using it - “correlation is not causation” is an expression of a logical fallacy as follows:

Correlation implies causation (logical fallacy)

Correlation implies causation, also known as cum hoc ergo propter hoc (Latin for "with this, therefore because of this") and false cause, is a logical fallacy by which two events that occur together are claimed to be cause and effect.

For example:

Teenage girls eat lots of chocolate.

Teenage girls have acne.

Therefore, chocolate causes acne.

This argument, and any of this pattern, is an example of a false categorical syllogism. One observation about it is that the fallacy ignores the possibility that the correlation is coincidence. But we can always pick an example where the correlation is as robust as we please. If chocolate-eating and acne were strongly correlated across cultures, and remained strongly correlated for decades or centuries, it probably is not a coincidence. In that case, the fallacy ignores the possibility that there is a common cause of eating chocolate and having acne.