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'correlation does not imply causation' is just the negation of 'if correlation, then causation'.

What do you think the relevant difference between the terms 'imply' and 'conclusively prove' is?

I view 'imply' as 'suggest' and 'prove' is 'this is a fact'. Correlation does in fact imply causation (which is why correlations are investigated). It just doesn't prove the causation. It may be that the two things you're looking at are both related to some other cause (e.g. ice cream sales and murders increase in summer, supposedly. This does not mean ice cream sales has a direct relation to murder but they probably both have a relation to outside tempature), it may even be pure coincidence. But if you see a correlation you see a place to begin your investigations.

I'm not going to suggest that 'imply' is clearer/less clear, but they both mean what you think 'prove' does. To quote a bunch of dictionaries, the phrase is using 'imply' to mean:

'to involve something or make it necessary'

'to have as a necessary consequence'

'to involve something as a logical consequence'

Thus XKCD's extension of the phrase to `Correlation doesn't imply causation, but it does waggle its eyebrows suggestively and gesture furtively while mouthing 'look over there'.` -- which is essentially what you're getting at.

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