Surprised to see such negative comments. I think this is a good piece.

When can inferential statistics really be applied? The requirements are onerous and almost never met:

There must be a designed experiment with randomisation of the inputs,

The experimental procedure must be carried out to the letter,

The statistical analysis must be of the preplanned format and no other analyses performed (e.g. no looking for other patterns p-hacking etc).

Smoking is a classic case, to 'prove' that smoking causes lung cancer we must:

Get a large bunch of people at random from the global population,

RANDOMLY assign then to smoking and non-smoking groups,

Force them to follow their assigned smoking/non-smoking lifestyle until death,

Finally we can perform the inferential statistic!

Needless to say this has never been done, we have never 'proved' that smoking causes lung cancer but the accumulation of evidence pointing to this being the case is overwhelming.

The discussion of correlation is also apt.

OK, correlation is just a descriptive statistic and means nothing, but in doing any scientific work we are searching for meaning - so what's the point?

If we find, eg, that smoking is correlated with lung cancer we are entitled to imagine that there might be a causual relationship and use it to inform our decisions, we will never have perfect proof and must decide based on the observation and our estimations of how the world might work.

Finally, I think there can be a moral dimension to our estimates of how things work. If we try and take a disinterested stance to the world we may come up with multiple plausible ideas about how it works. Different ideas might lead to different courses of action, some more morally abhorant then others. I think then it is the correct thing to do to weight your conclusions towards the least morally abhorant.