“Under no circumstances shall the company be liable to you or to any other person for any indirect, incidental, consequential or punitive damages arising out of…”
looks perfectly good in English, but it actually has no less than two linguistic quirks that come to the surface under translation. The first quirk is that the last one of the “damages” is a completely different beast than the first three ones. “Damage” is something unpleasant that happens to you and under that we can have indirect, incidental and consequential damage. “Damages”, on the other hand, are awarded by a court as monetary COMPENSATION for those unpleasant things, loss or injury, that happened to you. And they become “punitive” when they exceed the value of actual damage caused and are therefore a punishment. And actually, it’s not “they”, it’s “it”. Legal damages is a singular noun (see Wikipedia). Indeed in Danish we have two different words for the damage that happens to you vs. the damages you are awarded in court (the latter: more like compensation (“straferstatning”)).
The second quirky thing is the word “Punitive”. As I commented to my colleagues on the potential pitfalls of the above sentence when subjected to I18n internationalization, one of them said “but wait, I don’t see anything wrong, I can easily see how you can suffer damage that is punitive”. Indeed you can. But that has to do with the dual meaning in English of the word “punitive”: Punitive in this context, when attached to Damages, means: “as a punishment”, but the word Punitive is also used in non-legal speech to mean “terminal” or “decisive”, “grueling” or “inflictive”, like in a “punitive blow to the head”, i.e. a SERIOUS blow to the head (from which it is hard to recover).
So, YES, you can be damaged punitively (meaning: ~seriously, irrecoverably) as the result of something bad happening to you, but “punitive damages” is something else.