I would like to know what the difference is, if there is any, between sentences like:
I need this article to show the mistake
I need this article for showing the mistake
They went to see that film to prove their point
They went ot see that film for proving their point
I think that for+present participle+noun is wrong, but cannot find any arguments for that apart from that it does not feel right to me.
With for + gerund, you're talking about a general purpose: This is a case for keeping records in / A corkscrew is a tool for opening bottles*.
*A.J.Thomson and A.V. Martinet, “A Practical English Grammar”, Fourth Edition, rubric 334