Father says at dinner, “we are correcting history here.” what does he mean by that? is it possible to “correct” history? is there only one version of history? can you name circumstances when changing history has been a good thing?

Correcting history is a process in which new pieces of evidence are taken into consideration in the aftermath of a historical event, in order to show that facts unfolded in a different way in relation to what people believed before, thus changing history, and correcting it in a new series of event, different from what was believed previously.

It is possible to find new evidence that opens to different interpretations of the same event. It is also possible to uncover new facts that change the perception of that even. In this process, it is possible to correct history, in a sense that makes history more accurate and fact centred than before.
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No, there are multiple versions of history, considering the different point of view that people could have on a single event, due to different backgrounds, cultures, ways of interpreting facts, or simply because they saw a different aspect of the same event, thus making more versions of the same event. 

The discovery of Troy was a good way of changing history. Before the discovery, everyone believed that Troy was only a myth, but with the new pieces of evidence, people started to actually study the area, finding not one but nine cities where Troy should have been, thus contributing in a good way to re-write a piece of history.