But
“There is no doubt but that he is the greatest painter of the age.” The word but is superfluous. “He never doubted but that he was the best fisherman on the coast.” Omit but.
That
“He told me he would write as soon as he reached London.” Say, “He told me that he would write,” etc.
Than
“The Romans loved war better than the Greeks.” Such ambiguous forms should be avoided. As it is not probable that the speaker intended to say that the Romans loved war better than they loved the Greeks, he should have framed his sentence thus: “The Romans loved war better than the Greeks did.”
But that
“He suffered no inconvenience but that arising from the dust.” But that, or except that, is correct. Some persons improperly use than that after no.
“I don’t know but that I shall go to Europe.” Omit that. “I don’t know but I shall go,” etc.