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I get the theoretical difference between the 2 words, unarguably means you cannot question the point.

But, given the sentence "Unarguably he is an excellent _", how does replacing unarguably with arguably impact the meaning of the sentence?

My only guess is that with arguably the implication is that the statement is open to scrutiny but with unarguably you are required to trust the speaker.

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up vote 3 down vote accepted

It's not a matter of meaning, it's a matter of context.

Unarguably, Bob is an excellent teacher.

This is an assertion about Bob's teaching excellence. The speaker expects no one would either question or dispute how well Bob can teach.

Arguably, Bob is an excellent teacher.

Once again, Bob's teaching ability is being affirmed. However, this sentence seems like it's a little more likely to be followed by a but or a however:

Arguably, Bob is an excellent teacher. However, he doesn't get along with his coworkers very well.

Another difference is that unarguably doesn't work well when talking about greatness that cannot be measure objectively. For example, I think it's okay to say:

Arguably, Bobby Orr was the greatest hockey player ever.

because some believe that is true. However, it would be foolish to assert:

Unarguably, Bobby Orr was the greatest hockey player ever.

because many people would bestow that honor upon Wayne Gretzky instead.

In other words, avoid using unarguably to describe matters of opinion, but reserve it for matters of undisputed fact:

Unarguably, the world's population has increased since 1900.

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You've pretty much nailed it. Arguable is used in different senses in the two words.

Unarguably, he is excellent = Arguable here means ‘there is room or occasion for argument or disputation over the proposition’, so this means that there can be no disagreement with the assertion that he is excellent.

Arguably, he is excellent = Arguable means ‘the proposition can be argued=maintained and supported by evidence’, so this means that it is reasonable to suggest that he is excellent*.

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With arguably the implication is that your statement is true but there are some points to discuss about, while with unarguable the implication is that your statement is true without any doubt.

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