I think "also" translates "therefore" quite well here, better than "deshalb" or "darum" would.
That is because the meaning of the sentence more precisely put is not "I think and because of that I am". Instead it is: "I think. Based on that fact we can draw the conclusion that I am."
The latter is exactly what "also" means here, while "deshalb" or "darum" would point more to the former.
Nobody said it was a logical necessity for him to disappear. Actually, the bartender was quite surprised.
This may be an instructive read :) http://lesswrong.com/lw/ne/the_parable_of_the_dagger/