McCoy's Paradox

McCoy's Paradox was the name given to a philosophical problem raised by Leonard McCoy in 2269 regarding transporters.

McCoy theorized to Montgomery Scott that, since during the transporter process there was a time in which neither body nor consciousness existed, this meant that what the transporter actually did was destroy the body and create a duplicate which possessed the consciousness and memories of the original. When Scott rebutted with a phrase coined by Alfred Korzybski, that "a difference which makes no difference is no difference", McCoy responded that, if there was any difference, especially to the unconscious mind, he have know way of knowing it. As McCoy pointed out, the main question raised by the paradox was if the soul was also duplicated by the transporter. James T. Kirk theorized that the ability to worry about the question proved that it was, Scott argued that the soul was immortal by definition and therefore could not be destroyed, and Spock later added that, since there was no known way to prove the existence of the soul, the question was meaningless. 

In 2267, Zefram Cochrane, after having the properties of the transporter explained to him, at first thought that a person going through it was killed during the conversion from matter to energy, resulting in the creation of a duplicate that just thinks it's the original. It was then explained to him that that only applied to replicator technology, and that since the transporter process operated on a quantum level, the person's original molecules were simply moved to a new location, not destroyed and re-created.