 Although the first formal descriptions of natural deduction were in 1934, its acceptance and popularity weren’t manifested until the 1950s and 1960s when a huge number of elementary logic textbooks were published, different ones using variations on the central ideas of the foundational works from  1934.[1]  We shall only briefly touch on a few of the ways that the logical systems of these elementary textbooks differ from the original works, but it should be noted that some of these differences are thought (by some scholars) to be so important as to distinguish “true natural deduction” from some other types of formalisms that are sometimes also called natural deduction. (We describe such a system-wide difference in  §4.)