Systems of natural deduction as a method of theorem proving were first developed in detail by Gentzen and Jáskowski. The complex nature of the rules for quantification in these early systems of natural deduction, and in particular of the parallel rules of Universal Generalization (UG) and Existential Instantiation (El) led to an active research program in the period from the late 1950's to the late 1960's in an effort by Quine, Suppes, Leblanc, and Copi to develop simplified and correct rules of inferences for the quantified formulae of first-order functional logic. We explore the history of these efforts and examine the difficulties found in the "unnatural" natural deductive systems that were developed for first-order logic. Our survey covers roughly forty years, from 1929 to 1971, which includes the early work of Hertz on which Gentzen's work was based through the development of the quantifation rules in Copi's system of natural deduction as presented in the third edition of his textbook Symbolic logic. Also considered is the extent to which O. H. Mitchell made a start at developing a system of natural deduction in his 1883 paper On a new algebra

The late Nikolai Ivanovich Stiazhkin was born in Astrakhan on 1 October 1932. He studied in the Philosophy Faculty of Moscow State University, where beginning in 1964 he taught a fundamental course on history of logic in the logic department of the philosophy faculty. He was a leading historian of logic who specialized in the history of logic in the nineteenth century, writing his Candidate's thesis on that topic under the direction of S. A. lanovskaia in 1959, and his doctoral thesis on The Development of the Idea of Mathematical Logic in 1964. The latter, published by „Nauka" Press in Moscow in 1964 appeared in translation in several languages; it is known in English under the title History of Mathematical Logic from Leibniz to Peano and was published by MIT Press in 1969.

The author outlines the contents of one Stiazhkin's most important writings in history of logic. A detailed survey is given of the contents of his book, published in 1967, little known outside the USSR, Formirovanie matematiceskoj logiki (The Formation of Mathematical Logic, which was reviewed by Jean van Heijenoort in the Journal of Symbolic Logic 33 (1968), p. 465). Stiazhkin's encyclopedic and detailed but nonjudgemental work traces the entire panorama of the history of logic, from ancient China and India through the modern development of mathematical logic in the algebraic work of the nineteenth century, and ends with Peano.

A list of Stiazhkin's scientific writings is appended.