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ARISTOTLES SYLLOGISTIC (Greek & Roman philosophy)

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Jan Lukasiewicz (1878-1956) was learned in classical languages and gifted in mathematics. He earned a permanent niche in history of logic for the book under review and for his work in the 1920s on Stoic logic recounted in the 1961 book STOIC LOGIC by Benson Mates. He also earned a permanent niche in symbolic logic for creating the parenthesis-free notation somewhat unjustly known as "Polish Notation": it should be called "Lukasiewicz notation". In mathematical logic he is known for the classic 1930 paper co-authored with his former student Alfred Tarski (1901-1983). An English translation of this paper is still in print; it is article IV of Tarski's 1956 LOGIC, SEMANTICS, METAMATHEMATICS (second ed. 1983). Tarski, who studied under Lukasiewicz, is widely regarded as one of the top five logicians to date--the others being Aristotle (384-322 BCE), Boole (1815-1864), Frege (1848-1925), and Gödel (1906-1977).
In the book under review, Lukasiewicz reconstructs Aristotle's syllogistic as a system of modern symbolic logic modeled on the 1910 Russell-Whitehead PRINCIPIA MATHEMATICA. This reconstruction inspired generations of logicians to go back and restudy their Aristotle, and it inspired generations of philosophers and classicists to go back and study their symbolic logic. There is no way to understand the historical development of interpretations of Aristotle's PRIOR ANALYTICS without reading this book. However, if your goal is to understand Aristotle's PRIOR ANALYTICS itself, read the 1989 translation and commentary by Robin Smith.

In addition to Mr. Ole Anders' review, I would add that Lukasiewicz can also be credited with the invention of three-valued logic, and for being one of the first researchers on the principle of contradiction, also treated in this book. Concerning the book itself, it presents a nice and very readable exposition of Aristotle's work on logic. It can even be considered as a completion of the Organon, with a very sharp critical aparatus. Lukasiewicz worked all his life on Aristotle's syllogistic and this book, whose second edition was published shortly after his death, can be considered as a summary of his long time thinkings about that. Even if Lukasiewicz did not publish anything else, he would enter history because of this book. A note about editions: the second edition has enlarged the first with the addition of three chapters on the modal logic of Aristotle, so it differs deeply from the first.