Method of Logical Proof
When a proof is done by the Kalish and Montague method, the lines have an indentured structure of "proofs within proofs." The first line of the outermost proof always starts with the word "Show" followed by the statement to be proven. Additional "Show" lines can appear anywhere within the proof, thereby commencing sub-proofs. Immediately after a "Show" line, the subsequent lines are indented one level. When a proof at any level is completed, a box is drawn around the lines in that indentation, making them inaccessible thereafter, and the word "Show" is canceled, whereupon the statement after the canceled "Show" becomes an active line, accessible at the next level out. A proof is finished when all the lines except the first line are enclosed in one or more boxes, and the word "Show" on the first line is canceled. The method is extremely elegant and greatly aides the understanding and teaching of logic.
The proof system is set forth in detail in Logic: Techniques of Formal Reasoning by Richard Montague and Donald Kalish, which was published in 1964. Montague died tragically in 1971. Kalish published a second edition of the book in 1980 with Gary Mar. Since the late 1960s, these books have been used as a textbook at many universities, including UCLA.
Read more about this topic: Donald Kalish
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