{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,12]],"date-time":"2024-07-12T04:10:05Z","timestamp":1720757405584},"reference-count":146,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2018,11,6]],"date-time":"2018-11-06T00:00:00Z","timestamp":1541462400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2020,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Greek antiquity saw the development of two distinct systems of logic: Aristotle\u2019s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such as<jats:italic>reductio ad absurdum<\/jats:italic>. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In the 17th century, this Peripatetic program of reducing hypothetical to categorical logic was championed by Gottfried Wilhelm Leibniz. In an essay titled<jats:italic>Specimina calculi rationalis<\/jats:italic>, Leibniz develops a theory of propositional terms that allows him to derive the rule of<jats:italic>reductio ad absurdum<\/jats:italic>in a purely categorical calculus in which every proposition is of the form<jats:italic>A is B<\/jats:italic>. We reconstruct Leibniz\u2019s categorical calculus and show that it is strong enough to establish not only the rule of<jats:italic>reductio ad absurdum<\/jats:italic>, but all the laws of classical propositional logic. Moreover, we show that the propositional logic generated by the nonmonotonic variant of Leibniz\u2019s categorical calculus is a natural system of relevance logic known as RMI<jats:inline-formula><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S1755020318000266_inline1\"\/><jats:tex-math>$_{{}_ \\to ^\\neg }$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1017\/s1755020318000266","type":"journal-article","created":{"date-parts":[[2018,11,6]],"date-time":"2018-11-06T09:08:39Z","timestamp":1541495319000},"page":"141-205","source":"Crossref","is-referenced-by-count":3,"title":["THE PERIPATETIC PROGRAM IN CATEGORICAL LOGIC: LEIBNIZ ON PROPOSITIONAL 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