English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Gottfried Leibniz embarked on a research program to prove all the Aristoteliccategorical syllogisms by diagrammatic and algebraic methods. He succeeded inproving them by means of Euler diagrams, but didn't produce a manuscript withtheir algebraic proofs. We demonstrate how key excerpts scattered acrossvarious Leibniz's drafts on logic contained sufficient ingredients to provethem by an algebraic method -- which we call the Leibniz-Cayley (LC) system --without having to make use of the more expressive and complex machinery offirst-order quantificational logic. In addition, we prove the classiccategorical syllogisms again by a relational method -- which we call theMcColl-Ladd (ML) system -- employing categorical relations studied by HughMcColl and Christine Ladd. Finally, we show the connection of ML and LC withBoolean algebra, proving that ML is a consequence of LC, and that LC is aconsequence of the Boolean lattice axioms, thus establishing Leibniz'shistorical priority over George Boole in characterizing and applying (asufficient fragment of) Boolean algebra to effectively tackle categoricalsyllogistic.

Proofs of valid categorical syllogisms in one diagrammatic and two symbolic axiomatic systems