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Full Idea
It has often been claimed (e.g. by Leibniz) that a single rule governs all syllogistic validity, called 'dictum de omni et null', which says that what is affirmed or denied of any whole is affirmed or denied of any part of that whole.
Gist of Idea
Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts
Source
Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8)
Book Ref
Engelbretsen,G/Sayward,C: 'Philosophical Logic: Intro to Advanced Topics' [Continuum 2011], p.143
A Reaction
This seems to be the rule which is captured by Venn Diagrams.
| 13849 | Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward] |
| 13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |
| 13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward] |
| 13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward] |
| 13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward] |
| 13916 | Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward] |
| 13850 | In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward] |
| 13851 | Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward] |