Editing Laws of Form (section)

====Syllogisms====
Appendix 2 of ''LoF'' shows how to translate traditional [[syllogism]]s and [[polysyllogism|sorites]] into the ''primary algebra''. A valid syllogism is simply one whose ''primary algebra'' translation simplifies to an empty Cross. Let ''A''* denote a ''literal'', i.e., either ''A'' or <math>\overline{A |}</math>, indifferently. Then every syllogism that does not require that one or more terms be assumed nonempty is one of 24 possible permutations of a generalization of [[syllogism|Barbara]] whose ''primary algebra'' equivalent is <math>\overline{A^* \ B |} \ \ \overline{\overline{B |} \ C^* \Big|} \ A^* \ C^* </math>. These 24 possible permutations include the 19 syllogistic forms deemed valid in [[Aristotelian logic|Aristotelian]] and [[medieval logic]]. This ''primary algebra'' translation of syllogistic logic also suggests that the ''primary algebra'' can [[interpretation (logic)|interpret]] [[monadic logic|monadic]] and [[term logic]], and that the ''primary algebra'' has affinities to the [[Boolean term schema]]ta of {{harvp|Quine|1982|loc=Part II}}.