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- W3196502013 abstract "In both Classical Syllogistics and the biliteral sorites of Barbara, Darapti and Darii types, it is worth to examine only the fundamental patterns. Instead of writing the general premises of a Barbara type sorite as M1*⊆M2*⊆M3*⊆... ⊆Mn*, where Mi*∈{Mi,Mi'}, i=1,2,...,n, and examining 2n possible Barbara sorites, one may examine only Barbara's pattern M1⊆ M2⊆M3⊆...⊆Mn, implying the premises M1 M2'=Ø, M2 M3'=Ø,…, Mn-1 Mn'=Ø, where Mi' denotes the complement of Mi in the universe of discourse, U. Any different Barbara type sorite being true, simultaneously with the “pattern Barbara”, would impose conditions on U. For n=3, if the “pattern Barbara”, S⊆M⊆P, is valid, then none of the other seven Barbara type syllogisms could be valid without imposing conditions on U: if both Celarent, S⊆M⊆P', and Barbara are simultaneously valid, then S=M=Ø. If Camestres, S⊆M'⊆P', and Barbara are simultaneously valid, then P=M. Using term relabelings, all the other seven syllogisms of Barbara type can be reduced to the Barbara pattern. The relabelings are determined by which term is designated as being either S or S', which one is labeled as either P or P', which one is labeled either M or M’: none of the eight such relabelings, (nor the P↔S relabeling), influence the syllogism's logical analysis. A unique “partitioning subset of U” characterizes the logical consequence of each of the Barbara, Darapti or Darii sorites. One argues that all the valid syllogisms are equivalent to either Barbara, Darapti or Darii, and that the moods and figures of Classical Syllogistics have mainly a historical value." @default.
- W3196502013 created "2021-09-13" @default.
- W3196502013 creator A5070313957 @default.
- W3196502013 date "2020-07-11" @default.
- W3196502013 modified "2023-10-18" @default.
- W3196502013 title "Variation and Pattern in the 3-term Syllogisms and the Biliteral Sorites of Types Barbara, Darapti and Darii" @default.
- W3196502013 doi "https://doi.org/10.31219/osf.io/xry4f" @default.
- W3196502013 hasPublicationYear "2020" @default.
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