One presents the Set Theory Model (STM) of the valid categorical arguments (VCAs) as an improvement on the Classic Categorical Syllogistic (CCS) approach to the valid (categorical) syllogisms (VS) – a proper subset of the VCAs. The STM was initially developed by George Boole and Lewis Carroll, who worked with a “universe of discourse”, U, which contains the pairwise complementary sets, or categorical terms, S,S'(non-S),P,P'(non-P),M,M'(non-M), and is thus partitioned into 8 subsets: SPM:= S∩P∩M, S'PM,...,S'P'M'. In STM both the positive terms, S,P,M, and the negative terms, S',P',M', are allowed to appear in the pairs of categorical premises (PCPs) and their entailed logical consequences (LCs). One thus counts 64 distinct PCPs, out of which only 32 PCPs generate VCAs, and 32 PCPs do not entail any LC. By comparison, CCS admits PCPs worded only via the positive terms S,P,M, and accepts as VS LCs only the statements E(S,P), I(S,P), A(S,P), or O(S,P). It is easier to see on the VCA set, than on its VS proper subset, that there are only three distinct types of VCAs, (and of VS), and that all the VCAs of the same type are equivalent modulo the term relabelings p:= P↔P', s:=S↔S', m:=M↔M' and their compositions. Besides the VCAs and their LCs, one discusses VCA (or categorical) sorites, “VCA distribution conservation”, empty set constraints (ESC), and “VCA generalized versions” of the Rules of Valid Syllogisms (RofVS).