ABSTRACT
In this chapter, the author aims to defend the Aristotelian concept of distribution by expanding Robert Carnes’ application of it. In first section, the author applies distribution to k-quantity “fractional” syllogistic systems. In second section, the author considers unrestricted “proportional” syllogisms and sorites. In third section the author describes proportional systems with an infinite number of quantities. In fourth section, the author shows how the new understanding of distribution survives Geach’s criticisms. The basic idea in Carnes’ application of the traditional rules to the 5-quantity syllogism can be developed for the fractional syllogistic. Any proof of the soundness of RI-R6 must show that every form they deem valid possesses an algebraic proof and any proof of the completeness rules must show that every form which possesses an algebraic proof is deemed valid by RI-R6. The i-quantity system appears to be equivalent to Johnson’s (1994) syllogistic with “fractional quantifiers”.
