How to use Aristotelian Logic to Formalize Reasonings Expressed in Ordinary Language?

Phillip Peterson

The most efficient, accurate, and fruitful way to communicate reasonings is in natural languages. The proper way to approach the question of how human reasoning is expressed and communicated in natural languages is not via typical formal systems or analogous artificial languages, but with Aristotle’s syllogistic. The rules of quality and distribution are sound and complete methods for filtering the 24 correct reasonings from the 256 logical possibilities (existential import adopted). The syllogism fundamental reasoning-wise via complex and complicated reasonings being broken down into syllogistic steps (as polysyllogisms, sorites, and enthymemes illustrate). A 5-quantity syllogistic gives the basic logic of "few", "many", and "most". Syllogistic systems for as many intermediate quantities as you like can be constructed. The infinite-quantity (iQ) syllogistic is modeled on the finite higher-quantity fractional systems. To add relations to syllogistic systems, the Dictim di Omni (DDO) reformulated first as DDO P and then DDO I is developed to cover iQ syllogisms. Finally, DDO* results from extending DDO I to arguments wherein one or more iQ-categoricals is replaced by a (simple or complex) "basic relational categorical" (BRC). Challenges for further research DDO* include iterations, embedded terms due to n-place relations, VP-modifiers, and other clausal NPs.

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