### The Logic of Ordinary Language Conditionals

Claro R. Ceniza

**Discipline: **Languages

#### Abstract:

THE FORMULA, (p v r) <--> g, behaves like the long sought ordinary language conditional (OLC). The italicized r is a "ghost" proposition, which represents the disjunction of all propositions other than p which also imply q. r is ordinarily not uttered, but quietly presupposed in the OLe. The above form is valid for modus ponens, modus tollens, transposition, hypothetical syllogism, and absorption. It supports the fallacies of affirming the consequent and denying the antecedent. Furthermore, it is not subject to the paradoxes of material implication. It is also free from the likewise counter-intuitive "paradox" of the negation of the material conditional where-(p--> q) is logically equivalent to (p.-q). If used to symbolize universal propositions, particularly the A and the E propositions of traditional logic, it is also free from the paradox of confirmation involving the paradoxes of MC. The formula is based on the common observation that ceteris paribus, a conditional, is really a relative biconditional. For example, in the conditional, "If it rains, then the ground will be wet," it would be true to say that, ceteris paribus, "If it does not train, then the ground will not be wet." The denial of r in the above formula takes the place of the ceteris paribus clause.

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