Presuppositions and the Content Implication

In the 1950s Peter Strawson analyzed the works of Bertrand Russell regarding fundamental definitions of meaning, sentences and truth value. The debate between them uncovered many issues that Fregean, truth-functional logics have when defining concepts from natural language. To reconcile the Fregean paradigm with the reality of language use, Strawson proposed the concept of presuppositions  necessary preconditions for the truth of other sentences. We believe that his proposition stemmed primarily from the problem caused by the fact that Fregean, truth-functional logics are not sensitive to the contents of sentences and reduce them to their logical values. This is bound to produce a mismatch between the way logic models reasoning and the way language users reason since real-life reasoning is performed on the contents of sentences and not their logical values. Inspired by the ideas of Strawson and Roman Suszko, who initiated the paradigm of non-Fregean logics, we propose a new solution to the debate between Strawson and Russell. In our solution, the content implication connective is used to express content relations between sentences. We move away from truth and falsehood as the sole two semantic correlates of sentences and instead work in a system where the contents of sentences are their semantic correlates.