Contemporary logicians continue to address problems associated with the existential import of categorical propositions. One notable problem concerns invalid instances of subalternation in the case of a universal proposition with an empty subject term. To remedy problems, logicians restrict first-order predicate logics to exclude such terms. Examining the historical origins of contemporary discussions reveals that logicians continue to make various category mistakes. We now believe that no proposition per se has existential import as commonly understood and thus it is unnecessary (...) to restrict first-order predicate logics to non-empty classes. After introducing the problem, we trace some nineteenth century treatments of the issue to locate a source of misconstruing propositional import in misconceptions of ‘implies’ and ‘affirms’ and name the process/product fallacy, along with the translation of categorical sentences using quantifiers and accommodating an empty class. Next we treat some metalogical matters to orient our discussion by which we provide a more precise nomenclature about ‘sentence’ and ‘proposition’ to correct previous misconceptions; here we uncover a common category mistake in respect of a proposition’s efficacy. The semantic distinction between agent and force is helpful in this connection. We conclude by showing that logicians have reinserted existence as a predicate, a position previously excised by Kant, and that the Frege-Russell ambiguity thesis applies only to relationships within a categorical sentence between grammatical predicate and subject. (shrink)

A new theoretical approach to Aristotelian Logic based on three axioms has been recently introduced. This formalization of the theory allowed for the unification of its uncommunicated traditional branches, thus restoring the theoretical unity of AL. In this brief paper, the applicability of the three AL axioms to Propositional Logic is explored. First, it is shown how the AL axioms can be applied to some simple PL arguments in a straightforward manner. Second, the development of a proof method for PL (...) inspired by the AL axioms is presented. This method mimics the underlying mechanics of the proof method from AL, and offers a complementary alternative to proof methods such as truth trees. (shrink)

This presentation includes a complete bibliography of John Corcoran’s publications devoted at least in part to Aristotle’s logic. Sections I–IV list 20 articles, 43 abstracts, 3 books, and 10 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article that antedates Corcoran’s Aristotle’s studies and the Journal of Symbolic Logic article first reporting his original results; it ends with works published in 2015. A few of the items are annotated with endnotes connecting them with (...) other work. In addition, Section V “Discussions” is a nearly complete secondary bibliography of works describing, interpreting, extending, improving, supporting, and criticizing Corcoran’s work: 8 items published in the 1970s, 22 in the 1980s, 39 in the 1990s, 56 in the 2000s, and 65 in the current decade. The secondary bibliography is annotated with endnotes: some simply quoting from the cited item, but several answering criticisms and identifying errors. As is evident from the Acknowledgements sections, all of Corcoran’s publications benefited from correspondence with other scholars, most notably Timothy Smiley, Michael Scanlan, and Kevin Tracy. All of Corcoran’s Greek translations were done in consultation with two or more classicists. Corcoran never published a sentence without discussing it with his colleagues and students. REQUEST: Please send errors, omissions, and suggestions. I am especially interested in citations made in non-English publications. (shrink)