Logical diagrams have long been used to represent logical inferences. In the talk, I explore how the logical diagrams historically used for rendering syllogistic inferences might have affected the historical evolution of the debate on existential import and empty terms in logic. I propose to view the evolution of logical diagrams and the evolution of answers to the problem of existential import in parallel, drawing lines of possible mutual influences.

The problem of existential import, i.e., the question of whether the denotations of syllogistic terms must exist for syllogisms to be logically valid, was not explicitly stated in Aristotle’s work, but first addressed in Arabic logic, beginning with Al-Farabi. In Europe, it was debated in detail with the rise of nominalist philosophy, later resurfacing with Leibniz and gaining much of an attention with the development of Boolean algebra and modern formal calculi.

To better understand these historical shifts in attention, I propose to examine the parallel evolution of diagrams used for representing logical inferences. I take into account the Byzantine diagrams for syllogistic figures, Al-Barakāt’s Arabic linear diagrams, Leibniz’s and Lambert’s linear diagrams, Euler circles, and Venn and Venn-Peirce diagrams. By analyzing them in terms of their (in)ability to account for the (non)emptiness of terms, I aim to show how the use of different types of logical diagrams have led to the recognition of the problem of existence of logical terms at different points in history.

Coffee, tea, cake and fruit will be served before the colloquium @2 pm.