Ontological assumptions in the history of Western logic: from Aristotelian syllogistic to Boolean algebra
Karol Wapniarski
The purpose of the paper is to provide a thorough account of the issue of empty terms and ontological assumptions as they play throughout the history of Western logic, beginning with Aristotelian syllogistic and going up till the Boolean algebra and the emergence of modern formal logic. Modern formal logic, using the notion of the universe of discourse, does not allow for constructing interpretations of formal languages for empty universes. In contemporary discussions, it is widely assumed that the Aristotelian syllogistic did not allow for the use of empty terms as well. Upon closer examination, this view does not reflect the historical reality, and the issue of empty terms is much more complex. Throughout history, it has been extensively discussed both in relation to categorical statements and the Logical Square. In the paper, I relate those discussions. I assert 1) that the (non)emptiness of terms did not emerge as an issue in Aristotelian logic, and the dominant modern interpretation stems from the development of formal logic and attempts to render syllogistic using modern notation, 2) that the interest of Arabic philosophers in the issue can be explained by different ways of expressing existence and attribution in Indo-European and Semitic languages, 3) that the conditional treatment of existential assumptions proposed by Ockham serves as the origins of the universe of discourse idea. I end by asserting that, firstly, throughout the history we can observe a rising awareness of empty terms as an issue that needs to be addressed, secondly, in parallel to it, we can trace the origins of the modern universe of discourse idea.