Giovedì 22 giugno, dalle ore 14.30 alle ore 17.00, si terrà a Bologna il simposio di logica medievale: “Goat-stags, Chimeras and Other Fantastic Creatures. Empty Terms and Existential Import in Medieval Logic“.
Il simposio è inserito all’intero della conferenza internazionale SILFS 2017, di cui è possibile consultare l’intero programma online al sito: http://www.silfs.it/silfs-2017-programme/
Qui sotto la descrizione del simposio.
Irene Binini (Scuola Normale Superiore)
Julie Brumberg-Chaumont (CNRS, PSL Research University Paris, LEM/UMR 8584)
Graziana Ciola (Scuola Normale Superiore)
Wojciech Wciòrka (University of Warsaw)
When reading medieval logical texts, it is frequent to find discussions involving an appeal to inexistent entities. These entities could be of many sorts: we may find reference to actually inexistent but possible entities, such as Homerus or my future son, as well as to only imaginable entities like chimeras, goat-stags or golden mountains, to entities that are naturally impossible but are employed in philosophy or sciences as useful conceptual tools, such as instants of time or abstracted extensions, and finally to entities that are not only naturally but also logically impossible, inasmuch as they are constituted by contradictory or incompossible parts, such as dead men and rational stones. In logical contexts, this appeal to inexistent entities raised a number of difficulties, mainly concerning the issues of existential assumptions in logical formulas
and of the validity of usually accepted systems of inference in presence of non referring
Some of the rules of inference that constituted the core of medieval logic – rules that are
usually represented by means of the traditional Square of Opposition – seem to work unexpectedly in the case that some of the terms included in categorical propositions are empty. One well-known problem is related to the proper interpretation of universal affirmative propositions like “Every A is B”. Let us suppose a situation in which the term “A” has no actual referent.
This means that the particular proposition “Some A is B” is false, and that its contradictory claim “No A is B” is true. But if this is the case, the universal affirmative claim “Every A is B” must be false, and therefore we have that there could be no true universal affirmative proposition whose subject is an empty term, and that the existence of the subject’s referent is a necessary condition for the truth of propositions such as “Every A is B”. From the point of view of contemporary logic this sounds odd, for propositions of this form are usually taken to be vacuously true in case their subject(s) is empty. A second issue concerns the interpretation of the particular negative proposition “Some A is not B”. If we posit again a situation in which the term “A” fails to refer, we have that the particular affirmative proposition “Some A is B” is false, and that its contradictory “No A is B” is true. In virtue of the rules of subalternation, we should admit that the negative particular proposition “Some A is not B” is also true, which is again strange to modern ears, for if we were to interpret particular propositions as containing
an existential quantification, the existence of their subject’s referents should be a necessary condition for their truth.
Apart from the the rules embodied in the Square of Opposition, there are several other
laws of inferences that seem to be threatened by the presence of non referring terms, such as the rules of conversion by contraposition, the equipollence rules between possibility and necessity claims and some syllogistic forms. To explain how medieval logicians were able to overcome these difficulties, it is sometimes claimed that their logic implicitly admitted a number of existential assumptions, and particularly the assumption that all terms in categorical propositions referred to non-empty classes, and, in some cases, that all proper names have existing referents. This view is however far from obvious, and in some cases explicitly rejected by many medieval authors.
Just as contemporary logicians, medieval logicians were often worried about how to deal
with non-denoting terms within their systems. They frequently admitted the presence of terms that refer to empty classes and of constants that fail to denote, and their texts show an explicit concern about how terms with no recognized denotation must be interpreted and how can propositions including them can be said to be meaningful. Moreover, they often developed sophisticated theories to distinguish between the inferences whose validity required existential assumptions and those whose validity is maintained in presence of non referring terms. The aim of this symposium is to investigate the problem of existential import in latin logical texts from the 11th century to the 14th century, and to highlight some interesting developments in
the logical theories of the time that involved the reference to inexistent, abstract, imaginary or even impossible entities.