Thursday, June 18th, 2020, 11:00, on Zoom.
Paolo Maffezioli (University of Barcelona)
Intuitionistic mereology (j.w.w. A. Varzi)
Like any formal theory, mereology consists of axioms concerning the propositional connectives and quantifiers (logical axioms) and axioms concerning the parthood relation (proper axioms). Over the years, philosophical reasons have motivated interest in departing from the traditional axiomatization of mereology. Proper axioms such as the principle of strong supplementation or the principle of unrestricted composition have been weakened or rejected altogether and even elementary axioms like the anti-symmetry of parthood or its transitivity are no longer regarded as uncontentious. Logical axioms have been challenged, too. For example, many-valued logic, free logic and plural quantification have long been considered as sensible alternatives to classical first-order logic and, more recently, mereological theories based on paraconsistent logic have also been proposed. The two kinds of revisions are normally seen as independent from each other, but this isn’t always the case. For instance, I will show that developing an intuitionistic mereology by rejecting the law of excluded middle without touching the proper axioms would fails to validate nearly all the compelling principles of extensionality. If, one the other hand, the logical revision (from classical to intuitionistic logic) is accompanied by a suitable revision of the proper axioms, extensionality can be fully recovered. I will also show that change of the proper axioms can easily be made if the traditional mereological primitives are defined in terms of notions that have been investigated in constructive mathematics, mainly (though not exclusively) the notion of apartness (Brouwer, Heyting) and excess (von Plato).
The seminar will be held on Zoom. In order to get access to the Zoom meeting, please contact Peter Schuster.