On 18 October 2011, Peter Simons, Professor of Trinity College (Dublin, Ireland), delivered his lecture in Opole. The lecture, under the title On Multitudes, was organized by the Group of Logic, Language and Information and was held in the Hall of the Senate of Opole University, sited in Collegium Maius.
In the beginning, Professor Urszula Wybraniec-Skardowska and Professor Janusz Czelakowski welcomed the speaker of the day and the guests attending the lecture. Then, Professor Andrzej Ciuk, Director of the Institute of English and American Studies of Opole University, presented the scientific silhouette of the lecturer. Professor Peter Simons is an outstanding English and Austrian scholar of international renown, an expert in metaphysics and ontology, philosophy, history of philosophy and logic, including the Polish logic. Professor Peter Simons studied mathematics and philosophy at the University of Manchester. He began his professional career as a lecturer in philosophy in Bolton Institute of Technology (currently the University of Bolton), and then – for several years – worked as a lecturer at the University of Salzburg, where he obtained his Assistant Professor’s degree. He was a visiting professor at the University of California, Irvine and the University of Texas. He also taught at some Swiss universities. In the years 1995-2009, he worked as a professor of philosophy at the University in Leeds. He is a member of the British Academy and Academia Europaea. At present he is working for Trinity College in Dublin, where he holds the post of Head of the Chair of Moral Philosophy.
In the course of his lecture, Prof. P. Simons discussed the notion of a multitude as a certain type of collection which can be regarded as a nominalistic equivalent of a set. He emphasized the differences between sets as abstract units, and between multitudes as pluralities of concrete material objects. Moreover, he pointed to a few reasons why we should accept the existence of such objects as „multitudes” and also discussed selected axioms relating to multitudes. He, on the one hand, highlighted analogies with the set theory, and – on the other one – accentuated the differences.
The above-mentioned problems, i.e. the problem of the character of dependences between multitudes, sets and Leśniewski’s systems of ontology and mereology, aroused a great deal of discussion after the lecture. Prof. P. Simons is a declared nominalist – everything that exists is located in the causative world extended temporally and spatially. An important element of the lecture (as well as of a substantial part of the discussion that followed) was the question of a confrontation between the naturalistic and nominalisitc attitudes, whose emanation is the theory of multitudes and the world of creations of mathematics. The latter, in the framework of Platonists, are extra-temporal and extra-spatial. (Mathematicians speak of pure sets, totally devoid of any references to material objects.) During the lecture a series of standpoints concerning this issue was presented (Hilbert, Quine, Field, Leśniewski, Boolos and others). The solution proposed by Prof. P. Simons consists in introducing multitudes of higher orders as concrete objects accepted by nominalists. Multitudes, like sets, are extensional collections. Accordingly, a considerable part of the lecture was occupied by a heuristic explanation, illustrated with a number of examples, of differences and similarities between multitudes, sets, collectives, populations and meanings of similar plural terms.
The discussion continued at the open seminar held by the GLLI, following the lecture, with the participation of the guest of the day. During the meeting a number of themes outlined in the lecture were taken up and developed, particularly those relating to the foundations of mathematics.