Claiming Infinity: Tokens and spells in the foundations of the Moscow Mathematical School

The Moscow Mathematical School, led by Dmitri Egorov, made tremendous strides in the development of set theory in the period around the Russian Revolutions. The concepts of transfinite sets and absolute infinity have long had a controversial association with religion, namely in the explicit theological statements of the founder of set theory, Georg Cantor. However, several recent studies have argued that the Moscow School was instrumentally shaped by a sect called the “Name Worshippers”. Here we examine more precisely what the Name Worshippers meant by naming, and how their semantics might have, and might have not, shaped the views of the Moscow School. This paper is a review and severe corrective of the book Naming Infinity by Loren Graham and Jean-Michel Kantor, yet we also have our own analysis. Examining the Name Worshippers’ semantics as defined by themselves and their opponents argues for the greater theological influence being Cantor’s. However some aspects of their beliefs indicate that they tended to treat names as tokens, objects of incantation and instantiation. Finally, we show how this fascinating chapter in the history of theology and mathematics contributes to realistic versions of what contemporary neurologically-based semantics calls “meaning externalism” and a science of essences.