Krzysztof Dyrda
University of Warsaw
Coming as an ambitious response to Russell’s paradox, which aims not only to preserve the original Cantorian notion of multiplicity (Menge) but also to preserve laypeople’s everyday intuitions about mereological notions, Leśniewski’s axiomatic theory of sets expounded in The Foundations of General Set Theory is all but incomprehensible when put in the language of the formalisms that prevailed in the 20th century. Some of the definitions that he offers – all in natural (while still highly technical) language – are ambiguous, when translated into the modern language of first-order logic and set theory, others do not lend themselves to such adaptations altogether: the arity and other syntactic properties of the formulas that he apparently offers differ widely from one sentence to another, rendering large parts of his exposition all but meaningless to the modern ear.
These negative effects, as I will claim, are the result of forcing the formalisms that are straightforwardly implied by the text into the framework of logics much different from the one that Leśniewski himself developed (and actually applied). In my talk, having indicated what problems the modern reader encounters in approaching Leśniewski’s theory of sets, I will present his very original system of logic and explain how his words can be formalised in that system without turning out to be clearly nonsensical, as is the case when inappropriate logics are applied.
Such dramatic differences in the effects of applying one formal system over the other give grounds for reflection on the wider problem of relativity of individuation of senses and logical pluralism. What is ambiguous when put in the terms of standard first-order logic and set theory is not so when put in the terms of Leśniewski’s singular system. What makes either of those systems primary? And if none of them is, then how can there be an answer to the question whether a term or sentence is ambiguous?
Chair: tba
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SOPhiA 2026 