05/05/2026
Drodzy Państwo,
w najbliższy piątek (08.05) o godz. 14:00 w sali S336 odbędzie się seria wykładów zorganizowana przez studentów Koła Logicznego UG. Jest to wyjątkowa okazja, żeby zapoznać się z szczegółowymi zagadnieniami z filozofii matematyki i logiki.
W ramach wydarzenia przewidziane są dwa wykłady: o 14:00 wykład wygłosi dr Pablo Dopico, a o 15:30 dr Santiago Jockwich Martinez. Poniżej zamieszczamy abstrakty i tytuły obu wystąpień.
Pablo Dopico
Title: Indeterminacy and the concept of set
Abstract: The concept of set has sometimes been said to be semantically indeterminate. However, little has been said about what kind of indeterminacy this might be. In this paper, we offer one proposal to that effect. We first defend that the extension and the anti-extension of the concept of set can be seen as determined on the basis of a given axiomatic theory that suitably extends ZF. Then, we argue that, under this account, the concept of set is likely to be indefinitely precisifiable. That is, regardless of how one determines the (anti)extension of the concept of set, the concept is likely to remain imprecise and can be precisified further. In the account we defend, this is understood as the idea that, no matter how one axiomatically extends ZF, there will always remain collections that the theory cannot settle as belonging or not to the extension of the concept of set. We conclude by assessing a possible objection coming from the inner model program.
Santiago Jockwich Martinez:
Title: The modal logic of Boolean-valued models.
Abstract: This paper connects modal set theory with Boolean-valued models by giving a new way to understand modal notions such as possibility and necessity inside Boolean-valued universes. The basic idea is to treat elements of a Boolean algebra as local perspectives on truth, and to say that two perspectives are accessible to one another when they are mutually compatible. We use this idea to identify general modal principles, to study how these principles depend on the structure of the Boolean algebra, and to analyze the special case of complete atomic Boolean algebras. We conclude by proving that, under a natural translation-based semantics, the resulting modal logic is exactly KTB.
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