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30Lesniewski's Systems of Logic and Mereology; History and Re-EvaluationDissertation, University of Calgary. 2008.
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29Informal Provability, First-Order BAT Logic and First Steps Towards a Formal Theory of Informal ProvabilityLogic and Logical Philosophy 1-27. forthcoming.BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to be extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a c…Read more
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28Logic of informal provability with truth valuesLogic Journal of the IGPL 31 (1): 172-193. 2023.Classical logic of formal provability includes Löb’s theorem, but not reflection. In contrast, intuitions about the inferential behavior of informal provability (in informal mathematics) seem to invalidate Löb’s theorem and validate reflection (after all, the intuition is, whatever mathematicians prove holds!). We employ a non-deterministic many-valued semantics and develop a modal logic T-BAT of an informal provability operator, which indeed does validate reflection and invalidates Löb’s theore…Read more
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23Modal Quantifiers, Potential Infinity, and Yablo sequencesReview of Symbolic Logic 1-30. forthcoming.
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22The History and Philosophy of Polish Logic. Essays in Honour of Jan Woleński (review)History and Philosophy of Logic 38 (1): 95-97. 2017.This is a Festschrift volume dedicated to Jan Woleński, whose extensive work in the history of Polish logic indeed deserves one. Accordingly, it is mostly devoted to Woleński's main interests: the...
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15Informal provability and dialetheismTheoria 89 (2): 204-215. 2023.According to the dialetheist argument from the inconsistency of informal mathematics, the informal version of the Gödelian argument leads us to a true contradiction. On one hand, the dialetheist argues, we can prove that there is a mathematical claim that is neither provable nor refutable in informal mathematics. On the other, the proof of its unprovability is given in informal mathematics and proves that very sentence. We argue that the argument fails, because it relies on the unjustified and u…Read more
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14Neologicism for Real – Are We There Yet?In Bartłomiej Skowron (ed.), Contemporary Polish Ontology, De Gruyter. pp. 181-204. 2019.
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14Some non-standard interpretations of the axiomatic basis of Leśniewski’s OntologyAustralasian Journal of Logic 4 (5): 13-46. 2006.We propose an intuitive understanding of the statement: ‘an axiom (or: an axiomatic basis) determines the meaning of the only specific constant occurring in it.’ We introduce some basic semantics for functors of the category s/n,n of Lesniewski’s Ontology. Using these results we prove that the popular claim that the axioms of Ontology determine the meaning of the primitive constants is false.
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13An Assessment of Contemporary Polish OntologyIn Contemporary Polish Ontology, De Gruyter. pp. 271-294. 2019.
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11On representing sentential connectives of Lesniewski's elementary PrototheticJournal of Logic and Computation 16 (4): 451-460. 2006.After a brief presentation of Le[s]niewski's notation for 1- and 2-place sentential connectives of protothetic, the article discusses a method of extending this method to n [≥] 3-place sentential connectives. Such a method has been hinted at by Luschei, but in fact, no general effective method of defining such functors has been clearly and explicitly given. The purpose of this article is to provide such a method.
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8A Modern Modal Argument for the SoulIn Michael Bruce & Steven Barbone (eds.), Just the Arguments, Wiley‐blackwell. 2011-09-16.
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6Material Implication and Conversational Implicature in Lvov-Warsaw SchoolIn Urszula Wybraniec-Skardowska & Ángel Garrido (eds.), The Lvov-Warsaw School. Past and Present, Springer- Birkhauser,. pp. 117-132. 2018.The relation between indicative conditionals in natural language and material implication wasn’t a major topic in the Lvov-Warsaw school. However, a major defense of the claim that the truth conditions of these two are the same has been developed by Ajdukiewicz. The first major goal of this paper is to present, assess, and improve his strategy. It turns out that it is quite similar to the approach developed by Grice, so our second goal is to compare these two and to argue that the accuracy of Aj…Read more
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6Richard Kaye. The mathematics of logic: A guide to completeness theorems and their applications. Cambridge University Press, Cambridge, 2007, xi + 204 pp (review)Bulletin of Symbolic Logic 15 (2): 216-218. 2009.
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4Logics of ProvabilityIn Sven Ove Hansson & Vincent F. Hendricks (eds.), Introduction to Formal Philosophy, Springer. pp. 191-237. 2012.Provability logics are, roughly speaking, modal logics meant to capture the formal principles of various provability operators or predicates.
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2InductionIn Sven Ove Hansson & Vincent F. Hendricks (eds.), Introduction to Formal Philosophy, Springer. pp. 105-130. 2012.Inductive reasoning, initially identified with enumerative induction is nowadays commonly understood more widely as any reasoning based on only partial support that the premises give to the conclusion. This is a tad too sweeping, for this includes any inconclusive reasoning. A more moderate and perhaps more adequate characterization requires that inductive reasoning not only includes generalizations, but also any predictions or explanations obtained in absence of suitable deductive premises. Ind…Read more
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