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Modal-Epistemic Arithmetic and the problem of quantifying in

Synthese 190 (1):89-111 (2013)

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Conceptos de cognoscibilidad.Jan Heylen & Felipe Morales Carbonell - 2023 - Revista de Humanidades de Valparaíso 23:287-308.details Many philosophical discussions hinge on the concept of knowability. For example, there is a blooming literature on the so-called paradox of knowability. How to understand this notion, however? In this paper, we examine several approaches to the notion: the naive approach to take knowability as the possibility to know, the counterfactual approach endorsed by Edgington (1985) and Schlöder (2019) , approaches based on the notion of a capacity or ability to know (Fara 2010, Humphreys 2011), and finally, approaches that make (...) Download Export citation Bookmark
Proof systems for BAT consequence relations.Pawel Pawlowski - 2018 - Logic Journal of the IGPL 26 (1):96-108.details Download Export citation Bookmark 1 citation
Informal provability and dialetheism.Pawel Pawlowski & Rafal Urbaniak - 2023 - Theoria 89 (2):204-215.details 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 unlikely assumption (...) Download Export citation Bookmark
Informal Provability, First-Order BAT Logic and First Steps Towards a Formal Theory of Informal Provability.Pawel Pawlowski & Rafal Urbaniak - forthcoming - Logic and Logical Philosophy:1-27.details 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 couple of (...) Download Export citation Bookmark
The epistemic significance of numerals.Jan Heylen - 2014 - Synthese 198 (Suppl 5):1019-1045.details The central topic of this article is (the possibility of) de re knowledge about natural numbers and its relation with names for numbers. It is held by several prominent philosophers that (Peano) numerals are eligible for existential quantification in epistemic contexts (‘canonical’), whereas other names for natural numbers are not. In other words, (Peano) numerals are intimately linked with de re knowledge about natural numbers, whereas the other names for natural numbers are not. In this article I am looking for (...) Download Export citation Bookmark 2 citations
Closure of A Priori Knowability Under A Priori Knowable Material Implication.Jan Heylen - 2015 - Erkenntnis 80 (2):359-380.details The topic of this article is the closure of a priori knowability under a priori knowable material implication: if a material conditional is a priori knowable and if the antecedent is a priori knowable, then the consequent is a priori knowable as well. This principle is arguably correct under certain conditions, but there is at least one counterexample when completely unrestricted. To deal with this, Anderson proposes to restrict the closure principle to necessary truths and Horsten suggests to restrict it (...) Download Export citation Bookmark 3 citations

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