•  11
    Marton argues that that it follows from the standard antirealist theory of truth, which states that truth and possible knowledge are equivalent, that knowing possibilities is equivalent to the possibility of knowing, whereas these notions should be distinct. Moreover, he argues that the usual strategies of dealing with the Church–Fitch paradox of knowability are either not able to deal with his modal-epistemic collapse result or they only do so at a high price. Against this, I argue that Marton’…Read more
  •  18
    Antirealists who hold the knowability thesis, namely that all truths are knowable, have been put on the defensive by the Church-Fitch paradox of knowability. Rejecting the non-factivity of the concept of knowability used in that paradox, Edgington has adopted a factive notion of knowability, according to which only actual truths are knowable. She has used this new notion to reformulate the knowability thesis. The result has been argued to be immune against the Church-Fitch paradox, but it has en…Read more
  •  46
    Rosenkranz’s Logic of Justification and Unprovability
    Journal of Philosophical Logic 49 (6): 1243-1256. 2020.
    Rosenkranz has recently proposed a logic for propositional, non-factive, all-things-considered justification, which is based on a logic for the notion of being in a position to know, 309–338 2018). Starting from three quite weak assumptions in addition to some of the core principles that are already accepted by Rosenkranz, I prove that, if one has positive introspective and modally robust knowledge of the axioms of minimal arithmetic, then one is in a position to know that a sentence is not prov…Read more
  •  3
    In the first chapter I have introduced Carnapian intensional logic again st the background of Frege s and Quine s puzzles. The main body of the d issertation consists of two parts. In the first part I discussed Carnapi an modal logic and arithmetic with descriptions. In the second chapter, I have described three Carnapian theories, CCL, CFL, and CNL. All three theories have three things in common. F irst, they are formulated in languages containing description terms. Sec ond, they contain a syst…Read more
  •  2
    I will examine three claims made by Ackerman and Kripke. First, they claim that not any arithmetical terms is eligible for universal instantiation and existential generalisation in doxastic or epistemic contexts. Second, Ackerman claims that Peano numerals are eligible for universal instantiation and existential generalisation in doxastic or epistemic contexts. Kripke's position is a bit more subtle. Third, they claim that the successor relation and the smaller-than relation must be effectively …Read more
  •  47
    Apophatic Finitism and Infinitism
    Logique Et Analyse 62 (247): 319-337. 2019.
    This article is about the ontological dispute between finitists, who claim that only finitely many numbers exist, and infinitists, who claim that infinitely many numbers exist. Van Bendegem set out to solve the 'general problem' for finitism: how can one recast finite fragments of classical mathematics in finitist terms? To solve this problem Van Bendegem comes up with a new brand of finitism, namely so-called 'apophatic finitism'. In this article it will be argued that apophatic finitism is una…Read more
  •  123
    Within the context of the Quine–Putnam indispensability argument, one discussion about the status of mathematics is concerned with the ‘Enhanced Indispensability Argument’, which makes explicit in what way mathematics is supposed to be indispensable in science, namely explanatory. If there are genuine mathematical explanations of empirical phenomena, an argument for mathematical platonism could be extracted by using inference to the best explanation. The best explanation of the primeness of the …Read more
  •  122
    Factive knowability and the problem of possible omniscience
    Philosophical Studies 177 (1): 65-87. 2020.
    Famously, the Church–Fitch paradox of knowability is a deductive argument from the thesis that all truths are knowable to the conclusion that all truths are known. In this argument, knowability is analyzed in terms of having the possibility to know. Several philosophers have objected to this analysis, because it turns knowability into a nonfactive notion. In addition, they claim that, if the knowability thesis is reformulated with the help of factive concepts of knowability, then omniscience can…Read more
  •  139
    Russell's Revenge: A Problem for Bivalent Fregean Theories of Descriptions
    Pacific Philosophical Quarterly 98 (4): 636-652. 2017.
    Fregean theories of descriptions as terms have to deal with improper descriptions. To save bivalence various proposals have been made that involve assigning referents to improper descriptions. While bivalence is indeed saved, there is a price to be paid. Instantiations of the same general scheme, viz. the one and only individual that is F and G is G, are not only allowed but even required to have different truth values.
  •  82
    Zelfpredicatie: Middeleeuwse en hedendaagse perspectieven
    Tijdschrift Voor Filosofie 79 (2): 239-258. 2017.
    The focus of the article is the self-predication principle, according to which the/a such-and-such is such-and-such. We consider contemporary approaches (Frege, Russell, Meinong) to the self-predication principle, as well as fourteenth-century approaches (Burley, Ockham, Buridan). In crucial ways, the Ockham-Buridan view prefigures Russell’s view, and Burley’s view shows a striking resemblance to Meinong’s view. In short the Russell-Ockham-Buridan view holds: no existence, no truth. The Burley-M…Read more
  •  89
    Truth and Existence
    Thought: A Journal of Philosophy 6 (1): 106-114. 2017.
    Halbach has argued that Tarski biconditionals are not ontologically conservative over classical logic, but his argument is undermined by the fact that he cannot include a theory of arithmetic, which functions as a theory of syntax. This article is an improvement on Halbach's argument. By adding the Tarski biconditionals to inclusive negative free logic and the universal closure of minimal arithmetic, which is by itself an ontologically neutral combination, one can prove that at least one thing e…Read more
  • Carnapian Arithmetic with Descriptions
    In Erik Weber, Thierry Libert, Geert Vanpaemel & P. Marage (eds.), Logic, Philosophy and History of Science in Belgium. Proceedings of the Young Researchers Days 2008, Koninklijke Vlaamse Academie Van België Voor Wetenschappen En Kunsten. pp. 28-34. 2009.
  •  262
    Counterfactual theories of knowledge and the notion of actuality
    Philosophical Studies 173 (6): 1647-1673. 2016.
    The central question of this article is how to combine counterfactual theories of knowledge with the notion of actuality. It is argued that the straightforward combination of these two elements leads to problems, viz. the problem of easy knowledge and the problem of missing knowledge. In other words, there is overgeneration of knowledge and there is undergeneration of knowledge. The combination of these problems cannot be solved by appealing to methods by which beliefs are formed. An alternative…Read more
  •  137
    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 r…Read more
  •  277
    The subject of this article is Modal-Epistemic Arithmetic (MEA), a theory introduced by Horsten to interpret Epistemic Arithmetic (EA), which in turn was introduced by Shapiro to interpret Heyting Arithmetic. I will show how to interpret MEA in EA such that one can prove that the interpretation of EA is MEA is faithful. Moreover, I will show that one can get rid of a particular Platonist assumption. Then I will discuss models for MEA in light of the problems of logical omniscience and logical co…Read more
  •  239
    Carnapian Modal and Epistemic Arithmetic
    In Carrara Massimiliano & Morato Vittorio (eds.), Language, Knowledge, and Metaphysics. Selected papers from the First SIFA Graduate Conference, College Publications. pp. 97-121. 2009.
    The subject of the first section is Carnapian modal logic. One of the things I will do there is to prove that certain description principles, viz. the ''self-predication principles'', i.e. the principles according to which a descriptive term satisfies its own descriptive condition, are theorems and that others are not. The second section will be devoted to Carnapian modal arithmetic. I will prove that, if the arithmetical theory contains the standard weak principle of induction, modal truth coll…Read more
  •  296
    Strict conditionals: A negative result
    Philosophical Quarterly 56 (225). 2006.
    Jonathan Lowe has argued that a particular variation on C.I. Lewis' notion of strict implication avoids the paradoxes of strict implication. We show that Lowe's notion of implication does not achieve this aim, and offer a general argument to demonstrate that no other variation on Lewis' notion of constantly strict implication describes the logical behaviour of natural-language conditionals in a satisfactory way.
  •  538
    Carnap’s Theory of Descriptions and its Problems
    Studia Logica 94 (3): 355-380. 2010.
    Carnap's theory of descriptions was restricted in two ways. First, the descriptive conditions had to be non-modal. Second, only primitive predicates or the identity predicate could be used to predicate something of the descriptum . The motivating reasons for these two restrictions that can be found in the literature will be critically discussed. Both restrictions can be relaxed, but Carnap's theory can still be blamed for not dealing adequately with improper descriptions.
  •  33
    Syntactical Treatment of Modalities, 6 February
    with Lorenz Demey
    The Reasoner 7 (4): 45-45. 2013.
  •  114
    The epistemic significance of numerals
    Synthese 198 (Suppl 5): 1019-1045. forthcoming.
    The central topic of this article is de re knowledge about natural numbers and its relation with names for numbers. It is held by several prominent philosophers that numerals are eligible for existential quantification in epistemic contexts, whereas other names for natural numbers are not. In other words, 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 an explanation of this phenomeno…Read more
  •  378
    Descriptions and unknowability
    Analysis 70 (1): 50-52. 2010.
    In a recent paper Horsten embarked on a journey along the limits of the domain of the unknowable. Rather than knowability simpliciter, he considered a priori knowability, and by the latter he meant absolute provability, i.e. provability that is not relativized to a formal system. He presented an argument for the conclusion that it is not absolutely provable that there is a natural number of which it is true but absolutely unprovable that it has a certain property. The argument depends on a descr…Read more
  •  317
    Being in a Position to Know and Closure
    Thought: A Journal of Philosophy 5 (1): 63-67. 2016.
    The focus of this article is the question whether the notion of being in a position to know is closed under modus ponens. The question is answered negatively.