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Now showing items 1-17 of 17
(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2023)
Ordinarily, the order in which some objects are attached to a scale does not affect the total weight measured by the scale. This principle is shown to fail in certain cases involving infinitely many objects. In these cases, ...
(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2023)
According to Weyl, “‘inexhaustibility’ is essential to the infinite”. However, he distinguishes two kinds of inexhaustible, or merely potential, domains: those that are “extensionally determinate” and those that are not. ...
(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2023)
(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2023)
(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2023)
Abstract Thin Objects has two overarching ambitions. The first is to clarify and defend the idea that some objects are ‘thin’, in the sense that their existence does not make a substantive demand on reality. The second ...
(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2023)
Abstract
Bob Hale has defended a new conception of properties that is broadly Fregean in two key respects. First, like Frege, Hale insists that every property can be defined by an open formula. Second, like Frege, ...
(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2023)
Abstract In the literature, predicativism is connected not only with the Vicious Circle Principle but also with the idea that certain totalities are inherently potential. To explain the connection between these two aspects ...
(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2022)
Abstract
Modal logic has been used to analyze potential infinity and potentialism more generally. However, the standard analysis breaks down in cases of divergent possibilities, where there are two or more ...
(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2022)
What explains the truth of a universal generalization? Two types of explanation can be distinguished. While an ‘instance-based explanation’ proceeds via some or all instances of the generalization, a ‘generic explanation’ ...
(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2020)
Abstract
What is the relation between some things and the set of these things? Mathematical practice does not provide a univocal answer. On the one hand, it relies on ordinary plural talk, which is implicitly ...
(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2020)
The purpose of this article is to explore the use of modal logic and/or intuitionistic logic to explicate potentiality and incomplete or indeterminate domains in mathematics. Our primary applications are the traditional ...
(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2020)
Abstract
Peacocke’s recent The Primacy of Metaphysics covers a wide range of topics. This critical discussion focuses on the book’s novel account of extensive magnitudes and numbers. First, I further develop and defend ...
(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)
(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)
It is widely thought that the acceptability of an abstraction principle is a feature of the cardinalities at which it is satisfiable. This view is called into question by a recent observation by Richard Heck. We show that ...
(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)
According to a famous argument by Dummett, the concept of set is indefinitely extensible, and the logic appropriate for reasoning about the instances of any such concept is intuitionistic, not classical. But Dummett's ...
(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)
Dummetts notion of indefinite extensibility is influential but obscure. The notion figures centrally in an alternative Dummettian argument for intuitionistic logic and anti‐realism, distinct from his more famous, ...
(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)
The notion of potential infinity dominated in mathematical thinking about infinity from Aristotle until Cantor. The coherence and philosophical importance of the notion are defended. Particular attention is paid to the ...