Fair Countable Lotteries and Reflection

Acta Analytica, published online

Abstract: The main conclusion is this conditional: If the principle of reflection is a valid constraint on rational credences, then so is the principle of countable additivity. The argument for it is a variation on two arguments that are already in the literature, but with crucial differences. The conditional can be used for either a modus ponens or a modus tollens; some reasons for thinking that the former is most reasonable is given.

Keywords: Countable Additivity, Uniform Probability Distributions, Reflection

Published paper ● Pre-print

The Signalman Against the Glut and Gap Theorists

Synthese, 198 (2021), 10923–10937

Abstract: Radical glut and gap theorists deny—in opposite ways—that the liar sentence has exactly one of the two values true and not true. I describe a scenario where a signalman finds himself in a situation analogous to the liar paradox: if he lights a fire at a certain time, that is analogous to the liar being true, and if he does not, that is analogous to the liar not being true. It is obvious that he must make exactly one of those states of affairs come about. It is argued that there are no relevant differences between the liar and the signalman's dilemma, implying that the glut and gap theorists are wrong about the former. A further point is that whether or not the liar is true/the signalman lights the fire, language/the signalman is misleading relative to the conditions under which the liar/the fire "ought" to be true/lit.

Keywords: Liar Paradox, Gap Theory, Glut Theory, Communication

Published paper ● Pre-print

Choice Sequences and the Continuum

Erkenntnis, published online

Abstract: According to L.E.J. Brouwer, there is room for non-definable real numbers within the intuitionistic ontology of mental constructions. That room is allegedly provided by freely proceeding choice sequences, i.e., sequences created by repeated free choices of elements by a creating subject in a potentially infinite process. Through an analysis of the constitution of choice sequences, this paper argues against Brouwer's claim.

Keywords: Intuitionism, Potential Infinity, Choice Sequences, The Continuum, Platonism 

Published paper ● Pre-print

Two Envelopes and Binding

The Australasian Journal of Philosophy 96 (2018), 508-518

Abstract: This paper describes a way of defending a modification of Eckhardt's (2013) solution to the Two Envelopes Paradox. The defence is based on ideas from Arntzenius, Elga, and Hawthorne (2004).

Keywords: Two Envelopes Paradox, Binding, Decision Theory

Published paper ● Pre-print

On Fair Infinite Lotteries

Philosophical Studies 174 (2017), 2787-2794

Abstract: Two reverse supertasks—one new and one invented by Pérez Laraudogoitia (2014)—are discussed. Contra Kerkvliet (2016) and Pérez Laraudogoitia, it is argued that these supertasks cannot be used to conduct fair infinite lotteries, i.e., lotteries on the set of natural numbers with a uniform probability distribution. The new supertask involves an infinity of gods who collectively select a natural number by each removing one ball from a collection of initially infinitely many balls in a reverse omega-sequence of actions.

Keywords: Reverse Supertasks, Uniform Probability Distributions, Countable Additivity Axiom

Published paper ● Pre-print

Unified Grounding

Erkenntnis 81 (2016), 993-1010

Abstract: This paper offers a unification and systematization of the grounding approaches to truth, denotation, classes and abstraction. Its main innovation is a method for “kleenifying” bivalent semantics so as to ensure that the trivalent semantics used for various linguistic elements are perfectly analogous to the semantics used by Kripke, rather than relying on intuition to achieve similarity. The language of Kripke is extended to include a reference function, a definite-description operator, ordinary functions, class identity, class membership and class functions, and then applied to the paradoxes of Berry, König, Hilbert and Bernays, Richard, and Russell. The focus is on generalizing strong Kleene semantics, but one section is devoted to supervaluation, and the unification method also extends to weak Kleene semantics.

Keywords: Grounding, Truth, Denotation, Classes, Abstraction, Paradoxes

Published paper ● Pre-print

The Temperature Paradox and Meaning Postulates

Linguistic Inquiry 47 (2016), 695-705

Abstract: Lasersohn has argued that the use of Russell's analysis of the definite determiner in Montague Grammar, which is responsible for giving the correct prediction in the case of the Temperature Paradox, is also responsible for giving the wrong prediction in the case of the Gupta Syllogism. In this paper I argue against Lasersohn, and show that the problem of the Gupta Syllogism can be solved by making a minor addition to Intensional Montague Grammar. This solution is one that Lasersohn discusses but rejects. I will show that his critique of it is ill-founded.

Keywords: Montague Grammar, Intensionality, Temperature Paradox, Gupta Syllogism, Definite Determiner, Meaning Postulates

Published paper ● Pre-print

Brouwer’s Conception of Truth

Philosophia Mathematica 24 (2016), 379-400

Abstract: In this paper it is argued that the understanding of Brouwer as replacing truth conditions with assertability or proof conditions, in particular as codified in the so-called Brouwer-Heyting-Kolmogorov Interpretation, is misleading and conflates a weak and a strong notion of truth that have to be kept apart to understand Brouwer properly: truth-as-anticipation and truth-in-content. These notions are explained, exegetical documentation provided and semi-formal recursive definitions are given.

Keywords: Intuitionism, Truth, BHK-Interpretation, Bivalence

Published paper ● Pre-print

Double Up on Heaven

Thought 4 (2015), 213-214

Abstract: This paper describes a scenario in which a person in his afterlife will with probability 1 spend twice as many days in Heaven as in Hell, but, even though Heaven is as good as Hell is bad, his expected utility for any given day in that afterlife is negative.

Keywords: Decision Theory, Infinity, Probability, Expected Utility

Published paper ● Pre-print

Supervaluation on Trees for Kripke’s Theory of Truth

Review of Symbolic Logic 8 (2015), 46-74

Abstract: A method of supervaluation for Kripke's theory of truth is presented. It differs from Kripke's own method in that it employs trees; results in a compositional semantics; assigns the intuitively correct truth values to the sentences of a particularly tricky example of Gupta's; and – it is argued – is acceptable as an explication of the correspondence theory of truth.

Keywords: Truth, Paradoxes, Grounding, Kripke's Theory of Truth, Supervaluation, Compositionality, Correspondence Theory of Truth, Gupta’s Challenge

Published paper ● Pre-print

Grounded Ungroundedness

Inquiry 57 (2014), 216–243

Abstract: A modification of Kripke's theory of truth is proposed and it is shown how this modification solves some of the problems of expressive weakness in Kripke's theory. This is accomplished by letting truth values be grounded in facts about other sentences' ungroundedness.

Keywords: Truth, Paradoxes, Grounding, Kripke's Theory of Truth, Expressive Strength

Published paper ● Pre-print

A Kripkean Solution to Paradoxes of Denotation

Daniel Lassiter, Marija Slavkovik (Eds.): New Directions in Logic, Language, and Computation (2012), 212–220, Springer

Abstract: Kripke's solution to the Liar Paradox and other paradoxes of truth is generalized to the paradoxes of denotation. Berry's Paradox and Hilbert and Bernays' Paradox are treated in detail.

Keywords: Truth, Paradoxes, Grounding, Kripke's Theory of Truth, Expressive Strength

Published paper ● Pre-print

Review of "Plural Logic" by Alex Oliver and Timothy Smiley

Together with Thomas Brouwer

Studia Logica 103 (2015), 1095-1100

Published paper ● Pre-print