•  9
    Steps Towards a Minimalist Account of Numbers
    Mind 131 (523): 865-893. 2022.
    This paper outlines an account of numbers based on the numerical equivalence schema (NES), which consists of all sentences of the form ‘#x.Fx=n if and only if ∃nx Fx’, where # is the number-of operator and ∃n is defined in standard Russellian fashion. In the first part of the paper, I point out some analogies between the NES and the T-schema for truth. In light of these analogies, I formulate a minimalist account of numbers, based on the NES, which strongly parallels the minimalist (deflationary…Read more
  •  11
    This is a correction to: Thomas Schindler, Steps Towards a Minimalist Account of Numbers, Mind, 2021; fzab060, https://doi.org/10.1093/mind/fzab060.
  •  31
    Deflationary Theories of Properties and Their Ontology
    Australasian Journal of Philosophy 100 (3): 443-458. 2022.
    I critically examine some deflationary theories of properties, according to which properties are ‘shadows of predicates’ and quantification over them serves a mere quasi-logical function. I start by considering Hofweber’s internalist theory, and pose a problem for his account of inexpressible properties. I then introduce a theory of properties that closely resembles Horwich’s minimalist theory of truth. This theory overcomes the problem of inexpressible properties, but its formulation presuppose…Read more
  •  21
    The Proper Formulation of the Minimalist Theory of Truth
    Philosophical Quarterly 72 (3): 695-712. 2022.
    Minimalism about truth is one of the main contenders for our best theory of truth, but minimalists face the charge of being unable to properly state their theory. Donald Davidson incisively pointed out that minimalists must generalize over occurrences of the same expression placed in two different contexts, which is futile. In order to meet the challenge, Paul Horwich argues that one can nevertheless characterize the axioms of the minimalist theory. Sten Lindström and Tim Button have independent…Read more
  •  50
    Higher-Order Logic and Disquotational Truth
    Journal of Philosophical Logic 51 (4): 879-918. 2022.
    Truth predicates are widely believed to be capable of serving a certain logical or quasi-logical function. There is little consensus, however, on the exact nature of this function. We offer a series of formal results in support of the thesis that disquotational truth is a device to simulate higher-order resources in a first-order setting. More specifically, we show that any theory formulated in a higher-order language can be naturally and conservatively interpreted in a first-order theory with a…Read more
  •  261
    Steps Towards a Minimalist Account of Numbers
    Mind 131 (523): 863-891. 2021.
    This paper outlines an account of numbers based on the numerical equivalence schema, which consists of all sentences of the form ‘#x.Fx=n if and only if ∃nx Fx’, where # is the number-of operator and ∃n is defined in standard Russellian fashion. In the first part of the paper, I point out some analogies between the NES and the T-schema for truth. In light of these analogies, I formulate a minimalist account of numbers, based on the NES, which strongly parallels the minimalist account of truth. O…Read more
  •  343
    Unrestricted quantification and ranges of significance
    Philosophical Studies 180 (5): 1579-1600. 2022.
    Call a quantifier ‘unrestricted’ if it ranges over absolutely all objects. Arguably, unrestricted quantification is often presupposed in philosophical inquiry. However, developing a semantic theory that vindicates unrestricted quantification proves rather difficult, at least as long as we formulate our semantic theory within a classical first-order language. It has been argued that using a type theory as framework for our semantic theory provides a resolution of this problem, at least if a broad…Read more
  •  210
    What requirements must deflationary formal theories of truth satisfy? This chapter argues against the widely accepted view that compositional and Tarskian theories of truth are substantial or otherwise unacceptable to deflationists. First, two purposes that a formal truth theory can serve are distinguished: one descriptive, the other logical (i.e., to characterise the correctness of inferences involving ‘true’). The chapter argues that the most compelling arguments for the incompatibility of com…Read more
  •  265
    The Proper Formulation of the Minimalist Theory of Truth
    The Philosophical Quarterly. forthcoming.
    Minimalism about truth is one of the main contenders for our best theory of truth, but minimalists face the charge of being unable to properly state their theory. Donald Davidson incisively pointed out that minimalists must generalize over occurrences of the same expression placed in two different contexts, which is futile. In order to meet the challenge, Paul Horwich argues that one can nevertheless characterize the axioms of the minimalist theory. Sten Lindström and Tim Button have independent…Read more
  •  412
    Deflationary theories of properties and their ontology
    Australasian Journal of Philosophy 1-16. 2021.
  •  279
    Does Semantic Deflationism Entail Meta-Ontological Deflationism?
    Philosophical Quarterly 71 (1): 99-119. 2021.
    Deflationary positions have been defended in many areas of philosophy. Most prominent are semantic deflationism about truth and reference, and meta-ontological deflationism, according to which existence has no deep nature and the standard neo-Quinean approach to ontology is misguided. Although both kinds of views have generated much discussion, surprisingly little attention has been paid to the question of how they relate to each other. Are they independent, is it advisable to hold them all at o…Read more
  •  433
    Deflationism and the Function of Truth
    Philosophical Perspectives 32 (1): 326-351. 2018.
    Deflationists claim that the truth predicate was introduced into our language merely to full a certain logico-linguistic function. Oddly enough, the question what this function exactly consists in has received little attention. We argue that the best way of understanding the function of the truth predicate is as enabling us to mimic higher-order quantification in a first-order framework. Indeed, one can show that the full simple theory of types is reducible to disquotational principles of truth.…Read more
  •  112
    Disquotation and Infinite Conjunctions
    Erkenntnis 83 (5): 899-928. 2017.
    One of the main logical functions of the truth predicate is to enable us to express so-called ‘infinite conjunctions’. Several authors claim that the truth predicate can serve this function only if it is fully disquotational, which leads to triviality in classical logic. As a consequence, many have concluded that classical logic should be rejected. The purpose of this paper is threefold. First, we consider two accounts available in the literature of what it means to express infinite conjunctions…Read more
  •  37
    A note on Horwich’s notion of grounding
    Synthese 197 (5): 2029-2038. 2020.
    Horwich proposes a solution to the liar paradox that relies on a particular notion of grounding—one that, unlike Kripke’s notion of grounding, does not invoke any “Tarski-style compositional principles”. In this short note, we will formalize Horwich’s construction and argue that his solution to the liar paradox does not justify certain generalizations about truth that he endorses. We argue that this situation is not resolved even if one appeals to the \-rule. In the final section, we briefly dis…Read more
  •  83
    Classes, why and how
    Philosophical Studies 176 (2): 407-435. 2019.
    This paper presents a new approach to the class-theoretic paradoxes. In the first part of the paper, I will distinguish classes from sets, describe the function of class talk, and present several reasons for postulating type-free classes. This involves applications to the problem of unrestricted quantification, reduction of properties, natural language semantics, and the epistemology of mathematics. In the second part of the paper, I will present some axioms for type-free classes. My approach is…Read more
  •  84
    A graph-theoretic analysis of the semantic paradoxes
    with Timo Beringer
    Bulletin of Symbolic Logic 23 (4): 442-492. 2017.
    We introduce a framework for a graph-theoretic analysis of the semantic paradoxes. Similar frameworks have been recently developed for infinitary propositional languages by Cook and Rabern, Rabern, and Macauley. Our focus, however, will be on the language of first-order arithmetic augmented with a primitive truth predicate. Using Leitgeb’s notion of semantic dependence, we assign reference graphs (rfgs) to the sentences of this language and define a notion of paradoxicality in terms of acceptabl…Read more
  • Reference graphs and semantic paradox
    with Timo Beringer
    In Adam Arazim & Michal Dancak (eds.), Logica Yearbook 2015, College Publications. pp. 1-15. 2016.
  •  55
    Axioms for grounded truth
    Review of Symbolic Logic 7 (1): 73-83. 2014.
    We axiomatize Leitgeb's (2005) theory of truth and show that this theory proves all arithmetical sentences of the system of ramified analysis up to $\epsilon_0$. We also give alternative axiomatizations of Kripke's (1975) theory of truth (Strong Kleene and supervaluational version) and show that they are at least as strong as the Kripke-Feferman system KF and Cantini's VF, respectively.
  •  34
    Arithmetic with Fusions
    with Jeff Ketland
    Logique Et Analyse 234 207-226. 2016.
    In this article, the relationship between second-order comprehension and unrestricted mereological fusion (over atoms) is clarified. An extension PAF of Peano arithmetic with a new binary mereological notion of “fusion”, and a scheme of unrestricted fusion, is introduced. It is shown that PAF interprets full second-order arithmetic, Z_2.
  •  54
    Some Notes on Truths and Comprehension
    Journal of Philosophical Logic 47 (3): 449-479. 2018.
    In this paper we study several translations that map models and formulae of the language of second-order arithmetic to models and formulae of the language of truth. These translations are useful because they allow us to exploit results from the extensive literature on arithmetic to study the notion of truth. Our purpose is to present these connections in a systematic way, generalize some well-known results in this area, and to provide a number of new results. Sections 3 and 4 contain some recurs…Read more
  • La Paradoja de Cantor
    In Eduardo Barrio (ed.), Paradojas, Paradoxjas y más Paradojas, College Publications. pp. 199-212. 2014.
  •  92
    Type-free truth
    Dissertation, Ludwig Maximilians Universität München. 2015.
    This book is a contribution to the flourishing field of formal and philosophical work on truth and the semantic paradoxes. Our aim is to present several theories of truth, to investigate some of their model-theoretic, recursion-theoretic and proof-theoretic aspects, and to evaluate their philosophical significance. In Part I we first outline some motivations for studying formal theories of truth, fix some terminology, provide some background on Tarski’s and Kripke’s theories of truth, and then d…Read more
  •  49
    A Disquotational Theory of Truth as Strong as Z 2 −
    Journal of Philosophical Logic 44 (4): 395-410. 2015.
    T-biconditionals have often been regarded as insufficient as axioms for truth. This verdict is based on Tarski’s observation that the typed T-sentences suffer from deductive weakness. As indicated by McGee, the situation might change radically if we consider type-free disquotational theories of truth. However, finding a well-motivated set of untyped T-biconditionals that is consistent and recursively enumerable has proven to be very difficult. Moreover, some authors ) have argued that any soluti…Read more